# Polarization Spectroscopy: Principles, Theory, Techniques and Applications

I. C. Baianu, Editor

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Contents

Articles

Copyright @ 2009 by B ci2 x

Permission is granted to copy, distribute and/or modify this documentunder the terms of the GNU Free Documentation License, Version 1.2 orany later version published by the Free Software Foundation, with no

Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A

copy of the license is included in ;the section entitled "GNU Free

Edited by Bci2, with the contributors listed after the Common Use

Spectroscopy—An Introduction 4

Spectroscopy 4

Fourier transform spectroscopy 11

Spectroscopy Theory 15

Quantum mechanics 15

Quantum field theory 30

Algebraic quantum field theory 41

Local quantum field theory 42

Algebraic logic 43

Quantum logic 46

Quantum computer 53

Quantum chemistry 62

Density functional theory 66

Birefringence 73

Polarization spectroscopy 79

Polarized IR Spectroscopy 79

Circular dichroism 85

Vibrational circular dichroism 91

Optical rotatory dispersion 101

Raman spectroscopy 101

Coherent anti-Stokes Raman spectroscopy 107

Raman Microscopy 110

Imaging spectroscopy 110

Chemical imaging 114

Spin polarization 121

Polarized Neutron Spectroscopy 122

Polarized Muon Spectroscopy 124

Time-resolved spectroscopy 126

Terahertz spectroscopy 127

Applied spectroscopy 128

Amino acids 131

Proteins 144

Protein structure 159

Protein folding 167

Protein dynamics 174

Nucleic Acids 189

DNA 192

Molecular models of DNA 216

DNA structure 224

DNA Dynamics 232

Interactomics 239

References

Article Sources and Contributors 242

Image Sources, Licenses and Contributors 247

Permission is granted to copy, distribute

and/or modify this document under the terms

of the GNU Free Documentation License,

Version 1.2 or any later version published

by the Free Software Foundation, with no

Invariant Sections, no Front-Cover Texts,

and no Back-Cover Texts. A copy of the

license is included in ;the section entitled

"GNU Free Documentation License".

Edited by Bci2, with the contributors listedafter the Common Use License.

Spectroscopy—An Introduction

Spectroscopy

Spectroscopy was originally the study of the interaction between radiation and matter as a function of wavelength(A). In fact, historically, spectroscopy referred to the use of visible light dispersed according to its wavelength, e.g.by a prism. Later the concept was expanded greatly to comprise any measurement of a quantity as a function ofeither wavelength or frequency. Thus it also can refer to a response to an alternating field or varying frequency (v). Afurther extension of the scope of the definition added energy (E) as a variable, once the very close relationship E =hv for photons was realized (h is the Planck constant). A plot of the response as a function of wavelength—or morecommonly frequency—is referred to as a spectrum; see also spectral linewidth.

Spectrometry is the spectroscopic technique used to assess the concentration or amount of a given chemical(atomic, molecular, or ionic) species. In this case, the instrument that performs such measurements is a spectrometer,spectrophotometer, or spectrograph.

Spectroscopy/spectrometry is often used in physical and analytical chemistry for the identification of substancesthrough the spectrum emitted from or absorbed by them.

Spectroscopy/spectrometry is also heavily used in astronomy and remote sensing. Most large telescopes havespectrometers, which are used either to measure the chemical composition and physical properties of astronomicalobjects or to measure their velocities from the Doppler shift of their spectral lines.

Classification of methodsNature of excitation measured

The type of spectroscopy depends on the physical quantity measured. Normally, the quantity that is measured is anintensity, either of energy absorbed or produced.

• Electromagnetic spectroscopy involves interactions of matter with electromagnetic radiation, such as light.

• Electron spectroscopy involves interactions with electron beams. Auger spectroscopy involves inducing theAuger effect with an electron beam. In this case the measurement typically involves the kinetic energy of theelectron as variable.

• Acoustic spectroscopy involves the frequency of sound.

• Dielectric spectroscopy involves the frequency of an external electrical field

• Mechanical spectroscopy involves the frequency of an external mechanical stress, e.g. a torsion applied to a pieceof material.

Measurement process

Most spectroscopic methods are differentiated as either atomic or molecular based on whether or not they apply toatoms or molecules. Along with that distinction, they can be classified on the nature of their interaction:

• Absorption spectroscopy uses the range of the electromagnetic spectra in which a substance absorbs. Thisincludes atomic absorption spectroscopy and various molecular techniques, such as infrared, ultraviolet-visibleand microwave spectroscopy.

• Emission spectroscopy uses the range of electromagnetic spectra in which a substance radiates (emits). Thesubstance first must absorb energy. This energy can be from a variety of sources, which determines the name of

the subsequent emission, like luminescence. Molecular luminescence techniques include spectrofluorimetry.• Scattering spectroscopy measures the amount of light that a substance scatters at certain wavelengths, incidentangles, and polarization angles. One of the most useful applications of light scattering spectroscopy is Ramanspectroscopy.

Common typesAbsorption

Absorption spectroscopy is a technique in which the power of a beam of light measured before and after interactionwith a sample is compared. Specific absorption techniques tend to be referred to by the wavelength of radiationmeasured such as ultraviolet, infrared or microwave absorption spectroscopy. Absorption occurs when the energy ofthe photons matches the energy difference between two states of the material.

Fluorescence

Fluorescence spectroscopy uses higherenergy photons to excite a sample,which will then emit lower energyphotons. This technique has becomepopular for its biochemical andmedical applications, and can be usedfor confocal microscopy, fluorescenceresonance energy transfer, andfluorescence lifetime imaging.

X-ray

When X-rays of sufficient frequency(energy) interact with a substance,inner shell electrons in the atom are

Wavelength | nanometer*)

Spectrum of light from a fluorescent lamp showing prominent mercury peaks

excited to outer empty orbitals, or they may be removed completely, ionizing the atom. The inner shell "hole" willthen be filled by electrons from outer orbitals. The energy available in this de-excitation process is emitted asradiation (fluorescence) or will remove other less-bound electrons from the atom (Auger effect). The absorption oremission frequencies (energies) are characteristic of the specific atom. In addition, for a specific atom smallfrequency (energy) variations occur which are characteristic of the chemical bonding. With a suitable apparatus,these characteristic X-ray frequencies or Auger electron energies can be measured. X-ray absorption and emissionspectroscopy is used in chemistry and material sciences to determine elemental composition and chemical bonding.

X-ray crystallography is a scattering process; crystalline materials scatter X-rays at well-defined angles. If thewavelength of the incident X-rays is known, this allows calculation of the distances between planes of atoms withinthe crystal. The intensities of the scattered X-rays give information about the atomic positions and allow thearrangement of the atoms within the crystal structure to be calculated. However, the X-ray light is then not dispersedaccording to its wavelength, which is set at a given value, and X-ray diffraction is thus not a spectroscopy.

Flame

Liquid solution samples are aspirated into a burner or nebulizer/burner combination, desolvated, atomized, andsometimes excited to a higher energy electronic state. The use of a flame during analysis requires fuel and oxidant,typically in the form of gases. Common fuel gases used are acetylene (ethyne) or hydrogen. Common oxidant gasesused are oxygen, air, or nitrous oxide. These methods are often capable of analyzing metallic element analytes in thepart per million, billion, or possibly lower concentration ranges. Light detectors are needed to detect light with theanalysis information coming from the flame.

• Atomic Emission Spectroscopy - This method uses flame excitation; atoms are excited from the heat of theflame to emit light. This method commonly uses a total consumption burner with a round burning outlet. A highertemperature flame than atomic absorption spectroscopy (AA) is typically used to produce excitation of analyteatoms. Since analyte atoms are excited by the heat of the flame, no special elemental lamps to shine into the flameare needed. A high resolution polychromator can be used to produce an emission intensity vs. wavelengthspectrum over a range of wavelengths showing multiple element excitation lines, meaning multiple elements canbe detected in one run. Alternatively, a monochromator can be set at one wavelength to concentrate on analysis ofa single element at a certain emission line. Plasma emission spectroscopy is a more modern version of thismethod. See Flame emission spectroscopy for more details.

• Atomic absorption spectroscopy (often called AA) - This method commonly uses a pre-burner nebulizer (ornebulizing chamber) to create a sample mist and a slot-shaped burner which gives a longer pathlength flame. Thetemperature of the flame is low enough that the flame itself does not excite sample atoms from their ground state.The nebulizer and flame are used to desolvate and atomize the sample, but the excitation of the analyte atoms isdone by the use of lamps shining through the flame at various wavelengths for each type of analyte. In AA, theamount of light absorbed after going through the flame determines the amount of analyte in the sample. Agraphite furnace for heating the sample to desolvate and atomize is commonly used for greater sensitivity. Thegraphite furnace method can also analyze some solid or slurry samples. Because of its good sensitivity andselectivity, it is still a commonly used method of analysis for certain trace elements in aqueous (and other liquid)samples.

• Atomic Fluorescence Spectroscopy - This method commonly uses a burner with a round burning outlet. Theflame is used to solvate and atomize the sample, but a lamp shines light at a specific wavelength into the flame toexcite the analyte atoms in the flame. The atoms of certain elements can then fluoresce emitting light in adifferent direction. The intensity of this fluorescing light is used for quantifying the amount of analyte element inthe sample. A graphite furnace can also be used for atomic fluorescence spectroscopy. This method is not ascommonly used as atomic absorption or plasma emission spectroscopy.

Plasma Emission Spectroscopy In some ways similar to flame atomic emission spectroscopy, it has largelyreplaced it.

• Direct-current plasma (DCP)

A direct-current plasma (DCP) is created by an electrical discharge between two electrodes. A plasma support gas isnecessary, and Ar is common. Samples can be deposited on one of the electrodes, or if conducting can make up oneelectrode.

• Glow discharge-optical emission spectrometry (GD-OES)

• Inductively coupled plasma-atomic emission spectrometry (ICP-AES)

• Laser Induced Breakdown Spectroscopy (LIBS) (LIBS), also called Laser-induced plasma spectrometry (LIPS)

• Microwave-induced plasma (MIP)

Spark or arc (emission) spectroscopy - is used for the analysis of metallic elements in solid samples. Fornon-conductive materials, a sample is ground with graphite powder to make it conductive. In traditional arcspectroscopy methods, a sample of the solid was commonly ground up and destroyed during analysis. An electric arc

or spark is passed through the sample, heating the sample to a high temperature to excite the atoms in it. The excitedanalyte atoms glow emitting light at various wavelengths which could be detected by common spectroscopicmethods. Since the conditions producing the arc emission typically are not controlled quantitatively, the analysis forthe elements is qualitative. Nowadays, the spark sources with controlled discharges under an argon atmosphere allowthat this method can be considered eminently quantitative, and its use is widely expanded worldwide throughproduction control laboratories of foundries and steel mills.

Visible

Many atoms emit or absorb visible light. In order to obtain a fine line spectrum, the atoms must be in a gas phase.This means that the substance has to be vaporised. The spectrum is studied in absorption or emission. Visibleabsorption spectroscopy is often combined with UV absorption spectroscopy in UV/Vis spectroscopy. Although thisform may be uncommon as the human eye is a similar indicator, it still proves useful when distinguishing colours.

Ultraviolet

All atoms absorb in the Ultraviolet (UV) region because these photons are energetic enough to excite outer electrons.If the frequency is high enough, photoionization takes place. UV spectroscopy is also used in quantifying protein andDNA concentration as well as the ratio of protein to DNA concentration in a solution. Several amino acids usuallyfound in protein, such as tryptophan, absorb light in the 280 nm range and DNA absorbs light in the 260 nm range.For this reason, the ratio of 260/280 nm absorbance is a good general indicator of the relative purity of a solution interms of these two macromolecules. Reasonable estimates of protein or DNA concentration can also be made thisway using Beer's law.

Infrared

Infrared spectroscopy offers the possibility to measure different types of inter atomic bond vibrations at differentfrequencies. Especially in organic chemistry the analysis of IR absorption spectra shows what type of bonds arepresent in the sample. It is also an important method for analysing polymers and constituents like fillers, pigmentsand plasticizers.

Near Infrared (NIR)

The near infrared NIR range, immediately beyond the visible wavelength range, is especially important for practicalapplications because of the much greater penetration depth of NIR radiation into the sample than in the case of midIR spectroscopy range. This allows also large samples to be measured in each scan by NIR spectroscopy, and iscurrently employed for many practical applications such as: rapid grain analysis, medical diagnosispharmaceuticals/medicines , biotechnology, genomics analysis, proteomic analysis, interactomics research, inlinetextile monitoring, food analysis and chemical imaging/hyperspectral imaging of intact organisms , plastics,

textiles, insect detection, forensic lab application, crime detection, various military applications, and so on.

Raman

Raman spectroscopy uses the inelastic scattering of light to analyse vibrational and rotational modes of molecules.The resulting 'fingerprints' are an aid to analysis.

Coherent anti-Stokes Raman spectroscopy (CARS)

CARS is a recent technique that has high sensitivity and powerful applications for in vivo spectroscopy and

• [5]

imaging .

Nuclear magnetic resonance

Nuclear magnetic resonance spectroscopy analyzes the magnetic properties of certain atomic nuclei to determinedifferent electronic local environments of hydrogen, carbon, or other atoms in an organic compound or othercompound. This is used to help determine the structure of the compound.

Mossbauer

Transmission or conversion-electron (CEMS) modes of Mossbauer spectroscopy probe the properties of specificisotope nuclei in different atomic environments by analyzing the resonant absorption of characteristic energygamma-rays known as the Mossbauer effect.

Other types

There are many different types of materials analysis techniques under the broad heading of "spectroscopy", utilizinga wide variety of different approaches to probing material properties, such as absorbance, reflection, emission,scattering, thermal conductivity, and refractive index.

Acoustic spectroscopy

Auger spectroscopy is a method used to study surfaces of materials on a micro-scale. It is often used in

connection with electron microscopy.

Cavity ring down spectroscopy

Circular Dichroism spectroscopy

Deep-level transient spectroscopy measures concentration and analyzes parameters of electrically active defects in

semiconducting materials

Dielectric spectroscopy

Dual polarisation interferometry measures the real and imaginary components of the complex refractive index

Force spectroscopy

Fourier transform spectroscopy is an efficient method for processing spectra data obtained using interferometers.

Nearly all infrared spectroscopy techniques (such as FTIR) and nuclear magnetic resonance (NMR) are based on

Fourier transforms.

Fourier transform infrared spectroscopy (FTIR)

Hadron spectroscopy studies the energy/mass spectrum of hadrons according to spin, parity, and other particle

properties. Baryon spectroscopy and meson spectroscopy are both types of hadron spectroscopy.

Inelastic electron tunneling spectroscopy (IETS) uses the changes in current due to inelastic electron-vibration

interaction at specific energies which can also measure optically forbidden transitions.

Inelastic neutron scattering is similar to Raman spectroscopy, but uses neutrons instead of photons.

Laser spectroscopy uses lasers and other types of coherent emission sources, such as optical parametric

oscillators, for selective excitation of atomic or molecular species.

• Ultra fast laser spectroscopy

• Mechanical spectroscopy involves interactions with macroscopic vibrations, such as phonons. An example isacoustic spectroscopy, involving sound waves.

• Neutron spin echo spectroscopy measures internal dynamics in proteins and other soft matter systems

• Nuclear magnetic resonance (NMR)

• Photoacoustic spectroscopy measures the sound waves produced upon the absorption of radiation.

• Photothermal spectroscopy measures heat evolved upon absorption of radiation.

• Raman optical activity spectroscopy exploits Raman scattering and optical activity effects to reveal detailedinformation on chiral centers in molecules.

• Terahertz spectroscopy uses wavelengths above infrared spectroscopy and below microwave or millimeter wavemeasurements.

• Time-resolved spectroscopy is the spectroscopy of matter in situations where the properties are changing withtime.

• Thermal infrared spectroscopy measures thermal radiation emitted from materials and surfaces and is used todetermine the type of bonds present in a sample as well as their lattice environment. The techniques are widelyused by organic chemists, mineralogists, and planetary scientists.

Background subtraction

Background subtraction is a term typically used in spectroscopy when one explains the process of acquiring abackground radiation level (or ambient radiation level) and then makes an algorithmic adjustment to the data toobtain qualitative information about any deviations from the background, even when they are an order of magnitudeless decipherable than the background itself.

Background subtraction can affect a number of statistical calculations (Continuum, Compton, Bremsstrahlung)leading to improved overall system performance.

Applications

ro]

• Estimate weathered wood exposure times using Near infrared spectroscopy.

• Cure monitoring of composites using Optical fibers

Absorption cross section

Applied spectroscopy

Astronomical spectroscopy

Atomic spectroscopy

Nuclear magnetic resonance

2D-FT NMRI and Spectroscopy

2D correlation analysis

Near infrared spectroscopy

Coherent spectroscopy

Cold vapour atomic fluorescence spectroscopy

Deep-level transient spectroscopy

EPR spectroscopy

Gamma spectroscopy

Kelvin probe force microscope

Metamerism (color)

Rigid rotor

Spectroscopy 10

• Rotational spectroscopy

• Saturated spectroscopy

• Scanning tunneling spectroscopy

• Scattering theory

• Spectral power distributions

• Spectral reflectance

• Spectrophotometry

• Spectroscopic notation

• Spectrum analysis

• The Unscrambler (CAMO Software)

• Vibrational spectroscopy

• Vibrational circular dichroism spectroscopy

• Robert Bunsen

• Gustav Kirchhoff

• Joseph von Fraunhofer

[91

• Spectroscopy links at the Open Directory Project

• Amateur spectroscopy links at the Open Directory Project

• Timeline of Spectroscopy

• Chemometric Analysis for Spectroscopy

ri3i

• The Science of Spectroscopy - supported by NASA, includes OpenSpectrum, a Wiki-based learning tool forspectroscopy that anyone can edit

ri4i

• A Short Study of the Characteristics of two Lab Spectroscopes

• NIST government spectroscopy data

• Potentiodynamic Electrochemical Impedance Spectroscopy

References

[I] J. Dubois, G. Sando, E. N. Lewis, Near-Infrared Chemical Imaging, A Valuable Tool for the Pharmaceutical Industry, G.I.T. LaboratoryJournal Europe, No. 1-2, 2007

[2] http://www.malvern.com/LabEng/produc...bliography.htm E. N. Lewis, E. Lee and L. H. Kidder, Combining

Imaging and Spectroscopy: Solving Problems with Near-Infrared Chemical Imaging. Microscopy Today, Volume 12, No. 6, 11/2004.[3] Near Infrared Microspectroscopy, Fluorescence Microspectroscopy,Infrared Chemical Imaging and High Resolution Nuclear Magnetic

Resonance Analysis of Soybean Seeds, Somatic Embryos and Single Cells., Baianu, I.C. et al. 2004., In Oil Extraction and Analysis., D.

Luthria, Editor pp.241-273, AOCS Press., Champaign, IL.[4] Single Cancer Cell Detection by Near Infrared Microspectroscopy, Infrared Chemical Imaging and Fluorescence Microspectroscopy.2004.1.

C. Baianu, D. Costescu, N. E. Hofmann and S. S. Korban, q-bio/0407006 (July 2004) (http://arxiv.org/abs/q-bio/0407006)[5] C.L. Evans and X.S. Xie.2008. Coherent Anti-Stokes Raman Scattering Microscopy: Chemical Imaging for Biology and Medicine.,

doi:10.1146/annurev.anchem.l.031207.112754 AnnualReview of Analytical Chemistry, 1: 883-909.[6] W. Demtroder, Laser Spectroscopy, 3rd Ed. (Springer, 2003).

[7] F. J. Duarte (Ed.), Tunable Laser Applications, 2nd Ed. (CRC, 2009) Chapter 2. (http://www.opticsjournal.com/tla.htm)[8] "Using NIR Spectroscopy to Predict Weathered Wood Exposure Times" (http://www.fpl.fs.fed.us/documnts/pdf2006/

fpl_2006_wang002.pdf). .[9] http://www.dmoz.Org//Science/Physics...troscopy//[10] http://www.dmoz.Org//Science/Astrono...Spectroscopy//

[II] http ://spectroscopyonline. findanalytichem. com/spectroscopy/article/articleDetail.j sp?id=3 81944& sk=&date=&pageID=8[12] http://www.laboratoryequipment.com/a...ctroscopy.aspx

11

Fourier transform spectroscopy

Fourier transform spectroscopy is a measurement technique whereby spectra are collected based on measurementsof the coherence of a radiative source, using time-domain or space-domain measurements of the electromagneticradiation or other type of radiation. It can be applied to a variety of types of spectroscopy including opticalspectroscopy, infrared spectroscopy (FT IR, FT-NIRS), Fourier transform (FT) nuclear magnetic resonance , massspectrometry and electron spin resonance spectroscopy. There are several methods for measuring the temporalcoherence of the light, including the continuous wave Michelson or Fourier transform spectrometer and the pulsedFourier transform spectrograph (which is more sensitive and has a much shorter sampling time than conventionalspectroscopic techniques, but is only applicable in a laboratory environment).

Conceptual introduction

Measuring an emission spectrum

One of the most basic tasks in spectroscopy is to characterize thespectrum of a light source: How much light is emitted at each differentwavelength. The most straightforward way to measure a spectrum is topass the light through a monochromator, an instrument that blocks allof the light except the light at a certain wavelength (the un-blockedwavelength is set by a knob on the monochromator). Then the intensityof this remaining (single-wavelength) light is measured. The measuredintensity directly indicates how much light is emitted at thatwavelength. By varying the monochromator's wavelength setting, thefull spectrum can be measured. This simple scheme in fact describeshow some spectrometers work.

 Cj . C2 ** A ^X> aV J ^

400 500

Wavelength / nm

An example of a spectrum: The spectrum of lightemitted by the blue flame of a butane torch. Thehorizontal axis is the wavelength of light, and thevertical axis represents how much light is emittedby the torch at that wavelength.

Fourier transform spectroscopy is a less intuitive way to get the same

information. Rather than allowing only one wavelength at a time to

pass through to the detector, this technique lets through a beam

containing many different wavelengths of light at once, and measures the total beam intensity. Next, the beam is

modified to contain a different combination of wavelengths, giving a second data point. This process is repeated

many times. Afterwards, a computer takes all this data and works backwards to infer how much light there is at each

wavelength.

To be more specific, between the light source and the detector, there is a certain configuration of mirrors that allowssome wavelengths to pass through but blocks others (due to wave interference). The beam is modified for each newdata point by moving one of the mirrors; this changes the set of wavelengths that can pass through.

As mentioned, computer processing is required to turn the raw data (light intensity for each mirror position) into thedesired result (light intensity for each wavelength). The processing required turns out to be a common algorithmcalled the Fourier transform (hence the name, "Fourier transform spectroscopy"). The raw data is sometimes calledan "interferogram".

12

Measuring an absorption spectrum

The method of Fourier transform spectroscopy can also be used for

absorption spectroscopy. The primary example is "FTIR

Spectroscopy", a common technique in chemistry. In general, the goal

of absorption spectroscopy is to measure how well a sample absorbs or

transmits light at each different wavelength. However, any technique

for emission spectroscopy can also be used for absorption spectroscopy

as follows: Assume you have a working spectrometer that can measure

the spectrum of any light source shining into it (as described above).

Shine a broadband light source into the spectrometer, then shine the

same light source through the sample into the same spectrometer.

Comparing the two spectra, it will be obvious which wavelengths get

absorbed by the sample and which wavelengths can pass right through

the sample. (More precisely, the spectrum with the sample, divided by

the "background" spectrum without the sample, equals the fraction of light that the sample can transmit at each

wavelength.)

Accordingly, the technique of "Fourier transform spectroscopy" can be used both for measuring emission spectra (forexample, the emission spectrum of a star), and absorption spectra (for example, the absorption spectrum of a glass ofliquid).

10720 10700 10BS0 10600 10B40

relative Ortekocrrjn

An interferogram from a Fourier transform

spectrometer. The horizontal axis is the position

of the mirror, and the vertical axis is the amount

of light detected. This is the "raw data" which can

be transformed into an actual spectrum.

Continuous wave Michelson or Fourier transform spectrograph

coherentlight source

The Michelson spectrograph is similar to the

instrument used in the Michelson-Morley experiment.

Light from the source is split into two beams by a

half-silvered mirror, one is reflected off a fixed mirror

and one off a moving mirror which introduces a time

delay — the Fourier transform spectrometer is just a

Michelson interferometer with a movable mirror. The

beams interfere, allowing the temporal coherence of the

light to be measured at each different time delay

setting, effectively converting the time domain into a

spatial coordinate. By making measurements of the

signal at many discrete positions of the moving mirror,

the spectrum can be reconstructed using a Fourier

transform of the temporal coherence of the light.

Michelson spectrographs are capable of very high

spectral resolution observations of very bright sources.

The Michelson or Fourier transform spectrograph was

popular for infra-red applications at a time when

infra-red astronomy only had single pixel detectors.

Imaging Michelson spectrometers are a possibility, but in general have been supplanted by imaging Fabry-Perot

instruments which are easier to construct.

detector

The Fourier transform spectrometer is just a Michelson

interferometer but one of the two fully-reflecting mirrors is movable,

allowing a variable delay (in the travel-time of the light) to be

included in one of the beams.

Extracting the spectrum

The intensity as a function of the path length difference in the interferometer pand wavenumber y = 1 /\ is

Ifa V) = I(l>) [1 + COs(27TI>p)],

where 1(D) is the spectrum to be determined. Note that it is not necessary for 1(D) to be modulated by the samplebefore the interferometer. In fact, most FTIR spectrometers place the sample after the interferometer in the opticalpath. The total intensity at the detector is

I(p) = I{p,D)dD = I(D)[l + cos(2nDp)]dD.Jo Jo

This is just a Fourier cosine transform. The inverse gives us our desired result in terms of the measured quantity

("OO

Up) = 4 / [I(p) - \l{p = 0)] cos(27ri>p)dp.Jo

Pulsed Fourier transform spectrometer

A pulsed Fourier transform spectrometer does not employ transmittance techniques. In the most general descriptionof pulsed FT spectrometry, a sample is exposed to an energizing event which causes a periodic response. Thefrequency of the periodic response, as governed by the field conditions in the spectrometer, is indicative of themeasured properties of the analyte.

Examples of Pulsed Fourier transform spectrometry

In magnetic spectroscopy (EPR, NMR), an RF pulse in a strong ambient magnetic field is used as the energizingevent. This turns the magnetic particles at an angle to the ambient field, resulting in gyration. The gyrating spins theninduce a periodic current in a detector coil. Each spin exhibits a characteristic frequency of gyration (relative to thefield strength) which reveals information about the analyte.

In FT-mass spectrometry, the energizing event is the injection of the charged sample into the strong electromagneticfield of a cyclotron. These particles travel in circles, inducing a current in a fixed coil on one point in their circle.Each traveling particle exhibits a characteristic cyclotron frequency-field ratio revealing the masses in the sample.

The Free Induction Decay

Pulsed FT spectrometry gives the advantage of requiring a single, time-dependent measurement which can easilydeconvolute a set of similar but distinct signals. The resulting composite signal, is called a free induction decay,because typically the signal will decay due to inhomogeneities in sample frequency, or simply unrecoverable loss ofsignal due to entropic loss of the property being measured.

One of the most important advantages of Fourier transform spectroscopy was shown by P.B. Fellgett, an earlyadvocate of the method. The Fellgett advantage, also known as the multiplex principle, states that a multiplexspectrometer such as the Fourier transform spectroscopy will produce a gain of the order of the square root of m inthe signal-to-noise ratio of the resulting spectrum, when compared with an equivalent scanning monochromator,where m is the number of elements comprising the resulting spectrum when the measurement noise is dominated bydetector noise.

Fourier transform spectroscopy 14

Converting spectra from time domain to frequency domain

/•ooI(v)e-ilj2lTt dv-oo

The sum is performed over all contributing frequencies to give a signal S(t) in the time domain.

/■oos(ty"27rtdt-oo

gives non-zero value when S(t) contains a component that matches the oscillating function.Remember that

elx = cos x + i sin x

• Applied spectroscopy

• 2D-FT NMRI and Spectroscopy

• Forensic chemistry

• Forensic polymer engineering

• nuclear magnetic resonance

• Infra-red spectroscopy

• Ellis, D.I. and Goodacre, R. (2006). "Metabolic fingerprinting in disease diagnosis: biomedical applications ofinfrared and Raman spectroscopy". The Analyst 131: 875—885. doi:10.1039/b602376m.

T31

• Description of how a Fourier transform spectrometer works

• The Michelson or Fourier transform spectrograph

• Internet Journal of Vibrational Spectroscopy - How FTIR works

• Fourier Transform Spectroscopy Topical Meeting and Tabletop Exhibit

References

[1] Antoine Abragam. 1968. Principles of Nuclear Magnetic Resonance., 895 pp., Cambridge University Press: Cambridge, UK.

[2] Peter Atkins, Julio De Paula. 2006. Physical Chemistry., 8th ed. Oxford University Press: Oxford, UK.

Spectroscopy Theory

Quantum mechanics

Quantum mechanics (QM) is a set of scientificprinciples describing the known behavior ofenergy and matter that predominate at the atomicand subatomic scales. The name derives from theobservation that some physical quantities—suchas the energy of an electron—can be changedonly by set amounts, or quanta, rather than beingcapable of varying by any amount. Thewave—particle duality of energy and matter at theatomic scale provides a unified view of thebehavior of particles such as photons andelectrons. Photons are the quanta of light, andhave energy values proportional to theirfrequency via the Planck constant. An electronbound in an atomic orbital has quantized values ofangular momentum and energy. The unboundelectron does not exhibit quantized energy levels,but is associated with a quantum mechanicalwavelength, as are all massive particles. The fullsignificance of the Planck constant is expressed inphysics through the abstract mathematical notionof action.

o - m—4

Fig. 1: Probability densities corresponding to the wavefunctions of anelectron in a hydrogen atom possessing definite energy levels (increasing

from the top of the image to the bottom: n = 1,2, 3, ...) and angularmomentum (increasing across from left to right: s, p, d,...). Brighter areas

correspond to higher probability density in a position measurement.Wavefunctions like these are directly comparable to Chladni's figures of

acoustic modes of vibration classical physics and are indeed modes of

oscillation as well: they possess a sharp energy and thus a keen frequency.

The angular momentum and energy are quantized, and only take on discrete

values like those shown (as is the case for resonant frequencies in

acoustics).

The mathematical formulation of quantum

mechanics is abstract and its implications are

often non-intuitive. The centerpiece of this

mathematical system is the wavefunction. The

wavefunction is a mathematical function of time and space that can provide information about the position and

momentum of a particle, but only as probabilities, as dictated by the constraints imposed by the uncertainty principle.

Mathematical manipulations of the wavefunction usually involve the bra-ket notation, which requires an

understanding of complex numbers and linear functionals. Many of the results of QM can only be expressed

mathematically and do not have models that are as easy to visualize as those of classical mechanics. For instance, the

ground state in quantum mechanical model is a non-zero energy state that is the lowest permitted energy state of a

system, rather than a more traditional system that is thought of as simple being at rest with zero kinetic energy.

Overview

The word quantum derives from Latin meaning "how great" or "how much". In quantum mechanics, it refers to adiscrete unit that quantum theory assigns to certain physical quantities, such as the energy of an atom at rest (seeFigure 1). The discovery that particles are discrete packets of energy with wave-like properties led to the branch of

physics that deals with atomic and subatomic systems which is today called quantum mechanics. It is the underlyingmathematical framework of many fields of physics and chemistry, including condensed matter physics, solid-statephysics, atomic physics, molecular physics, computational physics, computational chemistry, quantum chemistry,particle physics, nuclear chemistry, and nuclear physics. The foundations of quantum mechanics were establishedduring the first half of the twentieth century by Werner Heisenberg, Max Planck, Louis de Broglie, Albert Einstein,Niels Bohr, Erwin Schrodinger, Max Born, John von Neumann, Paul Dirac, Wolfgang Pauli, David Hilbert, andothers. Some fundamental aspects of the theory are still actively studied.

Quantum mechanics is essential to understand the behavior of systems at atomic length scales and smaller. Forexample, if classical mechanics governed the workings of an atom, electrons would rapidly travel towards andcollide with the nucleus, making stable atoms impossible. However, in the natural world the electrons normallyremain in an uncertain, non-deterministic "smeared" (wave—particle wave function) orbital path around or throughthe nucleus, defying classical electromagnetism.

Quantum mechanics was initially developed to provide a better explanation of the atom, especially the spectra oflight emitted by different atomic species. The quantum theory of the atom was developed as an explanation for theelectron's staying in its orbital, which could not be explained by Newton's laws of motion and by Maxwell's laws ofclassical electromagnetism.

In the formalism of quantum mechanics, the state of a system at a given time is described by a complex wavefunction (sometimes referred to as orbitals in the case of atomic electrons), and more generally, elements of acomplex vector space. This abstract mathematical object allows for the calculation of probabilities of outcomes ofconcrete experiments. For example, it allows one to compute the probability of finding an electron in a particularregion around the nucleus at a particular time. Contrary to classical mechanics, one can never make simultaneouspredictions of conjugate variables, such as position and momentum, with accuracy. For instance, electrons may beconsidered to be located somewhere within a region of space, but with their exact positions being unknown.Contours of constant probability, often referred to as "clouds", may be drawn around the nucleus of an atom toconceptualize where the electron might be located with the most probability. Heisenberg's uncertainty principlequantifies the inability to precisely locate the particle given its conjugate.

The other exemplar that led to quantum mechanics was the study of electromagnetic waves such as light. When itwas found in 1900 by Max Planck that the energy of waves could be described as consisting of small packets orquanta, Albert Einstein further developed this idea to show that an electromagnetic wave such as light could bedescribed by a particle called the photon with a discrete energy dependent on its frequency. This led to a theory ofunity between subatomic particles and electromagnetic waves called wave—particle duality in which particles andwaves were neither one nor the other, but had certain properties of both. While quantum mechanics describes theworld of the very small, it also is needed to explain certain macroscopic quantum systems such as superconductorsand superfluids.

Broadly speaking, quantum mechanics incorporates four classes of phenomena for which classical physics cannotaccount: (I) the quantization (discretization) of certain physical quantities, (II) wave—particle duality, (III) theuncertainty principle, and (IV) quantum entanglement. Each of these phenomena is described in detail in subsequentsections.

History

The history of quantum mechanics began with the 1838 discovery of cathode rays by Michael Faraday, the 1859statement of the black body radiation problem by Gustav Kirchhoff, the 1877 suggestion by Ludwig Boltzmann thatthe energy states of a physical system could be discrete, and the 1900 quantum hypothesis by Max Planck.Planck's hypothesis stated that any energy is radiated and absorbed in quantities divisible by discrete "energyelements", such that each energy element E is proportional to its frequency v:

E = hv

where h is Planck's action constant. Planck insisted that this was simply an aspect of the processes of absorption and

ro"|

emission of radiation and had nothing to do with the physical reality of the radiation itself. However, at that time,this appeared not to explain the photoelectric effect (1839), i.e. that shining light on certain materials can ejectelectrons from the material. In 1905, basing his work on Planck's quantum hypothesis, Albert Einstein postulated thatlight itself consists of individual quanta.

In the mid-1920s, developments in quantum mechanics quickly led to it becoming the standard formulation foratomic physics. In the summer of 1925, Bohr and Heisenberg published results that closed the "Old QuantumTheory". Light quanta came to be called photons (1926). From Einstein's simple postulation was born a flurry ofdebating, theorizing and testing, and thus, the entire field of quantum physics, leading to its wider acceptance at theFifth Solvay Conference in 1927.

Quantum mechanics and classical physics

Predictions of quantum mechanics have been verified experimentally to a very high degree of accuracy. Thus, thecurrent logic of correspondence principle between classical and quantum mechanics is that all objects obey laws ofquantum mechanics, and classical mechanics is just a quantum mechanics of large systems (or a statistical quantummechanics of a large collection of particles). Laws of classical mechanics thus follow from laws of quantummechanics at the limit of large systems or large quantum numbers. However, chaotic systems do not have goodquantum numbers, and quantum chaos studies the relationship between classical and quantum descriptions in thesesystems.

The main differences between classical and quantum theories have already been mentioned above in the remarks onthe Einstein-Podolsky-Rosen paradox. Essentially the difference boils down to the statement that quantummechanics is coherent (addition of amplitudes), whereas classical theories are incoherent (addition of intensities).Thus, such quantities as coherence lengths and coherence times come into play. For microscopic bodies theextension of the system is certainly much smaller than the coherence length; for macroscopic bodies one expects thatit should be the other way round. An exception to this rule can occur at extremely low temperatures, whenquantum behavior can manifest itself on more macroscopic scales (see Bose-Einstein condensate).

This is in accordance with the following observations:

Many macroscopic properties of classical systems are direct consequences of quantum behavior of its parts. Forexample, the stability of bulk matter (which consists of atoms and molecules which would quickly collapse under

electric forces alone), the rigidity of solids, and the mechanical, thermal, chemical, optical and magnetic properties

ri2iof matter are all results of interaction of electric charges under the rules of quantum mechanics.

While the seemingly exotic behavior of matter posited by quantum mechanics and relativity theory become moreapparent when dealing with extremely fast-moving or extremely tiny particles, the laws of classical Newtonianphysics remain accurate in predicting the behavior of large objects—of the order of the size of large molecules and

ri3i

bigger—at velocities much smaller than the velocity of light.

18

Theory

There are numerous mathematically equivalent formulations of quantum mechanics. One of the oldest and mostcommonly used formulations is the transformation theory proposed by Cambridge theoretical physicist Paul Dirac,which unifies and generalizes the two earliest formulations of quantum mechanics, matrix mechanics (invented byWerner Heisenberg) and wave mechanics (invented by Erwin Schrodinger).

In this formulation, the instantaneous state of a quantum system encodes the probabilities of its measurableproperties, or "observables". Examples of observables include energy, position, momentum, and angular momentum.Observables can be either continuous (e.g., the position of a particle) or discrete (e.g., the energy of an electron

ri7i

bound to a hydrogen atom). Generally, quantum mechanics does not assign definite values to observables.Instead, it makes predictions using probability distributions; that is, the probability of obtaining possible outcomesfrom measuring an observable. Oftentimes these results are skewed by many causes, such as dense probabilityclouds or quantum state nuclear attraction. Naturally, these probabilities will depend on the quantum state

at the "instant" of the measurement. Hence, uncertainty is involved in the value. There are, however, certain states

that are associated with a definite value of a particular observable. These are known as eigenstates of the observable

1211("eigen" can be translated from German as inherent or as a characteristic). In the everyday world, it is natural and

intuitive to think of everything (every observable) as being in an eigenstate. Everything appears to have a definite

position, a definite momentum, a definite energy, and a definite time of occurrence. However, quantum mechanics

does not pinpoint the exact values of a particle for its position and momentum (since they are conjugate pairs) or its

energy and time (since they too are conjugate pairs); rather, it only provides a range of probabilities of where that

particle might be given its momentum and momentum probability. Therefore, it is helpful to use different words to

describe states having uncertain values and states having definite values (eigenstate).

For example, consider a free particle.

In quantum mechanics, there is

wave-particle duality so the properties

of the particle can be described as the

properties of a wave. Therefore, its

quantum state can be represented as a

wave of arbitrary shape and extending

over space as a wave function. The

position and momentum of the particle

are observables. The Uncertainty

Principle states that both the position

and the momentum cannot

simultaneously be measured with full

precision at the same time. However,

one can measure the position alone of a

moving free particle creating an eigenstate of position with a wavefunction that is very large (a Dirac delta) at a

particular position x and zero everywhere else. If one performs a position measurement on such a wavefunction, the

result x will be obtained with 100% probability (full certainty). This is called an eigenstate of position

(mathematically more precise: a generalized position eigenstate (eigendistribution)). If the particle is in an eigenstate

of position then its momentum is completely unknown. On the other hand, if the particle is in an eigenstate of

T221momentum then its position is completely unknown. In an eigenstate of momentum having a plane wave form, it

can be shown that the wavelength is equal to h/p, where h is Planck's constant and p is the momentum of the

* * [23]

eigenstate.

±J

Energy Level = #1

D=

Energy Level = #13 00 _l[j

■ H

3 opti

3D confined electron wave functions for each eigenstate in a Quantum Dot. Here,

rectangular and triangular-shaped quantum dots are shown. Energy states in rectangular

dots are more 's-type' and 'p-type'. However, in a triangular dot the wave functions are

mixed due to confinement symmetry.

Usually, a system will not be in an eigenstate of the observable we are interested in. However, if one measures theobservable, the wavefunction will instantaneously be an eigenstate (or generalized eigenstate) of that observable.

T241This process is known as wavefunction collapse, a debatable process. It involves expanding the system under

study to include the measurement device. If one knows the corresponding wave function at the instant before the

measurement, one will be able to compute the probability of collapsing into each of the possible eigenstates. For

example, the free particle in the previous example will usually have a wavefunction that is a wave packet centered

around some mean position x , neither an eigenstate of position nor of momentum. When one measures the position

[25]of the particle, it is impossible to predict with certainty the result. It is probable, but not certain, that it will be

near x , where the amplitude of the wave function is large. After the measurement is performed, having obtained

some result x, the wave function collapses into a position eigenstate centered at x.

Wave functions can change as time progresses. An equation known as the Schrodinger equation describes how wavefunctions change in time, a role similar to Newton's second law in classical mechanics. The Schrodinger equation,applied to the aforementioned example of the free particle, predicts that the center of a wave packet will movethrough space at a constant velocity, like a classical particle with no forces acting on it. However, the wave packetwill also spread out as time progresses, which means that the position becomes more uncertain. This also has the

effect of turning position eigenstates (which can be thought of as infinitely sharp wave packets) into broadened wave

T271packets that are no longer position eigenstates. Some wave functions produce probability distributions that are

constant or independent of time, such as when in a stationary state of constant energy, time drops out of the absolute

square of the wave function. Many systems that are treated dynamically in classical mechanics are described by such

"static" wave functions. For example, a single electron in an unexcited atom is pictured classically as a particle

moving in a circular trajectory around the atomic nucleus, whereas in quantum mechanics it is described by a static,

spherically symmetric wavefunction surrounding the nucleus (Fig. 1). (Note that only the lowest angular momentum

rofil

states, labeled s, are spherically symmetric).

The time evolution of wave functions is deterministic in the sense that, given a wavefunction at an initial time, it

[291makes a definite prediction of what the wavefunction will be at any later time. During a measurement, the change

of the wavefunction into another one is not deterministic, but rather unpredictable, i.e., random. A time-evolution

simulation can be seen here. [30]

The probabilistic nature of quantum mechanics thus stems from the act of measurement. This is one of the mostdifficult aspects of quantum systems to understand. It was the central topic in the famous Bohr-Einstein debates, inwhich the two scientists attempted to clarify these fundamental principles by way of thought experiments. In thedecades after the formulation of quantum mechanics, the question of what constitutes a "measurement" has beenextensively studied. Interpretations of quantum mechanics have been formulated to do away with the concept of"wavefunction collapse"; see, for example, the relative state interpretation. The basic idea is that when a quantumsystem interacts with a measuring apparatus, their respective wavefunctions become entangled, so that the originalquantum system ceases to exist as an independent entity. For details, see the article on measurement in quantummechanics.

Mathematical formulation

T321In the mathematically rigorous formulation of quantum mechanics, developed by Paul Dirac and John von

T331Neumann, the possible states of a quantum mechanical system are represented by unit vectors (called "state

vectors") residing in a complex separable Hilbert space (variously called the "state space" or the "associated Hilbert

space" of the system) well defined up to a complex number of norm 1 (the phase factor). In other words, the possible

states are points in the projectivization of a Hilbert space, usually called the complex projective space. The exact

nature of this Hilbert space is dependent on the system; for example, the state space for position and momentum

states is the space of square-integrable functions, while the state space for the spin of a single proton is just the

product of two complex planes. Each observable is represented by a maximally-Hermitian (precisely: by a

self-adjoint) linear operator acting on the state space. Each eigenstate of an observable corresponds to an eigenvector

of the operator, and the associated eigenvalue corresponds to the value of the observable in that eigenstate. If the

operator's spectrum is discrete, the observable can only attain those discrete eigenvalues.

The time evolution of a quantum state is described by the Schrodinger equation, in which the Hamiltonian, theoperator corresponding to the total energy of the system, generates time evolution.

The inner product between two state vectors is a complex number known as a probability amplitude. During ameasurement, the probability that a system collapses from a given initial state to a particular eigenstate is given bythe square of the absolute value of the probability amplitudes between the initial and final states. The possible resultsof a measurement are the eigenvalues of the operator — which explains the choice of Hermitian operators, for whichall the eigenvalues are real. We can find the probability distribution of an observable in a given state by computingthe spectral decomposition of the corresponding operator. Heisenberg's uncertainty principle is represented by thestatement that the operators corresponding to certain observables do not commute.

The Schrodinger equation acts on the entire probability amplitude, not merely its absolute value. Whereas theabsolute value of the probability amplitude encodes information about probabilities, its phase encodes informationabout the interference between quantum states. This gives rise to the wave-like behavior of quantum states.

It turns out that analytic solutions of Schrodinger's equation are only available for a small number of modelHamiltonians, of which the quantum harmonic oscillator, the particle in a box, the hydrogen molecular ion and thehydrogen atom are the most important representatives. Even the helium atom, which contains just one more electronthan hydrogen, defies all attempts at a fully analytic treatment. There exist several techniques for generatingapproximate solutions. For instance, in the method known as perturbation theory one uses the analytic results for asimple quantum mechanical model to generate results for a more complicated model related to the simple model by,for example, the addition of a weak potential energy. Another method is the "semi-classical equation of motion"approach, which applies to systems for which quantum mechanics produces weak deviations from classical behavior.The deviations can be calculated based on the classical motion. This approach is important for the field of quantumchaos.

An alternative formulation of quantum mechanics is Feynman's path integral formulation, in which aquantum-mechanical amplitude is considered as a sum over histories between initial and final states; this is thequantum-mechanical counterpart of action principles in classical mechanics.

Interactions with other scientific theories

The fundamental rules of quantum mechanics are very deep. They assert that the state space of a system is a Hilbertspace and the observables are Hermitian operators acting on that space, but do not tell us which Hilbert space orwhich operators, or if it even exists. These must be chosen appropriately in order to obtain a quantitative descriptionof a quantum system. An important guide for making these choices is the correspondence principle, which states thatthe predictions of quantum mechanics reduce to those of classical physics when a system moves to higher energiesor equivalently, larger quantum numbers. In other words, classical mechanics is simply a quantum mechanics oflarge systems. This "high energy" limit is known as the classical or correspondence limit. One can therefore startfrom an established classical model of a particular system, and attempt to guess the underlying quantum model thatgives rise to the classical model in the correspondence limit.

Unsolved problems in physics

^Q

In the correspondence limit of quantum mechanics: Is there a preferred interpretation of quantum mechanics? How does the quantumdescription of reality, which includes elements such as the "superposition of states" and "wavefunction collapse", give rise to the realitywe perceive?

When quantum mechanics was originally formulated, it was applied to models whose correspondence limit wasnon-relativistic classical mechanics. For instance, the well-known model of the quantum harmonic oscillator uses anexplicitly non-relativistic expression for the kinetic energy of the oscillator, and is thus a quantum version of theclassical harmonic oscillator.

Early attempts to merge quantum mechanics with special relativity involved the replacement of the Schrodingerequation with a covariant equation such as the Klein-Gordon equation or the Dirac equation. While these theorieswere successful in explaining many experimental results, they had certain unsatisfactory qualities stemming fromtheir neglect of the relativistic creation and annihilation of particles. A fully relativistic quantum theory required thedevelopment of quantum field theory, which applies quantization to a field rather than a fixed set of particles. Thefirst complete quantum field theory, quantum electrodynamics, provides a fully quantum description of theelectromagnetic interaction.

The full apparatus of quantum field theory is often unnecessary for describing electrodynamic systems. A simplerapproach, one employed since the inception of quantum mechanics, is to treat charged particles as quantummechanical objects being acted on by a classical electromagnetic field. For example, the elementary quantum modelof the hydrogen atom describes the electric field of the hydrogen atom using a classical —-^-—7 Coulomb

potential. This "semi-classical" approach fails if quantum fluctuations in the electromagnetic field play an importantrole, such as in the emission of photons by charged particles.

Quantum field theories for the strong nuclear force and the weak nuclear force have been developed. The quantumfield theory of the strong nuclear force is called quantum chromodynamics, and describes the interactions of thesubnuclear particles: quarks and gluons. The weak nuclear force and the electromagnetic force were unified, in their

quantized forms, into a single quantum field theory known as electroweak theory, by the physicists Abdus Salam,

T341Sheldon Glashow and Steven Weinberg. These three men shared the Nobel Prize in Physics in 1979 for this work.

It has proven difficult to construct quantum models of gravity, the remaining fundamental force. Semi-classicalapproximations are workable, and have led to predictions such as Hawking radiation. However, the formulation of acomplete theory of quantum gravity is hindered by apparent incompatibilities between general relativity, the mostaccurate theory of gravity currently known, and some of the fundamental assumptions of quantum theory. Theresolution of these incompatibilities is an area of active research, and theories such as string theory are among thepossible candidates for a future theory of quantum gravity.

In the 21st century classical mechanics has been extended into the complex domain and complex classical mechanics

T351exhibits behaviours very similar to quantum mechanics.

Example

The particle in a 1-dimensional potential energy box is the most simple example where restraints lead to thequantization of energy levels. The box is defined as zero potential energy inside a certain interval and infiniteeverywhere outside that interval. For the 1-dimensional case in the x direction, the time-independent Schrodingerequation can be written as:

2m dx2The general solutions are:

T)2k2if>(x) = Aelkx + Be-lkx E = ——

2m

or, from Euler's formula,

ip(x) — C sin kx + D cos kx.The presence of the walls of the box determines the values of C, D, and k. At each wall (x = 0 and x = L), \p = 0.Thus when x = 0,

^(0) =0 = CsinO + DcosO = Z)and so D = 0. When x = L,

i/j(L) =0 = Csin£;L.C cannot be zero, since this would conflict with the Born interpretation. Therefore sin kL = 0, and so it must be thatkL is an integer multiple of jt. Therefore,

k = — n = 1, 2, 3,....

LThe quantization of energy levels follows from this constraint on k, since

^ fcW n2h2E

2mL2 SmL2'

Attempts at a unified field theory

As of 2010 the quest for unifying the fundamental forces through quantum mechanics is still ongoing. Quantum

T371electrodynamics (or "quantum electromagnetism"), which is currently the most accurately tested physical theory,

has been successfully merged with the weak nuclear force into the electroweak force and work is currently being

done to merge the electroweak and strong force into the electrostrong force. Current predictions state that at around

10 GeV the three aforementioned forces are fused into a single unified field, Beyond this "grand unification", it

is speculated that it may be possible to merge gravity with the other three gauge symmetries, expected to occur at

19roughly 10 GeV. However— and while special relativity is parsimoniously incorporated into quantum

electrodynamics — the expanded general relativity, currently the best theory describing the gravitation force, has not

been fully incorporated into quantum theory.

Relativity and quantum mechanics

Main articles: Quantum gravity and Theory of everything

Even with the defining postulates of both Einstein's theory of general relativity and quantum theory beingindisputably supported by rigorous and repeated empirical evidence and while they do not directly contradict eachother theoretically (at least with regard to primary claims), they are resistant to being incorporated within onecohesive model.

Einstein himself is well known for rejecting some of the claims of quantum mechanics. While clearly contributing tothe field, he did not accept the more philosophical consequences and interpretations of quantum mechanics, such asthe lack of deterministic causality and the assertion that a single subatomic particle can occupy numerous areas ofspace at one time. He also was the first to notice some of the apparently exotic consequences of entanglement andused them to formulate the Einstein-Podolsky-Rosen paradox, in the hope of showing that quantum mechanics hadunacceptable implications. This was 1935, but in 1964 it was shown by John Bell (see Bell inequality) that Einstein'sassumption was correct, but had to be completed by hidden variables and thus based on wrong philosophicalassumptions. According to the paper of J. Bell and the Copenhagen interpretation (the common interpretation ofquantum mechanics by physicists since 1927), and contrary to Einstein's ideas, quantum mechanics was

• neither a "realistic" theory (since quantum measurements do not state pre-existing properties, but rather theyprepare properties)

• nor a local theory (essentially not, because the state vector \ip) determines simultaneously the probabilityamplitudes at all sites, Ujj\ —> ■j/.'fr), Vr)-

The Einstein-Podolsky-Rosen paradox shows in any case that there exist experiments by which one can measure thestate of one particle and instantaneously change the state of its entangled partner, although the two particles can bean arbitrary distance apart; however, this effect does not violate causality, since no transfer of information happens.These experiments are the basis of some of the most topical applications of the theory, quantum cryptography, whichhas been on the market since 2004 and works well, although at small distances of typically < 1000 km.

Gravity is negligible in many areas of particle physics, so that unification between general relativity and quantummechanics is not an urgent issue in those applications. However, the lack of a correct theory of quantum gravity is animportant issue in cosmology and physicists' search for an elegant "theory of everything". Thus, resolving theinconsistencies between both theories has been a major goal of twentieth- and twenty-first-century physics. Manyprominent physicists, including Stephen Hawking, have labored in the attempt to discover a theory underlyingeverything, combining not only different models of subatomic physics, but also deriving the universe's fourforces —the strong force, electromagnetism, weak force, and gravity— from a single force or phenomenon. One ofthe leaders in this field is Edward Witten, a theoretical physicist who formulated the groundbreaking M-theory,which is an attempt at describing the supersymmetrical based string theory.

Applications

Quantum mechanics has had enormous success in explaining many of the features of our world. The individualbehaviour of the subatomic particles that make up all forms of matter—electrons, protons, neutrons, photons andothers—can often only be satisfactorily described using quantum mechanics. Quantum mechanics has stronglyinfluenced string theory, a candidate for a theory of everything (see reductionism) and the multiverse hypothesis. It isalso related to statistical mechanics.

Quantum mechanics is important for understanding how individual atoms combine covalently to form chemicals ormolecules. The application of quantum mechanics to chemistry is known as quantum chemistry. (Relativistic)quantum mechanics can in principle mathematically describe most of chemistry. Quantum mechanics can providequantitative insight into ionic and covalent bonding processes by explicitly showing which molecules areenergetically favorable to which others, and by approximately how much. Most of the calculations performed in

24

computational chemistry rely on quantum mechanics

Much of modern technology operatesat a scale where quantum effects aresignificant. Examples include the laser,the transistor (and thus the microchip),the electron microscope, and magneticresonance imaging. The study ofsemiconductors led to the invention ofthe diode and the transistor, which areindispensable for modern electronics.

[41]

Result: iBands+Transmission+CurrentDensity+IV

-

0.3 ■

0.2 -

oj 0.1

0 -

±J

0 12 3

Composite Plot AxisBancls+Transmission+QiiTientDensity+IV = 1_Bias=0V

El =

J Optio

A working mechanism of a Resonant Tunneling Diode device, based on the phenomenonof quantum tunneling through the potential barriers.

Researchers are currently seeking

robust methods of directly

manipulating quantum states. Efforts

are being made to develop quantum

cryptography, which will allow

guaranteed secure transmission of

information. A more distant goal is the

development of quantum computers,

which are expected to perform certain

faster than classical computers. Another active research topic is quantum teleportation, which deals with techniques

to transmit quantum states over arbitrary distances.

Quantum tunneling is vital in many devices, even in the simple light switch, as otherwise the electrons in the electriccurrent could not penetrate the potential barrier made up of a layer of oxide. Flash memory chips found in USBdrives use quantum tunneling to erase their memory cells.

QM primarily applies to the atomic regimes of matter and energy, but some systems exhibit quantum mechanicaleffects on a large scale; superfluidity (the frictionless flow of a liquid at temperatures near absolute zero) is onewell-known example. Quantum theory also provides accurate descriptions for many previously unexplainedphenomena such as black body radiation and the stability of electron orbitals. It has also given insight into theworkings of many different biological systems, including smell receptors and protein structures. Even so,classical physics often can be a good approximation to results otherwise obtained by quantum physics, typically incircumstances with large numbers of particles or large quantum numbers. (However, some open questions remain inthe field of quantum chaos.)

Philosophical consequences

Since its inception, the many counter-intuitive results of quantum mechanics have provoked strong philosophicaldebate and many interpretations. Even fundamental issues such as Max Born's basic rules concerning probabilityamplitudes and probability distributions took decades to be appreciated.

The Copenhagen interpretation, due largely to the Danish theoretical physicist Niels Bohr, is the interpretation ofquantum mechanics most widely accepted amongst physicists. According to it, the probabilistic nature of quantummechanics predictions cannot be explained in terms of some other deterministic theory, and does not simply reflectour limited knowledge. Quantum mechanics provides probabilistic results because the physical universe is itselfprobabilistic rather than deterministic.

Albert Einstein, himself one of the founders of quantum theory, disliked this loss of determinism in measurement(this dislike is the source of his famous quote, "God does not play dice with the universe."). Einstein held that there

should be a local hidden variable theory underlying quantum mechanics and that, consequently, the present theorywas incomplete. He produced a series of objections to the theory, the most famous of which has become known asthe Einstein-Podolsky-Rosen paradox. John Bell showed that the EPR paradox led to experimentally testabledifferences between quantum mechanics and local realistic theories. Experiments have been performed confirming

the accuracy of quantum mechanics, thus demonstrating that the physical world cannot be described by local realistic

T431theories. The Bohr-Einstein debates provide a vibrant critique of the Copenhagen Interpretation from an

epistemological point of view.

The Everett many-worlds interpretation, formulated in 1956, holds that all the possibilities described by quantum

T441theory simultaneously occur in a multiverse composed of mostly independent parallel universes. This is not

accomplished by introducing some new axiom to quantum mechanics, but on the contrary by removing the axiom of

the collapse of the wave packet: All the possible consistent states of the measured system and the measuring

apparatus (including the observer) are present in a real physical (not just formally mathematical, as in other

interpretations) quantum superposition. Such a superposition of consistent state combinations of different systems is

called an entangled state.

While the multiverse is deterministic, we perceive non-deterministic behavior governed by probabilities, because wecan observe only the universe, i.e. the consistent state contribution to the mentioned superposition, we inhabit.Everett's interpretation is perfectly consistent with John Bell's experiments and makes them intuitivelyunderstandable. However, according to the theory of quantum decoherence, the parallel universes will never beaccessible to us. This inaccessibility can be understood as follows: Once a measurement is done, the measuredsystem becomes entangled with both the physicist who measured it and a huge number of other particles, some ofwhich are photons flying away towards the other end of the universe; in order to prove that the wave function did notcollapse one would have to bring all these particles back and measure them again, together with the system that wasmeasured originally. This is completely impractical, but even if one could theoretically do this, it would destroy anyevidence that the original measurement took place (including the physicist's memory).

Copenhagen interpretation

Correspondence rules

De Broglie—Bohm theory

Fine-structure constant

Interpretation of quantum mechanics

Introduction to quantum mechanics

Many-worlds interpretation

Measurement in quantum mechanics

Measurement problem

Photon dynamics in the double-slit experiment

Photon polarization

Physical ontology

Quantum chaos

Quantum chemistry

Quantum chemistry computer programs

Quantum chromodynamics

Quantum computers

Quantum decoherence

Quantum electrochemistry

Quantum electronics

Quantum field theory

Quantum information

Quantum mind

Quantum optics

Quantum pseudo-telepathy

Quantum thermodynamics

Quantum triviality

Quantum Zeno effect

Quasi-set theory

Relation between Schrodinger's equation and the path integral formulation of quantum mechanics

Schrodinger's cat

Theoretical and experimental justification for the Schrodinger equation

Theoretical chemistry

Transactional interpretation

Trojan wave packet

References

The following titles, all by working physicists, attempt to communicate quantum theory to lay people, using aminimum of technical apparatus.

• Chester, Marvin (1987) Primer of Quantum Mechanics. John Wiley. ISBN 0-486-42878-8

• Richard Feynman, 1985. QED: The Strange Theory of Light and Matter, Princeton University Press. ISBN0-691-08388-6. Four elementary lectures on quantum electrodynamics and quantum field theory, yet containingmany insights for the expert.

• Ghirardi, GianCarlo, 2004. Sneaking a Look at God's Cards, Gerald Malsbary, trans. Princeton Univ. Press. Themost technical of the works cited here. Passages using algebra, trigonometry, and bra-ket notation can be passedover on a first reading.

• N. David Mermin, 1990, "Spooky actions at a distance: mysteries of the QT" in his Boojums all the way through.Cambridge University Press: 110-76.

• Victor Stenger, 2000. Timeless Reality: Symmetry, Simplicity, and Multiple Universes. Buffalo NY: PrometheusBooks. Chpts. 5-8. Includes cosmological and philosophical considerations.

More technical:

• Bryce DeWitt, R. Neill Graham, eds., 1973. The Many-Worlds Interpretation of Quantum Mechanics, PrincetonSeries in Physics, Princeton University Press. ISBN 0-691-08131-X

• Dirac, P. A. M. (1930). The Principles of Quantum Mechanics. ISBN 0198520115. The beginning chapters makeup a very clear and comprehensible introduction.

• Hugh Everett, 1957, "Relative State Formulation of Quantum Mechanics," Reviews of Modern Physics 29:454-62.

• Feynman, Richard P.; Leighton, Robert B.; Sands, Matthew (1965). The Feynman Lectures on Physics. 1-3.Addison-Wesley. ISBN 0738200085.

• Griffiths, David J. (2004). Introduction to Quantum Mechanics (2nd ed.). Prentice Hall. ISBN 0-13-111892-7.OCLC 40251748. A standard undergraduate text.

• Max Jammer, 1966. The Conceptual Development of Quantum Mechanics. McGraw Hill.

• Hagen Kleinert, 2004. Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets,3rd ed. Singapore: World Scientific. Draft of 4th edition.

• Gunther Ludwig, 1968. Wave Mechanics. London: Pergamon Press. ISBN 0-08-203204-1

• George Mackey (2004). The mathematical foundations of quantum mechanics. Dover Publications. ISBN0-486-43517-2.

• Albert Messiah, 1966. Quantum Mechanics (Vol. I), English translation from French by G. M. Temmer. NorthHolland, John Wiley & Sons. Cf. chpt. IV, section III.

• Omnes, Roland (1999). Understanding Quantum Mechanics. Princeton University Press. ISBN 0-691-00435-8.OCLC 39849482.

• Scerri, Eric R., 2006. The Periodic Table: Its Story and Its Significance. Oxford University Press. Considers theextent to which chemistry and the periodic system have been reduced to quantum mechanics. ISBN0-19-530573-6

• Transnational College of Lex (1996). What is Quantum Mechanics? A Physics Adventure. Language ResearchFoundation, Boston. ISBN 0-9643504-1-6. OCLC 34661512.

• von Neumann, John (1955). Mathematical Foundations of Quantum Mechanics. Princeton University Press.ISBN 0691028931.

• Hermann Weyl, 1950. The Theory of Groups and Quantum Mechanics, Dover Publications.

• D. Greenberger, K. Hentschel, F. Weinert, eds., 2009. Compendium of quantum physics, Concepts, experiments,history and philosophy, Springer-Verlag, Berlin, Heidelberg.

• Bohm, David (1989). Quantum Theory. Dover Publications. ISBN 0-486-65969-0.

• Eisberg, Robert; Resnick, Robert (1985). Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles(2nd ed.). Wiley. ISBN 0-471-87373-X.

• Liboff, Richard L. (2002). Introductory Quantum Mechanics. Addison-Wesley. ISBN 0-8053-8714-5.

• Merzbacher, Eugen (1998). Quantum Mechanics. Wiley, John & Sons, Inc. ISBN 0-471-88702-1.

• Sakurai, J. J. (1994). Modern Quantum Mechanics. Addison Wesley. ISBN 0-201-53929-2.

• Shankar, R. (1994). Principles of Quantum Mechanics. Springer. ISBN 0-306-44790-8.

General

T471The Modern Revolution in Physics - an online textbook.

J. O'Connor and E. F. Robertson: A history of quantum mechanics.

[49]Introduction to Quantum Theory at Quantiki.

Quantum Physics Made Relatively Simple : three video lectures by Hans Bethe

H is for h-bar.

[52]

Quantum Mechanics Books Collection : Collection of free booksCourse material

[53]

Doron Cohen: Lecture notes in Quantum Mechanics (comprehensive, with advanced topics).

MIT OpenCourseWare: Chemistry [54]. See 5.61 [55], 5.73 [56], and 5.74 [57]

MIT OpenCourseWare: Physics [58]. See 8.04 [59], 8.05 [60], and 8.06 [61]

Stanford Continuing Education PHY 25: Quantum Mechanics by Leonard Susskind, see course description

[63] Fall 2007

5Vi Examples in Quantum Mechanics

Imperial College Quantum Mechanics Course.

Spark Notes - Quantum Physics.

Quantum Physics Online : interactive introduction to quantum mechanics (RS applets).

Experiments to the foundations of quantum physics with single photons.

Motion Mountain, Volume IV - A modern introduction to quantum theory, with several animations.

• AQME : Advancing Quantum Mechanics for Engineers — by T.Barzso, D.Vasileska and G.Klimeck online

learning resource with simulation tools on nanoHUB

[711

• Quantum Mechanics by Martin Plenio

T721

• Quantum Mechanics by Richard Fitzpatrick

FAQs

[731

• Many-worlds or relative-state interpretation.

T741

• Measurement in Quantum mechanics.

Media

T751

• Everything you wanted to know about the quantum world — archive of articles from New Scientist.

• Quantum Physics Research from Science Daily

[771

• "Quantum Trickery: Testing Einstein's Strangest Theory" . The New York Times. December 27, 2005.

Philosophy

T781

• ""Quantum Mechanics" article by Jenann Ismael. in the Stanford Encyclopedia of Philosophy

T781

• ""Measurement in Quantum Theory" article by Henry Krips. in the Stanford Encyclopedia of Philosophy

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[5] Greiner, Walter; Muller, Berndt (1994). Quantum Mechanics Symmetries, Second edition (http://books.google.com/

books?id=gCfvWx6vuzUC&pg=PA52). Springer-Verlag. p. 52. ISBN 3-540-58080-8. .,[6] AIP.org (http://www.aip.org/history/heisenberg/p08a.htm)

[7] J. Mehra and H. Rechenberg, The historical development of quantum theory, Springer-Verlag, 1982.[8] T.S. Kuhn, Black-body theory and the quantum discontinuity 1894-1912, Clarendon Press, Oxford, 1978.[9] A. Einstein, Uber einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt (On a heuristic point of view

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Einstein, John Stachel, editor, Princeton University Press, 1989, Vol. 2, pp. 149-166, in German; see also Einstein's early work on the

quantum hypothesis, ibid. pp. 134-148).[10] Scribd.com (http://www.scribd.com/doc/5998949/Qu...antummechanics)

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[15] Especially since Werner Heisenberg was awarded the Nobel Prize in Physics in 1932 for the creation of quantum mechanics, the role of Max

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books?id=W2J2IXgiZVgC&pg=PA265). Campbridge University Press, p. 265. ISBN 0-521-80412-4. .,[21] Dict.cc (http://www.dict.cc/german-english/eigen.html)

De.pons.eu (http://de.pons.eu/deutsch-englisch/eigen)[22] Davies, P. C. W.; Betts, David S. (1984). Quantum Mechanics, Second edition (http://books.google.com/books?id=XRyHCrGNstoC&

pg=PA79). Chapman and Hall. p. 79. ISBN 0-7487-4446-0..,[23] Books.Google.com (http://books.google.com/books?id=tKm-Ekwke_UC)[24] PHY.olemiss.edu (http://www.phy.olemiss.edu/~luca/Top.../collapse.html)[25] Greenstein, George; Zajonc, Arthur (2006). The Quantum Challenge: Modern Research on the Foundations of Quantum Mechanics, Second

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Parker, B. (1993). Overcoming some of the problems, pp. 259—279.

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Quantum mechanics 30

Quantum field theory

Quantum field theory (QFT) provides a theoretical framework for constructing quantum mechanical models ofsystems classically described by fields or (especially in a condensed matter context) many-body systems. It is widelyused in particle physics and condensed matter physics. Most theories in modern particle physics, including theStandard Model of elementary particles and their interactions, are formulated as relativistic quantum field theories.Quantum field theories are used in many circumstances, especially those where the number of particlesfluctuates—for example, in the BCS theory of superconductivity.

In perturbative quantum field theory, the forces between particles are mediated by other particles. Theelectromagnetic force between two electrons is caused by an exchange of photons. Intermediate vector bosonsmediate the weak force and gluons mediate the strong force. There is currently no complete quantum theory of theremaining fundamental force, gravity, but many of the proposed theories postulate the existence of a gravitonparticle which mediates it. These force-carrying particles are virtual particles and, by definition, cannot be detectedwhile carrying the force, because such detection will imply that the force is not being carried. In addition, the notionof "force mediating particle" comes from perturbation theory, and thus does not make sense in a context of boundstates.

In QFT photons are not thought of as 'little billiard balls', they are considered to be field quanta - necessarilychunked ripples in a field that 'look like' particles. Fermions, like the electron, can also be described as ripples in afield, where each kind of fermion has its own field. In summary, the classical visualisation of "everything is particlesand fields", in quantum field theory, resolves into "everything is particles", which then resolves into "everything isfields". In the end, particles are regarded as excited states of a field (field quanta).

History

Quantum field theory originated in the 1920s from the problem of creating a quantum mechanical theory of theelectromagnetic field. In 1926, Max Born, Pascual Jordan, and Werner Heisenberg constructed such a theory byexpressing the field's internal degrees of freedom as an infinite set of harmonic oscillators and by employing theusual procedure for quantizing those oscillators (canonical quantization). Max Plank, a physicist at the University ofKiels, observed the behavior at the atomic level of radiation and heat on matter. He observed that the energyabsorbed or emitted was contained in small, discrete (i.e. individual) energy packets called quanta. This theoryassumed that no electric charges or currents were present, and today would be called a free field theory. The firstreasonably complete theory of quantum electrodynamics, which included both the electromagnetic field andelectrically charged matter (specifically, electrons) as quantum mechanical objects, was created by Paul Dirac in

[21

1927. This quantum field theory could be used to model important processes such as the emission of a photon byan electron dropping into a quantum state of lower energy, a process in which the number of particles changes —one atom in the initial state becomes an atom plus a photon in the final state. It is now understood that the ability todescribe such processes is one of the most important features of quantum field theory.

It was evident from the beginning that a proper quantum treatment of the electromagnetic field had to somehowincorporate Einstein's relativity theory, which had after all grown out of the study of classical electromagnetism. Thisneed to put together relativity and quantum mechanics was the second major motivation in the development ofquantum field theory. Pascual Jordan and Wolfgang Pauli showed in 1928 that quantum fields could be made tobehave in the way predicted by special relativity during coordinate transformations (specifically, they showed thatthe field commutators were Lorentz invariant), and in 1933 Niels Bohr and Leon Rosenfeld showed that this result

could be interpreted as a limitation on the ability to measure fields at space-like separations, exactly as required byrelativity. A further boost for quantum field theory came with the discovery of the Dirac equation, a single-particleequation obeying both relativity and quantum mechanics, when it was shown that several of its undesirableproperties (such as negative-energy states) could be eliminated by reformulating the Dirac equation as a quantumfield theory. This work was performed by Wendell Furry, Robert Oppenheimer, Vladimir Fock, and others.

The third thread in the development of quantum field theory was the need to handle the statistics of many-particlesystems consistently and with ease. In 1927, Jordan tried to extend the canonical quantization of fields to themany-body wavefunctions of identical particles, a procedure that is sometimes called second quantization. In 1928,Jordan and Eugene Wigner found that the quantum field describing electrons, or other fermions, had to be expandedusing anti-commuting creation and annihilation operators due to the Pauli exclusion principle. This thread ofdevelopment was incorporated into many-body theory, and strongly influenced condensed matter physics andnuclear physics.

Despite its early successes, quantum field theory was plagued by several serious theoretical difficulties. Manyseemingly-innocuous physical quantities, such as the energy shift of electron states due to the presence of theelectromagnetic field, gave infinity — a nonsensical result — when computed using quantum field theory. This"divergence problem" was solved during the 1940s by Bethe, Tomonaga, Schwinger, Feynman, and Dyson, throughthe procedure known as renormalization. This phase of development culminated with the construction of the moderntheory of quantum electrodynamics (QED). Beginning in the 1950s with the work of Yang and Mills, QED wasgeneralized to a class of quantum field theories known as gauge theories. The 1960s and 1970s saw the formulationof a gauge theory now known as the Standard Model of particle physics, which describes all known elementaryparticles and the interactions between them. The weak interaction part of the standard model was formulated bySheldon Glashow, with the Higgs mechanism added by Steven Weinberg and Abdus Salam. The theory was shownto be renormalizable and hence consistent by Gerardus 't Hooft and Martinus Veltman.

Also during the 1970s, parallel developments in the study of phase transitions in condensed matter physics led LeoKadanoff, Michael Fisher and Kenneth Wilson (extending work of Ernst Stueckelberg, Andre Peterman, MurrayGell-Mann and Francis Low) to a set of ideas and methods known as the renormalization group. By providing abetter physical understanding of the renormalization procedure invented in the 1940s, the renormalization groupsparked what has been called the "grand synthesis" of theoretical physics, uniting the quantum field theoreticaltechniques used in particle physics and condensed matter physics into a single theoretical framework.

The study of quantum field theory is alive and flourishing, as are applications of this method to many physicalproblems. It remains one of the most vital areas of theoretical physics today, providing a common language to manybranches of physics.

Principles of quantum field theoryClassical fields and quantum fields

Quantum mechanics, in its most general formulation, is a theory of abstract operators (observables) acting on anabstract state space (Hilbert space), where the observables represent physically-observable quantities and the statespace represents the possible states of the system under study. Furthermore, each observable corresponds, in atechnical sense, to the classical idea of a degree of freedom. For instance, the fundamental observables associatedwith the motion of a single quantum mechanical particle are the position and momentum operators x and P ■Ordinary quantum mechanics deals with systems such as this, which possess a small set of degrees of freedom.(It is important to note, at this point, that this article does not use the word "particle" in the context of wave—particleduality. In quantum field theory, "particle" is a generic term for any discrete quantum mechanical entity, such as anelectron or photon, which can behave like classical particles or classical waves under different experimentalconditions.)

A quantum field is a quantum mechanical system containing a large, and possibly infinite, number of degrees offreedom. This is not as exotic a situation as one might think (e.g., in an infinite-dimensional vector space, a vector isjust a function as ordinary as f(x) = xA2; which is, of course, familiar territory). A classical field contains a set ofdegrees of freedom at each point of space; for instance, the classical electromagnetic field defines two vectors — theelectric field and the magnetic field — that can in principle take on distinct values for each position r . When thefield as a whole is considered as a quantum mechanical system, its observables form an infinite (in fact uncountable)set, because r is continuous.

Furthermore, the degrees of freedom in a quantum field are arranged in "repeated" sets. For example, the degrees offreedom in an electromagnetic field can be grouped according to the position r, with exactly two vectors for eachr ■ Note that r is an ordinary number that "indexes" the observables; it is not to be confused with the positionoperator x encountered in ordinary quantum mechanics, which is an observable. (Thus, ordinary quantummechanics is sometimes referred to as "zero-dimensional quantum field theory", because it contains only a single setof observables.)

It is also important to note that there is nothing special about r because, as it turns out, there is generally more thanone way of indexing the degrees of freedom in the field.

In the following sections, we will show how these ideas can be used to construct a quantum mechanical theory withthe desired properties. We will begin by discussing single-particle quantum mechanics and the associated theory ofmany-particle quantum mechanics. Then, by finding a way to index the degrees of freedom in the many-particleproblem, we will construct a quantum field and study its implications.

Single-particle and many-particle quantum mechanics

In ordinary quantum mechanics, the time-dependent one-dimensional Schrodinger equation describing the timeevolution of the quantum state of a single non-relativistic particle is

\m) = ^t\m),

2m. dx1where mis the particle's mass, 1/is the applied potential, and \ip\ denotes the quantum state (we are using

bra-ket notation).

We wish to consider how this problem generalizes to TV"particles. There are two motivations for studying the

many-particle problem. The first is a straightforward need in condensed matter physics, where typically the number

23

of particles is on the order of Avogadro's number (6.0221415 x 10 ). The second motivation for the many-particleproblem arises from particle physics and the desire to incorporate the effects of special relativity. If one attempts toinclude the relativistic rest energy into the above equation (in quantum mechanics where position is an observable),the result is either the Klein-Gordon equation or the Dirac equation. However, these equations have manyunsatisfactory qualities; for instance, they possess energy eigenvalues which extend to — °°, so that there seems to beno easy definition of a ground state. It turns out that such inconsistencies arise from relativistic wavefunctionshaving a probabilistic interpretation in position space, as probability conservation is not a relativistically covariantconcept. In quantum field theory, unlike in quantum mechanics, position is not an observable, and thus, one does notneed the concept of a position-space probability density. For quantum fields whose interaction can be treatedperturbatively, this is equivalent to neglecting the possibility of dynamically creating or destroying particles, whichis a crucial aspect of relativistic quantum theory. Einstein's famous mass-energy relation allows for the possibilitythat sufficiently massive particles can decay into several lighter particles, and sufficiently energetic particles cancombine to form massive particles. For example, an electron and a positron can annihilate each other to createphotons. This suggests that a consistent relativistic quantum theory should be able to describe many-particledynamics.

Furthermore, we will assume that the _/yparticles are indistinguishable. As described in the article on identicalparticles, this implies that the state of the entire system must be either symmetric (bosons) or antisymmetric

(fermions) when the coordinates of its constituent particles are exchanged. These multi-particle states are rathercomplicated to write. For example, the general quantum state of a system of _/\T bosons is written as

|0i• -• 0w) = y 3m3' J2 l0P(i))---l0P(iv)>3

p£SN

where 10^) are the single-particle states, Nj is the number of particles occupying state j , and the sum is taken

over all possible permutations p acting on JV elements. In general, this is a sum of j\M( iV factorial) distinctterms, which quickly becomes unmanageable as _/y increases. The way to simplify this problem is to turn it into aquantum field theory.

Second quantization

In this section, we will describe a method for constructing a quantum field theory called second quantization. Thisbasically involves choosing a way to index the quantum mechanical degrees of freedom in the space of multipleidentical-particle states. It is based on the Hamiltonian formulation of quantum mechanics; several other approachesexist, such as the Feynman path integral, which uses a Lagrangian formulation. For an overview, see the article onquantization.

Second quantization of bosons

For simplicity, we will first discuss second quantization for bosons, which form perfectly symmetric quantum states.Let us denote the mutually orthogonal single-particle states by |0i), 102), |03)iand so on- For example, the3-particle state with one particle in state $$j)i) and two in state |02) is ^ [|01>|02}|02> + |02}|0l)|02) + |02)|02)|0l)] • The first step in second quantization is to express such quantum states in terms of occupation numbers, by listingthe number of particles occupying each of the single-particle states 10]), |02),etc- This is simply another way oflabelling the states. For instance, the above 3-particle state is denoted as |1,2,0,0,0,---).The next step is to expand the _/y -particle state space to include the state spaces for all possible values of _/y . Thisextended state space, known as a Fock space, is composed of the state space of a system with no particles (theso-called vacuum state), plus the state space of a 1-particle system, plus the state space of a 2-particle system, and soforth. It is easy to see that there is a one-to-one correspondence between the occupation number representation andvalid boson states in the Fock space. At this point, the quantum mechanical system has become a quantum field in the sense we described above. Thefield's elementary degrees of freedom are the occupation numbers, and each occupation number is indexed by anumber j ■ ■ ■, indicating which of the single-particle states |0i), 102} 1 " ' ' 107'} ' ' -it refers to.The properties of this quantum field can be explored by defining creation and annihilation operators, which add andsubtract particles. They are analogous to "ladder operators" in the quantum harmonic oscillator problem, whichadded and subtracted energy quanta. However, these operators literally create and annihilate particles of a givenquantum state. The bosonic annihilation operator Q^and creation operator a> have the following effects: a2\Nu N2, N3,---) = Jn~2\ Nu (JV2 - 1), N3, ■ ■ ■}, 4\NUN2, N3, ...) = JN2 + 1\ Nu (N2 + 1), JV3, ■ ■ ■}.It can be shown that these are operators in the usual quantum mechanical sense, i.e. linear operators acting on theFock space. Furthermore, they are indeed Hermitian conjugates, which justifies the way we have written them. Theycan be shown to obey the commutation relation [at,aj] = 0 , a],a] =0 , at,a] = Sij} where § stands for the Kronecker delta. These are precisely the relations obeyed by the ladder operators for aninfinite set of independent quantum harmonic oscillators, one for each single-particle state. Adding or removingbosons from each state is therefore analogous to exciting or de-exciting a quantum of energy in a harmonicoscillator. The Hamiltonian of the quantum field (which, through the Schrodinger equation, determines its dynamics) can bewritten in terms of creation and annihilation operators. For instance, the Hamiltonian of a field of free(non-interacting) bosons is H = ^Eka\ak, kwhere Ek is the energy of the fc -th single-particle energy eigenstate. Note that a\ak\ ■■ -,Nk,-- ■) = Nk\ ■ ■■ ,Nk,- ■■}. Second quantization of fermions It turns out that a different definition of creation and annihilation must be used for describing fermions. According tothe Pauli exclusion principle, fermions cannot share quantum states, so their occupation numbers AT; can only takeon the value 0 or 1. The fermionic annihilation operators c and creation operators ct are defined by their actions ona Fock state thus > = o ) = (-l){Ni+-+N^)\N1,N2,---,N3 = 0r--)} = (-l)^+-+N^\N1,N2,...,NJ = l,...) )=0.These obey an anticommutation relation: {cl} Cj} = 0 , {cj, cj} = 0 , {c8, cj} = Sij.One may notice from this that applying a fermionic creation operator twice gives zero, so it is impossible for theparticles to share single-particle states, in accordance with the exclusion principle. Field operators We have previously mentioned that there can be more than one way of indexing the degrees of freedom in a quantumfield. Second quantization indexes the field by enumerating the single-particle quantum states. However, as we havediscussed, it is more natural to think about a "field", such as the electromagnetic field, as a set of degrees of freedomindexed by position. To this end, we can define field operators that create or destroy a particle at a particular point in space. In particlephysics, these operators turn out to be more convenient to work with, because they make it easier to formulatetheories that satisfy the demands of relativity. Single-particle states are usually enumerated in terms of their momenta (as in the particle in a box problem.) We canconstruct field operators by applying the Fourier transform to the creation and annihilation operators for these states.For example, the bosonic field annihilation operator d>(r) is  c,-|JVi N2,- ■,N3 = 0, CjWi N2,- ■,Nj = 1, c}\Nl N2,- -,iV, = 0, c}\Nl N2,- -,N3 = 1, 0(r)^f5>^. 3The bosonic field operators obey the commutation relation [0(r),0(rO]=O , [0t(r),0t(r')]=O , [0(r), 0t(r')] = S\r - r') where S(x) stands for the Dirac delta function. As before, the fermionic relations are the same, with the commutators replaced by anticommutators. It should be emphasized that the field operator is not the same thing as a single-particle wavefunction. The former isan operator acting on the Fock space, and the latter is just a scalar field. However, they are closely related, and areindeed commonly denoted with the same symbol. If we have a Hamiltonian with a space representation, say where the indices \ and j run over all particles, then the field theory Hamiltonian is h2 H = 2m d\ 0f(r)VV(r) + f&r fdV (f>\r)<j)i{r')U(\r -r'$$(f>{r')(j)(r).

This looks remarkably like an expression for the expectation value of the energy, with (j) playing the role of thewavefunction. This relationship between the field operators and wavefunctions makes it very easy to formulate fieldtheories starting from space-projected Hamiltonians.

Implications of quantum field theory

Unification of fields and particles

The "second quantization" procedure that we have outlined in the previous section takes a set of single-particlequantum states as a starting point. Sometimes, it is impossible to define such single-particle states, and one mustproceed directly to quantum field theory. For example, a quantum theory of the electromagnetic field must be aquantum field theory, because it is impossible (for various reasons) to define a wavefunction for a single photon. Insuch situations, the quantum field theory can be constructed by examining the mechanical properties of the classicalfield and guessing the corresponding quantum theory. For free (non-interacting) quantum fields, the quantum fieldtheories obtained in this way have the same properties as those obtained using second quantization, such aswell-defined creation and annihilation operators obeying commutation or anticommutation relations.

Quantum field theory thus provides a unified framework for describing "field-like" objects (such as theelectromagnetic field, whose excitations are photons) and "particle-like" objects (such as electrons, which are treatedas excitations of an underlying electron field), so long as one can treat interactions as "perturbations" of free fields.There are still unsolved problems relating to the more general case of interacting fields which may or may not beadequately described by perturbation theory. For more on this topic, see Haag's theorem.

Physical meaning of particle indistinguishability

The second quantization procedure relies crucially on the particles being identical. We would not have been able toconstruct a quantum field theory from a distinguishable many-particle system, because there would have been noway of separating and indexing the degrees of freedom.

Many physicists prefer to take the converse interpretation, which is that quantum field theory explains what identicalparticles are. In ordinary quantum mechanics, there is not much theoretical motivation for using symmetric(bosonic) or antisymmetric (fermionic) states, and the need for such states is simply regarded as an empirical fact.From the point of view of quantum field theory, particles are identical if and only if they are excitations of the sameunderlying quantum field. Thus, the question "why are all electrons identical?" arises from mistakenly regardingindividual electrons as fundamental objects, when in fact it is only the electron field that is fundamental.

Particle conservation and non-conservation

During second quantization, we started with a Hamiltonian and state space describing a fixed number of particles (j\T), and ended with a Hamiltonian and state space for an arbitrary number of particles. Of course, in many commonsituations _/y is an important and perfectly well-defined quantity, e.g. if we are describing a gas of atoms sealed in abox. From the point of view of quantum field theory, such situations are described by quantum states that areeigenstates of the number operator jy, which measures the total number of particles present. As with any quantummechanical observable, jCris conserved if it commutes with the Hamiltonian. In that case, the quantum state istrapped in the _/V -particle subspace of the total Fock space, and the situation could equally well be described byordinary _/y -particle quantum mechanics.

For example, we can see that the free-boson Hamiltonian described above conserves particle number. Whenever theHamiltonian operates on a state, each particle destroyed by an annihilation operator fflfc is immediately put back bythe creation operator a ■

On the other hand, it is possible, and indeed common, to encounter quantum states that are not eigenstates of pj,which do not have well-defined particle numbers. Such states are difficult or impossible to handle using ordinaryquantum mechanics, but they can be easily described in quantum field theory as quantum superpositions of stateshaving different values of _/\T. For example, suppose we have a bosonic field whose particles can be created ordestroyed by interactions with a fermionic field. The Hamiltonian of the combined system would be given by theHamiltonians of the free boson and free fermion fields, plus a "potential energy" term such as

HI = Yu Vl(ai + a-q)Ck+qCk,

k,q

where a and ak denotes the bosonic creation and annihilation operators, A and C^ denotes the fermioniccreation and annihilation operators, and V^is a parameter that describes the strength of the interaction. This"interaction term" describes processes in which a fermion in state & either absorbs or emits a boson, thereby beingkicked into a different eigenstate k + q. (In fact, this type of Hamiltonian is used to describe interaction betweenconduction electrons and phonons in metals. The interaction between electrons and photons is treated in a similarway, but is a little more complicated because the role of spin must be taken into account.) One thing to notice here isthat even if we start out with a fixed number of bosons, we will typically end up with a superposition of states with

different numbers of bosons at later times. The number of fermions, however, is conserved in this case.

In condensed matter physics, states with ill-defined particle numbers are particularly important for describing the

various superfluids. Many of the defining characteristics of a superfluid arise from the notion that its quantum state is

a superposition of states with different particle numbers. In addition, the concept of a coherent state (used to model

the laser and the BCS ground state) refers to a state with an ill-defined particle number but a well-defined phase.

Axiomatic approaches

The preceding description of quantum field theory follows the spirit in which most physicists approach the subject.However, it is not mathematically rigorous. Over the past several decades, there have been many attempts to putquantum field theory on a firm mathematical footing by formulating a set of axioms for it. These attempts fall intotwo broad classes.

The first class of axioms, first proposed during the 1950s, include the Wightman, Osterwalder-Schrader, andHaag-Kastler systems. They attempted to formalize the physicists' notion of an "operator-valued field" within thecontext of functional analysis, and enjoyed limited success. It was possible to prove that any quantum field theorysatisfying these axioms satisfied certain general theorems, such as the spin-statistics theorem and the CPT theorem.Unfortunately, it proved extraordinarily difficult to show that any realistic field theory, including the StandardModel, satisfied these axioms. Most of the theories that could be treated with these analytic axioms were physicallytrivial, being restricted to low-dimensions and lacking interesting dynamics. The construction of theories satisfyingone of these sets of axioms falls in the field of constructive quantum field theory. Important work was done in this

area in the 1970s by Segal, Glimm, Jaffe and others.

During the 1980s, a second set of axioms based on geometric ideas was proposed. This line of investigation, whichrestricts its attention to a particular class of quantum field theories known as topological quantum field theories, isassociated most closely with Michael Atiyah and Graeme Segal, and was notably expanded upon by Edward Witten,Richard Borcherds, and Maxim Kontsevich. However, most physically-relevant quantum field theories, such as theStandard Model, are not topological quantum field theories; the quantum field theory of the fractional quantum Halleffect is a notable exception. The main impact of axiomatic topological quantum field theory has been onmathematics, with important applications in representation theory, algebraic topology, and differential geometry.

Finding the proper axioms for quantum field theory is still an open and difficult problem in mathematics. One of theMillennium Prize Problems—proving the existence of a mass gap in Yang-Mills theory—is linked to this issue.

Phenomena associated with quantum field theory

In the previous part of the article, we described the most general properties of quantum field theories. Some of thequantum field theories studied in various fields of theoretical physics possess additional special properties, such asrenormalizability, gauge symmetry, and supersymmetry. These are described in the following sections.

Renormalization

Early in the history of quantum field theory, it was found that many seemingly innocuous calculations, such as theperturbative shift in the energy of an electron due to the presence of the electromagnetic field, give infinite results.The reason is that the perturbation theory for the shift in an energy involves a sum over all other energy levels, andthere are infinitely many levels at short distances which each give a finite contribution.

Many of these problems are related to failures in classical electrodynamics that were identified but unsolved in the19th century, and they basically stem from the fact that many of the supposedly "intrinsic" properties of an electronare tied to the electromagnetic field which it carries around with it. The energy carried by a single electron—its selfenergy—is not simply the bare value, but also includes the energy contained in its electromagnetic field, its attendantcloud of photons. The energy in a field of a spherical source diverges in both classical and quantum mechanics, butas discovered by Weisskopf, in quantum mechanics the divergence is much milder, going only as the logarithm ofthe radius of the sphere.

The solution to the problem, presciently suggested by Stueckelberg, independently by Bethe after the crucialexperiment by Lamb, implemented at one loop by Schwinger, and systematically extended to all loops by Feynmanand Dyson, with converging work by Tomonaga in isolated postwar Japan, is called renormalization. The techniqueof renormalization recognizes that the problem is essentially purely mathematical, that extremely short distances areat fault. In order to define a theory on a continuum, first place a cutoff on the fields, by postulating that quantacannot have energies above some extremely high value. This has the effect of replacing continuous space by astructure where very short wavelengths do not exist, as on a lattice. Lattices break rotational symmetry, and one ofthe crucial contributions made by Feynman, Pauli and Villars, and modernized by 't Hooft and Veltman, is asymmetry preserving cutoff for perturbation theory. There is no known symmetrical cutoff outside of perturbationtheory, so for rigorous or numerical work people often use an actual lattice.

On a lattice, every quantity is finite but depends on the spacing. When taking the limit of zero spacing, we make surethat the physically-observable quantities like the observed electron mass stay fixed, which means that the constantsin the Lagrangian defining the theory depend on the spacing. Hopefully, by allowing the constants to vary with thelattice spacing, all the results at long distances become insensitive to the lattice, defining a continuum limit.

The renormalization procedure only works for a certain class of quantum field theories, called renormalizablequantum field theories. A theory is perturbatively renormalizable when the constants in the Lagrangian onlydiverge at worst as logarithms of the lattice spacing for very short spacings. The continuum limit is then well defined

in perturbation theory, and even if it is not fully well defined non-perturbatively, the problems only show up atdistance scales which are exponentially small in the inverse coupling for weak couplings. The Standard Model ofparticle physics is perturbatively renormalizable, and so are its component theories (quantumelectrodynamics/electroweak theory and quantum chromodynamics). Of the three components, quantumelectrodynamics is believed to not have a continuum limit, while the asymptotically free SU(2) and SU(3) weakhypercharge and strong color interactions are nonperturbatively well defined.

The renormalization group describes how renormalizable theories emerge as the long distance low-energy effectivefield theory for any given high-energy theory. Because of this, renormalizable theories are insensitive to the precisenature of the underlying high-energy short-distance phenomena. This is a blessing because it allows physicists toformulate low energy theories without knowing the details of high energy phenomenon. It is also a curse, becauseonce a renormalizable theory like the standard model is found to work, it gives very few clues to higher energyprocesses. The only way high energy processes can be seen in the standard model is when they allow otherwiseforbidden events, or if they predict quantitative relations between the coupling constants.

Gauge freedom

A gauge theory is a theory that admits a symmetry with a local parameter. For example, in every quantum theory theglobal phase of the wave function is arbitrary and does not represent something physical. Consequently, the theory isinvariant under a global change of phases (adding a constant to the phase of all wave functions, everywhere); this is aglobal symmetry. In quantum electrodynamics, the theory is also invariant under a local change of phase, that is -one may shift the phase of all wave functions so that the shift may be different at every point in space-time. This is alocal symmetry. However, in order for a well-defined derivative operator to exist, one must introduce a new field,the gauge field, which also transforms in order for the local change of variables (the phase in our example) not toaffect the derivative. In quantum electrodynamics this gauge field is the electromagnetic field. The change of localgauge of variables is termed gauge transformation.

In quantum field theory the excitations of fields represent particles. The particle associated with excitations of thegauge field is the gauge boson, which is the photon in the case of quantum electrodynamics.

The degrees of freedom in quantum field theory are local fluctuations of the fields. The existence of a gaugesymmetry reduces the number of degrees of freedom, simply because some fluctuations of the fields can betransformed to zero by gauge transformations, so they are equivalent to having no fluctuations at all, and theytherefore have no physical meaning. Such fluctuations are usually called "non-physical degrees of freedom" or gaugeartifacts; usually some of them have a negative norm, making them inadequate for a consistent theory. Therefore, ifa classical field theory has a gauge symmetry, then its quantized version (i.e. the corresponding quantum fieldtheory) will have this symmetry as well. In other words, a gauge symmetry cannot have a quantum anomaly. If agauge symmetry is anomalous (i.e. not kept in the quantum theory) then the theory is non-consistent: for example, inquantum electrodynamics, had there been a gauge anomaly, this would require the appearance of photons withlongitudinal polarization and polarization in the time direction, the latter having a negative norm, rendering thetheory inconsistent; another possibility would be for these photons to appear only in intermediate processes but notin the final products of any interaction, making the theory non unitary and again inconsistent (see optical theorem).

In general, the gauge transformations of a theory consist of several different transformations, which may not becommutative. These transformations are together described by a mathematical object known as a gauge group.Infinitesimal gauge transformations are the gauge group generators. Therefore the number of gauge bosons is thegroup dimension (i.e. number of generators forming a basis).

All the fundamental interactions in nature are described by gauge theories. These are:

• Quantum electrodynamics, whose gauge transformation is a local change of phase, so that the gauge group isU(l). The gauge boson is the photon.

• Quantum chromodynamics, whose gauge group is SU(3). The gauge bosons are eight gluons.

39

• The electroweak Theory, whose gauge group is f7(l) ® SU(2) (a direct product of U(l) and SU(2)).

• Gravity, whose classical theory is general relativity, admits the equivalence principle which is a form of gaugesymmetry, however it is explicitly non-renormalizable.

Supersymmetry

Supersymmetry assumes that every fundamental fermion has a superpartner that is a boson and vice versa. It wasintroduced in order to solve the so-called Hierarchy Problem, that is, to explain why particles not protected by anysymmetry (like the Higgs boson) do not receive radiative corrections to its mass driving it to the larger scales (GUT,Planck...)- It was soon realized that supersymmetry has other interesting properties: its gauged version is anextension of general relativity (Supergravity), and it is a key ingredient for the consistency of string theory.

The way supersymmetry protects the hierarchies is the following: since for every particle there is a superpartner withthe same mass, any loop in a radiative correction is cancelled by the loop corresponding to its superpartner,rendering the theory UV finite.

Since no superpartners have yet been observed, if supersymmetry exists it must be broken (through a so-called softterm, which breaks supersymmetry without ruining its helpful features). The simplest models of this breaking requirethat the energy of the superpartners not be too high; in these cases, supersymmetry is expected to be observed byexperiments at the Large Hadron Collider.

List of quantum field theoriesFeynman path integral

Quantum chromodynamicsQuantum electrodynamicsQuantum flavordynamicsQuantum geometrodynamics

Quantum hydrodynamics

Quantum magnetodynamics

Quantum triviality

Schwinger-Dyson equation

Relation between Schrodinger's equation and the path integral formulation of

quantum mechanics

Basic concepts of quantum mechanics

Relationship between string theory and quantum field

theory

Abraham-Lorentz force

Form factor

Photon polarization

Theoretical and experimental justification for the

Schrodinger equation

Invariance mechanics

Green—Kubo relations

Green's function (many-body theory)

Common integrals in quantum field theory

• Feynman, R.P. (2001) [1964]. The Character of Physical Law. MIT Press. ISBN 0262560038.

• Feynman, R.P. (2006) [1985]. QED: The Strange Theory of Light and Matter. Princeton University Press.ISBN 0691125759.

• Gribbin, J. (1998). Q is for Quantum: Particle Physics from A to Z. Weidenfeld & Nicolson. ISBN 0297817523.

• Schumm, Bruce A. (2004) Deep Down Things. Johns Hopkins Univ. Press. Chpt. 4.

Introductory texts:

• Bogoliubov, N; Shirkov, D. (1982). Quantum Fields. Benjamin-Cummings. ISBN 0805309837.

• Frampton, P.H. (2000). Gauge Field Theories. Frontiers in Physics (2nd ed.). Wiley.

• Greiner, W; Muller, B. (2000). Gauge Theory of Weak Interactions. Springer. ISBN 3-540-67672-4.

• Itzykson, C; Zuber, J.-B. (1980). Quantum Field Theory. McGraw-Hill. ISBN 0-07-032071-3.

• Kane, G.L. (1987). Modern Elementary Particle Physics. Perseus Books. ISBN 0-201-11749-5.

• Kleinert, H.; Schulte-Frohlinde, Verena (2001). Critical Properties ofq> -Theories . World Scientific.ISBN 981-02-4658-7.

• Kleinert, H. (2008). Multivalued Fields in Condensed Matter, Electrodynamics, and Gravitation . WorldScientific. ISBN 978-981-279-170-2.

• Loudon, R (1983). The Quantum Theory of Light. Oxford University Press. ISBN 0-19-851155-8.

• Mandl, F.; Shaw, G. (1993). Quantum Field Theory. John Wiley & Sons. ISBN 0-0471-94186-7.

• Peskin, M.; Schroeder, D. (1995). An Introduction to Quantum Field Theory. Westview Press.ISBN 0-201-50397-2.

• Ryder, L.H. (1985). Quantum Field Theory. Cambridge University Press. ISBN 0-521-33859-X.

• Srednicki, Mark (2007) Quantum Field Theory. Cambridge Univ. Press.

• Yndurain, F.J. (1996). Relativistic Quantum Mechanics and Introduction to Field Theory (1st ed.). Springer.ISBN 978-3540604532.

• Zee, A. (2003). Quantum Field Theory in a Nutshell. Princeton University Press. ISBN ISBN 0-691-01019-6.

• Bogoliubov, N; Logunov, A. A.; Oksak, A.I.; Todorov, I.T. (1990). General Principles of Quantum Field Theory.Kluwer Academic Publishers. ISBN 978-0792305408.

• Weinberg, S. (1995). The Quantum Theory of Fields. 1—3. Cambridge University Press.

Articles:

• Gerard 't Hooft (2007) "The Conceptual Basis of Quantum Field Theory in Butterfield, J., and John Earman,

Frank Wilczek (1999) "Quantum field theory, [8]" Reviews of Modern Physics 71: S83-S95. Also

eds., Philosophy of Physics, Part A. Elsevier: 661-730

• Frank Wilczek (1999) "Quantumdoi=10.1103/Rev. Mod. Phys. 71 .

• Stanford Encyclopedia of Philosophy: "Quantum Field Theory, by Meinard Kuhlmann.

• Siegel, Warren, 2005. Fields. A free text, also available from arXiv:hep-th/9912205.

• Pedagogic Aids to Quantum Field Theory . Click on "Introduction" for a simplified introduction suitable forsomeone familiar with quantum mechanics.

• Free condensed matter books and notes .

ri3i

• Quantum field theory texts , a list with links to amazon.com.

• Quantum Field Theory by P. J. Mulders

• Quantum Field Theory by David Tong

• Quantum Field Theory Video Lectures by David Tong

ri7i

• Quantum Field Theory Lecture Notes by Michael Luke

n si

• Quantum Field Theory Video Lectures by Sidney R. Coleman

Quantum field theory 41

References

[I] Weinberg, S. Quantum Field Theory, Vols. I to III, 2000, Cambridge University Press: Cambridge, UK.

[2] Dirac, P.A.M. (1927). The Quantum Theory of the Emission and Absorption of Radiation, Proceedings of the Royal Society of London, Series

A, Vol. 114, p. 243.[3] Abraham Pais, Inward Bound: Of Matter and F orces in the Physical World ISBN 0-19-851997-4. Pais recounts how his astonishment at the

rapidity with which Feynman could calculate using his method. Feynman's method is now part of the standard methods for physicists.[4] http://users.physik.fu-berlin.de/~kleinert/re.html#B6

Algebraic quantum field theory

The Haag-Kastler axiomatic framework for quantum field theory, named after Rudolf Haag and Daniel Kastler, isan application to local quantum physics of C*-algebra theory. It is therefore also known as Algebraic QuantumField Theory (AQFT). The axioms are stated in terms of an algebra given for every open set in Minkowski space,and mappings between those.

Let Mink be the category of open subsets of Minkowski space M with inclusion maps as morphisms. We are given acovariant functor j\ from Mink to uC*alg, the category of unital C* algebras, such that every morphism in Minkmaps to a monomorphism in uC*alg {isotony).

The Poincare group acts continuously on Mink. There exists a pullback of this action, which is continuous in thenorm topology of J\iM) (Poincare covariance).

Minkowski space has a causal structure. If an open set V lies in the causal complement of an open set U, then theimage of the maps

A{iu,uiiv)

and

•A{iv,uuv)

commute (spacelike commutativity). If TJ is the causal completion of an open set U, then *A(ijjxj)is an

isomorphism (primitive causality).

A state with respect to a C*-algebra is a positive linear functional over it with unit norm. If we have a state over

AiM), we can take the "partial trace" to get states associated with J^.(UMor each open set via the net

monomorphism. It's easy to show the states over the open sets form a presheaf structure.

According to the GNS construction, for each state, we can associate a Hilbert space representation of j[(M). Pure

states correspond to irreducible representations and mixed states correspond to reducible representations. Each

irreducible (up to equivalence) is called a superselection sector. We assume there is a pure state called the vacuum

such that the Hilbert space associated with it is a unitary representation of the Poincare group compatible with the

Poincare covariance of the net such that if we look at the Poincare algebra, the spectrum with respect to

Algebraic quantum field theory 42

energy-momentum (corresponding to spacetime translations) lies on and in the positive light cone. This is thevacuum sector.

• Haag, Rudolf (1992). Local Quantum Physics: Fields, Particles, Algebras. Springer.

• Local Quantum Physics Crossroads - A network of scientists working on Local Quantum Physics

• Algebraic Quantum Field Theory - AQFT resources at the University of Hamburg

References

Local quantum field theory

The Haag-Kastler axiomatic framework for quantum field theory, named after Rudolf Haag and Daniel Kastler, isan application to local quantum physics of C*-algebra theory. It is therefore also known as Algebraic QuantumField Theory (AQFT). The axioms are stated in terms of an algebra given for every open set in Minkowski space,and mappings between those.

Let Mink be the category of open subsets of Minkowski space M with inclusion maps as morphisms. We are given acovariant functor J^ from Mink to uC*alg, the category of unital C* algebras, such that every morphism in Minkmaps to a monomorphism in uC*alg (isotony).

The Poincare group acts continuously on Mink. There exists a pullback of this action, which is continuous in thenorm topology of j\,(M) (Poincare covariance).

Minkowski space has a causal structure. If an open set V lies in the causal complement of an open set U, then theimage of the maps

A{iu,uiiv)

and

A(iv,Uuv)commute (spacelike commutativity). If jjk the causal completion of an open set U, then Jk.{ijjxj)K an

isomorphism (primitive causality).

A state with respect to a C*-algebra is a positive linear functional over it with unit norm. If we have a state over

AiM), we can take the "partial trace" to get states associated with J[,(U\fov each open set via the net

monomorphism. It's easy to show the states over the open sets form a presheaf structure.

According to the GNS construction, for each state, we can associate a Hilbert space representation of j[(M). Pure

states correspond to irreducible representations and mixed states correspond to reducible representations. Each

irreducible (up to equivalence) is called a superselection sector. We assume there is a pure state called the vacuum

such that the Hilbert space associated with it is a unitary representation of the Poincare group compatible with the

Poincare covariance of the net such that if we look at the Poincare algebra, the spectrum with respect to

energy-momentum (corresponding to spacetime translations) lies on and in the positive light cone. This is the

vacuum sector.

Local quantum field theory

43

• Haag, Rudolf (1992). Local Quantum Physics: Fields, Particles, Algebras. Springer.

in

Local Quantum Physics Crossroads - A network of scientists working on Local Quantum PhysicsAlgebraic Quantum Field Theory - AQFT resources at the University of Hamburg

Algebraic logic

In mathematical logic, algebraic logic is the study of logic presented in an algebraic style.

Algebras as models of logics

Algebraic logic treats algebraic structures, often bounded lattices, as models (interpretations) of certain logics,making logic a branch of order theory.

In algebraic logic:

• Variables are tacitly universally quantified over some universe of discourse. There are no existentially quantifiedvariables or open formulas;

• Terms are built up from variables using primitive and defined operations. There are no connectives;

• Formulas, built from terms in the usual way, can be equated if they are logically equivalent. To express atautology, equate a formula with a truth value;

• The rules of proof are the substitution of equals for equals, and uniform replacement. Modus ponens remainsvalid, but is seldom employed.

In the table below, the left column contains one or more logical or mathematical systems, and the algebraic structurewhich are its models are shown on the right in the same row. Some of these structures are either Boolean algebras orproper extensions thereof. Modal and other nonclassical logics are typically modeled by what are called "Booleanalgebras with operators."

Algebraic formalisms going beyond first-order logic in at least some respects include:

• Combinatory logic, having the expressive power of set theory;

• Relation algebra, arguably the paradigmatic algebraic logic, can express Peano arithmetic and most axiomatic settheories, including the canonical ZFC.

 logical system its models Classical sentential logic Lindenbaum-Tarski algebra Two-element Boolean algebra Intuitionistic propositional logic Heyting algebra Lukasiewicz logic MV-algebra Modal logic K Modal algebra Lewis's S4 Interior algebra Lewis's S5; Monadic predicate logic Monadic Boolean algebra First-order logic Cylindric algebra Polyadic algebraPredicate functor logic Set theory Combinatory logic Relation algebra

History

On the history of algebraic logic before World War II, see Brady (2000) and Grattan-Guinness (2000) and theirample references. On the postwar history, see Maddux (1991) and Quine (1976).

Algebraic logic has at least two meanings:

• The study of Boolean algebra, begun by George Boole, and of relation algebra, begun by Augustus DeMorgan,extended by Charles Sanders Peirce, and taking definitive form in the work of Ernst Schroder;

• Abstract algebraic logic, a branch of contemporary mathematical logic.

Perhaps surprisingly, algebraic logic is the oldest approach to formal logic, arguably beginning with a number ofmemoranda Leibniz wrote in the 1680s, some of which were published in the 19th century and translated intoEnglish by Clarence Lewis in 1918. But nearly all of Leibniz's known work on algebraic logic was published only in1903, after Louis Couturat discovered it in Leibniz's Nachlass. Parkinson (1966) and Loemker (1969) translatedselections from Couturat's volume into English.

Brady (2000) discusses the rich historical connections between algebraic logic and model theory. The founders ofmodel theory, Ernst Schroder and Leopold Loewenheim, were logicians in the algebraic tradition. Alfred Tarski, thefounder of set theoretic model theory as a major branch of contemporary mathematical logic, also:

• Co-discovered Lindenbaum-Tarski algebra;

• Invented cylindric algebra;

• Wrote the 1940 paper that revived relation algebra, and that can be seen as the starting point of abstract algebraiclogic.

Modern mathematical logic began in 1847, with two pamphlets whose respective authors were Augustus DeMorganand George Boole. They, and later C.S. Peirce, Hugh MacColl, Frege, Peano, Bertrand Russell, and A. N. Whiteheadall shared Leibniz's dream of combining symbolic logic, mathematics, and philosophy. Relation algebra is arguablythe culmination of Leibniz's approach to logic. With the exception of some writings by Leopold Loewenheim andThoralf Skolem, algebraic logic went into eclipse soon after the 1910-13 publication of Principia Mathematica, notto revive until Tarski's 1940 reexposition of relation algebra.

Leibniz had no influence on the rise of algebraic logic because his logical writings were little studied before theParkinson and Loemker translations. Our present understanding of Leibniz the logician stems mainly from the workof Wolfgang Lenzen, summarized in Lenzen (2004). To see how present-day work in logic and metaphysics candraw inspiration from, and shed light on, Leibniz's thought, see Zalta (2000).

Abstract algebraic logicAlgebraic structureBoolean algebra (logic)Boolean algebra (structure)Cylindric algebraLindenbaum-Tarski algebraMathematical logicModel theoryMonadic Boolean algebraPredicate functor logicRelation algebraUniversal algebra

Algebraic logic 45

References

• Brady, Geraldine, 2000. From Peirce to Skolem: A neglected chapter in the history of logic.

T31North-Holland/Elsevier Science BV: catalog page , Amsterdam, Netherlands, 625 pages.

• Burris, Stanley, 2009. The Algebra of Logic Tradition . Stanford Encyclopedia of Philosophy.

• Ivor Grattan-Guinness, 2000. The Search for Mathematical Roots. Princeton Univ. Press.

• Lenzen, Wolfgang, 2004, "Leibniz's Logic in Gabbay, D., and Woods, J., eds., Handbook of the History ofLogic, Vol. 3: The Rise of Modern Logic from Leibniz to Frege. North-Holland: 1-84.

• Loemker, Leroy (1969 (1956)), Leibniz: Philosophical Papers and Letters, Reidel.

• Roger Maddux, 1991, "The Origin of Relation Algebras in the Development and Axiomatization of the Calculusof Relations," Studia Logica 50: 421-55.

• Parkinson, G.H.R., 1966. Leibniz: Logical Papers. Oxford Uni. Press.

• Willard Quine, 1976, "Algebraic Logic and Predicate Functors" in The Ways of Paradox. Harvard Univ. Press:283-307.

• Zalta, E. N., 2000, "A (Leibnizian) Theory of Concepts ," Philosophiegeschichte und logische Analyse /Logical Analysis and History of Philosophy 3: 137-183.

• Stanford Encyclopedia of Philosophy: "Propositional Consequence Relations and Algebraic Logic — byRamon Jansana.

References

Quantum logic

In quantum mechanics, quantum logic is a set of rules for reasoning about propositions which takes the principles ofquantum theory into account. This research area and its name originated in the 1936 paper by Garrett Birkhoff andJohn von Neumann, who were attempting to reconcile the apparent inconsistency of classical boolean logic with thefacts concerning the measurement of complementary variables in quantum mechanics, such as position andmomentum.

Quantum logic can be formulated either as a modified version of propositional logic or as a noncommutative andnon-associative many-valued (MV) logic .

Quantum logic has some properties which clearly distinguish it from classical logic, most notably, the failure of thedistributive law of propositional logic:

p and (q or r) = (p and q) or (p and r),

where the symbols p, q and r are propositional variables. To illustrate why the distributive law fails, consider aparticle moving on a line and let

p = "the particle is moving to the right"

q = "the particle is in the interval [-1,1]"

r = "the particle is not in the interval [-1,1]"

then the proposition "q or r" is true, so

p and (q or r) = p

On the other hand, the propositions "p and q" and "p and r" are both false, since they assert tighter restrictions onsimultaneous values of position and momentum than is allowed by the uncertainty principle. So,

(p and q) or (p and r) = false

Thus the distributive law fails.

Quantum logic has been proposed as the correct logic for propositional inference generally, most notably by thephilosopher Hilary Putnam, at least at one point in his career. This thesis was an important ingredient in Putnam'spaper Is Logic Empirical? in which he analysed the epistemological status of the rules of propositional logic. Putnamattributes the idea that anomalies associated to quantum measurements originate with anomalies in the logic ofphysics itself to the physicist David Finkelstein. However, this idea had been around for some time and had beenrevived several years earlier by George Mackey's work on group representations and symmetry.

The more common view regarding quantum logic, however, is that it provides a formalism for relating observables,system preparation filters and states. In this view, the quantum logic approach resembles more closely theC*-algebraic approach to quantum mechanics; in fact with some minor technical assumptions it can be subsumed byit. The similarities of the quantum logic formalism to a system of deductive logic may then be regarded more as acuriosity than as a fact of fundamental philosophical importance. A more modern approach to the structure ofquantum logic is to assume that it is a diagram — in the sense of category theory — of classical logics (see DavidEdwards).

Introduction

In his classic treatise Mathematical Foundations of Quantum Mechanics, John von Neumann noted that projectionson a Hilbert space can be viewed as propositions about physical observables. The set of principles for manipulatingthese quantum propositions was called quantum logic by von Neumann and Birkhoff. In his book (also calledMathematical Foundations of Quantum Mechanics) G Mackey attempted to provide a set of axioms for thispropositional system as an orthocomplemented lattice. Mackey viewed elements of this set as potential yes or no

questions an observer might ask about the state of a physical system, questions that would be settled by somemeasurement. Moreover Mackey defined a physical observable in terms of these basic questions. Mackey's axiomsystem is somewhat unsatisfactory though, since it assumes that the partially ordered set is actually given as theorthocomplemented closed subspace lattice of a separable Hilbert space. Piron, Ludwig and others have attempted togive axiomatizations which do not require such explicit relations to the lattice of subspaces.

The remainder of this article assumes the reader is familiar with the spectral theory of self-adjoint operators on aHilbert space. However, the main ideas can be understood using the finite-dimensional spectral theorem.

Projections as propositions

The so-called Hamiltonian formulations of classical mechanics have three ingredients: states, observables anddynamics. In the simplest case of a single particle moving in R , the state space is the position-momentum space R .We will merely note here that an observable is some real-valued function / on the state space. Examples ofobservables are position, momentum or energy of a particle. For classical systems, the value/(x), that is the value of/for some particular system state x, is obtained by a process of measurement of /. The propositions concerning aclassical system are generated from basic statements of the form

• Measurement off yields a value in the interval [a, b] for some real numbers a, b.

It follows easily from this characterization of propositions in classical systems that the corresponding logic isidentical to that of some Boolean algebra of subsets of the state space. By logic in this context we mean the rules thatrelate set operations and ordering relations, such as de Morgan's laws. These are analogous to the rules relatingboolean conjunctives and material implication in classical propositional logic. For technical reasons, we will alsoassume that the algebra of subsets of the state space is that of all Borel sets. The set of propositions is ordered by thenatural ordering of sets and has a complementation operation. In terms of observables, the complement of theproposition {/> a] is {/< a}.

We summarize these remarks as follows:

• The proposition system of a classical system is a lattice with a distinguished orthocomplementation operation:The lattice operations of meet and join are respectively set intersection and set union. The orthocomplementationoperation is set complement. Moreover this lattice is sequentially complete, in the sense that any sequence {E.}. ofelements of the lattice has a least upper bound, specifically the set-theoretic union:

00LVB({Ei}) = (JEi.i=\In the Hilbert space formulation of quantum mechanics as presented by von Neumann, a physical observable is

represented by some (possibly unbounded) densely-defined self-adjoint operator A on a Hilbert space H. A has aspectral decomposition, which is a projection-valued measure E defined on the Borel subsets of R. In particular, forany bounded Borel function/, the following equation holds:

f(A)= /"/(A)dE(A).

Jr

In case / is the indicator function of an interval [a, b], the operator/(A) is a self-adjoint projection, and can beinterpreted as the quantum analogue of the classical proposition

• Measurement of A yields a value in the interval [a, b].

The propositional lattice of a quantum mechanical system

This suggests the following quantum mechanical replacement for the orthocomplemented lattice of propositions inclassical mechanics. This is essentially Mackey's Axiom VII:

• The orthocomplemented lattice Q of propositions of a quantum mechanical system is the lattice of closedsubspaces of a complex Hilbert space H where orthocomplementation of V is the orthogonal complement V .

Q is also sequentially complete: any pairwise disjoint sequencef V.}. of elements of Q has a least upper bound. Here

_L ' '

disjointness of W and W means W is a subspace of W . The least upper bound of {V}. is the closed internal directsum.

Henceforth we identify elements of Q with self-adjoint projections on the Hilbert space H.

The structure of Q immediately points to a difference with the partial order structure of a classical propositionsystem. In the classical case, given a proposition/?, the equations

I = pV q

0 = p A qhave exactly one solution, namely the set-theoretic complement of p. In these equations / refers to the atomicproposition which is identically true and 0 the atomic proposition which is identically false. In the case of the latticeof projections there are infinitely many solutions to the above equations.

Having made these preliminary remarks, we turn everything around and attempt to define observables within theprojection lattice framework and using this definition establish the correspondence between self-adjoint operatorsand observables: A Mackey observable is a countably additive homomorphism from the orthocomplemented latticeof the Borel subsets of R to Q. To say the mapping cp is a countably additive homomorphism means that for anysequence {S.}. of pairwise disjoint Borel subsets of R, {cp(5.)}.are pairwise orthogonal projections and

i i

oo \ oo

Theorem. There is a bijective correspondence between Mackey observables and densely-defined self-adjointoperators on H.

This is the content of the spectral theorem as stated in terms of spectral measures.

Statistical structure

Imagine a forensics lab which has some apparatus to measure the speed of a bullet fired from a gun. Under carefullycontrolled conditions of temperature, humidity, pressure and so on the same gun is fired repeatedly and speedmeasurements taken. This produces some distribution of speeds. Though we will not get exactly the same value foreach individual measurement, for each cluster of measurements, we would expect the experiment to lead to the samedistribution of speeds. In particular, we can expect to assign probability distributions to propositions such as {a <speed < b}. This leads naturally to propose that under controlled conditions of preparation, the measurement of aclassical system can be described by a probability measure on the state space. This same statistical structure is alsopresent in quantum mechanics.

A quantum probability measure is a function P defined on Q with values in [0,1] such that P(0)=0, P(I)=1 and if{£■.}. is a sequence of pairwise orthogonal elements of Q then

(oo \ oo

i=l / i=l

The following highly non-trivial theorem is due to Andrew Gleason:

Theorem. Suppose H is a separable Hilbert space of complex dimension at least 3. Then for any quantumprobability measure on Q there exists a unique trace class operator S such that

P(E) = Ti(SE)for any self-adjoint projection E.

The operator S is necessarily non-negative (that is all eigenvalues are non-negative) and of trace 1. Such an operatoris often called a density operator.

Physicists commonly regard a density operator as being represented by a (possibly infinite) density matrix relative tosome orthonormal basis.

For more information on statistics of quantum systems, see quantum statistical mechanics.

Automorphisms

An automorphism of Q is a bijective mapping a:Q —> Q which preserves the orthocomplemented structure of Q, that

is

(00 \ 00

J2EA=J2a(Et)i=l / i=\

for any sequence {£.}. of pairwise orthogonal self-adjoint projections. Note that this property implies monotonicityof a. If P is a quantum probability measure on Q, then E —> a(E) is also a quantum probability measure on Q. By theGleason theorem characterizing quantum probability measures quoted above, any automorphism a induces amapping a* on the density operators by the following formula:

Ti(a*(S)E) =Tr(Sa(E)).

The mapping a* is bijective and preserves convex combinations of density operators. This means

a*(riSx + r2S2) — r1o;*(51) + r2a*(S2)whenever 1 - r + r and r , r are non-negative real numbers. Now we use a theorem of Richard V. Kadison:

Theorem. Suppose (3 is a bijective map from density operators to density operators which is convexity preserving.Then there is an operator U on the Hilbert space which is either linear or conjugate-linear, preserves the innerproduct and is such that

/?(£) = USU*

for every density operator S. In the first case we say U is unitary, in the second case U is anti-unitary.

Remark. This note is included for technical accuracy only, and should not concern most readers. Theresult quoted above is not directly stated in Kadison's paper, but can be reduced to it by noting first thatp extends to a positive trace preserving map on the trace class operators, then applying duality andfinally applying a result of Kadison's paper.

The operator U is not quite unique; if r is a complex scalar of modulus 1, then r U will be unitary or anti-unitary if Uis and will implement the same automorphism. In fact, this is the only ambiguity possible.

It follows that automorphisms of Q are in bijective correspondence to unitary or anti-unitary operators modulomultiplication by scalars of modulus 1. Moreover, we can regard automorphisms in two equivalent ways: asoperating on states (represented as density operators) or as operating on Q.

Non-relativistic dynamics

In non-relativistic physical systems, there is no ambiguity in referring to time evolution since there is a global timeparameter. Moreover an isolated quantum system evolves in a deterministic way: if the system is in a state S at time tthen at time s > t, the system is in a state F (S). Moreover, we assume

• The dependence is reversible: The operators F are bijective.

• The dependence is homogeneous: F = F

r b s,t s - tfi

• The dependence is convexity preserving: That is, each F (S) is convexity preserving.

• The dependence is weakly continuous: The mapping R—> R given by t —> Tr(F (S) E) is continuous for every Eing.

By Kadison's theorem, there is a 1-parameter family of unitary or anti-unitary operators {U } such that

Fs,t(s) = ua.tsu;_t

In fact,

Theorem. Under the above assumptions, there is a strongly continuous 1-parameter group of unitary operators {U }such that the above equation holds.

Note that it easily from uniqueness from Kadison's theorem that

Ut+a = tr{t,s)UtUa

where o(t,s) has modulus 1. Now the square of an anti-unitary is a unitary, so that all the U are unitary. Theremainder of the argument shows that o(t,s) can be chosen to be 1 (by modifying each U by a scalar of modulus 1.)

Pure states

A convex combinations of statistical states S and S is a state of the form S = p S +p S where p , p arenon-negative and p + p =1. Considering the statistical state of system as specified by lab conditions used for itspreparation, the convex combination S can be regarded as the state formed in the following way: toss a biased coinwith outcome probabilities PVP1 and depending on outcome choose system prepared to S or S

Density operators form a convex set. The convex set of density operators has extreme points; these are the densityoperators given by a projection onto a one-dimensional space. To see that any extreme point is such a projection,note that by the spectral theorem S can be represented by a diagonal matrix; since S is non-negative all the entries arenon-negative and since S has trace 1, the diagonal entries must add up to 1. Now if it happens that the diagonalmatrix has more than one non-zero entry it is clear that we can express it as a convex combination of other densityoperators.

The extreme points of the set of density operators are called pure states. If S is the projection on the 1-dimensionalspace generated by a vector i|> of norm 1 then

Tt(SE) = <£ty#)

for any E in Q. In physics jargon, if

s = |VWI,

where o|> has norm 1, then

Tr(SE) = (ij>\E\\l>).Thus pure states can be identified with rays in the Hilbert space H.

The measurement process

Consider a quantum mechanical system with lattice Q which is in some statistical state given by a density operator S.This essentially means an ensemble of systems specified by a repeatable lab preparation process. The result of acluster of measurements intended to determine the truth value of proposition E, is just as in the classical case, aprobability distribution of truth values T and F. Say the probabilities are p for T and q = 1 - p for F. By the previoussection p = Tr(5 E) and q = Tr(5 (7 - £)).

Perhaps the most fundamental difference between classical and quantum systems is the following: regardless of whatprocess is used to determine E immediately after the measurement the system will be in one of two statistical states:

• If the result of the measurement is T

1 -ESE.

Tv(ES)

If the result of the measurement is F

1

(I-E)S(I-E).

Tr{(7 - E)S)

(We leave to the reader the handling of the degenerate cases in which the denominators may be 0.) We now form theconvex combination of these two ensembles using the relative frequencies p and q. We thus obtain the result that themeasurement process applied to a statistical ensemble in state S yields another ensemble in statistical state:

ME(S) = ESE +(I- E)S(I - E).

We see that a pure ensemble becomes a mixed ensemble after measurement. Measurement, as described above, is aspecial case of quantum operations.

Limitations

Quantum logic derived from propositional logic provides a satisfactory foundation for a theory of reversible quantumprocesses. Examples of such processes are the covariance transformations relating two frames of reference, such aschange of time parameter or the transformations of special relativity. Quantum logic also provides a satisfactoryunderstanding of density matrices. Quantum logic can be stretched to account for some kinds of measurementprocesses corresponding to answering yes-no questions about the state of a quantum system. However, for moregeneral kinds of measurement operations (that is quantum operations), a more complete theory of filtering processesis necessary. Such an approach is provided by the consistent histories formalism. On the other hand, quantum logicsderived from MV-logic extend its range of applicability to irreversible quantum processes and/or 'open' quantumsystems.

In any case, these quantum logic formalisms must be generalized in order to deal with super-geometry (which isneeded to handle Fermi-fields) and non-commutative geometry (which is needed in string theory and quantumgravity theory). Both of these theories use a partial algebra with an "integral" or "trace". The elements of the partialalgebra are not observables; instead the "trace" yields "greens functions" which generate scattering amplitudes. Onethus obtains a local S-matrix theory (see D. Edwards).

Since around 1978 the Flato school (see F. Bayen) has been developing an alternative to the quantum logicsapproach called deformation quantization (see Weyl quantization).

In 2004, Prakash Panangaden described how to capture the kinematics of quantum causal evolution using SystemBV, a deep inference logic originally developed for use in structural proof theory. Alessio Guglielmi, LutzStraBburger, and Richard Blute have also done work in this area.

• Mathematical formulation of quantum mechanics

• Multi-valued logic

• Quasi-set theory

• HPO formalism (An approach to temporal quantum logic)

• Quantum field theory

• S. Auyang, How is Quantum Field Theory Possible?, Oxford University Press, 1995.

• F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz and D. Sternheimer, Deformation theory and quantization I,II,Ann. Phys. (N.Y.), 111 (1978) pp. 61-110, 111-151.

• G. Birkhoff and J. von Neumann, The Logic of Quantum Mechanics, Annals of Mathematics, Vol. 37, pp.823-843, 1936.

• D. Cohen, An Introduction to Hilbert Space and Quantum Logic, Springer-Verlag, 1989. This is a thorough butelementary and well-illustrated introduction, suitable for advanced undergraduates.

• David Edwards,The Mathematical Foundations of Quantum Mechanics, Synthese, Volume 42, Number1/September, 1979, pp. 1-70.

• D. Edwards, The Mathematical Foundations of Quantum Field Theory: Fermions, Gauge Fields, andSuper-symmetry, Part I: Lattice Field Theories, International J. of Theor. Phys., Vol. 20, No. 7 (1981).

• D. Finkelstein, Matter, Space and Logic, Boston Studies in the Philosophy of Science Vol. V, 1969

• A. Gleason, Measures on the Closed Subspaces of a Hilbert Space, Journal of Mathematics and Mechanics, 1957.

• R. Kadison, Isometries of Operator Algebras, Annals of Mathematics, Vol. 54, pp. 325—338, 1951

• G. Ludwig, Foundations of Quantum Mechanics, Springer-Verlag, 1983.

• G. Mackey, Mathematical Foundations of Quantum Mechanics, W. A. Benjamin, 1963 (paperback reprint byDover 2004).

• J. von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton University Press, 1955. Reprintedin paperback form.

• R. Omnes, Understanding Quantum Mechanics, Princeton University Press, 1999. An extraordinarily luciddiscussion of some logical and philosophical issues of quantum mechanics, with careful attention to the history ofthe subject. Also discusses consistent histories.

• N. Papanikolaou, Reasoning Formally About Quantum Systems: An Overview, ACM SIGACT News, 36(3), pp.51-66,2005.

• C. Piron, Foundations of Quantum Physics, W. A. Benjamin, 1976.

• H. Putnam, Is Logic Empirical?, Boston Studies in the Philosophy of Science Vol. V, 1969

• H. Weyl, The Theory of Groups and Quantum Mechanics, Dover Publications, 1950.

Quantum logic

53

• Stanford Encyclopedia of Philosophy entry on Quantum Logic and Probability Theory

[8]

References

[1] http://arxiv.org/PS_cache/quant-ph/p.../0101028v2.pdf Maria Luisa Dalla Chiara and Roberto Giuntini. 2008. Quantum Logic,

102 pages PDF

[2] Dalla Chiara, M. L. and Giuntini, R.: 1994, Unsharp quantum logics, Foundations of Physics,, 24, 1161—1177.

[3] http://planetphysics.org/encyclopedi...raicLogic.html I. C. Baianu. 2009. Quantum LMn Algebraic Logic.

[4] Georgescu, G. and C. Vraciu. 1970, On the characterization of centered Lukasiewicz algebras., J. Algebra, 16: 486-495.

[5] Georgescu, G. 2006, N-valued Logics and Lukasiewicz-Moisil Algebras, Axiomathes, 16 (1-2): 123-

Quantum computer

A quantum computer is a device for computation that makes directuse of quantum mechanical phenomena, such as superposition andentanglement, to perform operations on data. Quantum computers aredifferent from traditional computers based on transistors. The basicprinciple behind quantum computation is that quantum properties canbe used to represent data and perform operations on these data. Atheoretical model is the quantum Turing machine, also known as theuniversal quantum computer.

Although quantum computing is still in its infancy, experiments havebeen carried out in which quantum computational operations wereexecuted on a very small number of qubits (quantum bit). Bothpractical and theoretical research continues, and many nationalgovernment and military funding agencies support quantum computingresearch to develop quantum computers for both civilian and national

security purposes, such as cryptanalysis

[21

The Bloch sphere is a representation of a qubit,

the fundamental building block of quantum

computers.

If large-scale quantum computers can be built, they will be able to solve certain problems much faster than anycurrent classical computers (for example Shor's algorithm). Quantum computers however do not allow one tocompute functions that are not theoretically computable by classical computers, i.e. they do not alter theChurch—Turing thesis. The gain is only in efficiency.

Basis

A classical computer has a memory made up of bits, where each bit represents either a one or a zero. A quantumcomputer maintains a sequence of qubits. A single qubit can represent a one, a zero, or, crucially, any quantumsuperposition of these; moreover, a pair of qubits can be in any quantum superposition of 4 states, and three qubits inany superposition of 8. In general a quantum computer with n qubits can be in an arbitrary superposition of up to2"different states simultaneously (this compares to a normal computer that can only be in one of these 2n states atany one time). A quantum computer operates by manipulating those qubits with a fixed sequence of quantum logicgates. The sequence of gates to be applied is called a quantum algorithm.

54

An example of an implementation of qubits for a quantum computer could start with the use of particles with twospin states: "down" and "up" (typically written M ) and ||) , or IfJ) and |1) ). But in fact any system possessingan observable quantity A which is conserved under time evolution and such that A has at least two discrete andsufficiently spaced consecutive eigenvalues, is a suitable candidate for implementing a qubit. This is true becauseany such system can be mapped onto an effective spin-1/2 system.

Bits vs. qubits

Consider first a classical computer that operates on a three-bitregister. The state of the computer at any time is a probabilitydistribution over the 23 = gdifferent three-bit strings 000,001, 010, 011, 100, 101, 110, 111. If it is adeterministic computer, then it is in exactly one of these stateswith probability 1. However, if it is a probabilistic computer, thenthere is a possibility of it being in any one of a number of differentstates. We can describe this probabilistic state by eightnonnegative numbers a,b,c,d,ef,g,h (where a = probabilitycomputer is in state 0 0 0, b = probability computer is in state 0 01,etc.). There is a restriction that these probabilities sum to 1.

4

o i°>

^ |0101) ^ |B)

<=> l*H5»

qubits can be in a superposition of all theclassically allowed states

Qubits are made up of controlled particles and the

means of control (e.g. devices that trap particles and

[3]switch them from one state to another).

The state of a three-qubit quantum computer is similarly described by an eight-dimensional vector (a,b,c,d,ef,g,h),called a ket. However, instead of adding to one, the sum of the squares of the coefficient magnitudes,

lal2 + |p|2 + ... + |/l|2> must equal one. Moreover, the coefficients are complex numbers. Since states arerepresented by complex wavefunctions, two states being added together will undergo interference. This is a keydifference between quantum computing and probabilistic classical computing.

If you measure the three qubits, then you will observe a three-bit string. The probability of measuring a string willequal the squared magnitude of that string's coefficients (using our example, probability that we read state as 000 =

|a|2, probability that we read state as 001 = Ifjl2, etc.). Thus a measurement of the quantum state with

coefficients (a,b,...,h) gives the classical probability distribution (lal2 |6|2 ... l/il2)- We say that the quantum

state "collapses" to a classical state.

Note that an eight-dimensional vector can be specified in many different ways, depending on what basis you choose

for the space. The basis of three-bit strings 000, 001, ..., Ill is known as the computational basis, and is often

convenient, but other bases of unit-length, orthogonal vectors can also be used. Ket notation is often used to make

explicit the choice of basis. For example, the state (a,b,c,d,ej,g,h) in the computational basis can be written as

a |000) + b |001) + c |010) + d |011) + e 1100} + / |101) + g |110) + h |111) , where, e.g.,

|010)= (0,0,1,0,0,0,0,0).The computational basis for a single qubit (two dimensions) is IfJ) = (1,0), |1) = (0,1), but another common basisare the eigenvectors of the Pauli-x operator: |+) = —^ (1, ljand |—) = —7= (1, —1).

Note that although recording a classical state of n bits, a 2 -dimensional probability distribution, requires anexponential number of real numbers, practically we can always think of the system as being exactly one of the n-bitstrings—we just don't know which one. Quantum mechanically, this is not the case, and all 2" complex coefficients

need to be kept track of to see how the quantum system evolves. For example, a 300-qubit quantum computer has a

300 90

state described by 2 (approximately 10 ) complex numbers, more than the number of atoms in the observableuniverse.

Operation

While a classical three-bit state and a quantum three-qubit state are both eight-dimensional vectors, they aremanipulated quite differently for classical or quantum computation. For computing in either case, the system must beinitialized, for example into the all-zeros string, 1000) , corresponding to the vector (1,0,0,0,0,0,0,0). In classicalrandomized computation, the system evolves according to the application of stochastic matrices, which preserve thatthe probabilities add up to one (i.e., preserve the LI norm). In quantum computation, on the other hand, allowedoperations are unitary matrices, which are effectively rotations (they preserve that the sum of the squares add up toone, the Euclidean or L2 norm). (Exactly what unitaries can be applied depend on the physics of the quantumdevice.) Consequently, since rotations can be undone by rotating backward, quantum computations are reversible.(Technically, quantum operations can be probabilistic combinations of unitaries, so quantum computation really doesgeneralize classical computation. See quantum circuit for a more precise formulation.)

Finally, upon termination of the algorithm, the result needs to be read off. In the case of a classical computer, wesample from the probability distribution on the three-bit register to obtain one definite three-bit string, say 000.Quantum mechanically, we measure the three-qubit state, which is equivalent to collapsing the quantum state downto a classical distribution (with the coefficients in the classical state being the squared magnitudes of the coefficientsfor the quantum state, as described above) followed by sampling from that distribution. Note that this destroys theoriginal quantum state. Many algorithms will only give the correct answer with a certain probability, however byrepeatedly initializing, running and measuring the quantum computer, the probability of getting the correct answercan be increased.

For more details on the sequences of operations used for various quantum algorithms, see universal quantumcomputer, Shor's algorithm, Graver's algorithm, Deutsch-Jozsa algorithm, amplitude amplification, quantum Fouriertransform, quantum gate, quantum adiabatic algorithm and quantum error correction.

Potential

Integer factorization is believed to be computationally infeasible with an ordinary computer for large integers thatare the product of only a few prime numbers (e.g., products of two 300-digit primes). By comparison, a quantumcomputer could efficiently solve this problem using Shor's algorithm to find its factors. This ability would allow aquantum computer to decrypt many of the cryptographic systems in use today, in the sense that there would be apolynomial time (in the number of digits of the integer) algorithm for solving the problem. In particular, most of thepopular public key ciphers are based on the difficulty of factoring integers (or the related discrete logarithm problemwhich can also be solved by Shor's algorithm), including forms of RSA. These are used to protect secure Web pages,encrypted email, and many other types of data. Breaking these would have significant ramifications for electronicprivacy and security.

However, other existing cryptographic algorithms don't appear to be broken by these algorithms. Some

public-key algorithms are based on problems other than the integer factorization and discrete logarithm problems towhich Shor's algorithm applies, like the McEliece cryptosystem based on a problem in coding theory. Lattice

based cryptosystems are also not known to be broken by quantum computers, and finding a polynomial timealgorithm for solving the dihedral hidden subgroup problem, which would break many lattice based cryptosystems,is a well-studied open problem. It has been proven that applying Graver's algorithm to break a symmetric (secretkey) algorithm by brute force requires roughly 2 invocations of the underlying cryptographic algorithm, comparedwith roughly 2n in the classical case, meaning that symmetric key lengths are effectively halved: AES-256 wouldhave the same security against an attack using Graver's algorithm that AES-128 has against classical brute-force

search (see Key size). Quantum cryptography could potentially fulfill some of the functions of public keycryptography.

Besides factorization and discrete logarithms, quantum algorithms offering a more than polynomial speedup over thebest known classical algorithm have been found for several problems, including the simulation of quantumphysical processes from chemistry and solid state physics, the approximation of Jones polynomials, and solvingPell's equation. No mathematical proof has been found that shows that an equally fast classical algorithm cannot bediscovered, although this is considered unlikely. For some problems, quantum computers offer a polynomialspeedup. The most well-known example of this is quantum database search, which can be solved by Grover'salgorithm using quadratically fewer queries to the database than are required by classical algorithms. In this case theadvantage is provable. Several other examples of provable quantum speedups for query problems have subsequentlybeen discovered, such as for finding collisions in two-to-one functions and evaluating NAND trees.

Consider a problem that has these four properties:

1. The only way to solve it is to guess answers repeatedly and check them,

2. There are n possible answers to check,

3. Every possible answer takes the same amount of time to check, and

4. There are no clues about which answers might be better: generating possibilities randomly is just as good aschecking them in some special order.

An example of this is a password cracker that attempts to guess the password for an encrypted file (assuming that thepassword has a maximum possible length).

For problems with all four properties, the time for a quantum computer to solve this will be proportional to thesquare root of n. That can be a very large speedup, reducing some problems from years to seconds. It can be used toattack symmetric ciphers such as Triple DES and AES by attempting to guess the secret key.

Grover's algorithm can also be used to obtain a quadratic speed-up [over a brute-force search] for a class of problemsknown as NP-complete.

Since chemistry and nanotechnology rely on understanding quantum systems, and such systems are impossible tosimulate in an efficient manner classically, many believe quantum simulation will be one of the most importantapplications of quantum computing.

There are a number of practical difficulties in building a quantum computer, and thus far quantum computers haveonly solved trivial problems. David DiVincenzo, of IBM, listed the following requirements for a practical quantum

t [13]

computer:

• scalable physically to increase the number of qubits;

• qubits can be initialized to arbitrary values;

• quantum gates faster than decoherence time;

• universal gate set;

• qubits can be read easily.

Quantum decoherence

One of the greatest challenges is controlling or removing quantum decoherence. This usually means isolating thesystem from its environment as the slightest interaction with the external world would cause the system to decohere.This effect is irreversible, as it is non-unitary, and is usually something that should be avoided, if not highlycontrolled. Decoherence times for candidate systems, in particular the transverse relaxation time T (for NMR andMRI technology, also called the dephasing time), typically range between nanoseconds and seconds at lowtemperature.

These issues are more difficult for optical approaches as the timescales are orders of magnitude lower and an oftencited approach to overcoming them is optical pulse shaping. Error rates are typically proportional to the ratio of

operating time to decoherence time, hence any operation must be completed much more quickly than thedecoherence time.

If the error rate is small enough, it is thought to be possible to use quantum error correction, which corrects errorsdue to decoherence, thereby allowing the total calculation time to be longer than the decoherence time. An often

_4

cited figure for required error rate in each gate is 10 . This implies that each gate must be able to perform its task inone 10,000th of the decoherence time of the system.

Meeting this scalability condition is possible for a wide range of systems. However, the use of error correction bringswith it the cost of a greatly increased number of required qubits. The number required to factor integers using Shor's

2

algorithm is still polynomial, and thought to be between L and L , where L is the number of bits in the number to befactored; error correction algorithms would inflate this figure by an additional factor of L. For a 1000-bit number,

4 ri4i

this implies a need for about 10 qubits without error correction. With error correction, the figure would rise to

■7

about 10 qubits. Note that computation time is about £2or about ]^Q7steps and on 1 MHz, about 10 seconds.

A very different approach to the stability-decoherence problem is to create a topological quantum computer withanyons, quasi-particles used as threads and relying on braid theory to form stable logic gates.

Developments

There are a number of quantum computing candidates, among those:

ri7i

Superconductor-based quantum computers (including SQUID-based quantum computers)Trapped ion quantum computer

Optical lattices

n siTopological quantum computer

Quantum dot on surface (e.g. the Loss-DiVincenzo quantum computer)

Nuclear magnetic resonance on molecules in solution (liquid NMR)

Solid state NMR Kane quantum computers

Electrons on helium quantum computers

Cavity quantum electrodynamics (CQED)

Molecular magnet

Fullerene-based ESR quantum computer

Optic-based quantum computers (Quantum optics)

Diamond-based quantum computer

Bose—Einstein condensate-based quantum computer

Transistor-based quantum computer - string quantum computers with entrainment of positive holes using an

electrostatic trap

Spin-based quantum computer

T231

[241 [25]

Rare-earth-metal-ion-doped inorganic crystal based quantum computers

The large number of candidates shows explicitly that the topic, in spite of rapid progress, is still in its infancy. But atthe same time there is also a vast amount of flexibility.

In 2005, researchers at the University of Michigan built a semiconductor chip which functioned as an ion trap. Suchdevices, produced by standard lithography techniques, may point the way to scalable quantum computing tools.An improved version was made in 2006.

In 2009, researchers at Yale University created the first rudimentary solid-state quantum processor. The two-qubitsuperconducting chip was able to run elementary algorithms. Each of the two artificial atoms (or qubits) were made

[97] [2S]

up of a billion aluminum atoms but they acted like a single one that could occupy two different energy states.

58

Another team, working at the University of Bristol, also created a silicon-based quantum computing chip, based on

[291quantum optics. The team was able to run Shor's algorithm on the chip.

Relation to computational complexity theory

The class of problems that can be efficiently solved by quantumcomputers is called BQP, for "bounded error, quantum, polynomialtime". Quantum computers only run probabilistic algorithms, so BQPon quantum computers is the counterpart of BPP on classicalcomputers. It is defined as the set of problems solvable with apolynomial-time algorithm, whose probability of error is boundedaway from one half. A quantum computer is said to "solve" aproblem if, for every instance, its answer will be right with highprobability. If that solution runs in polynomial time, then that problemis in BQP.

PSPACE problems

NP Problems

BQP

The suspected relationship of BQP to other

l3°]problem spaces.

BQP is contained in the complexity class #P (or more precisely in theassociated class of decision problems P ), which is a subclass ofPSPACE.

BQP is suspected to be disjoint from NP-complete and a strict superset of P, but that is not known. Both integerfactorization and discrete log are in BQP. Both of these problems are NP problems suspected to be outside BPP, andhence outside P. Both are suspected to not be NP-complete. There is a common misconception that quantumcomputers can solve NP-complete problems in polynomial time. That is not known to be true, and is generallysuspected to be false

[31]

Although quantum computers may be faster than classical computers, those described above can't solve anyproblems that classical computers can't solve, given enough time and memory (however, those amounts might bepractically infeasible). A Turing machine can simulate these quantum computers, so such a quantum computer couldnever solve an undecidable problem like the halting problem. The existence of "standard" quantum computers doesnot disprove the Church—Turing thesis. It has been speculated that theories of quantum gravity, such as M-theoryor loop quantum gravity, may allow even faster computers to be built. Currently, it's an open problem to even definecomputation in such theories due to the problem of time, i.e. there's no obvious way to describe what it means for anobserver to submit input to a computer and later receive output

132]

Timeline of quantum computing

Quantum bus

Post-quantum cryptography

Chemical computer

Optical computer

DNA computer

Molecular computer

List of emerging technologies

References

[I] " Quantum Computing with Molecules (http://www.media.mit.edu/physics/pub...rshenfeld.html)"article in Scientific American by Neil Gershenfeld and Isaac L. Chuang - a generally accessible overview of quantum computing and so on.

[2] Quantum Information Science and Technology Roadmap (http://qist.lanl.gov/qcomp_map.shtml) for a sense of where the research is

heading.[3] Waldner, Jean-Baptiste (2007). Nanocomputers and Swarm Intelligence. London: ISTE. p. 157. ISBN 2746215160.[4] David P. DiVincenzo (1995). "Quantum Computation". Science 270 (5234): 255-261. doi:10.1126/science.270.5234.255.[5] Integer Factoring (http://modular.fas.harvard.edu/edu/F..._factoring.pdf) By ARJEN K. LENSTRA -

Designs, Codes and Cryptography, 19, 101—128 (2000) Kluwer Academic Publishers[6] Daniel J. Bernstein, Introduction to Post-Quantum Cryptography (http://pqcrypto.org/www.springer.com...tent/document/

cda_downloaddocument/9783540887010-cl.pdf). Introduction to Daniel J. Bernstein, Johannes Buchmann, Erik Dahmen (editors).

Post-quantum cryptography. Springer, Berlin, 2009. ISBN 978-3-540-88701-0[7] See also pqcrypto.org (http://pqcrypto.org/), a bibliography maintained by Daniel J. Bernstein and Tanja Lange on cryptography not known

to be broken by quantum computing.[8] Robert J. McEliece. " A public-key cryptosystem based on algebraic coding theory (http://ipnpr.jpl.nasa.gov/progress_report2/42-44/

44N.PDF)." Jet Propulsion Laboratory DSN Progress Report 42-44, 114-116.[9] Kobayashi, H.; Gall, F.L. (2006), "Dihedral Hidden Subgroup Problem: A Survey", Information and Media Technologies (J-STAGE) 1 (1):

178-185[10] Bennett C.H., Bernstein E., Brassard G., Vazirani U., The strengths and weaknesses of quantum computation (http://www.es.berkeley.

edu/~vazirani/pubs/bbbv.ps). SIAM Journal on Computing 26(5): 1510-1523 (1997).

[II] Quantum Algorithm Zoo (http://www.its.caltech.edu/~sjordan/zoo.html) - Stephen Jordan's Homepage

[12] The Father of Quantum Computing (http://www.wired.com/science/discove.../2007/02/72734) By Quinn Norton 02.15.2007,

Wired.com[13] David P. DiVincenzo, IBM (2000-04-13). "The Physical Implementation of Quantum Computation" (http://arxiv.org/abs/quant-ph/

0002077). . Retrieved 2006-11-17.[14] M. I. Dyakonov, Universite Montpellier (2006-10-14). "Is Fault-Tolerant Quantum Computation Really Possible?" (http://arxiv.org/abs/

quant-ph/0610117). . Retrieved 2007-02-16.[15] Freedman, Michael; Alexei Kitaev, Michael Larsen, Zhenghan Wang (2002-10-20). "Topological Quantum Computation". Bulletin of the

American Mathematical Society 40 (1): 31-38. doi:10.1090/S0273-0979-02-00964-3.[16] Monroe, Don, Anyons: The breakthrough quantum computing needs? (http://www.newscientist.com/channel/fundamentals/

mg20026761.700-anyons-the-breakthrough-quantum-computing-needs.html), New Scientist, 1 October 2008[17] Clarke, John; Wilhelm, Frank (June 19, 2008). "Superconducting quantum bits" (http://www.nature.com/nature/journal/v453/n7198/

fulVnature07128.html). Nature 453 (7198): 1031-1042. doi:10.1038/nature07128. ISSN 0028-0836. PMID 18563154..[18] Nayak, Chetan; Simon, Steven; Stern, Ady (2008). "Nonabelian Anyons and Quantum Computation" (http://arxiv.org/abs/0707.1889).

Rev Mod Phys 80: 1083..[19] Nizovtsev, A. P.; Kilin, S. Ya.; Jelezko, F.; Gaebal, T.; Popa, I.; Gruber, A.; Wrachtrup, J. (October 19, 2004). "A quantum computer based

on NV centers in diamond: Optically detected nutations of single electron and nuclear spins" (http://www.springerlink.com/content/

5p65541g35716085/). Optics and Spectroscopy 99 (2): 248-260. doi:10.1134/1.2034610. .[20] Wolfgang Gruener, TG Daily (2007-06-01). "Research indicates diamonds could be key to quantum storage" (http://www.tgdaily.com/

content/view/32306/118/). . Retrieved 2007-06-04.[21] Neumann, P.; Mizuochi, N.; Rempp, F.; Hemmer, P.; Watanabe, H.; Yamasaki, S.; Jacques, V.; Gaebel, T. et al. (June 6, 2008).

"Multipartite Entanglement Among Single Spins in Diamond" (http://www.sciencemag.org/cgi/conten.../320/5881/1326).

Science 320 (5881): 1326-1329. doi:10.1126/science.H57233. PMID 18535240. .[22] Rene Millman, IT PRO (2007-08-03). "Trapped atoms could advance quantum computing" (http://www.itpro.co.uk/news/121086/

trapped-atoms-could-advance-quantum-computing.html). . Retrieved 2007-07-26.[23] William M Kaminsky, MIT (Date Unknown). "Scalable Superconducting Architecture for Adiabatic Quantum Computation" (http://arxiv.

org/pdf/quant-ph/0403090).. Retrieved 2007-02-19.[24] Ohlsson, N.; Mohan, R. K.; Kroll, S. (January 1, 2002). "Quantum computer hardware based on rare-earth-ion-doped inorganic crystals"

(http://www.sciencedirect.eom/science...b8281f76f89138). Opt. Commun. 201 (1-3):

71-77. doi:10.1016/S0030-4018(01)01666-2..[25] Longdell, J. J.; Sellars, M. J.; Manson, N. B. (September 23, 2004). "Demonstration of conditional quantum phase shift between ions in a

solid" (http://prola.aps.org/abstract/PRL/v93/il3/el30503). Phys. Rev. Lett. 93 (13): 130503. doi:10.1103/PhysRevLett.93.130503.

PMID 15524694..[26] Ann Arbor (2005-12-12). "U-M develops scalable and mass-producible quantum computer chip" (http://www.umich.edu/news/index.

html?Releases/2005/Dec05/rl21205b).. Retrieved 2006-11-17.[27] Dicarlo, L; Chow, JM; Gambetta, JM; Bishop, LS; Johnson, BR; Schuster, DI; Majer, J; Blais, A et al. (2009-06-28). "Demonstration of

two-qubit algorithms with a superconducting quantum processor" (http://www.nature.com/nature/journal.../ncurrent/pdf/

nature08121.pdf). Nature 460 (7252): 240-4. doi:10.1038/nature08121. ISSN 0028-0836. PMID 19561592.. Retrieved 2009-07-02.

[28] "Scientists Create First Electronic Quantum Processor" (http://opa.yale.edu/news/article.aspx?id=6764). 2009-07-02. . Retrieved2009-07-02.

[29] New Scientist (2009-09-04). "Code-breaking quantum algorithm runs on a silicon chip" (http://www.newscientist.com/article/...icon-chip.html).. Retrieved 2009-10-14.

[30] Michael Nielsen and Isaac Chuang (2000). Quantum Computation and Quantum Information. Cambridge: Cambridge University Press.ISBN 0-521-63503-9. OCLC 174527496.

[31] Bernstein and Vazirani, Quantum complexity theory, SIAM Journal on Computing, 26(5):1411-1473, 1997. (http://www.cs.berkeley.edu/-vazirani/bv.ps)

[32] Scott Aaronson, NP-complete Problems and Physical Reality (http://arxiv.org/abs/quant-ph/0502072), ACM SIGACT News, Vol. 36,No. 1. (March 2005), pp. 30-52, section 7 "Quantum Gravity": "[...] to anyone who wants a test or benchmark for a favorite quantum gravitytheory,[author's footnote: That is, one without all the bother of making numerical predictions and comparing them to observation] let mehumbly propose the following: can you define Quantum Gravity Polynomial-Time? [...] until we can say what it means for a 'user' to specifyan 'input' and 'later' receive an 'output'—there is no such thing as computation, not even theoretically." (emphasis in original)

General references

• Derek Abbott, Charles R. Doering, Carlton M. Caves, Daniel M. Lidar, Howard E. Brandt, Alexander R.Hamilton, David K. Ferry, Julio Gea-Banacloche, Sergey M. Bezrukov, and Laszlo B. Kish (2003). "Dreamsversus Reality: Plenary Debate Session on Quantum Computing". Quantum Information Processing 2 (6):449-472. doi:10.1023/B:QINP.0000042203.24782.9a. arXiv:quant-ph/0310130. (Alternative Location (free) atMichigan university's repository Deep Blue (http://hdl.handle.net/2027.42/45526))

David P. DiVincenzo (2000). "The Physical Implementation of Quantum Computation". Experimental Proposalsfor Quantum Computation. arXiv:quant-ph/0002077

David P. DiVincenzo (1995). "Quantum Computation". Science 270 (5234): 255-261.doi:10.1126/science.270.5234.255. Table 1 lists switching and dephasing times for various systems.Richard Feynman (1982). "Simulating physics with computers". International Journal of Theoretical Physics 21:467. doi:10.1007/BF02650179.

Gregg Jaeger (2006). Quantum Information: An Overview. Berlin: Springer. ISBN 0-387-35725-4.OCLC 255569451.

Michael Nielsen and Isaac Chuang (2000). Quantum Computation and Quantum Information. Cambridge:Cambridge University Press. ISBN 0-521-63503-9. OCLC 174527496.

Stephanie Frank Singer (2005). Linearity, Symmetry, and Prediction in the Hydrogen Atom. New York: Springer.ISBN 0-387-24637-1. OCLC 253709076.

Giuliano Benenti (2004). Principles of Quantum Computation and Information Volume 1. New Jersey: WorldScientific. ISBN 9-812-38830-3. OCLC 179950736.

David P. DiVincenzo (2000). "The Physical Implementation of Quantum Computation". Experimental Proposalsfor Quantum Computation. arXiv:quant-ph/0002077.

Sam Lomonaco Four Lectures on Quantum Computing given at Oxford University in July 2006 (http://www.csee. umbc. edu/~lomonaco/Lectures .html#OxfordLectures)C. Adami, N.J. Cerf. (1998). "Quantum computation with linear optics". arXiv:quant-ph/9806048vl.

Joachim Stolze,; Dieter Suter, (2004). Quantum Computing. Wiley-VCH. ISBN 3527404384.

Ian Mitchell, (1998). "Computing Power into the 21st Century: Moore's Law and Beyond" (http://citeseer.ist.psu.edu/mitchell98computing.html).

Rolf Landauer, (1961). "Irreversibility and heat generation in the computing process" (http://www.research.ibm.com/journal/...ibmrd0503C.pdf).

Gordon E. Moore (1965). Cramming more components onto integrated circuits.

R.W. Keyes, (1988). Miniaturization of electronics and its limits.

M. A. Nielsen,; E. Knill, ; R. Laflamme,. "Complete Quantum Teleportation By Nuclear Magnetic Resonance"(http://citeseer.ist.psu.edu/595490.html).

Quantum computer 61

• Lieven M.K. Vandersypen,; Constantino S. Yannoni, ; Isaac L. Chuang, (2000). Liquid state NMR QuantumComputing.

• Imai Hiroshi,; Hayashi Masahito, (2006). Quantum Computation and Information. Berlin: Springer.ISBN 3540331328.

• Andre Berthiaume, (1997). "Quantum Computation" (http://citeseer.ist.psu.edu/article/...97quantum.html).

• Daniel R. Simon, (1994). "On the Power of Quantum Computation" (http://citeseer.ist.psu.edu/simon94power.html). Institute of Electrical and Electronic Engineers Computer Society Press.

• "Seminar Post Quantum Cryptology" (http://www.crypto.rub.de/its_seminar_ss08.html). Chair forcommunication security at the Ruhr-University Bochum.

• Laura Sanders, (2009). "First programmable quantum computer created" (http://www.sciencenews.org/view/gene...mputer_created).

• Stanford Encyclopedia of Philosophy: " Quantum Computing (http://plato.stanford.edu/entries/qt-quantcomp/)" by Amit Hagar.

• Quantiki (http://www.quantiki.org/) - Wiki and portal with free-content related to quantum informationscience.

• jQuantum: Java quantum circuit simulator (http://jquantum.sourceforge.net/jQuantumApplet.html)

• C++ Quantum Library (https://gna.org/projects/quantumlibrary)

• Haskell Library for Quantum computations (http://hackage.haskell.org/cgi-bin/h.../quantum-arrow)

• Video Lectures by David Deutsch (http://www.quiprocone.org/Protected/DD_lectures.htm)

• Lectures at the Institut Henri Poincare (slides and videos) (http://www.quantware.ups-tlse.fr/IHP2006/)

Quantum chemistry

Quantum chemistry is a branch of theoretical chemistry, which applies quantum mechanics and quantum fieldtheory to address problems in chemistry. The description of the electronic behavior of atoms and molecules aspertaining to their reactivity is one of the applications of quantum chemistry. Quantum chemistry lies on the borderbetween chemistry and physics, and significant contributions have been made by scientists from both fields. It has astrong and active overlap with the field of atomic physics and molecular physics, as well as physical chemistry.

Quantum chemistry mathematically describes the fundamental behavior of matter at the molecular scale. It is, inprinciple, possible to describe all chemical systems using this theory. In practice, only the simplest chemical systemsmay realistically be investigated in purely quantum mechanical terms, and approximations must be made for mostpractical purposes (e.g., Hartree-Fock, post Hartree-Fock or Density functional theory, see computational chemistryfor more details). Hence a detailed understanding of quantum mechanics is not necessary for most chemistry, as theimportant implications of the theory (principally the orbital approximation) can be understood and applied in simplerterms.

In quantum mechanics the Hamiltonian, or the physical state, of a particle can be expressed as the sum of twooperators, one corresponding to kinetic energy and the other to potential energy. The Hamiltonian in the Schrodingerwave equation used in quantum chemistry does not contain terms for the spin of the electron.

Solutions of the Schrodinger equation for the hydrogen atom gives the form of the wave function for atomic orbitals,and the relative energy of the various orbitals. The orbital approximation can be used to understand the other atomse.g. helium, lithium and carbon.

History

The history of quantum chemistry essentially began with the 1838 discovery of cathode rays by Michael Faraday, the1859 statement of the black body radiation problem by Gustav Kirchhoff, the 1877 suggestion by Ludwig Boltzmannthat the energy states of a physical system could be discrete, and the 1900 quantum hypothesis by Max Planck thatany energy radiating atomic system can theoretically be divided into a number of discrete energy elements e suchthat each of these energy elements is proportional to the frequency v with which they each individually radiateenergy, as defined by the following formula:

e = hvwhere h is a numerical value called Planck's Constant. Then, in 1905, to explain the photoelectric effect (1839), i.e.,that shining light on certain materials can function to eject electrons from the material, Albert Einstein postulated,based on Planck's quantum hypothesis, that light itself consists of individual quantum particles, which later came tobe called photons (1926). In the years to follow, this theoretical basis slowly began to be applied to chemicalstructure, reactivity, and bonding.

Electronic structure

The first step in solving a quantum chemical problem is usually solving the Schrodinger equation (or Dirac equationin relativistic quantum chemistry) with the electronic molecular Hamiltonian. This is called determining theelectronic structure of the molecule. It can be said that the electronic structure of a molecule or crystal impliesessentially its chemical properties. An exact solution for the Schrodinger equation can only be obtained for thehydrogen atom. Since all other atomic, or molecular systems, involve the motions of three or more "particles", theirSchrodinger equations cannot be solved exactly and so approximate solutions must be sought.

Wave model

The foundation of quantum mechanics and quantum chemistry is the wave model, in which the atom is a small,dense, positively charged nucleus surrounded by electrons. Unlike the earlier Bohr model of the atom, however, thewave model describes electrons as "clouds" moving in orbitals, and their positions are represented by probabilitydistributions rather than discrete points. The strength of this model lies in its predictive power. Specifically, itpredicts the pattern of chemically similar elements found in the periodic table. The wave model is so named becauseelectrons exhibit properties (such as interference) traditionally associated with waves. See wave-particle duality.

Valence bond

Although the mathematical basis of quantum chemistry had been laid by Schrodinger in 1926, it is generallyaccepted that the first true calculation in quantum chemistry was that of the German physicists Walter Heitler andFritz London on the hydrogen (H ) molecule in 1927. Heitler and London's method was extended by the Americantheoretical physicist John C. Slater and the American theoretical chemist Linus Pauling to become theValence-Bond (VB) [or Heitler-London-Slater-Pauling (HLSP)] method. In this method, attention is primarilydevoted to the pairwise interactions between atoms, and this method therefore correlates closely with classicalchemists' drawings of bonds.

Molecular orbital

An alternative approach was developed in 1929 by Friedrich Hund and Robert S. Mulliken, in which electrons aredescribed by mathematical functions delocalized over an entire molecule. The Hund-Mulliken approach ormolecular orbital (MO) method is less intuitive to chemists, but has turned out capable of predicting spectroscopicproperties better than the VB method. This approach is the conceptional basis of the Hartree-Fock method andfurther post Hartree-Fock methods.

Density functional theory

The Thomas-Fermi model was developed independently by Thomas and Fermi in 1927. This was the first attemptto describe many-electron systems on the basis of electronic density instead of wave functions, although it was notvery successful in the treatment of entire molecules. The method did provide the basis for what is now known asdensity functional theory. Though this method is less developed than post Hartree-Fock methods, its significantlylower computational requirements (scaling typically no worse than ^3-with respect to n basis functions) allow it totackle larger polyatomic molecules and even macromolecules. This computational affordability and oftencomparable accuracy to MP2 and CCSD (post-Hartree—Fock methods) has made it one of the most popular methodsin computational chemistry at present.

Chemical dynamics

A further step can consist of solving the Schrodinger equation with the total molecular Hamiltonian in order to studythe motion of molecules. Direct solution of the Schrodinger equation is called quantum molecular dynamics, withinthe semiclassical approximation semiclassical molecular dynamics, and within the classical mechanics frameworkmolecular dynamics (MD). Statistical approaches, using for example Monte Carlo methods, are also possible.

In adiabatic dynamics, interatomic interactions are represented by single scalar potentials called potential energysurfaces. This is the Born-Oppenheimer approximation introduced by Born and Oppenheimer in 1927. Pioneeringapplications of this in chemistry were performed by Rice and Ramsperger in 1927 and Kassel in 1928, andgeneralized into the RRKM theory in 1952 by Marcus who took the transition state theory developed by Eyring in

1935 into account. These methods enable simple estimates of unimolecular reaction rates from a few characteristicsof the potential surface.

Non-adiabatic dynamics consists of taking the interaction between several coupled potential energy surface(corresponding to different electronic quantum states of the molecule). The coupling terms are called vibroniccouplings. The pioneering work in this field was done by Stueckelberg, Landau, and Zener in the 1930s, in theirwork on what is now known as the Landau-Zener transition. Their formula allows the transition probability betweentwo diabatic potential curves in the neighborhood of an avoided crossing to be calculated.

Quantum chemistry and quantum field theory

The application of quantum field theory (QFT) to chemical systems and theories has become increasingly commonin the modern physical sciences. One of the first and most fundamentally explicit appearances of this is seen in thetheory of the photomagneton. In this system, plasmas, which are ubiquitous in both physics and chemistry, arestudied in order to determine the basic quantization of the underlying bosonic field. However, quantum field theoryis of interest in many fields of chemistry, including: nuclear chemistry, astrochemistry, sonochemistry, and quantumhydrodynamics. Field theoretic methods have also been critical in developing the ab initio Effective Hamiltoniantheory of semi-empirical pi-electron methods.

Atomic physics

Computational chemistry

Condensed matter physics

International Academy of Quantum Molecular Science

Molecular modelling

Physical chemistry

Quantum chemistry computer programs

Quantum electrochemistry

QMC@Home

Theoretical physics

• Atkins, P.W. Friedman, R. (2005). Molecular Quantum Mechanics , Oxford University Press, 4th edition. ISBN978-0199274987

• Atkins, P.W. Physical Chemistry (Oxford University Press) ISBN 0-19-879285-9

• Atkins, P.W. Friedman, R. (2008). Quanta, Matter and Change: A Molecular Approach to Physical Change , W.H. Freeman. ISBN 978-0716761174

• Bernard Pullman and Alberte Pullman. 1963. Quantum Biochemistry, New York and London: Academic Press.

• Eric R. Scerri, The Periodic Table: Its Story and Its Significance, Oxford University Press, 2006. Considers theextent to which chemistry and especially the periodic system has been reduced to quantum mechanics. ISBN0-19-530573-6.

• McWeeny, R. Coulson's Valence (Oxford Science Publications) ISBN 0-19-855144-4

• Karplus M., Porter R.N. (1971). Atoms and Molecules. An introduction for students of physical chemistry ,Benjamin-Cummings Publishing Company, ISBN 978-0805352184

Quantum chemistry 65

• Landau, L.D. and Lifshitz, E.M. Quantum Mechanics:Non-relativistic Theory (Course of Theoretical Physicsvol.3) (Pergamon Press)

• Levine, I. (2008). Physical Chemistry , McGraw-Hill Science, 6th edition. ISBN 978-0072538625 (Hardcover) orISBN 978-0071276368 (Paperback)

• Pauling, L. (1954). General Chemistry. Dover Publications. ISBN 0-486-65622-5.

• Pauling, L., and Wilson, E. B. (1935/1963). Introduction to Quantum Mechanics with Applications to Chemistry(Dover Publications) ISBN 0-486-64871-0

• Simon, Z. (1976). Quantum Biochemistry and Specific Interactions., Taylor & Francis; ISBN 978-0856260872and ISBN 0-85-6260878 .

• The Sherrill Group - Notes [2]

• ChemViz Curriculum Support Resources

• Early ideas in the history of quantum chemistry

• The Particle Adventure

Nobel lectures by quantum chemists

• Walter Kohn's Nobel lecture

T71

• Rudolph Marcus' Nobel lecture

ro]

• Robert Mulliken's Nobel lecture

• Linus Pauling's Nobel lecture

• John Pople's Nobel lecture

References

[1] "Quantum Chemistry" (http://cmm.cit.nih.gov/modeling/guid..._document.html). The N1H Guide to

Molecular Modeling. National Institutes of Health.. Retrieved 2007-09-08.[2] http://vergil.chemistry.gatech.edu/n.../index.html[3] http://www.shodor.org/chemviz/[4] http://www.quantum-chemistry-history.com/[5] http://particleadventure.org/

Density functional theory

Electronic structure methods

Tight binding

Nearly-free electron model

Hartree—Fock

Modern valence bond

Generalized valence bond

M0ller—Plesset perturbation theory

Configuration interaction

Coupled cluster

Multi-configurational self-consistent field

Density functional theory

Quantum chemistry composite methods

Quantum Monte Carlo

kp perturbation theory

Muffin-tin approximation

LCAO method

Density functional theory (DFT) is a quantum mechanical theory used in physics and chemistry to investigate theelectronic structure (principally the ground state) of many-body systems, in particular atoms, molecules, and thecondensed phases. With this theory, the properties of a many-electron system can be determined by usingfunctionals, i.e. functions of another function, which in this case is the spatially dependent electron density. Hencethe name density functional theory comes from the use of functionals of the electron density. DFT is among the mostpopular and versatile methods available in condensed-matter physics, computational physics, and computationalchemistry.

DFT has been very popular for calculations in solid state physics since the 1970s. In many cases the results of DFTcalculations for solid-state systems agreed quite satisfactorily with experimental data. Also, the computational costswere relatively low when compared to traditional ways which were based on the complicated many-electronwavefunction, such as Hartree-Fock theory and its descendants. However, DFT was not considered accurate enoughfor calculations in quantum chemistry until the 1990s, when the approximations used in the theory were greatlyrefined to better model the exchange and correlation interactions. DFT is now a leading method for electronicstructure calculations in chemistry and solid-state physics.

Despite the improvements in DFT, there are still difficulties in using density functional theory to properly describeintermolecular interactions, especially van der Waals forces (dispersion); charge transfer excitations; transitionstates, global potential energy surfaces and some other strongly correlated systems; and in calculations of the bandgap in semiconductors. Its poor treatment of dispersion renders DFT unsuitable (at least when used alone) for thetreatment of systems which are dominated by dispersion (e.g., interacting noble gas atoms) or where dispersioncompetes significantly with other effects (e.g. in biomolecules). The development of new DFT methods designed toovercome this problem, by alterations to the functional or by the inclusion of additive terms, is a current researchtopic.

Overview of method

Although density functional theory has its conceptual roots in the Thomas-Fermi model, DFT was put on a firmtheoretical footing by the two Hohenberg-Kohn theorems (H-K). The original H-K theorems held only fornon-degenerate ground states in the absence of a magnetic field, although they have since been generalized toencompass these.

The first H-K theorem demonstrates that the ground state properties of a many-electron system are uniquelydetermined by an electron density that depends on only 3 spatial coordinates. It lays the groundwork for reducing themany-body problem of N electrons with 3N spatial coordinates to 3 spatial coordinates, through the use offunctionals of the electron density. This theorem can be extended to the time-dependent domain to developtime-dependent density functional theory (TDDFT), which can be used to describe excited states.

The second H-K theorem defines an energy functional for the system and proves that the correct ground stateelectron density minimizes this energy functional.

Within the framework of Kohn-Sham DFT, the intractable many-body problem of interacting electrons in a staticexternal potential is reduced to a tractable problem of non-interacting electrons moving in an effective potential. Theeffective potential includes the external potential and the effects of the Coulomb interactions between the electrons,e.g., the exchange and correlation interactions. Modeling the latter two interactions becomes the difficulty within KSDFT. The simplest approximation is the local-density approximation (LDA), which is based upon exact exchangeenergy for a uniform electron gas, which can be obtained from the Thomas-Fermi model, and from fits to thecorrelation energy for a uniform electron gas. Non-interacting systems are relatively easy to solve as thewavefunction can be represented as a Slater determinant of orbitals. Further, the kinetic energy functional of such asystem is known exactly. The exchange-correlation part of the total-energy functional remains unknown and must beapproximated.

Another approach, less popular than Kohn-Sham DFT (KS-DFT) but arguably more closely related to the spirit ofthe original H-K theorems, is orbital-free density functional theory (OFDFT), in which approximate functionals arealso used for the kinetic energy of the non-interacting system.

Derivation and formalism

As usual in many-body electronic structure calculations, the nuclei of the treated molecules or clusters are seen asfixed (the Born-Oppenheimer approximation), generating a static external potential V in which the electrons aremoving. A stationary electronic state is then described by a wavefunction ^(r*!, . . . , Fjv) satisfying themany-electron Schrodinger equation

HV

T + V + U

vp

N ^2 N N

Ira . t-t

■qj = E^

where j^ is the electronic molecular Hamiltonian, _/V"is the number of electrons, jus the J\T -electron kinetic

energy, f/is the _/\T -electron potential energy from the external field, and fj is the electron-electron interaction

energy for the _/\T -electron system. The operators j1 and jj are so-called universal operators as they are the same

for any system, while f/is system dependent, i.e. non-universal. The difference between having separable

single-particle problems and the much more complicated many-particle problem arises from the interaction term fj .There are many sophisticated methods for solving the many-body Schrodinger equation based on the expansion of

the wavefunction in Slater determinants. While the simplest one is the Hartree-Fock method, more sophisticated

approaches are usually categorized as post-Hartree-Fock methods. However, the problem with these methods is the

huge computational effort, which makes it virtually impossible to apply them efficiently to larger, more complex

systems.

68

Here DFT provides an appealing alternative, being much more versatile as it provides a way to systematically mapthe many-body problem, with fj, onto a single-body problem without jj . In DFT the key variable is the particledensity n(r), which for a normalized \J> is given by

n{f) =N I d3r2 / d3r3 ■ ■ ■ / d3rN^*(f, r2,..., rN)V{r, r2)..., fN)

This relation can be reversed, i.e. for a given ground-state density no(r)it is possible, in principle, to calculate the

corresponding ground-state wavefunction ^qOti, . . . , fjv)- in other words, ty^is a unique functional of 71q,

^o = * [no]and consequently the ground-state expectation value of an observable q is also a functional of Uq

O[n0] = (y[no]\6\y[n0])In particular, the ground-state energy is a functional of Uq

T + V + U

*["o]

V

v[r [n0] \ can be written explicitly in terms of the

V

l[Mcan be written explicitly in terms of the

E0 = E[n0] = (V[n0]where the contribution of the external potential /^[riglground-state density TIq

V[n0] = I V(r)n0(r)d3r

More generally, the contribution of the external potential /\p

density n,

V[n] = I V(r)n{r)d3r

The functionals T^land ?7[rilare called universal functionals, while ^/[rjlis called a non-universal functional,as it depends on the system under study. Having specified a system, i.e., having specified y', one then has tominimize the functional

E[n] = T[n] + U[n] + / V(r)n(r)d3r

with respect to n(r), assuming one has got reliable expressions for T[n] and U[n] ■ A successful minimization of

the energy functional will yield the ground-state density fioand thus all other ground-state observables.

The variational problems of minimizing the energy functional E[n] can be solved by applying the Lagrangian

method of undetermined multipliers. First, one considers an energy functional that doesn't explicitly have anelectron-electron interaction energy term,

EB[n] = (®s[n\

Ts + Vs

ys[n]

where J1 denotes the non-interacting kinetic energy and \/ is an external effective potential in which the particlesare moving. Obviously, n f^\ = n(^\ if \T is chosen to be

vs = v + u+(f-t)

Thus, one can solve the so-called Kohn-Sham equations of this auxiliary non-interacting system,

L^+v-^

4>i{r) = £i<t>i{r)which yields the orbitals (f>t that reproduce the density n{r) of the original many-body system

N

n(r) = ns(r) = ^|0,(f)|2

i

The effective single-particle potential can be written in more detail as

Vs(r) = V(r) + /' t^J. dV + VfccM?)]

]3

where the second term denotes the so-called Hartree term describing the electron-electron Coulomb repulsion, whilethe last term Vxcis called the exchange-correlation potential. Here, VxcmclU(les all the many-particleinteractions. Since the Hartree term and Vxc^epend on n{r), which depends on the (j)^, which in turn depend onVs, the problem of solving the Kohn-Sham equation has to be done in a self-consistent (i.e., iterative) way. Usuallyone starts with an initial guess for n{r), then calculates the corresponding V^and solves the Kohn-Sham equationsfor the (f>t. From these one calculates a new density and starts again. This procedure is then repeated untilconvergence is reached.

Approximations (Exchange-correlation functionals)

The major problem with DFT is that the exact functionals for exchange and correlation are not known except for thefree electron gas. However, approximations exist which permit the calculation of certain physical quantities quiteaccurately. In physics the most widely used approximation is the local-density approximation (LDA), where thefunctional depends only on the density at the coordinate where the functional is evaluated:

Exc[n] = / exc(n)n(r)d3

The local spin-density approximation (LSDA) is a straightforward generalization of the LDA to include electronspin:

Exc[nhnl\ = J exc^T'^M^d3^

Highly accurate formulae for the exchange-correlation energy density £xc(nU n\ )have been constructed from

quantum Monte Carlo simulations of a free electron model.

Generalized gradient approximations (GGA) are still local but also take into account the gradient of the density at the

same coordinate:

Exc[nhnt] = j eXc(nh nh Wnh Vfi|)n(r)d3r.Using the latter (GGA) very good results for molecular geometries and ground-state energies have been achieved.

Potentially more accurate than the GGA functionals are meta-GGA functions. These functionals include a furtherterm in the expansion, depending on the density, the gradient of the density and the Laplacian (second derivative) ofthe density.

Difficulties in expressing the exchange part of the energy can be relieved by including a component of the exactexchange energy calculated from Hartree-Fock theory. Functionals of this type are known as hybrid functionals.

Generalizations to include magnetic fields

The DFT formalism described above breaks down, to various degrees, in the presence of a vector potential, i.e. amagnetic field. In such a situation, the one-to-one mapping between the ground-state electron density andwavefunction is lost. Generalizations to include the effects of magnetic fields have led to two different theories:current density functional theory (CDFT) and magnetic field functional theory (BDFT). In both these theories, thefunctional used for the exchange and correlation must be generalized to include more than just the electron density.In current density functional theory, developed by Vignale and Rasolt, the functionals become dependent on boththe electron density and the paramagnetic current density. In magnetic field density functional theory, developed bySalsbury, Grayce and Harris, the functionals depend on the electron density and the magnetic field, and thefunctional form can depend on the form of the magnetic field. In both of these theories it has been difficult todevelop functionals beyond their equivalent to LDA, which are also readily implementable computationally.

70

Applications

In practice, Kohn-Sham theory can be applied in several distinct ways

depending on what is being investigated. In solid state calculations, the

local density approximations are still commonly used along with plane

wave basis sets, as an electron gas approach is more appropriate for

electrons delocalised through an infinite solid. In molecular calculations,

however, more sophisticated functionals are needed, and a huge variety of

exchange-correlation functionals have been developed for chemical

applications. Some of these are inconsistent with the uniform electron gas

approximation, however, they must reduce to LDA in the electron gas limit.

Among physicists, probably the most widely used functional is the revised

Perdew-Burke-Ernzerhof exchange model (a direct generalized-gradient

parametrization of the free electron gas with no free parameters); however,

this is not sufficiently calorimetrically accurate for gas-phase molecular calculations. In the chemistry community,

one popular functional is known as BLYP (from the name Becke for the exchange part and Lee, Yang and Parr for

the correlation part). Even more widely used is B3LYP which is a hybrid functional in which the exchange energy,

in this case from Becke's exchange functional, is combined with the exact energy from Hartree-Fock theory. Along

with the component exchange and correlation functionals, three parameters define the hybrid functional, specifying

how much of the exact exchange is mixed in. The adjustable parameters in hybrid functionals are generally fitted to a

'training set' of molecules. Unfortunately, although the results obtained with these functionals are usually sufficiently

accurate for most applications, there is no systematic way of improving them (in contrast to some of the traditional

wavefunction-based methods like configuration interaction or coupled cluster theory). Hence in the current DFT

approach it is not possible to estimate the error of the calculations without comparing them to other methods or

experiments.

C with isosurface of ground-state electron60

density as calculated with DFT.

For molecular applications, in particular for hybrid functionals, Kohn-Sham DFT methods are usually implementedjust like Hartree-Fock itself.

Thomas—Fermi model

The predecessor to density functional theory was the Thomas—Fermi model, developed by Thomas and Fermi in1927. They used a statistical model to approximate the distribution of electrons in an atom. The mathematical basispostulated that electrons are distributed uniformly in phase space with two electrons in every /],3of volume. Foreach element of coordinate space volume ^3rwe can fill out a sphere of momentum space up to the Fermi

[7]

momentum Pf

(4/3)7rj>J(f)Equating the number of electrons in coordinate space to that in phase space gives:

,-f. 87T r.

Solving for P/and substituting into the classical kinetic energy formula then leads directly to a kinetic energyrepresented as a functional of the electron density:

tTF[n]TTF[n]

V

1rat

-CF

\ n

l/3\2

CK

oc n

2/3

ime

(r)

n(r)n2'd(r)ddr = CF

n

5/3

(r)d3r

where CF = f — |

10me V87r/

As such, they were able to calculate the energy of an atom using this kinetic energy functional combined with theclassical expressions for the nuclear-electron and electron-electron interactions (which can both also be representedin terms of the electron density).

Although this was an important first step, the Thomas—Fermi equation's accuracy is limited because the resultingkinetic energy functional is only approximate, and because the method does not attempt to represent the exchangeenergy of an atom as a conclusion of the Pauli principle. An exchange energy functional was added by Dirac in1928.

However, the Thomas—Fermi—Dirac theory remained rather inaccurate for most applications. The largest source oferror was in the representation of the kinetic energy, followed by the errors in the exchange energy, and due to thecomplete neglect of electron correlation.

Teller (1962) showed that Thomas—Fermi theory cannot describe molecular bonding. This can be overcome byimproving the kinetic energy functional.

The kinetic energy functional can be improved by adding the Weizsacker (1935) correction:

Tw[n] = 8 m ./ ~wr

Hohenberg-Kohn Theorem

l.For N-interacting electrons, E[n] is only functional of the electron density.

2. E\nGS] = EGS

Eqs^s the real ground state energy,and TlQsis the real ground state electron density.

Software supporting DFT

DFT is supported by many Quantum chemistry and solid state physics codes, often along with other methods.

Basis set (chemistry)

Gas in a box

Helium atom

Kohn—Sham equations

Local density approximation

Molecule

Molecular design software

Molecular modelling

Quantum chemistry

List of quantum chemistry and solid state physics software

List of software for molecular mechanics modeling

Thomas—Fermi model

Time-dependent density functional theory

Books on DFT

• R. Dreizler, E. Gross, Density Functional Theory (Plenum Press, New York, 1995).

• C. Fiolhais, F. Nogueira, M. Marques (eds.), A Primer in Density Functional Theory (Springer-Verlag, 2003).[10]

• Kohanoff, J., Electronic Structure Calculations for Solids and Molecules: Theory and Computational Methods(Cambridge University Press, 2006).

• W. Koch, M. C. Holthausen, A Chemist's Guide to Density Functional Theory (Wiley-VCH, Weinheim, ed. 2,2002).

• R. G. Parr, W. Yang, Density-Functional Theory of Atoms and Molecules (Oxford University Press, New York,1989), ISBN 0-19-504279-4, ISBN 0-19-509276-7 (pbk.).

• N.H. March, Electron Density Theory of Atoms and Molecules (Academic Press, 1992), ISBN 0-12-470525-1.

• Richard M. Martin, Electronic Structure: Basic Theory and Practical Methods, Cambridge University Press, 2004

• D. Sholl, J. A. Steckel, Density Functional Theory: A Practical Introduction, Wiley-Interscience, 2009

Key papers

L.H. Thomas, The calculation of atomic fields, Proc. Camb. Phil. Soc, 23 542-548

P. Hohenberg and W. Kohn, Phys. Rev. 136 (1964) B864 [11]

W. Kohn and L. J. Sham, Phys. Rev. 140 (1965) A1133 [12]

A. D. Becke, J. Chem. Phys. 98 (1993) 5648 [13]

C. Lee, W. Yang, and R. G. Parr, Phys. Rev. B 37 (1988) 785 [14]

P. J. Stephens, F. J. Devlin, C. F. Chabalowski, and M. J. Frisch, J. Phys. Chem. 98 (1994) 11623 [15]

K. Burke, J. Werschnik, and E. K. U. Gross, Time-dependent density functional theory: Past, present, and future.

J. Chem. Phys. 123, 062206 [16] (2005). OAI: arXiv.org:cond-mat/0410362 [17].

n 8i

• Walter Kohn, Nobel Laureate Freeview video interview with Walter on his work developing density

functional theory by the Vega Science Trust.

Klaus Capelle, A bird's-eye view of density-functional theory

Walter Kohn, Nobel Lecture [20]

T211Density functional theory on arxiv.org

T221FreeScience Library -> Density Functional Theory

TheABCofDFT[23]

T241Density Functional Theory — an introduction

1251Electron Density Functional Theory - Lecture Notes

References

[1] Hohenberg, Pierre; Walter Kohn (1964). "Inhomogeneous electron gas". Physical Review 136 (3B): B864—B871.

doi:10.1103/PhysRev.l36.B864.[2] Levy, Mel (1979). "Universal variational functional of electron densities, first-order density matrices, and natural spin-orbitals and solution

of the v-representability problem". Proceedings of the National Academy of Sciences (United States National Academy of Sciences) 76 (12):

6062-6065. doi: 10.1073/pnas.76.12.6062.[3] Vignale, G.; Mark Rasolt (1987). "Density-functional theory in strong magnetic fields". Physical Review Letters (American Physical Society)

59 (20): 2360-2363. doi:10.1103/PhysRevLett.59.2360.[4] Kohn, W.; Sham, L. J. (1965). "Self-consistent equations including exchange and correlation effects". Phys. Rev. 140 (4A): A1133—A1138.

doi:10.1103/PhysRev.l40.A1133.[5] John P. Perdew, Adrienn Ruzsinszky, Jianmin Tao, Viktor N. Staroverov, Gustavo Scuseria and Gabor I. Csonka (2005). "Prescriptions for

the design and selection of density functional approximations: More constraint satisfaction with fewer fits". J. Chem. Phys. 123: 062201.

doi:10.1063/l.1904565.

Density functional theory 73

[6] Parr and Yang 1989, p.47

[7] March 1992, p.24

[8] Weizsacker, C. F. v. (1935). "Zur Theorie der Kernmassen". Zeitschriftfur Physik 96 (7-8): 431-58. doi:10.1007/BF01337700.

[9] Parr and Yang 1989, p. 127

[18] http ://www. vega.org. uk/video/programme/23

Birefringence

Birefringence, or double refraction,

is the decomposition of a ray of light

into two rays (the ordinary ray and

the extraordinary ray) when it passes

through certain types of material, such

as calcite crystals or boron nitride,

depending on the polarization of the

light. This effect can occur only if the

structure of the material is anisotropic

(directionally dependent). If the

material has a single axis of anisotropy

or optical axis, (i.e. it is uniaxial) birefringence can be formalized by assigning two different refractive indices to the

material for different polarizations. The birefringence magnitude is then defined by

An = ne — n0

where n and n are the refractive indices for polarizations parallel (extraordinary) and perpendicular (ordinary) to

e ° [11

the axis of anisotropy respectively.

The reason for birefringence is the fact that in anisotropic media the electric field vector pj and the dielectricdisplacement jj can be nonparallel (namely for the extraordinary polarisation), although being linearly related.Birefringence can also arise in magnetic, not dielectric, materials, but substantial variations in magnetic permeabilityof materials are rare at optical frequencies. Liquid crystal materials as used in Liquid Crystal Displays (LCDs) are

[21

also birefringent.

74

Creation

While birefringence is often found naturally (especially in crystals), there are several ways to create it in opticallyisotropic materials.

• Birefringence results when isotropic materials are deformed such that the isotropy is lost in one direction (i.e.,

131stretched or bent). Example

• Applying an electric field can induce molecules to line up or behave asymmetrically, introducing anisotropy andresulting in birefringence, (see Pockels effect)

• Applying a magnetic field can cause a material to be circularly birefringent, with different indices of refractionfor oppositely-handed circular polarizations

• Self alignment of highly polar molecules such as lipids and some surfactants will generate highly birefringent thinfilms (see also Liquid crystal)

Examples of uniaxial birefringent materials

Uniaxial materials, at 590 nm

[4]

Material

beryl Be3Al2(Si03)6

n n An

o e

1.602 1.557 -0.045

calcite CaCO,

calomel Hg CI

1.658 1.486 -0.1721.973 2.656 +0.683

ice H2Q

lithium niobate LiNbO,

1.309 1.313 +0.0042.272 2.187 -0.085

magnesium fluoride MgFquartz SiO

1.380 1.385 +0.0061.544 1.553 +0.009

ruby A1203rutile TiO„

1.770 1.762 -0.0082.616 2.903 +0.287

peridot (Mg, Fe)2Si04sapphire Al O

1.690 1.654 -0.0361.768 1.760 -0.008

sodium nitrate NaNO,

1.587 1.336 -0.251

tourmaline (complex silicate ) 1.669 1.638 -0.031

zircon, high ZrSiO,

zircon, low ZrSiO,

1.960 2.015 +0.0551.920 1.967 +0.047

Many plastics are birefringent, because their molecules are 'frozen' in a stretched conformation when the plastic ismoulded or extruded. For example, cellophane is a cheap birefringent material, and Polaroid sheets are commonlyused to examine for orientation in birefringent plastics like polystyrene and polycarbonate. Birefringent materials areused in many devices which manipulate the polarization of light, such as wave plates, polarizing prisms, and Lyotfilters.

There are many birefringent crystals: birefringence was first described in calcite crystals by the Danish scientistRasmus Bartholin in 1669.

Birefringence can be observed in amyloid plaque deposits such as are found in the brains of Alzheimer's patients.Modified proteins such as immunoglobulin light chains abnormally accumulate between cells, forming fibrils.Multiple folds of these fibers line up and take on a beta-pleated sheet conformation. Congo red dye intercalates

75

between the folds and, when observed under polarized light, causes birefringence.

Cotton (Gossypium hirsutum) fiber is birefringent because of high levels of cellulosic material in the fiber'ssecondary cell wall.

Slight imperfections in optical fiber can cause birefringence, which can cause distortion in fiber-opticcommunication; see polarization mode dispersion. The imperfections can be geometrically based, or a result ofphotoelastic effects from loading on the optical fiber.

Silicon carbide, also known as Moissanite, is strongly birefringent.

The refractive indices of several (uniaxial) birefringent materials are listed below (at wavelength ~ 590 nm)

[4]

Biaxial birefringence

Biaxial materials, at 590 nm

[4]

 Material na \ nY borax 1.447 1.469 1.472 epsom salt MgS04-7(H20) 1.433 1.455 1.461 mica, biotite 1.595 1.640 1.640 mica, muscovite 1.563 1.596 1.601 olivine (Mg, Fe)2Si04 1.640 1.660 1.680 perovskite CaTiO 2.300 2.340 2.380 topaz 1.618 1.620 1.627 ulexite 1.490 1.510 1.520

Biaxial birefringence, also known as trirefringence, describes an anisotropic material that has more than one axis

of anisotropy. For such a material, the refractive index tensor n, will in general have three distinct eigenvalues that

can be labeled n , n„ and n .a p y

Measurement

Birefringence and related optical effects (such as optical rotation and linear or circular dichroism) can be measuredby measuring the changes in the polarization of light passing through the material. These measurements are knownas polarimetry.

Birefringence of lipid bilayers can be measured using dual polarisation interferometry. This provides a measure ofthe degree of order within these fluid layers and how this order is disrupted when the layer interacts with otherbiomolecules.

A common feature of optical microscopes is a pair of crossed polarizing filters. Between the crossed polarizers, abirefringent sample will appear bright against a dark (isotropic) background.

For a fixed composition such as calcium carbonate, a crystal such as calcite or its polymorphs, the index of refractiondepends on the direction of light through the crystal structure. The refraction also depends on composition, and canbe calculated using the Gladstone-Dale relation.

76

Applications

Birefringence is widely used in optical devices, such as liquid crystal displays, light modulators, color filters, waveplates, optical axis gratings, etc. It also plays an important role in second harmonic generation and many othernonlinear processes. It is also utilized in medical diagnostics: needle aspiration of fluid from a gouty joint will revealnegatively birefringent urate crystals. In ophthalmology, scanning laser polarimetry utilises the birefringence of theretinal nerve fibre layer to indirectly quantify its thickness, which is of use in the assessment and monitoring ofglaucoma. Birefringence characteristics in sperm heads allow for the selection of spermatozoa for intracytoplasmic

• • ♦■ [6]

sperm injection.

Birefringent filters are also used as spatial low-pass filters in electronic cameras, where the thickness of the crystal iscontrolled to spread the image in one direction, thus increasing the spot-size. This is essential to the proper workingof all television and electronic film cameras, to avoid spatial aliasing, the folding back of frequencies higher than canbe sustained by the pixel matrix of the camera.

Elastic birefringence

Another form of birefringence is observed in anisotropic elastic materials. In these materials, shear waves splitaccording to similar principles as the light waves discussed above. The study of birefringent shear waves in the earthis a part of seismology. Birefringence is also used in optical mineralogy to determine the chemical composition, andhistory of minerals and rocks.

Electromagnetic waves in an anisotropic material

Effective refractive indices in uniaxial materials

 Propagationdirection Ordinary ray Extraordinary ray Polarization eff Polarization "eff z xy-plane n0 n/a n/a ry-plane xy-plane n0 Z ne xz-plane y n0 Jtz-plane ne < n < n0 other analogous to *z-plane

The behavior of a light ray that propagates through an anisotropic material is dependent on its polarization. For agiven propagation direction, there are generally two perpendicular polarizations for which the medium behaves as ifit had a single effective refractive index. In a uniaxial material, rays with these polarizations are called theextraordinary and the ordinary ray (e and o rays), corresponding to the extraordinary and ordinary refractive indices.In a biaxial material, there are three refractive indices a, /3, and y, yet only two rays, which are called the fast and theslow ray. The slow ray is the ray that has the highest effective refractive index.

For a uniaxial material with the z axis defined to be the optical axis, the effective refractive indices are as in the tableon the right. For rays propagating in the xz plane, the effective refractive index of the e polarization variescontinuously between n0and ne, depending on the angle with the z axis. The effective refractive index can beconstructed from the Index ellipsoid.

77

Mathematical description

More generally, birefringence can be defined by considering a dielectric permittivity and a refractive index that aretensors. Consider a plane wave propagating in an anisotropic medium, with a relative permittivity tensor e, where therefractive index n, is defined by n ■ n = e . If the wave has an electric vector of the form:

E = E0expz(k-r-c^t) (2)where r is the position vector and t is time, then the wave vector k and the angular frequency w must satisfyMaxwell's equations in the medium, leading to the equations:

-V x V x E

1. d2Ew?

— (e ■ ) (3a)

c2 V dt2 '

V - (e ■ E) = 0 (3b)where c is the speed of light in a vacuum. Substituting eqn. 2 in eqns. 3a-b leads to the conditions:

|k|2Eo-(k-Eo)k = ^(e-E0)Wk ■ (e ■ E0) = 0 (4b)

For the matrix product (<e ■ E)often a separate name is used, the dielectric displacement vector TJ). So essentially

birefringence concerns the general theory of linear relationships between these two vectors in anisotropic media.

To find the allowed values of k, E can be eliminated from eq 4a. One way to do this is to write eqn 4a in Cartesian

coordinates, where the x, y and z axes are chosen in the directions of the eigenvectors of e, so that

^2 0 0

e: = u n2. 0

K0

0

0

(4c)

Hence eqn 4a becomes

-K -K +

w2nl.

)EX ~t Kxky£jy -j- kxkzhjz

0 (5a)

kxky£i/x -\- { kx kz -\-

u!2n2

y-)Ey + kykzEz = 0 (5b)

kxkztjx -j- kykzhjy + \— kx — k +

Up-Tpi.

Er = a (5c)

where E ,E ,E ,k ,k and k are the components of E. and k. This is a set of linear equations in E , E , E , and they

xyzxyz * 0 l xyz^

have a non-trivial solution if their determinant is zero:

det

(-*; - k2z +

KxKy

KxfCy

i-kl - hi +

rl )

™y'vz

kxkz

If z

i-kl - kl +

0(6)

Multiplying out eqn (6), and rearranging the terms, we obtain

UJ

UJ

2 (kl + kl . kl + kl . kl + kl\

+

c4 c2 y n2. ny

n-

+

hi

J \nlnl

+

/..'2

K_v

nlnl

k

,r,2l(kl+kl+kl) = 0(7)

nxny

In the case of a uniaxial material, where n =

X

(kl kl kl

n =n and n =n say, eqn 7 can be factorised into-j o z e

kl

■2

/•2,2

,2

UJ

= 0.(8)n* n^ n^ cL I \n* n^ n^ c* I

Each of the factors in eqn 8 defines a surface in the space of vectors k — the surface of wave normals. The first

factor defines a sphere and the second defines an ellipsoid. Therefore, for each direction of the wave normal, two

wavevectors k are allowed. Values of k on the sphere correspond to the ordinary rays while values on the ellipsoid

correspond to the extraordinary rays.

Birefringence 78

For a biaxial material, eqn (7) cannot be factorized in the same way, and describes a more complicated pair ofwave-normal surfaces.

Birefringence is often measured for rays propagating along one of the optical axes (or measured in atwo-dimensional material). In this case, n has two eigenvalues which can be labeled n and n . n can be diagonalizedby:

n = R(X)

R-(x)T m

'nj 0"0 n2^

where R(x) is the rotation matrix through an angle X- Rather than specifying the complete tensor n, we may nowsimply specify the magnitude of the birefringence An, and extinction angle x, where An = n - n .

• Cotton-Mouton effect

• Crystal optics

• John Kerr

• Periodic poling

• Dichroism

• [8] Video of stress birefringence in Polymethylmethacrylate (PMMA or Plexiglas).

• Application note on the theory of birefringence (see no. 14)

References

[1] Eric Weisstein's World of Science on Birefringence (http://scienceworld.wolfram.com/phys...fringence.html)

[2] The Science of Color, by Steven K. Shevell, Optical Society of America. Published 2003. ISBN 0444512519

[4] Elert, Glenn. "Refraction" (http://hypertextbook.com/physics/waves/refraction/). The Physics Hypertextbook. .

[5] The Use of Birefringence for Predicting the Stiffness of Injection Moulded Polycarbonate Discs (http://www.dep.uminho.pt/home/

rec_humanos/mostra_curriculum.php3?pessoa=12&&menu=5&&idcategoria=l)[6] Gianaroli L, Magli MC, Ferraretti AP, et al. (December 2008). "Birefringence characteristics in sperm heads allow for the selection of reacted

spermatozoa for intracytoplasmic sperm injection". Fertil. Steril. doi:10.1016/j.fertnstert.2008.10.024. PMID 19064263.[7] Born M, and Wolf E, Principles of Optics, 7th Ed. 1999 (Cambridge University Press), §15.3.3[8] http://www.youtube.com/watch?v=BEClYQbuG7U[9] http://www.campoly.com/application_notes.html

Polarization spectroscopy 79

Polarization spectroscopy

Polarization spectroscopy comprises a set of spectroscopic techniques based on polarization properties of light (notnecessarily visible one; UV, X-ray, infrared, or in any other frequency range of the electromagnetic radiation). Byanalyzing the polarization properties of light, decisions can be made about the media that emitted the light (or themedia the light passes/scatters through). Alternatively, a source of polarized light may be used to probe a media; inthis case, the changes in the light polarization (comparing to the incidental one) allow to infer the media properties.

In general, any kind of anisotropy in the media results in some sort of light polarization. Such an anisotropy can beeither inherent to the media (e.g., in the case of a crystal substance), or imposed externally (e.g., in the presence ofmagnetic field in plasma).

• Zeeman effect

• Stark effect

• Plasma diagnostics

Polarized IR Spectroscopy

Infrared spectroscopy (IR spectroscopy) is the subset of spectroscopy that deals with the infrared region of theelectromagnetic spectrum. It covers a range of techniques, the most common being a form of absorptionspectroscopy. As with all spectroscopic techniques, it can be used to identify compounds and investigate samplecomposition. A common laboratory instrument that uses this technique is an infrared spectrophotometer.

The infrared portion of the electromagnetic spectrum is usually divided into three regions; the near-, mid- and far-infrared, named for their relation to the visible spectrum. The far-infrared, approximately 400—10 cm"(1000—30 |im), lying adjacent to the microwave region, has low energy and may be used for rotational spectroscopy.The mid-infrared, approximately 4000—400 cm- (30—2.5 u,m) may be used to study the fundamental vibrations andassociated rotational-vibrational structure. The higher energy near-IR, approximately 14000—4000 cm"(2.5—0.8 |im) can excite overtone or harmonic vibrations. The names and classifications of these subregions aremerely conventions. They are neither strict divisions nor based on exact molecular or electromagnetic properties.

Theory

Infrared spectroscopy exploits the fact that molecules absorb specific frequencies that are characteristic of theirstructure. These absorptions are resonant frequencies, i.e. the frequency of the absorbed radiation matches thefrequency of the bond or group that vibrates. The energies are determined by the shape of the molecular potentialenergy surfaces, the masses of the atoms, and the associated vibronic coupling.

In particular, in the Born—Oppenheimer and harmonic approximations, i.e. when the molecular Hamiltoniancorresponding to the electronic ground state can be approximated by a harmonic oscillator in the neighborhood of theequilibrium molecular geometry, the resonant frequencies are determined by the normal modes corresponding to themolecular electronic ground state potential energy surface. Nevertheless, the resonant frequencies can be in a firstapproach related to the strength of the bond, and the mass of the atoms at either end of it. Thus, the frequency of thevibrations can be associated with a particular bond type.

80

Number of vibrational modes

In order for a vibrational mode in a molecule to be "IR active," it must be associated with changes in the permanentdipole.

A molecule can vibrate in many ways, and each way is called a vibrational mode. Linear molecules have 3N-5degrees of vibrational modes whereas nonlinear molecules have 3N-6 degrees of vibrational modes (also calledvibrational degrees of freedom). As an example HO, a non-linear molecule, will have 3*3-6 = 3 degrees ofvibrational freedom, or modes.

Simple diatomic molecules have only one bond and only one vibrational band. If the molecule is symmetrical, e.g.N2, the band is not observed in the IR spectrum, but only in the Raman spectrum. Unsymmetrical diatomicmolecules, e.g. CO, absorb in the IR spectrum. More complex molecules have many bonds, and their vibrationalspectra are correspondingly more complex, i.e. big molecules have many peaks in their IR spectra.

The atoms in a CH group, commonly found in organic compounds can vibrate in six different ways: symmetricaland antisymmetrical stretching, scissoring, rocking, wagging and twisting:

 Symmetricalstretching Antisymmetricalstretching Scissoring Rocking Wagging Twisting V K?- V K?- V V V

Special effects

The simplest and most important IR bands arise from the "normal modes," the simplest distortions of the molecule.In some cases, "overtone bands" are observed. These bands arise from the absorption of a photon that leads to adoubly excited vibrational state. Such bands appear at approximately twice the energy of the normal mode. Somevibrations, so-called 'combination modes," involve more than one normal mode. The phenomenon of Fermiresonance can arise when two modes are similar in energy, Fermi resonance results in an unexpected shift in energyand intensity of the bands.

Practical IR spectroscopy

The infrared spectrum of a sample is recorded by passing a beam of infrared light through the sample. Examinationof the transmitted light reveals how much energy was absorbed at each wavelength. This can be done with amonochromatic beam, which changes in wavelength over time, or by using a Fourier transform instrument tomeasure all wavelengths at once. From this, a transmittance or absorbance spectrum can be produced, showing atwhich IR wavelengths the sample absorbs. Analysis of these absorption characteristics reveals details about themolecular structure of the sample. When the frequency of the IR is the same as the vibrational frequency of a bond,absorption occurs.

This technique works almost exclusively on samples with covalent bonds. Simple spectra are obtained from sampleswith few IR active bonds and high levels of purity. More complex molecular structures lead to more absorptionbands and more complex spectra. The technique has been used for the characterization of very complex mixtures.

81

Sample preparation

Gaseous samples require a sample cell with a long pathlength (typically 5—10 cm), to compensate for the diluteness.

Liquid samples can be sandwiched between two plates of a salt (commonly sodium chloride, or common salt,although a number of other salts such as potassium bromide or calcium fluoride are also used). The plates aretransparent to the infrared light and do not introduce any lines onto the spectra.

Solid samples can be prepared in a variety of ways. One common method is to crush the sample with an oily mullingagent (usually Nujol) in a marble or agate mortar, with a pestle. A thin film of the mull is smeared onto salt platesand measured. The second method is to grind a quantity of the sample with a specially purified salt (usuallypotassium bromide) finely (to remove scattering effects from large crystals). This powder mixture is then pressed ina mechanical die press to form a translucent pellet through which the beam of the spectrometer can pass. A thirdtechnique is the "cast film" technique, which is used mainly for polymeric materials. The sample is first dissolved ina suitable, non hygroscopic solvent. A drop of this solution is deposited on surface of KBr or NaCl cell. The solutionis then evaporated to dryness and the film formed on the cell is analysed directly. Care is important to ensure that thefilm is not too thick otherwise light cannot pass through. This technique is suitable for qualitative analysis. The finalmethod is to use microtomy to cut a thin (20—100 micrometre) film from a solid sample. This is one of the mostimportant ways of analysing failed plastic products for example because the integrity of the solid is preserved.

It is important to note that spectra obtained from different sample preparation methods will look slightly differentfrom each other due to differences in the samples' physical states.

Conventional apparatus

A beam of infrared light is producedand split into two separate beams. Oneis passed through the sample, the otherpassed through a reference which isoften the substance the sample isdissolved in. The beams are bothreflected back towards a detector,however first they pass through asplitter which quickly alternates whichof the two beams enters the detector.The two signals are then compared anda printout is obtained.

IRsource

 Processor Printout

Typical apparatus

A reference prevents fluctuations in the output of the source affecting the data. The reference also allows the effectsof the solvent to be cancelled out (the reference is usually a pure form of the solvent the sample is in)

FT-IR method

Fourier transform infrared (FTIR) spectroscopy is a measurement technique for collecting infrared spectra.Instead of recording the amount of energy absorbed when the frequency of the infra-red light is varied(monochromator), the IR light is guided through an interferometer. After passing through the sample, the measuredsignal is the interferogram. Performing a Fourier transform on this signal data results in a spectrum identical to thatfrom conventional (dispersive) infrared spectroscopy.

FTIR spectrometers are cheaper than conventional spectrometers because building an interferometer is easier thanthe fabrication of a monochromator. In addition, measurement of a single spectrum is faster for the FTIR techniquebecause the information at all frequencies is collected simultaneously. This allows multiple samples to be collectedand averaged together resulting in an improvement in sensitivity. Virtually all modern infrared spectrometers are

FTIR instruments.

Absorptions bands

Wavenumbers listed in cm .

Uses and applications

Infrared spectroscopy is widely used in both research and industry as a simple and reliable technique formeasurement, quality control and dynamic measurement. It is of especial use in forensic analysis in both criminaland civil cases, enabling identification of polymer degradation for example.

The instruments are now small, and can be transported, even for use in field trials. With increasing technology incomputer filtering and manipulation of the results, samples in solution can now be measured accurately (waterproduces a broad absorbance across the range of interest, and thus renders the spectra unreadable without thiscomputer treatment). Some instruments will also automatically tell you what substance is being measured from astore of thousands of reference spectra held in storage.

By measuring at a specific frequency over time, changes in the character or quantity of a particular bond can bemeasured. This is especially useful in measuring the degree of polymerization in polymer manufacture. Modernresearch instruments can take infrared measurements across the whole range of interest as frequently as 32 times asecond. This can be done whilst simultaneous measurements are made using other techniques. This makes theobservations of chemical reactions and processes quicker and more accurate.

Techniques have been developed to assess the quality of tea-leaves using infrared spectroscopy. This will mean thathighly trained experts (also called 'noses') can be used more sparingly, at a significant cost saving.

Infrared spectroscopy has been highly successful for applications in both organic and inorganic chemistry. Infraredspectroscopy has also been successfully utilized in the field of semiconductor microelectronics : for example,infrared spectroscopy can be applied to semiconductors like silicon, gallium arsenide, gallium nitride, zinc selenide,amorphous silicon, silicon nitride, etc.

Isotope effects

The different isotopes in a particular species may give fine detail in infrared spectroscopy. For example, the 0-0stretching frequency (in reciprocal centimeters) of oxyhemocyanin is experimentally determined to be 832 and788 cm- for v( O- O) and v( O- O) respectively.

By considering the 0-0 as a spring, the wavenumber of absorbance, v can be calculated:

1

2ttc v fiwhere k is the spring constant for the bond, c is the speed of light, and j.iis the reduced mass of the A-B system:

mAmB

t*=

m,A + rug

( TTli is the mass of atom { ).

\f\ \f\ 1 R 18

The reduced masses for O- O and O- O can be approximated as 8 and 9 respectively. Thus

83

^1Bo _

I/1B0

Where v is the wavenumber [wavenumber = frequency/(speed of light)]

The effect of isotopes, both on the vibration and the decay dynamics, has been found to be stronger than previouslythought. In some systems, such as silicon and germanium, the decay of the anti-symmetric stretch mode of interstitialoxygen involves the symmetric stretch mode with a strong isotope dependence. For example, it was shown that for anatural silicon sample, the lifetime of the anti-symmetric vibration is 11.4 ps. When the isotope of one of the siliconatoms is increased to 29Si, the lifetime increases to 19 ps, similarly, when the silicon atom is changed to 30Si, thelifetime becomes 27 ps

[4]

Two-dimensional IR

Two-dimensional infrared correlation spectroscopy analysis is the application of 2D correlation analysis oninfrared spectra. By extending the spectral information of a perturbed sample, spectral analysis is simplified andresolution is enhanced. The 2D synchronous and 2D asynchronous spectra represent a graphical overview of thespectral changes due to a perturbation (such as a changing concentration or changing temperature) as well as therelationship between the spectral changes at two different wavenumbers.

Nonlinear two-dimensional infrared

spectroscopy is the infrared version of

correlation spectroscopy. Nonlinear

two-dimensional infrared spectroscopy is a

technique that has become available with the

development of femtosecond infrared laser

pulses. In this experiment first a set of pump

pulses are applied to the sample. This is

followed by a waiting time, where the

system is allowed to relax. The waiting time

typically lasts from zero to several

picoseconds and the duration can be

controlled with a resolution of tens of

femtoseconds. A probe pulse is then applied

resulting in the emission of a signal from the sample. The nonlinear two-dimensional infrared spectrum is a

two-dimensional correlation plot of the frequency U)\ that was excited by the initial pump pulses and the frequency

Cl^3 excited by the probe pulse after the waiting time. This allows the observation of coupling between different

vibrational modes; because of its extremely high time resolution it can be used to monitor molecular dynamics on a

picosecond timescale. It is still a largely unexplored technique and is becoming increasingly popular for fundamental

research.

time

Pulse Sequence used to obtain a two-dimensional Fourier transform infrared

spectrum. The time period T\ is usually referred to as the coherence time and the

second time period 7~2 is known as the waiting time. The excitation frequency is

obtained by Fourier transforming along the T\ axis.

Like in two-dimensional nuclear magnetic resonance (2DNMR) spectroscopy this technique spreads the spectrum intwo dimensions and allow for the observation of cross peaks that contain information on the coupling betweendifferent modes. In contrast to 2DNMR nonlinear two-dimensional infrared spectroscopy also involve the excitationto overtones. These excitations result in excited state absorption peaks located below the diagonal and cross peaks. In2DNMR two distinct techniques, COSY and NOESY, are frequently used. The cross peaks in the first are related tothe scalar coupling, while in the later they are related to the spin transfer between different nuclei. In nonlineartwo-dimensional infrared spectroscopy analogs have been drawn to these 2DNMR techniques. Nonlineartwo-dimensional infrared spectroscopy with zero waiting time corresponds to COSY and nonlinear two-dimensionalinfrared spectroscopy with finite waiting time allowing vibrational population transfer corresponds to NOESY. The

Polarized IR Spectroscopy

84

COSY variant of nonlinear two-dimensional infrared spectroscopy has been used for determination of the secondarystructure content proteins.

• Infrared spectroscopy correlation table

• Fourier transform spectroscopy

• Near infrared spectroscopy

• Vibrational spectroscopy

• Rotational spectroscopy

Time-resolved spectroscopySpectroscopyQuantum vibrationRaman spectroscopyInfrared microscopyPhotothermal microspectroscopy

Polymer degradationInfrared astronomyFar infrared astronomyForensic chemistryForensic engineeringForensic polymerengineeringForensic scienceApplied spectroscopy

• A useful gif animation of different vibrational modes: here

[8]

Infrared spectroscopy for organic chemistsOrganic compounds spectrum database

[91

References

[1] Laurence M. Harwood, Christopher J. Moody. Experimental organic chemistry: Principles and Practice (Illustrated edition ed.). pp. 292.[2] Luypaert, J.; Zhang, M.H.; Massart, D.L. (2003), "Feasibility study for the use of near infrared spectroscopy in the qualitative and

quantitative analysis of green tea, Camellia sinensis (L.)", Analytica Chimica Acta, 478(2), Elsevier, pp. 303—312[3] Lau, W.S. (1999). Infrared characterization for microelectronics. World Scientific.[4] Isotope Dependence of the Lifetime of the 1136-cm[sup -1] Vibration of Oxygen in Silicon K. K. Kohli, Gordon Davies, N. Q. Vinh, D.

West, S. K. Estreicher, T. Gregorkiewicz, I. Izeddin, and K. M. Itoh, Phys. Rev. Lett. 96, 225503 (2006),

DOI:10.1103/PhysRevLett.96.225503[5] P. Hamm, M. H. Lim, R. M. Hochstrasser (1998). "Structure of the amide I band of peptides measured by femtosecond nonlinear-infrared

spectroscopy". J. Phys. Chem. B 102: 6123. doi:10.1021/jp9813286.[6] S. Mukamel (2000). "Multidimensional Fentosecond Correlation Spectroscopies of Electronic and Vibrational Excitations". Annual Review of

Physics and Chemistry 51: 691. doi:10.1146/annurev.physchem.51.1.691.[7] N. Demirdoven, C. M. Cheatum, H. S. Chung, M. Khalil, J. Knoester, A. Tokmakoff (2004). "Two-dimensional infrared spectroscopy of

antiparallel beta-sheet secondary structure". Journal of the American Chemical Society 126: 7981. doi: 10.1021/ja04981 lj.[8] http://www.shu.ac.uk/schools/sci/che...irspecl.htm[9] http: //w w w. organic world wide, net/infrared[10] http://riodb01.ibase.aist.go.jp/sdbs...x.cgi?lang=eng

85

Circular dichroism

First pioneered by Jean-Baptiste Biot, Augustin Fresnel, and Aime Cotton

[2] [3]

[1]

circular dichroism (CD) refers to thedifferential absorption of left and right circularly polarized light. L^J L'J . This phenomenon is exhibited in theabsorption bands of optically active chiral molecules. CD spectroscopy has a wide range of applications in manydifferent fields. Most notably, UV CD is used to investigate the secondary structure of proteins . UV/Vis CD isused to investigate charge-transfer transitions . Near-infrared CD is used to investigate geometric and electronicstructure by probing metal d—>d transitions . Vibrational circular dichroism, which uses light from the infraredenergy region, is used for structural studies of small organic molecules, and most recently proteins and DNA .

Physical Principles

Circular polarization of light

Electromagnetic radiation consists of an electric and magnetic field that oscillate perpendicular to one another and to

ro]

the propagating direction . While linearly polarized light occurs when the electric field vector oscillates only inone plane and changes in magnitude, circularly polarized light occurs when the electric field vector rotates about itspropagation direction and retains constant magnitude. Hence, it forms a helix in space while propagating. For leftcircularly polarized light (LCP) with propagation towards the observer, the electric vector rotates counterclockwise. For right circularly polarized light (RCP), the electric vector rotates clockwise.

[9]

Linearly polarized

Circularly polari;

Interaction of circularly polarized light with matter

When circularly polarized light passes through an absorbing optically active medium, the speeds between right and

left polarizations differ (c * c ) as well as their wavelength (X * X ) and the extent to which they are absorbed

rioi

(e *e ). Circular dichroism is the difference Ae = eT - e_ . The electric field of a light beam causes a linear

L R L R

displacement of charge when interacting with a molecule (electric dipole), whereas the magnetic field of it causes acirculation of charge (magnetic dipole). These two motions combined cause an excitation of an electron in a helicalmotion, which includes translation and rotation and their associated operators. The experimentally determinedrelationship between the rotational strength (R) of a sample and the As is given by

R

3hcl03ln(10)

c.rp

—dv

v

32n3NAThe rotational strength has also been determined theoretically,

We see from these two equations that in order to have non-zero /\^, the electric and magnetic dipole momentoperators ( M( i a- i \and Mi j i \) must transform as the same irreducible representation. C*nand Dn

are the only point groups where this can occur, making only chiral molecules CD active.

Simply put, since circularly polarized light itself is "chiral", it interacts differently with chiral molecules. That is, thetwo types of circularly polarized light are absorbed to different extents. In a CD experiment, equal amounts of leftand right circularly polarized light of a selected wavelength are alternately radiated into a (chiral) sample. One of thetwo polarizations is absorbed more than the other one, and this wavelength-dependent difference of absorption ismeasured, yielding the CD spectrum of the sample. Due to the interaction with the molecule, the electric field vectorof the light traces out an elliptical path after passing through the sample.

Delta absorbance

By definition,

AA = AL - AR

where AA (Delta Absorbance) is the difference between absorbance of left circularly polarized (LCP) and rightcircularly polarized (RCP) light (this is what is usually measured). AA is a function of wavelength, so for ameasurement to be meaningful the wavelength it was performed at must be known.

Molar circular dichroism

It can also be expressed, by applying Beer's law, as:

AA = (eL-eR)Clwhere

e and e are the molar extinction coefficients for LCP and RCP light,

C is the molar concentration

/ is the path length in centimeters (cm).Then

Ae = eL - eRis the molar circular dichroism. This intrinsic property is what is usually meant by the circular dichroism of thesubstance. Since /\^ is a function of wavelength, a molar circular dichroism value ( /\^) must specify thewavelength at which it is valid.

Extrinsic effects on circular dichroism

In many practical applications of circular dichroism (CD), as discussed below, the measured CD is not simply anintrinsic property of the molecule, but rather depends on the molecular conformation. In such a case the CD may alsobe a function of temperature, concentration, and the chemical environment, including solvents. In this case thereported CD value must also specify these other relevant factors in order to be meaningful.

Molar ellipticity

Although AA is usually measured, for historical reasons most measurements are reported in degrees of ellipticity.Molar circular dichroism and molar ellipticity, [9], are readily interconverted by the equation:

87

Elliptical polarized light (purple) is composed of

unequal contributions of right (blue) and left (red)

circular polarized light.

[B] = 3298.2 Ae.

This relationship is derived by defining the ellipticity of the polarization as:

Er — EL

tan# =

ER + EL

where

E and E are the magnitudes of the electric field vectors of the right-circularly and left-circularly polarized

R Ij

light, respectively.When E equals E (when there is no difference in the absorbance of right- and left-circular polarized light), 6 is 0°

R L

and the light is linearly polarized. When either E or E is equal to zero (when there is complete absorbance of the

R L

circular polarized light in one direction), 6 is 45° and the light is circularly polarized.

Generally, the circular dichroism effect is small, so tanB is small and can be approximated as 6 in radians. Since theintensity or irradiance, I, of light is proportional to the square of the electric-field vector, the ellipticity becomes:

, ,-1/2 r1^# (radians)

(j? - ff)

Then by substituting for I using Beer's law in natural logarithm form:

I = I0e-M0The ellipticity can now be written as:

(e1

-In 10

lnlON

e 2

1

^lnlO

fLlnlO>

,AA±

(e^Inl0 + e^lnl°) e^HT + 1Since A A « 1, this expression can be approximated by expanding the exponentials in a Taylor series to first-orderand then discarding terms of AA in comparison with unity and converting from radians to degrees:

'lnl0\ /180x

# (degrees) = A A

4 j \ nThe linear dependence of solute concentration and pathlength is removed by defining molar ellipticity as,

H = —

L J CIThen combining the last two expression with Beer's law, molar ellipticity becomes:

= mAe(^\m\= 3298.2 A,

\ 4 y \ 7r /

Mean residue ellipticity

Methods for estimating secondary structure in polymers, proteins and polypeptides in particular, often require thatthe measured molar ellipticity spectrum be converted to a normalized value, specifically a value independent of thepolymer length. Mean residue ellipticity is used for this purpose; it is simply the measured molar ellipticity of themolecule divided by the number of monomer units (residues) in the molecule.

Application to biological molecules

In general, this phenomenon will be exhibited in absorption bands of any optically active molecule. As aconsequence, circular dichroism is exhibited by biological molecules, because of their dextrorotary and levorotarycomponents. Even more important is that a secondary structure will also impart a distinct CD to its respectivemolecules. Therefore, the alpha helix of proteins and the double helix of nucleic acids have CD spectral signaturesrepresentative of their structures.

CD is closely related to the optical rotatory dispersion (ORD) technique, and is generally considered to be moreadvanced. CD is measured in or near the absorption bands of the molecule of interest, while ORD can be measuredfar from these bands. CD's advantage is apparent in the data analysis. Structural elements are more clearlydistinguished since their recorded bands do not overlap extensively at particular wavelengths as they do in ORD. Inprinciple these two spectral measurements can be interconverted through an integral transform (Kramers—Kronigrelation), if all the absorptions are included in the measurements.

The far-UV (ultraviolet) CD spectrum of proteins can reveal important characteristics of their secondary structure.CD spectra can be readily used to estimate the fraction of a molecule that is in the alpha-helix conformation, thebeta-sheet conformation, the beta-turn conformation, or some other (e.g. random coil) conformation. These

fractional assignments place important constraints on the possible secondary conformations that the protein can bein. CD cannot, in general, say where the alpha helices that are detected are located within the molecule or evencompletely predict how many there are. Despite this, CD is a valuable tool, especially for showing changes inconformation. It can, for instance, be used to study how the secondary structure of a molecule changes as a functionof temperature or of the concentration of denaturing agents, e.g. Guanidinium hydrochloride or urea. In this way itcan reveal important thermodynamic information about the molecule (such as the enthalpy and Gibbs free energy ofdenaturation) that cannot otherwise be easily obtained. Anyone attempting to study a protein will find CD a valuabletool for verifying that the protein is in its native conformation before undertaking extensive and/or expensiveexperiments with it. Also, there are a number of other uses for CD spectroscopy in protein chemistry not related toalpha-helix fraction estimation.

The near-UV CD spectrum (>250 nm) of proteins provides information on the tertiary structure. The signals obtainedin the 250-300 nm region are due to the absorption, dipole orientation and the nature of the surrounding environmentof the phenylalanine, tyrosine, cysteine (or S-S disulfide bridges) and tryptophan amino acids. Unlike in far-UV CD,the near-UV CD spectrum cannot be assigned to any particular 3D structure. Rather, near-UV CD spectra providestructural information on the nature of the prosthetic groups in proteins, e.g., the heme groups in hemoglobin andcytochrome c.

Visible CD spectroscopy is a very powerful technique to study metal—protein interactions and can resolve individuald-d electronic transitions as separate bands. CD spectra in the visible light region are only produced when a metalion is in a chiral environment, thus, free metal ions in solution are not detected. This has the advantage of onlyobserving the protein-bound metal, so pH dependence and stoichiometrics are readily obtained. Optical activity intransition metal ion complexes have been attributed to configurational, conformational and the vicinal effects.Klewpatinond and Viles (2007) have produced a set of empirical rules for predicting the appearance of visible CD

spectra for Cu and Ni square-planar complexes involving histidine and main-chain coordination.

CD gives less specific structural information than X-ray crystallography and protein NMR spectroscopy, forexample, which both give atomic resolution data. However, CD spectroscopy is a quick method that does not requirelarge amounts of proteins or extensive data processing. Thus CD can be used to survey a large number of solventconditions, varying temperature, pH, salinity, and the presence of various cofactors.

CD spectroscopy is usually used to study proteins in solution, and thus it complements methods that study the solidstate. This is also a limitation, in that many proteins are embedded in membranes in their native state, and solutionscontaining membrane structures are often strongly scattering. CD is sometimes measured in thin films.

Experimental limitations

CD has also been studied in carbohydrates, but with limited success due to the experimental difficulties associatedwith measurement of CD spectra in the vacuum ultraviolet (VUV) region of the spectrum (100-200 nm), where thecorresponding CD bands of unsubstituted carbohydrates lie. Substituted carbohydrates with bands above the VUVregion have been successfully measured.

Measurement of CD is also complicated by the fact that typical aqueous buffer systems often absorb in the rangewhere structural features exhibit differential absorption of circularly polarized light. Phosphate, sulfate, carbonate,and acetate buffers are generally incompatible with CD unless made extremely dilute e.g. in the 10-50 mM range.The TRIS buffer system should be completely avoided when performing far-UV CD. Borate and Onium compoundsare often used to establish the appropriate pH range for CD experiments. Some experimenters have substitutedfluoride for chloride ion because fluoride absorbs less in the far UV, and some have worked in pure water. Another,almost universal, technique is to minimize solvent absorption by using shorter path length cells when working in thefar UV, 0.1 mm path lengths are not uncommon in this work.

In addition to measuring in aqueous systems, CD, particularly far-UV CD, can be measured in organic solvents e.g.ethanol, methanol, trifluoroethanol (TFE). The latter has the advantage to induce structure formation of proteins,inducing beta-sheets in some and alpha helices in others, which they would not show under normal aqueousconditions. Most common organic solvents such as acetonitrile, THF, chloroform, dichloromethane are however,incompatible with far-UV CD.

It may be of interest to note that the protein CD spectra used in secondary structure estimation are related to the n tojt*orbital absorptions of the amide bonds linking the amino acids. These absorption bands lie partly in the so-calledvacuum ultraviolet (wavelengths less than about 200 nm). The wavelength region of interest is actually inaccessiblein air because of the strong absorption of light by oxygen at these wavelengths. In practice these spectra aremeasured not in vacuum but in an oxygen-free instrument (filled with pure nitrogen gas).

Once oxygen has been eliminated, perhaps the second most important technical factor in working below 200 nm is todesign the rest of the optical system to have low losses in this region. Critical in this regard is the use of aluminizedmirrors whose coatings have been optimized for low loss in this region of the spectrum.

The usual light source in these instruments is a high pressure, short-arc xenon lamp. Ordinary xenon arc lamps areunsuitable for use in the low UV. Instead, specially constructed lamps with envelopes made from high-puritysynthetic fused silica must be used.

Light from synchrotron sources has a much higher flux at short wavelengths, and has been used to record CD downto 160 nm. Recently the CD spectrometer at the electron storage ring facility ISA at the University of Aarhus inDenmark was used to record solid state CD spectra down to 120 nm.

At the quantum mechanical level, the information content of circular dichroism and optical rotation are identical.

Circular dichroism 90

• Circular polarization in nature

• Dichroism

• Linear dichroism

• Magnetic circular dichroism

• Optical activity

• Optical isomerism

• Optical rotation

• Optical rotatory dispersion

ri3i

1. Alison Rodger and Bengt Norden, Circular Dichroism and Linear Dichroism (1997) Oxford UniversityPress, Oxford, UK. ISBN 019855897X.

2. Fasman, G.D., Circular Dichroism and the Conformational Analysis of Biomolecules (1996) Plenum Press, NewYork.

rd

3. Hecht, E., Optics 3 Edition (1998) Addison Wesley Longman, Massachusetts.

4. Klewpatinond, M. and Viles, J.H. (2007) Empirical rules for rationalising visible circular dichroism of Cu andNi histidine complexes: Applications to the prion protein. FEBS Letters 581, 1430-1434.

ri4i

• Circular Dichroism explained

• Circular Dichroism at UMDNJ - a good site for information on structure estimation software

• Electromagnetic waves - Animated electromagnetic waves. The Emanim program is a teaching resource forhelping students understand the nature of electromagnetic waves and their interaction with birefringent and

dichroic samples

ri7i

• An Introduction to Circular Dichroism Spectroscopy - a very good tutorial on circular dichroism spectroscopy

References

[I] G. D. Fasman (1996). Plenum Press, p. 3.

[2] P. Atkins and J. de Paula (2005). Elements of Physical Chemistry, 4th ed.. Oxford University Press.

[3] E. I. Solomon and A. B. P. Lever (2006). 1. Wiley, p. 78.

[4] R. W. Woody (1994). K. Nakanishi, N. Berova, R. W. Woody, ed. VCH Publishers, Inc.. p. 473.

[5] Solomon, Neidig; A. T. Wecksler, G. Schenk, and T. R. Holman (2007). "Kinetic and Spectroscopic Studies of N694C Lipoxygenase: A

Probe of the Substrate Activation Mechanism of a Nonheme Ferric Enzyme". JACS 129: 7531—7537.[6] E. I. Solomon and A. B. P. Lever (2006). 1. Wiley, p. 78.[7] K. Nakanishi, N. Berova, R. W. Woody, ed (1994). VCH Publishers, Inc..

[8] A. Rodger and B. Norden (1997). Circular Dichroism and Linear Dichroism. Oxford University Press.[9] E. I. Solomon and A. B. P. Lever (2006). 1. Wiley, p. 78.[10] Woody,R.W.1994

[II] Whitmore L, Wallace BA (2008). "Protein secondary structure analyses from circular dichroism spectroscopy: methods and referencedatabases". Biopolymers 89 (5): 392-400. doi:10.1002/bip.20853. PMID 17896349.

[12] Greenfield NJ (2006). "Using circular dichroism spectra to estimate protein secondary structure". Nature protocols 1 (6): 2876—90.

doi:10.1038/nprot.2006.202. PMID 17406547.

91

Vibrational circular dichroism

Vibrational circular dichroism (VCD) is a spectroscopic technique which detects differences in attenuation of leftand right circularly polarized light passing through a sample. It is basically circular dichroism spectroscopy in theinfrared and near infrared ranges .

Because VCD is sensitive to the mutual orientation of distinct groups in a molecule, it provides three-dimensionalstructural information. Thus, it is a powerful technique as VCD spectra of enantiomers can be simulated using abinitio calculations, thereby allowing the identification of absolute configurations of small molecules in solution fromVCD spectra. Among such quantum computations of VCD spectra resulting from the chiral properties of smallorganic molecules are those based on density functional theory (DFT) and gauge-invariant atomic orbitals (GIAO).As a simple example of the experimental results that were obtained by VCD are the spectral data obtained within thecarbon-hydrogen (C-H) stretching region of 21 amino acids in heavy water solutions. Measurements of vibrationaloptical activity (VOA) have thus numerous applications, not only for small molecules, but also for large andcomplex biopolymers such as muscle proteins (myosin, for example) and DNA.

Vibrational modes

K?

K*

Theory of VCD

While the fundamental quantity associated with the infrared absorption is the dipole strength, the differentialabsorption is proportional also to the rotational strength, a quantity which depends on both the electric and magneticdipole transition moments. Sensitivity of the handedness of a molecule toward circularly polarized light results fromthe form of the rotational strength.

VCD of peptides and proteins

Extensive VCD studies have been reported for both polypeptides and several proteins in solution ; several

recent reviews were also compiled . An extensive but not comprehensive VCD publications list is also

provided in the "References" section. The published reports over the last 22 years have established VCD as apowerful technique with improved results over those previously obtained by visible/UV circular dichroism (CD) oroptical rotatory dispersion (ORD) for proteins and nucleic acids.

92

Amino acid and polypeptide structures

 + H,NX /CpT -CH, 0 - 0 H,C- -\c-0 Na+

=^*>

Cation Zuitterion Anion

:»fr£&** |

Bcl-2 Family

§=!=

93

VCD of nucleic acids

VCD spectra of nucleotides, synthetic polynucleotides and several nucleic acids, including DNA, have been reportedand assigned in terms of the type and number of helices present in A-, B-, and Z- DNA.

VCD Instrumentation

For biopolymers such as proteins and nucleic acids, the difference in absorbance between the levo- and dextro-configurations is five orders of magnitude smaller than the corresonding (unpolarized) absorbance. Therefore, VCDof biopolymers requires the use of very sensitive, specially built instrumentation as well as time-averaging overrelatively long intervals of time even with such sensitive VCD spectrometers. Most CD instruments produce left- andright- circularly polarized light which is then either sine-wave or square-wave modulated, with subsequentphase-sensitive detection and lock-in amplification of the detected signal. In the case of FT-VCD, a photo-elasticmodulator (PEM) is employed in conjunction with an FT-IR interferometer set-up. An example is that of a Bomemmodel MB-100 FT-IR interferometer equipped with additional polarizing optics/ accessories needed for recordingVCD spectra. A parallel beam emerges through a side port of the interferometer which passes first through a wiregrid linear polarizer and then through an octagonal-shaped ZnSe crystal PEM which modulates the polarized beam ata fixed, lower frequency such as 37.5 kHz. A mechanically stressed crystal such as ZnSe exhibits birefringence whenstressed by an adjacent piezoelectric transducer. The linear polarizer is positioned close to, and at 45 degrees, withrespect to the ZnSe crystal axis. The polarized radiation focused onto the detector is doubly modulated, both by thePEM and by the interferometer setup. A very low noise detector, such as MCT (HgCdTe), is also selected for theVCD signal phase-sensitive detection. Quasi-complete commercial FT-VCD instruments are also available from afew manufacturers but these are quite expensive and also have to be still considered as being at the prototype stage.To prevent detector saturation an appropriate, long wave pass filter is placed before the very low noise MCTdetector, which allows only radiation below 1750 cm- to reach the MCT detector; the latter however measuresradiation only down to 750 cm- . FT-VCD spectra accumulation of the selected sample solution is then carried out,digitized and stored by an in-line computer. Published reviews that compare various VCD methods are also

available

[9] [10]

n;in

^WfM

 m. 1 J , (l«™H« ™™, - 1

94

BjNj 7759 An 90.48°

Magnetic VCD

VCD spectra have also been reported in the presence of an applied external magnetic field1enhance the VCD spectral resolution for small molecules

[ll]

This method can

Raman optical activity (ROA)

-i

ROA is a technique complementary to VCD especially useful in the 50—1600 cm spectral region; it is consideredas the technique of choice for determining optical activity for photon energies less than 600 cm- .

References

Peptides and proteins

• Huang R, Wu L, McElheny D, Bour P, Roy A, Keiderling TA. Cross-Strand Coupling and Site-SpecificUnfolding Thermodynamics of a Trpzip beta-Hairpin Peptide Using (13)C Isotopic Labeling and IRSpectroscopy. The journal of physical chemistry. B. 2009 Apr;113(16):5661-74.

• "Vibrational Circular Dichroism of Poly alpha-Benzyl-L-Glutamate," R. D. Singh, and T. A. Keiderling,Biopolymers, 20, 237-40 (1981).

• "Vibrational Circular Dichroism of Polypeptides II. Solution Amide II and Deuteration Results," A. C. Sen and T.A. Keiderling, Biopolymers, 23, 1519-32 (1984).

• "Vibrational Circular Dichroism of Polypeptides III. Film Studies of Several alpha-Helical and 6-SheetPolypeptides," A. C. Sen and T. A. Keiderling, Biopolymers, 23, 1533-46 (1984).

• "Vibrational Circular Dichroism of Polypeptides IV. Film Studies of L-Alanine Homo Oligopeptides," U.Narayanan, T. A. Keiderling, G. M. Bonora, and C. Toniolo, Biopolymers 24, 1257-63 (1985).

• "Vibrational Circular Dichroism of Polypeptides, T. A. Keiderling, S. C. Yasui, A. C. Sen, C. Toniolo, G. M.Bonora, in Peptides Structure and Function, Proceedings of the 9th American Peptide Symposium," ed. C. M.Deber, K. Kopple, V. Hruby; Pie rce Chemical: Rockford, IL; 167-172 (1985).

• "Vibrational Circular Dichroism of Polypeptides V. A Study of 310 Helical-Octapeptides" S. C. Yasui, T. A.Keiderling, G M. Bonora, C. Toniolo, Biopolymers 25, 79-89 (1986).

• "Vibrational Circular Dichroism of Polypeptides VI. Polytyrosine alpha-helical and Random Coil Results," S. C.Yasui and T. A. Keiderling, Biopolymers 25, 5-15 (1986).

• "Vibrational Circular Dichroism of Polypeptides VII. Film and Solution Studies of alpha-formingHomo-Oligopeptides," U. Narayanan, T. A. Keiderling, G M. Bonora, C. Toniolo, Journal of the AmericanChemical Society, 108, 2431-2437 (1986).

• "Vibrational Circular Dichroism of Polypeptides VIII. Poly Lysine Conformations as a Function of pH inAqueous Solution," S. C. Yasui, T. A. Keiderling, Journal of the American Chemical Society, 108, 5576-5581(1986).

• "Vibrational Circular Dichroism of Polypeptides IX. A Study of Chain Length Dependence for 310-HelixFormation in Solution." S. C. Yasui, T. A. Keiderling, F. Formaggio, G M. Bonora, C. Toniolo, Journal of theAmerican Chemical Society 108, 4988-499 3 (1986).

• "Vibrational Circular Dichroism of Biopolymers." T. A. Keiderling, Nature, 322, 851-852 (1986).

• "Vibrational Circular Dichroism of Polypeptides X. A Study of alpha-Helical Oligopeptides in Solution." S. C.Yasui, T. A. Keiderling, R. Katachai, Biopolymers 26, 1407-1412 (1987).

• "Vibrational Circular Dichroism of Polypeptides XL Conformation of

Poly(L-Lysine(Z)-L-Lysine(Z)-L-1 -Pyrenylalanine) and Poly(L-Lysine(Z)-L-Lysine(Z)-L-1 -Napthylala-nine) inSolution" S. C. Yasui, T. A. Keiderling, and M. Sisido, Macromolecules 20, 2 403-2406 (1987).

• "Vibrational Circular Dichroism of Biopolymers" T. A. Keiderling, S. C. Yasui, A. C. Sen, U. Narayanan, A.Annamalai, P. Malon, R. Kobrinskaya, L. Yang, in "F.E.C.S. Second International Conference on CircularDichroism, Conference Proceedings," ed. M. Kajtar, L. Eotvos Univ., Budapest, 1987, p. 155-161.

• "Vibrational Circular Dichroism of Poly-L-Proline and Other Helical Poly-peptides," R. Kobrinskaya, S. C.Yasui, T. A. Keiderling, in "Peptides: Chemistry and Biology, Proceedings of the 10th American PeptideSymposium," ed. G. R. Marshall, ESCOM, L eiden, 1988, p. 65-67.

• "Vibrational Circular Dichroism of Polypeptides with Aromatic Side Chains," S. C. Yasui, T. A. Keiderling, in"Peptides: Chemistry and Biology, Proceedings of the 10th American Peptide Symposium," ed. G. R. Marshall,ESCOM, Leiden, 1988, p. 90-92.

• "Vibrational Circular Dichroism of Polypeptides XII. Re-evaluation of the Fourier Transform Vibrational CircularDichroism of Poly-gamma-Benzyl-L-Glutamate," P. Malon, R. Kobrinskaya, T. A. Keiderling, Biopolymers 27,733-746 (1988).

• "Vibrational Circular Dichroism of Biopolymers," T. A. Keiderling, S. C. Yasui, U. Narayanan, A. Annamalai, P.Malon, R. Kobrinskaya, L. Yang, in Spectroscopy of Biological Molecules New Advances ed. E. D. Schmid, F. W.Schneider, F. Siebert, p. 73-76 (1988).

• "Vibrational Circular Dichroism of Polypeptides and Proteins," S. C. Yasui, T. A. Keiderling, Mikrochimica Acta,II, 325-327, (1988).

• "(lR,7R)-7-Methyl-6,9,-Diazatricyclo[6,3,0,01,6]Tridecanne-5,10-Dione, A Tricyclic Spirodilactam ContainingNon-planar Amide Groups: Synthesis, NMR, Crystal Structure, Absolute Configuration, Electronic andVibrational Circular Dichroism" P. Malon, C . L. Barness, M. Budesinsky, R. K. Dukor, D. van der Helm, T. A.Keiderling, Z. Koblicova, F. Pavlikova, M. Tichy, K. Blaha, Collections of Czechoslovak ChemicalCommunications 53, 2447-2472 (1988).

• "Vibrational Circular Dichroism of Poly Glutamic Acid" R. K. Dukor, T. A. Keiderling, in Peptides 1988 (ed. GJung, E. Bayer) Walter de Gruyter, Berlin (1989) pp 519-521.

• "Biopolymer Conformational Studies with Vibrational Circular Dichroism" T. A. Keiderling, S. C. Yasui, P.Pancoska, R. K. Dukor, L. Yang, SPIE Proceeding 1057, ("Biomolecular Spectroscopy," ed. H. H. Mantsch, R. R.Birge) 7-14 (1989).

• "Vibrational Circular Dichroism. Comparison of Techniques and Practical Considerations" T. A. Keiderling, in"Practical Fourier Transform Infrared Spectroscopy. Industrial and Laboratory Chemical Analysis," ed. J. R.Ferraro, K. Krishnan (Academic Press, San Diego, 1990) p. 203-284.

• "Vibrational Circular Dichroism Study of Unblocked Proline Oligomers," R. K. Dukor, T. A. Keiderling, V. Gut,International Journal of Peptide and Protein Research, 38, 198-203 (1991).

• "Reassessment of the Random Coil Conformation. Vibrational CD Study of Proline Oligopeptides and RelatedPolypeptides" R. K. Dukor and T. A. Keiderling, Biopolymers 31 1747-1761 (1991).

• "Vibrational CD of the Amide II band in Some Model Polypeptides and Proteins" V. P. Gupta, T. A. Keiderling,Biopolymers 32 239-248 (1992).

• "Vibrational Circular Dichroism of Proteins Polysaccharides and Nucleic Acids" T. A. Keiderling, Chapter 8 inPhysical Chemistry of Food Processes, Vol. 2 Advanced Techniques, Structures and Applications., eds. I.C.Baianu, H. Pessen, T. Kumosinski, Van Norstrand—Reinhold, New York (1993), pp 307—337.

• "Structural Studies of Biological Macromolecules using Vibrational Circular Dichroism" T. A. Keiderling, P.Pancoska, Chapter 6 in Advances in Spectroscopy Vol. 21, Biomolecular Spectroscopy Part B eds. R. E. Hester,R. J. H. Clarke, John W iley Chichester (1993) pp 267-315.

• "Ab Initio Simulations of the Vibrational Circular Dichroism of Coupled Peptides" P. Bour and T. A. Keiderling,Journal of the American Chemical Society 115 9602-9607 (1993).

• "Ab initio Simulations of Coupled Peptide Vibrational Circular Dichroism" P. Bour, T. A. Keiderling in "FifthInternational Conference on The Spectroscopy of Biological Molecules" Th. Theophanides, J. Anastassopoulou,N. Fotopoulos (Eds), Kluwen Aca demic Publ., Dortrecht, 1993, p. 29-30.

• "Vibrational Circular Dichroism Spectroscopy of Peptides and Proteins" T. A. Keiderling, in "Circular DichroismInterpretations and Applications," K. Nakanishi, N. Berova, R. Woody, Eds., VCH Publishers, New York, (1994)pp 497-521.

• "Conformational Study of Sequential Lys-Leu Based Polymers and Oligomers using Vibrational and ElectronicCircular Dichroism Spectra" V. Baumruk, D. Huo, R. K. Dukor, T. A. Keiderling, D. LeLeivre and A. BrackBiopolymers 34, 1115-1121 (1994).

• "Vibrational Optical Activity of Oligopeptides" T. B. Freedman, L. A. Nafie, T. A. Keiderling Biopolymers(Peptide Science) 37 (ed. C. Toniolo) 265-279 (1995).

• "Characterization of 6-bend ribbon spiral forming peptides using electronic and vibrational circular dichroism" G.Yoder, T. A. Keiderling, F. Formaggio, M. Crisma, C. Toniolo Biopolymers 35, 103-111 (1995).

• "Vibrational Circular Dichroism as a Tool for Determination of Peptide Secondary Structure" P. Bour, T. A.Keiderling, P. Malon, in "Peptides 1994 (Proceedings of the 23rd European Peptide Symposium, 1994," (H.L.S.Maia, ed.), Escom, Le iden 1995, p. 517-518.

• "Helical Screw Sense of homo-oligopeptides of C-alpha-methylated alpha-amino acids as Determined withVibrational Circular Dichroism." G. Yoder, T. A. Keiderling, M. Crisma, F. Formaggio, C. Toniolo, J. Kamphuis,Tetrahedron Asymmetry 6, 687 -690 (1995).

• "Conformational Study of Linear Alternating and Mixed D- and L-Proline Oligomers Using Electronic andVibrational CD and Fourier Transform IR." W. M&#228stle, R. K. Dukor, G Yoder, T. A. KeiderlingBiopolymers 36, 623-631 (1995).

• Review: "Vibrational Circular Dichroism Applications to Conformational Analysis of Biomolecules" T. A.Keiderling in Circular Dichroism and the Conformational Analysis of Biomolecules ed. G D. Fasman, Plenum,New York (1996) p. 555-585.

• "Mutarotation studies of Poly L-Proline using FT-IR, Electronic and Vibrational Circular Dichroism" R. K.Dukor, T. A. Keiderling, Biospectroscopy 2, 83-100 (1996).

• "Vibrational Circular Dichroism Applications in Proteins and Peptides" T. A. Keiderling, Proceedings of theNATO ASI in Biomolecular Structure and Dynamics, Loutrakii Greece, May 1996, Ed. G Vergoten (delayedsecond volume to 1998).

• "Transfer of Molecular Property Tensors in Cartesian Coordinates: A new algorithm for simulation of vibrationalspectra" Petr Bour, Jana Sopkova, Lucie Bednarova, Petr Malon, T. A. Keiderling, Journal of ComputationalChemistry 18, 6 46-659 (1997).

• "Vibrational Circular Dichroism Characterization of Alanine-Rich Peptides." Gorm Yoder and Timothy A.Keiderling, "Spectroscopy of Biological Molecules: Modern Trends," Ed. P. Carmona, R. Navarro, A. Hernanz,Kluwer Acad. Pub., Netherlands (1997) p p. 27-28.

• "Ionic strength effect on the thermal unfolding of alpha-spectrin peptides." D. Lusitani, N. Menhart, T.A.Keiderling and L. W. M. Fung. Biochemistry 37(1998)16546-16554.

• "In search of the earliest events of hCGb folding: structural studies of the 60-87 peptide fragment" S. Sherman, L.Kirnarsky, O. Prakash, H. M. Rogers, R.A.G.D. Silva, T.A. Keiderling, D. Smith, A.M. Hanly, F. Perini, andR.W. Ruddon, American Pep tide Symposium Proceedings, 1997.

• "Cold Denaturation Studies of (LKELPKEL)n Peptide Using Vibrational Circular Dichroism and FT-IR". R. A.G D. Silva, Vladimir Baumruk, Petr Pancoska, T. A. Keiderling, Eric Lacassie, and Yves Trudelle, AmericanPeptide Symposium Proceedings, 1997.

• "Simulations of oligopeptide vibrational CD. Effects of isotopic labeling." Petr Bour, Jan Kubelka,T. A.Keiderling Biopolymers 53, 380-395 (2000).

• "Site specific conformational determination in thermal unfolding studies of helical peptides using vibrationalcircular dichroism with isotopic substitution" R. A. G. D. Silva, Jan Kubelka, Petr Bour, Sean M. Decatur,Timothy A. Keiderling, Proceedings of the National Academy of Sciences (PNAS:USA) 97, 8318-8323 (2000).

• "Folding studies on the human chorionic gonadotropin b -subunit using optical spectroscopy of peptidefragments" R. A. G. D. Silva, S. A. Sherman, F. Perini, E. Bedows, T. A. Keiderling, Journal of the AmericanChemical Society, 122, 8623-8630 (2000).

• "Peptide and Protein Conformational Studies with Vibrational Circular Dichroism and Related Spectroscopies",Timothy A. Keiderling, (Revised and Expanded Chapter) In Circular Dichroism: Principles and Applications, 2ndEdition. (Eds. K. Nakanishi, N. Berova and R. A. Woody, John Wiley & Sons, New York (2000) p. 621-666.

• "Conformation studies with Optical Spectroscopy of peptides taken from hairpin sequences in the HumanChorionic Gonadotropin " R. A. G D. Silva, S. A. Sherman, E. Bedows, T. A. Keiderling, Peptides for the NewMillenium, Proceedings of the 16th American Peptide Symposium, (June, 1999 Minneapolis, MN) Ed.G B.Fields, J. P. Tam, G. Barany, Kluwer Acad. Pub., Dordrecht,(2000) p. 325-326.

• "Analysis of Local Conformation within Helical Peptides via Isotope-Edited Vibrational Spectroscopy." S. M.Decatur, T. A. Keiderling, R. A. G D.Silva, and P. Bour, Peptides for the New Millenium, Proceedings of the16th American Peptide Symposium, (June, 1999 Minneapolis, MN) Ed. Ed.G. B. Fields, J. P. Tam, G Barany,Kluwer Acad. Pub., Dordrecht, (2000) p. 414-416.

• "The anomalous infrared amide I intensity distribution in C-13 isotopically labeled peptide beta-sheets comesfrom extended, multiple stranded structures. An Ab Initio study." Jan Kubelka and T. A. Keiderling , Journal ofthe American Chemical Society. 123, 6142-6150 (2001).

• "Vibrational Circular Dichroism of Peptides and Proteins: Survey of Techniques, Qualitative and QuantitativeAnalyses, and Applications" Timothy A. Keiderling, Chapter in Infrared and Raman Spectroscopy of BiologicalMaterials, Ed. Bing Yan and H.-U. Gremlich, Marcel Dekker, New York (2001) p. 55-100.

• "Chirality in peptide vibrations. Ab initio computational studies of length, solvation, hydrogen bond, dipolecoupling and isotope effects on vibrational CD. " Jan Kubelka, Petr Bour, R. A. Gangani D. Silva, Sean M.Decatur, Timothy A. Keiderling, ACS Symposium Series 810, ["Chirality: Physical Chemistry," (Ed. JaniceHicks) American Chemical Society, Washington, DC] (2002), pp. 50—64.

• "Spectroscopic Characterization of Selected b-Sheet Hairpin Models", J. Hilario, J. Kubelka, F. A. Syud, S. H.Gellman, and T. A. Keiderling. Biopolymers (Biospectroscopy) 67: 233-236 (2002)

• " Discrimination between peptide 3 - and alpha-helices. Theoretical analysis of the impact of alpha-methylsubstitution on experimental spectra " Jan Kubelka, R. A. Gangani D. Silva, and T. A. Keiderling, Journal of theAmerican Chemical Society, 124, 5325-5332 (2002).

• "Ab Initio Quantum Mechanical Models of Peptide Helices and their Vibrational Spectra" Petr Bour, Jan Kubelkaand T. A. Keiderling, Biopolymers 65, 45-59 (2002).

• "Discriminating 3 - from alpha-helices. Vibrational and electronic CD and IR Absorption study of relatedAib-contining oligopeptides" R. A. Gangani D. Silva, Sritana Yasui, Jan Kubelka, Fernando Formaggio, MarcoCrisma, Claudio Toniolo, and Timothy A. Keiderling, Biopolymers 65, 229-243 (2002).

• "Spectroscopic characterization of Unfolded peptides and proteins studied with infrared absorption andvibrational circular dichroism spectra" T. A. Keiderling and Qi Xu, Advances in Protein Chemistry Volume 62,[Unfolded Proteins, Dedicated to John Edsall, Ed.: George Rose, Academic Press:New York] (2002),

pp. 111-161.

• "Protein and Peptide Secondary Structure and Conformational Determination with Vibrational Circular Dichroism" Timothy A. Keiderling, Current Opinions in Chemical Biology (Ed. Julie Leary and Mark Arnold) 6, 682-688(2002).

• Review: Conformational Studies of Peptides with Infrared Techniques. Timothy A. Keiderling and R. A. G. D.Silva, in Synthesis of Peptides and Peptidomimetics, Ed. M. Goodman and G. Herrman, Houben-Weyl, Vol 22Eb,Georg Thiem Verlag, New York (2002) pp. 715—738, (written and accepted in 2000).

• "Spectroscopic Studies of Structural Changes in Two beta-Sheet Forming Peptides Show an Ensemble ofStructures That Unfold Non-Cooperatively" Serguei V. Kuznetsov, Jovencio Hilario, T. A. Keiderling, AnjumAnsari, Biochemistry, 42 :4321-4332, (2003).

• "Optical spectroscopic investigations of model beta-sheet hairpins in aqueous solution" Jovencio Hilario, JanKubelka, T. A. Keiderling, Journal of the American Chemical Society 125, 7562-757'4 (2003).

• "Synthesis and conformational study of homopeptides based on (S)-Bin, a C2-symmetric binapthyl-derivedCaa-disubstituted glycine with only axial chirality" J.-P. Mazaleyrat, K. Wright, A. Gaucher, M. Wakselman, S.Oancea, F. Formaggio, C. Toniolo, V. Setnicka, J. Kapitan, T. A. Keiderling, Tetrahedron Asymmetry, 14,1879-1893 (2003).

• "Empirical modeling of the peptide amide I band IR intensity in water solution," Petr Bour, Timothy A.Keiderling, Journal of Chemical Physics, 119, 11253-11262 (2003)

• "The Nature of Vibrational Coupling in Helical Peptides: An Isotope Labeling Study" by R. Huang, J. Kubelka,W. Barber-Armstrong, R. A. G D Silva, S. M. Decatur, and T. A. Keiderling, Journal of the American ChemicalSociety, 126, 2346-2354 (2004).

• "The Complete Chirospectroscopic Signature of the Peptide 3 Helix in Aqueous Solution" Claudio Toniolo,Fernando Formaggio, Sabrina Tognon, Quirinus B. Broxterman, Bernard Kaptein, Rong Huang, VladimirSetnicka, Timothy A. Keiderling, Iain H. McColl, Lutz Hecht, Laurence D. Barron, Biopolymers 75, 32-45(2004).

• "Induced axial chirality in the biphenyl core for the Ca-tetrasubstituted a-amino acid residue Bip and subsequentpropagation of chirality in (Bip)n/Val oligopeptides" J.-P. Mazaleyrat, K. Wright, A. Gaucher, N. Toulemonde,M. Wakselman, S. Oancea, C. Peggion, F. Formaggio, V. Setnicka, T. A. Keiderling, C. Toniolo, Journal of theAmerican Chemical Society 126; 12874-12879 (2004).

• Ab initio modeling of amide I coupling in anti-parallel b-sheets and the effect of the 13C isotopic labeling onvibrational spectra" Petr Bour, Timothy A. Keiderling, Journal of Physical Chemistry B, 109, 5348-5357 (2005)

• Solvent Effects on IR And VCD Spectra of Helical Peptides: Insights from Ab Initio Spectral Simulations withExplicit Water" Jan Kubelka and Timothy A. Keiderling, Journal of Physical Chemistry B 109, 8231-8243 (2005)

• IR Study of Cross-Strand Coupling in a beta-Hairpin Peptide Using Isotopic Labels., Vladimir Setnicka, RongHuang, Catherine L. Thomas, Marcus A. Etienne, Jan Kubelka, Robert P. Hammer, Timothy A. KeiderlingJournal of the American Chemical Society 127, 4992-4993 (2005).

• Vibrational spectral simulation for peptides of mixed secondary structure: Method comparisons with the trpzipmodel hairpin. Petr Bour and Timothy A. Keiderling, Journal of Physical Chemistry B 109, 232687-23697(2005).

• Isotopically labeled peptides provide site-resolved structural data with infrared spectra. Probing the structurallimit of optical spectroscopy, Timothy A. Keiderling, Rong Huang, Jan Kubelka, Petr Bour, Vladimir Setnicka,Robert P. Hammer, Marcus *A. Etienne, R. A. Gangani D. Silva, Sean M. Decatur Collections SymposiumSeries, 8, 42-49 (2005)—["Biologically Active Peptides" IXth Conference, Prague Czech Republic, April 20-22,2005.

Nucleic acids and polynucleotides

• "Application of Vibrational Circular Dichroism to Synthetic Polypeptides and Polynucleic Acids" T. A.Keiderling, S. C. Yasui, R. K. Dukor, L. Yang, Polymer Preprints 30, 423-424 (1989).

• "Vibrational Circular Dichroism of Polyribonucleic Acids. A Comparative Study in Aqueous Solution." A.Annamalai and T. A. Keiderling, Journal of the American Chemical Society, 109, 3125-3132 (1987).

• "Conformational phase transitions (A-B and B-Z) of DNA and models using vibrational circular dichroism" L.Wang, L. Yang, T. A. Keiderling in Spectroscopy of Biological Molecules., eds. R. E. Hester, R. B. Girling,Special Publication 94 Roya 1 Society of Chemistry, Cambridge (1991) p. 137-38.

• "Vibrational Circular Dichroism of Proteins Polysaccharides and Nucleic Acids" T. A. Keiderling, Chapter 8 inPhysical Chemistry of Food Processes, Vol. 2 Advanced Techniques, Structures and Applications eds. I. C.Baianu, H. Pessen, T. Kumosinski, Van Norstrand—Reinhold, New York (1993) pp. 307—337.

• "Structural Studies of Biological Macromolecules using Vibrational Circular Dichroism" T. A. Keiderling, P.Pancoska, Chapter 6 in Advances in Spectroscopy Vol. 21, "Biomolecular Spectroscopy Part B" ed. R. E. Hester,R. J. H. Clarke, John W iley Chichester (1993) pp 267-315.

• "Detection of Triple Helical Nucleic Acids with Vibrational Circular Dichroism," L. Wang, P. Pancoska, T. A.Keiderling in "Fifth International Conference on The Spectroscopy of Biological Molecules" Th. Theophanides, J.Anastassopoulou, N. Fotopoul os (Eds), Kluwen Academic Publ., Dortrecht, 1993, p. 81-82.

• "Helical Nature of Poly (dl-dC) ♦ Poly (dl-dC). Vibrational Circular Dichroism Results" L. Wang and T. A.Keiderling Nucleic Acids Research 21 4127-4132 (1993).

• "Detection and Characterization of Triple Helical Pyrimidine-Purine-Pyrimidine Nucleic Acids with VibrationalCircular Dichroism" L. Wang, P. Pancoska, T. A. Keiderling, Biochemistry 33 8428-8435 (1994).

• "Vibrational Circular Dichroism of A-, B- and Z- form Nucleic Acids in the P02- Stretching Region" L. Wang, L.Yang, T. A. Keiderling, Biophysical Journal 67, 2460-2467 (1994).

• "Studies of multiple stranded RNA and DNA with FTIR, vibrational and electronic circular dichroism," ZhihuaHuang, Lijiang Wang and Timothy A. Keiderling, in Spectrosopy of Biological Molecules, Ed. J. C. Merlin,Kluwer Acad. Pub., Dordrecht, 1995, pp . 321-322.

• "Vibrational Circular Dichroism Applications to Conformational Analysis of Biomolecules" T. A. Keiderling in"Circular Dichroism and the Conformational Analysis of Biomolecules" ed G. D. Fasman, Plenum, New York(1996) pp. 555-598.

• "Vibrational Circular Dichroism Techniques and Application to Nucleic Acids" T. A. Keiderling, In"Biomolecular Structure and Dynamics", NATO ASI series, Series E: Applied Sciences- Vol.342, Eds: GVergoten and T. Theophanides, Kluwer Academ ic Publishers, Dordrecht, The Netherlands,pp. 299—317 (1997).

Circular dichroism

Birefringence

Optical rotatory dispersion

IR spectroscopy

Polarization

Proteins

Nucleic Acids

DNA

Molecular models of DNA

DNA structure

Protein structure

Amino acids

Vibrational circular dichroism 100

• Density functional theory

• Quantum chemistry

• Raman optical activity (ROA)

References

[I] http://planetphysics.org/?op=getobj;...objects;id=410 Principles of IR and NIR Spectroscopy

[2] *"Vibrational Circular Dichroism of Polypeptides XII. Re-evaluation of the Fourier Transform Vibrational Circular Dichroism of

Poly-gamma-Benzyl-L-Glutamate," P. Malon, R. Kobrinskaya, T. A. Keiderling, Biopolymers 27, 733-746 (1988).[3] *"Vibrational Circular Dichroism of Biopolymers," T. A. Keiderling, S. C. Yasui, U. Narayanan, A. Annamalai, P. Malon, R. Kobrinskaya,

L. Yang, in Spectroscopy of Biological Molecules New Advances ed. E. D. Schmid, F. W. Schneider, F. Siebert, p. 73-76 (1988).[4] *"Vibrational Circular Dichroism of Polypeptides and Proteins," S. C. Yasui, T. A. Keiderling, Mikrochimica Acta, II, 325-327, (1988).[5] *"Vibrational Circular Dichroism of Proteins Polysaccharides and Nucleic Acids" T. A. Keiderling, Chapter 8 in Physical Chemistry of Food

Processes, Vol. 2 Advanced Techniques, Structures and Applications., eds. I.C. Baianu, H. Pessen, T. Kumosinski, Van Norstrand—Reinhold,

New York (1993), pp 307-337.[6] "Spectroscopic characterization of Unfolded peptides and proteins studied with infrared absorption and vibrational circular dichroism spectra"

T. A. Keiderling and Qi Xu, Advances in Protein Chemistry Volume 62, [Unfolded Proteins, Dedicated to John Edsall, Ed.: George Rose,

Academic Press:New York] (2002), pp. 111-161.[7] *"Protein and Peptide Secondary Structure and Conformational Determination with Vibrational Circular Dichroism " Timothy A. Keiderling,

Current Opinions in Chemical Biology (Ed. Julie Leary and Mark Arnold) 6, 682-688 (2002).[8] *Review: Conformational Studies of Peptides with Infrared Techniques. Timothy A. Keiderling and R. A. G. D. Silva, in Synthesis of

Peptides and Peptidomimetics, Ed. M. Goodman and G. Herrman, Houben-Weyl, Vol 22Eb, Georg Thiem Verlag, New York (2002) pp.

715-738, (written and accepted in 2000).[9] "Polarization Modulation Fourier Transform Infrared Spectroscopy with Digital SignalProcessing: Comparison of Vibrational Circular

Dichroism Methods." Jovencio Hilario, DavidDrapcho, Raul Curbelo, Timothy A. Keiderling, Applied Spectroscopy 55, 1435-1447(2001)—[10] "Vibrational circular dichroism of biopolymers. Summary of methods and applications.", Timothy A. Keiderling, Jan Kubelka, Jovencio

Hilario, in Vibrational spectroscopy of polymers and biological systems, Ed. Mark Braiman, Vasilis Gregoriou, Taylor&Francis, Atlanta

(CRC Press, Boca Raton, FL) (2006) pp. 253-324 (originally written in 2000, updated in 2003)

[II] "Observation of Magnetic Vibrational Circular Dichroism," T. A. Keiderling, Journal of Chemical Physics, 75, 3639-41 (1981).

[12] "Vibrational Spectral Assignment and Enhanced Resolution Using Magnetic Vibrational Circular Dichroism," T. R. Devine and T. A.

Keiderling, Spectrochimica Acta, 43A, 627-629 (1987).[13] "Magnetic Vibrational Circular Dichroism with an FTIR" P. V. Croatto, R. K. Yoo, T. A. Keiderling, SPIE Proceedings 1145 (7th

International Conference on FTS, ed. D. G. Cameron) 152-153 (1989).[14] "Direct Measurement of the Rotational g-Value in the Ground State of Acetylene by Magnetic Vibrational Circular Dichroism." C. N. Tarn

and T. A. Keiderling, Chemical Physics Letters, 243, 55-58 (1995).[15] . "Ab initio calculation of the vibrational magnetic dipole moment" P. Bour, C. N. Tarn, T. A. Keiderling, Journal of Physical Chemistry 99,

17810-17813 (1995)[16] "Rotationally Resolved Magnetic Vibrational Circular Dichroism. Experimental Spectra and Theoretical Simulation for Diamagnetic

Molecules." P. Bour, C. N. Tarn, B. Wang, T. A. Keiderling, Molecular Physics 87, 299-318, (1996).

Optical rotatory dispersion

101

Optical rotatory dispersion

Optical rotatory dispersion is the variation in the optical rotation of a substance with a change in the wavelength oflight. Optical rotatory dispersion can be used to find the absolute configuration of metal complexes. For example,when plane-polarized white light from an overhead projector is passed through a cylinder of sucrose solution, aspiral rainbow is observed perpendicular to the cylinder.

When white light passes through a polarizer, the extent of rotation of light depends on its wavelength. Shortwavelengths are rotated more than longer wavelengths. Because the wavelength of light determines its color, thevariation of color with distance through the tube is observed. This dependence of specific rotation on wavelength iscalled optical rotatory dispersion.

• Circular dichroism

Raman spectroscopy

Raman spectroscopy (named after C.V. Raman, pronounced /'ra:m9n/) is aspectroscopic technique used to studyvibrational, rotational, and otherlow-frequency modes in a system. Itrelies on inelastic scattering, or Ramanscattering, of monochromatic light,usually from a laser in the visible, nearinfrared, or near ultraviolet range. Thelaser light interacts with phonons orother excitations in the system,resulting in the energy of the laserphotons being shifted up or down. Theshift in energy gives information aboutthe phonon modes in the system.Infrared spectroscopy yields similar,but complementary, information.

Virtual

energy

states

J

Vibrationalenergy states

±

A

I

I

I— 0

Infrared Rayleigh Stokes Anti-Stokes

absorption scattering Raman Raman

scattering scattering

Energy level diagram showing the states involved in Raman signal. The line thickness isroughly proportional to the signal strength from the different transitions.

Typically, a sample is illuminated with

a laser beam. Light from the illuminated spot is collected with a lens and sent through a monochromator.Wavelengths close to the laser line, due to elastic Rayleigh scattering, are filtered out while the rest of the collectedlight is dispersed onto a detector.

Spontaneous Raman scattering is typically very weak, and as a result the main difficulty of Raman spectroscopy isseparating the weak inelastically scattered light from the intense Rayleigh scattered laser light. Historically, Ramanspectrometers used holographic gratings and multiple dispersion stages to achieve a high degree of laser rejection. Inthe past, photomultipliers were the detectors of choice for dispersive Raman setups, which resulted in longacquisition times. However, modern instrumentation almost universally employs notch or edge filters for laserrejection and spectrographs (either axial transmissive (AT), Czerny-Turner (CT) monochromator) or FT (Fouriertransform spectroscopy based), and CCD detectors.

There are a number of advanced types of Raman spectroscopy, including surface-enhanced Raman, tip-enhancedRaman, polarised Raman, stimulated Raman (analogous to stimulated emission), transmission Raman,spatially-offset Raman, and hyper Raman.

Basic theory

The Raman effect occurs when light impinges upon a molecule and interacts with the electron cloud and the bonds ofthat molecule. For the spontaneous Raman effect, a photon excites the molecule from the ground state to a virtualenergy state. When the molecule relaxes it emits a photon and it returns to a different rotational or vibrational state.The difference in energy between the original state and this new state leads to a shift in the emitted photon'sfrequency away from the excitation wavelength.

If the final vibrational state of the molecule is more energetic than the initial state, then the emitted photon will beshifted to a lower frequency in order for the total energy of the system to remain balanced. This shift in frequency isdesignated as a Stokes shift. If the final vibrational state is less energetic than the initial state, then the emittedphoton will be shifted to a higher frequency, and this is designated as an Anti-Stokes shift. Raman scattering is anexample of inelastic scattering because of the energy transfer between the photons and the molecules during theirinteraction.

A change in the molecular polarization potential — or amount of deformation of the electron cloud — with respectto the vibrational coordinate is required for a molecule to exhibit a Raman effect. The amount of the polarizabilitychange will determine the Raman scattering intensity. The pattern of shifted frequencies is determined by therotational and vibrational states of the sample.

History

Although the inelastic scattering of light was predicted by Adolf Smekal in 1923, it was not until 1928 that it wasobserved in practice. The Raman effect was named after one of its discoverers, the Indian scientist Sir C. V. Ramanwho observed the effect by means of sunlight (1928, together with K. S. Krishnan and independently by GrigoryLandsberg and Leonid Mandelstam). Raman won the Nobel Prize in Physics in 1930 for this discoveryaccomplished using sunlight, a narrow band photographic filter to create monochromatic light and a "crossed" filterto block this monochromatic light. He found that light of changed frequency passed through the "crossed" filter.

Systematic pioneering theory of the Raman effect was developed by Czechoslovak physicist George Placzek

T21between 1930 and 1934. The mercury arc became the principal light source, first with photographic detection and

then with spectrophotometric detection. Currently lasers are used as light sources.

Applications

Raman spectroscopy is commonly used in chemistry, since vibrational information is specific to the chemical bondsand symmetry of molecules. It therefore provides a fingerprint by which the molecule can be identified. For instance,the vibrational frequencies of SiO, Si O , and Si O were identified and assigned on the basis of normal coordinate

2 2 3 3

analyses using infrared and Raman spectra. The fingerprint region of organic molecules is in the (wavenumber)range 500—2000 cm- . Another way that the technique is used is to study changes in chemical bonding, e.g., when asubstrate is added to an enzyme.

Raman gas analyzers have many practical applications. For instance, they are used in medicine for real-timemonitoring of anaesthetic and respiratory gas mixtures during surgery.

In solid state physics, spontaneous Raman spectroscopy is used to, among other things, characterize materials,measure temperature, and find the crystallographic orientation of a sample. As with single molecules, a given solidmaterial has characteristic phonon modes that can help an experimenter identify it. In addition, Raman spectroscopycan be used to observe other low frequency excitations of the solid, such as plasmons, magnons, and

superconducting gap excitations. The spontaneous Raman signal gives information on the population of a givenphonon mode in the ratio between the Stokes (downshifted) intensity and anti-Stokes (upshifted) intensity.

Raman scattering by an anisotropic crystal gives information on the crystal orientation. The polarization of theRaman scattered light with respect to the crystal and the polarization of the laser light can be used to find theorientation of the crystal, if the crystal structure (specifically, its point group) is known.

Raman active fibers, such as aramid and carbon, have vibrational modes that show a shift in Raman frequency withapplied stress. Polypropylene fibers also exhibit similar shifts. The radial breathing mode is a commonly usedtechnique to evaluate the diameter of carbon nanotubes. In nanotechnology, a Raman microscope can be used toanalyze nanowires to better understand the composition of the structures.

Spatially-offset Raman spectroscopy (SORS), which is less sensitive to surface layers than conventional Raman, canbe used to discover counterfeit drugs without opening their internal packaging, and for non-invasive monitoring of

Ml

biological tissue. Raman spectroscopy can be used to investigate the chemical composition of historical documents

such as the Book of Kells and contribute to knowledge of the social and economic conditions at the time thedocuments were produced. This is especially helpful because Raman spectroscopy offers a non-invasive way todetermine the best course of preservation or conservation treatment for such materials.

Raman spectroscopy is being investigated as a means to detect explosives for airport security.

Microspectroscopy

Raman spectroscopy offers several advantages for microscopic analysis. Since it is a scattering technique, specimensdo not need to be fixed or sectioned. Raman spectra can be collected from a very small volume (< 1 pm in diameter);these spectra allow the identification of species present in that volume. Water does not generally interfere withRaman spectral analysis. Thus, Raman spectroscopy is suitable for the microscopic examination of minerals,materials such as polymers and ceramics, cells and proteins. A Raman microscope begins with a standard opticalmicroscope, and adds an excitation laser, a monochromator, and a sensitive detector (such as a charge-coupleddevice (CCD), or photomultiplier tube (PMT)). FT-Raman has also been used with microscopes.

In direct imaging, the whole field of view is examined for scattering over a small range of wavenumbers (Ramanshifts). For instance, a wavenumber characteristic for cholesterol could be used to record the distribution ofcholesterol within a cell culture.

The other approach is hyperspectral imaging or chemical imaging, in which thousands of Raman spectra areacquired from all over the field of view. The data can then be used to generate images showing the location andamount of different components. Taking the cell culture example, a hyperspectral image could show the distributionof cholesterol, as well as proteins, nucleic acids, and fatty acids. Sophisticated signal- and image-processingtechniques can be used to ignore the presence of water, culture media, buffers, and other interferents.

Raman microscopy, and in particular confocal microscopy, has very high spatial resolution. For example, the lateraland depth resolutions were 250 nm and 1.7 |am, respectively, using a confocal Raman microspectrometer with the632.8 nm line from a He-Ne laser with a pinhole of 100 |jm diameter. Since the objective lenses of microscopesfocus the laser beam to several micrometres in diameter, the resulting photon flux is much higher than achieved inconventional Raman setups. This has the added benefit of enhanced fluorescence quenching. However, the highphoton flux can also cause sample degradation, and for this reason some setups require a thermally conductingsubstrate (which acts as a heat sink) in order to mitigate this process.

By using Raman microspectroscopy, in vivo time- and space-resolved Raman spectra of microscopic regions ofsamples can be measured. As a result, the fluorescence of water, media, and buffers can be removed. Consequentlyin vivo time- and space-resolved Raman spectroscopy is suitable to examine proteins, cells and organs.

Raman microscopy for biological and medical specimens generally uses near-infrared (NIR) lasers (785 nm diodesand 1064 nm Nd:YAG are especially common). This reduces the risk of damaging the specimen by applying higher

4

energy wavelengths. However, the intensity of NIR Raman is low (owing to the m dependence of Raman scatteringintensity), and most detectors required very long collection times. Recently, more sensitive detectors have becomeavailable, making the technique better suited to general use. Raman microscopy of inorganic specimens, such asrocks and ceramics and polymers, can use a broader range of excitation wavelengths.

Polarized analysis

The polarization of the Raman scattered light also contains useful information. This property can be measured using(plane) polarized laser excitation and a polarization analyzer. Spectra acquired with the analyzer set at bothperpendicular and parallel to the excitation plane can be used to calculate the depolarization ratio. Study of thetechnique is pedagogically useful in teaching the connections between group theory, symmetry, Raman activity andpeaks in the corresponding Raman spectra.

The spectral information arising from this analysis gives insight into molecular orientation and vibrational symmetry.In essence, it allows the user to obtain valuable information relating to the molecular shape, for example in syntheticchemistry or polymorph analysis. It is often used to understand macromolecular orientation in crystal lattices, liquid

ro]

crystals or polymer samples.

Variations

Several variations of Raman spectroscopy have been developed. The usual purpose is to enhance the sensitivity (e.g.,surface-enhanced Raman), to improve the spatial resolution (Raman microscopy), or to acquire very specificinformation (resonance Raman).

• Surface Enhanced Raman Spectroscopy (SERS) - Normally done in a silver or gold colloid or a substratecontaining silver or gold. Surface plasmons of silver and gold are excited by the laser, resulting in an increase inthe electric fields surrounding the metal. Given that Raman intensities are proportional to the electric field, thereis large increase in the measured signal (by up to 10 ). This effect was originally observed by MartinFleischmann but the prevailing explanation was proposed by Van Duyne in 1977.

• Resonance Raman spectroscopy - The excitation wavelength is matched to an electronic transition of themolecule or crystal, so that vibrational modes associated with the excited electronic state are greatly enhanced.This is useful for studying large molecules such as polypeptides, which might show hundreds of bands in"conventional" Raman spectra. It is also useful for associating normal modes with their observed frequencyshifts.™

• Surface Enhanced Resonance Raman Spectroscopy (SERRS) - A combination of SERS and resonance Ramanspectroscopy which uses proximity to a surface to increase Raman intensity, and excitation wavelength matchedto the maximum absorbance of the molecule being analysed.

• Hyper Raman - A non-linear effect in which the vibrational modes interact with the second harmonic of theexcitation beam. This requires very high power, but allows the observation of vibrational modes which arenormally "silent". It frequently relies on SERS-type enhancement to boost the sensitivity.

• Spontaneous Raman Spectroscopy - Used to study the temperature dependence of the Raman spectra ofmolecules.

• Optical Tweezers Raman Spectroscopy (OTRS) - Used to study individual particles, and even biochemicalprocesses in single cells trapped by optical tweezers.

• Stimulated Raman Spectroscopy - A spatially coincedent, two color pulse (with polarization either parallel orperpendicular) transfers the population from ground to a rovibrationally excited state, if the difference in energycorresponds to an allowed Raman transition, and if neither frequency corresponds to an electronic resonance. Twophoton UV ionization, applied after the population transfer but before relaxation, allows the intra-molecular orinter-molecular Raman spectrum of a gas or molecular cluster (indeed, a given conformation of molecular cluster)to be collected. This is a useful molecular dynamics technique.

• Spatially Offset Raman Spectroscopy (SORS) - The Raman scatter is collected from regions laterally offsetaway from the excitation laser spot, leading to significantly lower contributions from the surface layer than with

ri2i

• Coherent anti-Stokes Raman spectroscopy (CARS) - Two laser beams are used to generate a coherentanti-Stokes frequency beam, which can be enhanced by resonance.

• Raman optical activity (ROA) - Measures vibrational optical activity by means of a small difference in theintensity of Raman scattering from chiral molecules in right- and left-circularly polarized incident light or,

ri3i

equivalently, a small circularly polarized component in the scattered light.

• Transmission Raman - Allows probing of a significant bulk of a turbid material, such as powders, capsules,

ri4iliving tissue, etc. It was largely ignored following investigations in the late 1960s but was rediscovered in

2006 as a means of rapid assay of pharmaceutical dosage forms. There are also medical diagnostic

applications.

• Inverse Raman spectroscopy.

• Tip-Enhanced Raman Spectroscopy (TERS) - Uses a metallic (usually silver-/gold-coated AFM or STM) tip toenhance the Raman signals of molecules situated in its vicinity. The spatial resolution is approximately the size ofthe tip apex (20-30 nm). TERS has been shown to have sensitivity down to the single molecule level.

ri7i

• An introduction to Raman spectroscopy , horiba.com

n si

• Raman Application examples , horiba.com

• A introduction on Raman Scattering , d3technologies.co.uk

• Raman Spectroscopy Applications , renishaw.com

T211

• Romanian Database of Raman Spectroscopy - This database contains mineral species (natural and synthetic)

with description of crystal structure, sample image, number of sample, origin, Raman spectrum and vibrations,Raman discussion and references. Also, this site contains artefacts sample with sample image and pigmentspectrum; black, red, white or blue pigment, rdrs.uaic.ro

["221

• Chemical Imaging Without Dyeing , witec.de

• DoITPoMS Teaching and Learning Package - Raman Spectroscopy - an introduction, aimed at undergraduate

level, doitpoms.ac.uk

T241

• Raman Spectroscopy Tutorial - A detailed explanation of Raman Spectroscopy including

Resonance-Enhanced Raman Scattering and Surface-Enhanced Raman Scattering. 161.25.205.25

• The Science Show, ABC Radio National - Interview with Scientist on NASA funded project to build RamanSpectrometer for the 2009 Mars mission: a cellular phone size device to detect almost any substance known, withcommercial <USD\$5000 commercial spin-off, prototyped by June 2006. abc.net.au/rn

• Raman spectroscopy for medical diagnosis from the June 1, 2007 issue of Analytical Chemistrypubs.acs.org

no]

• Spontaneous Raman Scattering (SRS) , lavision.de

Raman spectroscopy 106

References

[I] Gardiner, DJ. (1989). Practical Raman spectroscopy. Springer-Verlag. ISBN 978-0387502540.

[2] Placzek G.: "Rayleigh Streeung und Raman Effekt", In: Hdb. der Radiologie, Vol. VI., 2, 1934, p. 209

[3] Khanna, R.K. (1981). "Raman-spectroscopy of oligomeric SiO species isolated in solid methane". Journal of Chemical Physics.

doi: 10.1063/1.441393.[4] . BBC News. 2007-01-31. http://news.bbc.co.Uk/2/hi/health/6314287.stm. Retrieved 2008-12-08.[5] Irish classic is still a hit (in calfskin, not paperback) - New York Times (http://www.nytimes.com/2007/05/28/wo...europe/28kells.

html), nytimes.com[6] Ben Vogel (29 August 2008). "Raman spectroscopy portends well for standoff explosives detection" (http://www.janes.com/news/

transport/business/jar/jar080829_l_n.shtml). Jane's.. Retrieved 2008-08-29.[7] Ellis DI, Goodacre R (August 2006). "Metabolic fingerprinting in disease diagnosis: biomedical applications of infrared and Raman

spectroscopy". Analyst 131 (8): 875-85. doi:10.1039/b602376m. PMID 17028718.[8] Khanna, R.K. (1957). Evidence of ion-pairing in the polarized Raman spectra of a Ba2+CrO doped KI single crystal. John Wiley & Sons,

Ltd. doi:10.1002/jrs.l250040104.[9] Jeanmaire DL, van Duyne RP (1977). "Surface Raman Electrochemistry Part I. Heterocyclic, Aromatic and Aliphatic Amines Adsorbed on

the Anodized Silver Electrode". Journal of Electroanalytical Chemistry (Elsevier Sequouia S.A.) 84: 1—20.

doi:10.1016/S0022-0728(77)80224-6.[10] Chao RS, Khanna RK, Lippincott ER (1974). "Theoretical and experimental resonance Raman intensities for the manganate ion". J Raman

Spectroscopy 3: 121. doi:10.1002/jrs.l250030203.

[II] Kneipp K, et al. (1999). "Surface-Enhanced Non-Linear Raman Scattering at the Single Molecule Level". Chem. Phys. 247: 155—162.doi:10.1016/S0301-0104(99)00165-2.

[12] Matousek P, Clark IP, Draper ERC, et al. (2005). "Subsurface Probing in Diffusely Scattering Media using Spatially Offset Raman

Spectroscopy". Applied Spectroscopy 59: 393. doi: 10.1366/000370205775142548.[13] Barron LD, Hecht L, McColl IH, Blanch EW (2004). "Raman optical activity comes of age". Molec. Phys. 102 (8): 731-744.

doi: 10.1080/00268970410001704399.[14] B. Schrader, G. Bergmann, Fresenius. Z. (1967). Anal. Chem.: 225—230.[15] P. Matousek, A. W. Parker (2006). "Bulk Raman Analysis of Pharmaceutical Tablets". Applied Spectroscopy 60: 1353—1357.

doi: 10.1366/000370206779321463.[16] P. Matousek, N. Stone (2007). "Prospects for the diagnosis of breast cancer by noninvasive probing of calcifications using transmission

Raman spectroscopy". Journal of Biomedical Optics 12: 024008. doi: 10.1117/1.2718934.[17] http://www.horiba.com/us/en/scientif...-tutorial/[18] http://www.horiba.com/scientific/pro...ion-notes/[19] http://www.d3technologies.co.uk/en/10371.aspx[20] http://www.renishaw.com/en/raman-spe...ions--6259[21] http://rdrs.uaic.ro

107

Coherent anti-Stokes Raman spectroscopy

Coherent anti-Stokes Raman spectroscopy, also called Coherent anti-Stokes Raman scattering spectroscopy

(CARS), is a form of spectroscopy used primarily in chemistry, physics and related fields. It is sensitive to the same

vibrational signatures of molecules as seen in Raman spectroscopy, typically the nuclear vibrations of chemical

bonds. Unlike Raman spectroscopy, CARS employs multiple photons to address the molecular vibrations, and

produces a signal in which the emitted waves are coherent with one another. As a result, CARS is orders of

magnitude stronger than spontaneous Raman emission. CARS is a third-order nonlinear optical process involving

three laser beams: a pump beam of frequency co , a Stokes beam of frequency co and a probe beam at frequency co .

These beams interact with the sample and generate a coherent optical signal at the anti-Stokes frequency

(co -co +co ). The latter is resonantly enhanced when the frequency difference between the pump and the Stokes

beams (co -co ) coincides with the frequency of a Raman resonance, which is the basis of the technique's intrinsic

P s in m

vibrational contrast mechanism.

History

The acronym CARS, which invokes a seemingly inadvertent relation to automobiles, is actually closely related to thebirth story of the technique. In 1965, a paper was published by two researchers of the Scientific Laboratory at theFord Motor Company, P. D. Maker and R. W. Terhune, in which the CARS phenomenon was reported for the firsttime. Maker and Terhune used a pulsed ruby laser to investigate the third order response of several materials. Theyfirst passed the ruby beam of frequency co through a Raman shifter to create a second beam at co-co , and thendirected the two beams simultaneously onto the sample. When the pulses from both beams overlapped in space andtime, the Ford researchers observed a signal at co+co , which is the blue-shifted CARS signal. They alsodemonstrated that the signal increases significantly when the difference frequency co between the incident beamsmatches a Raman frequency of sample. Maker and Terhune called their technique simply 'three wave mixingexperiments'. The name coherent anti-Stokes Raman spectroscopy was assigned almost ten years later, by Begley etal. at Stanford University in 1974. Since then, this vibrationally sensitive nonlinear optical technique is commonlyknown as CARS.

Principle

The CARS process can be physically explained by

using either a classical oscillator model or by using a

quantum mechanical model that incorporates the

energy levels of the molecule. Classically, the Raman

active vibrator is modeled as a (damped) harmonic

oscillator with a characteristic frequency of co . In

CARS, this oscillator is not driven by a single optical

wave, but by the difference frequency (co -co ) between

p s

the pump and the Stokes beams instead. This drivingmechanism is similar to hearing the low combinationtone when striking two different high tone piano keys:your ear is sensitive to the difference frequency of thehigh tones. Similarly, the Raman oscillator issusceptible to the difference frequency of two optical

waves. When the difference frequency to -co„ approaches to , the oscillator is driven very efficiently. On a molecularlevel, this implies that the electron cloud surrounding the chemical bond is vigorously oscillating with the frequencyto -co . These electron motions alter the optical properties of the sample, i.e. there is a periodic modulation of therefractive index of the material. This periodic modulation can be probed by a third laser beam, the probe beam.When the probe beam is propagating through the periodically altered medium, it acquires the same modulation. Partof the probe, originally at to will now get modified to to +to -to„, which is the observed anti-Stokes emission.

r ° J pr ° pr p S

Under certain beam geometries, the anti-Stokes emission may diffract away from the probe beam, and can bedetected in a separate direction.

While intuitive, this classical picture does not take into account the quantum mechanical energy levels of themolecule. Quantum mechanically, the CARS process can be understood as follows. Our molecule is initially in theground state, the lowest energy state of the molecule. The pump beam excites the molecule to a Virtual State. Avirtual state is not an eigenstate of the molecule and it can not be occupied but it does allow for transitions betweenotherwise uncoupled real states. If a Stokes beam is simultaneously present along with the pump, the virtual state canbe used as an instantaneous gateway to address a vibrational eigenstate of the molecule. The joint action of the pumpand the Stokes has effectively established a coupling between the ground state and the vibrationally excited state ofthe molecule. The molecule is now in two states at the same time: it resides in a coherent superposition of states.This coherence between the states can be probed by the probe beam, which promotes the system to a virtual state.Again, the molecule cannot stay in the virtual state and will fall back instantaneously to the ground state under theemission of a photon at the anti-Stokes frequency. The molecule is no longer in a superposition, as it resides again inone state, the ground state. In the quantum mechanical model, no energy is deposited in the molecule during theCARS process. Instead, the molecule acts like a medium for converting the frequencies of the three incoming wavesinto a CARS signal (a parametric process). There are, however, related coherent Raman process that occursimultaneously which do deposit energy into the molecule.

Comparison to Raman spectroscopy

CARS is often compared to Raman spectroscopy as both techniques probe the same Raman active modes. Ramancan be done using a single continuous wave (CW) laser whereas CARS requires (generally) two pulsed laser sources.The Raman signal is detected on the red side of the incoming radiation where it might have to compete with otherfluorescent processes. The CARS signal is detected on the blue side, which is free from fluorescence, but it comeswith a non-resonant contribution. The differences between the signals from Raman and CARS (there are manyvariants of both techniques) stems largely from the fact that Raman relies on a spontaneous transition whereas CARSrelies on a coherently driven transition. The total Raman signal collected from a sample is the incoherent addition ofthe signal from individual molecules. It is therefore linear in the concentration of those molecules and the signal isemitted in all directions. The total CARS signal comes from a coherent addition of the signal from individualmolecules. For the coherent addition to be additive, phase-matching must be fulfilled. For tight focusing conditionsthis is generally not a restriction. Once phase-matching is fulfilled the signal amplitude grows linear with distance sothat the power grows quadratically. This signal forms a collimated beam that is therefore easily collected. The factthat the CARS signal is quadratic in the distance makes it quadratic with respect to the concentration and thereforeespecially sensitive to the majority constituent. The total CARS signal also contains an inherent non-resonantbackground. This non-resonant signal can be considered as the result of (several) far off-resonance transitions thatalso add coherently. The resonant amplitude contains a phase shift of Pi over the resonance whereas the non-resonantpart does not. The spectral line shape of the CARS intensity therefore resembles a Fano-profile which is shifted withrespect to the Raman signal. To compare the spectra from multi-component compounds, the (resonant) CARSspectral amplitude should be compared to the Raman spectral intensity.

Theoretically Raman spectroscopy and CARS spectroscopy are equally sensitive as they use the same moleculartransitions. However, given the limits on input power (damage threshold) and detector noise (integration time), the

signal from a single transition can be collected much faster in practical situation (a factor of 10 ) using CARS.Imaging of known substances (known spectra) is therefore often done using CARS. Given the fact that CARS is ahigher order nonlinear process, the CARS signal from a single molecule is larger than the Raman signal from asingle molecule for a sufficiently high driving intensity. However at very low concentrations, the advantages of thecoherent addition for CARS signal reduces and the presence of the incoherent background becomes an increasingproblem.

Since CARS is such a nonlinear process there are not really any 'typical' experimental numbers. One example isgiven below under the explicit warning that just changing the pulse duration by one order of magnitude changes theCARS signal by three orders of magnitude. The comparison should only be used as an indication of the order ofmagnitude of the signals. 200 mW average power input (CW for the Raman), in a 0.9NA objective with a center

2

wavelength around 800 nm, constitutes a power density of 26 MW/cm, (focal length =1.5 micrometre, focal

3 -19

volume =1.16 micrometre , photon energy = 2.31 10 J or 1.44 eV). The Raman cross section for the vibration of

-1 -29 2

the aromatic ring in Toluene around 1000 cm is on the order of 10 cm /molecule*steradian. Therefore the Raman

-22 -21

signal is around 26 10 W/molecule*steradian or 3.3 10 W/molecule (over 4Pi). That is 0.014

3 3 -3

photon/sec*molecule. The density of Toluene = 0.8668 10 kg/m , Molecular mass = 92.14 10 kg/mol. Therefore

9the focal volume (~1 cubic micrometre) contains 6 10 molecules. Those molecules together generate a Raman

signal in the order of 2 10 W (20pW) or roughly one hundred million photons/sec (over a 4Pi solid angle). A

CARS experiment with similar parameters (150 mW at 1064 nm, 200 mW at 803.5 nm, 15ps pulses at 80Mhz

repetition frequency, same objective lens) yields roughly 17.5 10" W (on the 3000 cm" line, which has 1/3 of the

strength and roughly 3 times the width). This CARS power is roughly 10 higher than the Raman but since there are

6 10 molecules, the signal per molecule from CARS is only 4 10 W/molecule*sec or 1.7 10

photons/molecule*sec. If we allow for two factors of three (line strength and line width) than the spontaneous

Raman signal per molecule still exceeds the CARS per molecule by a more than two orders of magnitude. The

coherent addition of the CARS signal from the molecules however yields a total signal that is much higher than the

Raman.

The sensitivity in many CARS experiments is not limited by the detection of CARS photons but rather by thedistinction between the resonant and non-resonant part of the CARS signal.

Applications

CARS is used for species selective microscopy and combustion diagnostics. The first exploits the selectivity ofvibrational spectroscopy whereas the latter is aimed at temperature measurements; the CARS signal is temperaturedependent. The strength of the signal scales (non-linearly) with the difference in the ground state population and thevibrationally excited state population. Since the population of states follows the temperature dependent BoltzmannDistribution, the CARS signal carries an intrinsic temperature dependence as well. This temperature dependencemakes CARS a popular technique for monitoring the temperature of hot gases and flames.

Coherent anti-Stokes Raman spectroscopy

110

• Coherent Stokes Raman spectroscopy

• Raman spectroscopy

• Four-wave mixing

References

[1] A Review of the Theory and Application of Coherent Anti-Stokes Raman Spectroscopy (CARS) Applied Spectroscopy, Volume 31, Number

4, July/August 1977, pp. 253-271(19) (http://www.ingentaconnect.com/conten...00004/art00001)[2] Coherent anti-Stokes Raman scattering: from proof-of-the-principle experiments to femtosecond CARS and higher order wave-mixing

generalizations Journal of Raman Spectroscopy, Volume 31, Issue 8-9 , pp. 653 - 667 (http://www3.interscience.wiley.com/cgi-bin/

abstract/73500427/ABSTRACT?CRETRY=l&SRETRY=0)[3] Study of Optical Effects Due to an Induced Polarization Third Order in the Electric Field Strength Physical Review, Volume 137, Issue 3A,

pp. 801-818 (http://prola.aps.org/abstract/PR/vl37/i3A/pA801_l)[4] Coherent anti-Stokes Raman spectroscopy Applied Physics Letters, Volume 25, Issue 7 , pp. 387-390 (http://scitation.aip.org/getabs/

servlet/GetabsServlet?prog=normal&id=APPLAB000025000007000387000001&idtype=cvips&gifs=yes)

Raman Microscopy

Raman microscope begins with a standard optical microscope, and adds an excitation laser, a monochromator, anda optical sensitive detector such as a charge-coupled device (CCD), or photomultiplier tube, (PMT)), and has beenimplemented for Raman spectroscopy in direct chemical imaging, the whole field of view on 3D sample.

Imaging spectroscopy

Imaging spectroscopy (also spectral imaging,

chemical imaging, or microspectroscopy) is similar tocolor photography, but each pixel acquires many bandsof light intensity data from the spectrum, instead of justthe three bands of the RGB color model. Moreprecisely, it is the simultaneous acquisition of spatiallycoregistered images in many spectrally contiguousbands.

Ash plumes on Kamchatka Peninsula, eastern Russia. A MODISimage.

Some spectral images contain only a few image planes of spectral data, while others are better thought of as fullspectra at every location in the image. For example, solar physicists use the spectroheliograph, to make images of theSun built up by scanning the slit of a spectrograph, to study the behavior of surface features on the Sun; such aspectroheliogram may have a spectral resolution of over 100,000 ( A/AA ) and be used to measure local motion(via the Doppler shift) and even the magnetic field (via the Zeeman splitting or Hanle effect) at each location in theimage plane. The multispectral images collected by the Opportunity rover, in contrast, have only four wavelength

bands and hence are only a little more than 3-color images.

To be scientifically useful, such measurement should be done using an internationally recognized system of units.

One example application is geophysical spectral imaging, which allows quantitative and qualitative characterizationof both, the surface and the atmosphere, using geometrically coherent spectrodirectional radiometric measurements.These measurements can then be used for the unambiguous direct and indirect identification of surface materials andatmospheric trace gases, the measurement of their relative concentrations, subsequently the assignment of theproportional contribution of mixed pixel signals (e.g., the spectral unmixing problem), the derivation of their spatialdistribution (mapping problem), and finally their study over time (multi-temporal analysis). The Moon MineralogyMapper on Chandrayaan-1 was an imaging spectrometer.

Background

About 300 years ago, in 1704, Sir Isaac Newton published in his 'Treatise of Light' (Newton, 1704) the concept ofdispersion of light. He demonstrated that white light could be split up into component colours by means of a prism,and found that each pure colour is characterized by a specific refrangibility. The corpuscular theory by Newton wasgradually succeeded over time by the wave theory. Consequently, the substantial summary of past experiencesperformed by Maxwell (1873), resulted in his equations of electromagnetic waves. But it was not until the 19thcentury that the quantitative measurement of dispersed light was recognized and standardized.

A major contribution was Fraunhofer's discovery of the dark lines in the solar spectrum (Fraunhofer, 1817); and theirinterpretation as absorption lines on the basis of experiments by Bunsen and Kirchhoff (1863). The term"spectroscopy" was first used in the late 19th century and provides the empirical foundations for atomic andmolecular physics (Born & Wolf, 1999). Significant achievements in imaging spectroscopy are attributed to airborneinstruments, particularly arising in the early 1980s and 1990s (Goetz et al., 1985; Vane et al., 1984). However, it wasnot until 1999 that the first imaging spectrometer was launched in space (the NASA Moderate-resolution ImagingSpectroradiometer, or MODIS).

Terminology and definitions evolve over time. At one time, >10 spectral bands sufficed to justify the term "imagingspectrometer" but presently the term is seldom defined by a total minimum number of spectral bands, rather by acontiguous (or redundant) statement of spectral bands.

The term hyperspectral imaging is sometimes used interchangeably with imaging spectroscopy. Due to its heavy usein military related applications, the civil world has established a slight preference for using the term imagingspectroscopy.

Unmixing

Hyperspectral data is often used to determine what materials are present in a scene. Materials of interest couldinclude roadways, vegetation, and specific targets (i.e. pollutants, hazardous materials, etc). Trivially, each pixel of ahyperpsectral image could be compared to a material database to determine the type of material making up the pixel.However, many hyperspectral imaging platforms have low resolution (>5m per pixel) causing each pixel to be amixture of several materials. The process of unmixing one of these 'mixed' pixels is called hyperspectral imageunmixing or simply hyperspectral unmixing.

Models

A solution to hyperspectral unmixing is to reverse the mixing process. Generally, two models of mixing areassumed: linear and nonlinear. Linear mixing models the ground as being flat and incident sunlight on the groundcauses the materials to radiate some amount of the incident energy back to the sensor. Each pixel then, is modeled asa linear sum of all the radiated energy curves of materials making up the pixel. Therefore, each material contributesto the sensor's observation in a positive linear fashion. Additionally, a conservation of energy constraint is often

observed thereby forcing the weights of the linear mixture to sum to one in addition to being positive. The model canbe described mathematically as follows:

p = A * Xwhere p represents a pixel observed by the sensor, J\_ is a matrix of material reflectance signatures (each signatureis a column of the matrix), and x is the proportion of material present in the observed pixel. This type of model isalso referred to as a simplex.

With x satisfying the two constraints: 1. Abundance Nonnegativty Constraint (ANC) - each element of x is positive.2. Abundance Sum-to-one Constraint (ASC) - the elements of x must sum to one.

Non-linear mixing results from multiple scattering often due to non-flat surface such as buildings and vegetation.

Unmixing (Endmember Detection) Algorithms

There are many algorithms to unmix hyperspectral data each with their own strengths and weaknesses. Manyalgorithms assume that pure pixels (pixels which contain only one materials) are present in a scene. Some algorithmsto perform unmixing are listed below:

• Pixel Purity Index (PPI) - Works by projecting each pixel onto one vector from a set of random vectors spanningthe reflectance space. A pixel receives a score when it represent an extremum of all the projections. Pixels withthe highest scores are deemed to be spectrally pure.

• NFINDR

• Gift Wrapping Algorithm

• Independent Component Analysis Endmember Extraction Algorithm (ICA-EEA) - Works by assuming that purepixels occur independently than mixed pixels. Assumes pure pixels are present.

• Vertex Component Analysis (VCA) - Works on the fact that the affine transformation of a simplex is anothersimplex which helps to find hidden (folded) verticies of the simplex. Assumes pure pixels are present.

• Principal component analysis -(PCA) could also be used to determine endmembers, projection on principal axescould permit endmember selection [ Smith,Johnson et Adams (1985), Bateson et Curtiss (1996) ]

• Multi Endmembers Spatial Mixture Analysis (MESMA) based on the SMA algorithm

Non-linear unmixing algortithm also exist (Support Vector Machines (SVM)) or Analytical Neural Network (ANN).Probabilistics methods have also been attempted to unmix pixel through Monte Carlo Unmixing (MCU) algorithm.

Abundance Maps

Once the fundamental materials of a scene are determined, it is often useful to construct an abundance map of eachmaterial which displays the fractional amount of material present at each pixel. Often linear programming is done toobserved ANC and ASC.

Sensors

AVIRIS — aircraft, (224 bands)

Telops Hyper-Cam — Commercial infrared hyperspectral camera, ground-based or aircraft

MODIS — on board EOS Terra and Aqua platforms

MERIS — on board Envisat

HyDice

Hyperion — on board the Earth Observing 1 satellite

Imaging spectroscopy 113

Remote sensing

Hyperspectral

Full Spectral Imaging

List of Earth observation satellites

Chemical Imaging

Imaging spectrometer

Infrared Microscopy

References

[1] Large quantities of water found on the Moon (http://www.telegraph.co.uk/science/space/6224974/

Large-quantities-of-water-found-on-the-Moon.html)[2] http://www.hyper-cam.com/

• Born, M. & Wolf, E. (1999) Principles of Optics, 7 edn. Cambridge University Press, Cambridge.

• Bunsen, R. & Kirchhoff, G. (1863) Untersuchungen iiber das Sonnenspektrum und die Spektren der ChemischenElemente. Abh. kgl. Akad. Wiss., 1861.

• Fraunhofer, J. (1817) Bestimmung des Brechungs- und Farbenzerstreuungs-Vermogens verschiedener Glasarten,in Bezug auf die Vervollkommnung achromatischer Fernrohre, Vol. 56, pp. 264—313. Gilberts Annalen derPhysik.

• Goetz, A.F.H., Vane, G, Solomon, J.E., & Rock, B.N. (1985) Imaging spectrometry for earth remote sensing.Science, 228, 1147.

• Maxwell, J.C. (1873) A Treatise on Electricity and Magnetism Clarendon Press, Oxford.

• Newton, I. (1704) Opticks: Or, a Treatise of the Reflexions, Refractions, Inflexions and Colours of Light SamSmith and Benj. Walford, London.

• Schaepman, M. (2005) Spectrodirectional Imaging: From Pixels to Processes. Inaugural address, WageningenUniversity, Wageningen (NL).

• Vane, G., Chrisp, M., Emmark, H., Macenka, S., & Solomon, J. (1984) Airborne Visible Infrared ImagingSpec-trometer (AVIRIS): An Advanced Tool for Earth Remote Sensing. European Space Agency, (SpecialPublication) ESA SP, 2, 751.

• Link to resources (OKSI): http://www.techexpo.com/WWW/opto-kno...resources.html

• Special Interest Group Imaging Spectroscopy (EARSeL): http://www.op.dlr.de/dais/SIGTS/SIG-IS.html

• Applications of Spectroscopic and Chemical Imaging in Research: http://www3.imperial.ac.uk/vibration...aging/research

Chemical imaging

Chemical imaging is the analytical capability (as quantitative - mapping) to create a visual image from simultaneousmeasurement of spectra (as quantitative - chemical) and spatial, time informations. The technique is most often

applied to either solid or gel samples, and has applications in chemistry, biology , medicine

rm r22i ri2i ri3i

pharmacy (see also for example: Chemical Imaging Without Dyeing ), food science, biotechnology

ri4i

agriculture and industry (see for example:NIR Chemical Imaging in Pharmaceutical Industry and PharmaceuticalProcess Analytical Technology: ). NIR, IR and Raman chemical imaging is also referred to as hyperspectral,spectroscopic, spectral or multispectral imaging (also see microspectroscopy). However, other ultra-sensitive andselective, chemical imaging techniques are also in use that involve either UV-visible or fluorescencemicrospectroscopy. Chemical imaging techniques can be used to analyze samples of all sizes, from the singlemolecule to the cellular level in biology and medicine , and to images of planetary systems in

astronomy, but different instrumentation is employed for making observations on such widely different systems.

Chemical imaging instrumentation is composed of three components: a radiation source to illuminate the sample, aspectrally selective element, and usually a detector array (the camera) to collect the images. When many stackedspectral channels (wavelengths) are collected for different locations of the microspectrometer focus on a line orplanar array in the focal plane, the data is called hyperspectral; fewer wavelength data sets are called multispectral.The data format is called a hypercube. The data set may be visualized as a three-dimensional block of data spanningtwo spatial dimensions (x and y), with a series of wavelengths (lambda) making up the third (spectral) axis. Thehypercube can be visually and mathematically treated as a series of spectrally resolved images (each image planecorresponding to the image at one wavelength) or a series of spatially resolved spectra. The analyst may choose toview the spectrum measured at a particular spatial location; this is useful for chemical identification. Alternatively,selecting an image plane at a particular wavelength can highlight the spatial distribution of sample components,provided that their spectral signatures are different at the selected wavelength.

Many materials, both manufactured and naturally occurring, derive their functionality from the spatial distribution ofsample components. For example, extended release pharmaceutical formulations can be achieved by using a coatingthat acts as a barrier layer. The release of active ingredient is controlled by the presence of this barrier, andimperfections in the coating, such as discontinuities, may result in altered performance. In the semi-conductorindustry, irregularities or contaminants in silicon wafers or printed micro-circuits can lead to failure of thesecomponents. The functionality of biological systems is also dependent upon chemical gradients — a single cell,tissue, and even whole organs function because of the very specific arrangement of components. It has been shownthat even small changes in chemical composition and distribution may be an early indicator of disease.

Any material that depends on chemical gradients for functionality may be amenable to study by an analyticaltechnique that couples spatial and chemical characterization. To efficiently and effectively design and manufacturesuch materials, the 'what' and the 'where' must both be measured. The demand for this type of analysis is increasingas manufactured materials become more complex. Chemical imaging techniques not only permit visualization of thespatially resolved chemical information that is critical to understanding modern manufactured products, but it is alsoa non-destructive technique so that samples are preserved for further testing.

History

Commercially available laboratory-based chemical imaging systems emerged in the early 1990s (ref. 1-5). Inaddition to economic factors, such as the need for sophisticated electronics and extremely high-end computers, asignificant barrier to commercialization of infrared imaging was that the focal plane array (FPA) needed to read IRimages were not readily available as commercial items. As high-speed electronics and sophisticated computersbecame more commonplace, and infrared cameras became readily commercially available, laboratory chemicalimaging systems were introduced.

Initially used for novel research in specialized laboratories, chemical imaging became a more commonplaceanalytical technique used for general R&D, quality assurance (QA) and quality control (QC) in less than a decade.The rapid acceptance of the technology in a variety of industries (pharmaceutical, polymers, semiconductors,security, forensics and agriculture) rests in the wealth of information characterizing both chemical composition andmorphology. The parallel nature of chemical imaging data makes it possible to analyze multiple samplessimultaneously for applications that require high throughput analysis in addition to characterizing a single sample.

Principles

Chemical imaging shares the fundamentals of vibrational spectroscopic techniques, but provides additionalinformation by way of the simultaneous acquisition of spatially resolved spectra. It combines the advantages ofdigital imaging with the attributes of spectroscopic measurements. Briefly, vibrational spectroscopy measures theinteraction of light with matter. Photons that interact with a sample are either absorbed or scattered; photons ofspecific energy are absorbed, and the pattern of absorption provides information, or a fingerprint, on the moleculesthat are present in the sample.

On the other hand, in terms of the observation setup, chemical imaging can be carried out in one of the followingmodes: (optical) absorption, emission (fluorescence), (optical) transmission or scattering (Raman). A consensuscurrently exists that the fluorescence (emission) and Raman scattering modes are the most sensitive and powerful,but also the most expensive.

In a transmission measurement, the radiation goes through a sample and is measured by a detector placed on the farside of the sample. The energy transferred from the incoming radiation to the molecule(s) can be calculated as thedifference between the quantity of photons that were emitted by the source and the quantity that is measured by thedetector. In a diffuse reflectance measurement, the same energy difference measurement is made, but the source anddetector are located on the same side of the sample, and the photons that are measured have re-emerged from theilluminated side of the sample rather than passed through it. The energy may be measured at one or multiplewavelengths; when a series of measurements are made, the response curve is called a spectrum.

A key element in acquiring spectra is that the radiation must somehow be energy selected — either before or afterinteracting with the sample. Wavelength selection can be accomplished with a fixed filter, tunable filter,spectrograph, an interferometer, or other devices. For a fixed filter approach, it is not efficient to collect a significantnumber of wavelengths, and multispectral data are usually collected. Interferometer-based chemical imaging requiresthat entire spectral ranges be collected, and therefore results in hyperspectral data. Tunable filters have the flexibilityto provide either multi- or hyperspectral data, depending on analytical requirements.

Spectra may be measured one point at a time using a single element detector (single-point mapping), as a line-imageusing a linear array detector (typically 16 to 28 pixels) (linear array mapping), or as a two-dimensional image using aFocal Plane Array (FPA)(typically 256 to 16,384 pixels) (FPA imaging). For single-point the sample is moved in thex and y directions point-by-point using a computer-controlled stage. With linear array mapping, the sample is movedline-by-line with a computer-controlled stage. FPA imaging data are collected with a two-dimensional FPA detector,hence capturing the full desired field-of-view at one time for each individual wavelength, without having to movethe sample. FPA imaging, with its ability to collected tens of thousands of spectra simultaneously is orders ofmagnitude faster than linear arrays which are can typically collect 16 to 28 spectra simultaneously, which are in turnmuch faster than single-point mapping.

116

Terminology

Some words common in spectroscopy, optical microscopy and photography have been adapted or their scopemodified for their use in chemical imaging. They include: resolution, field of view and magnification. There are twotypes of resolution in chemical imaging. The spectral resolution refers to the ability to resolve small energydifferences; it applies to the spectral axis. The spatial resolution is the minimum distance between two objects that isrequired for them to be detected as distinct objects. The spatial resolution is influenced by the field of view, aphysical measure of the size of the area probed by the analysis. In imaging, the field of view is a product of themagnification and the number of pixels in the detector array. The magnification is a ratio of the physical area of thedetector array divided by the area of the sample field of view. Higher magnifications for the same detector image asmaller area of the sample.

Types of vibrational chemical imaging instruments

Chemical imaging has been implemented for mid-infrared, near-infrared spectroscopy and Raman spectroscopy. Aswith their bulk spectroscopy counterparts, each imaging technique has particular strengths and weaknesses, and arebest suited to fulfill different needs.

Mid-infrared chemical imaging

Mid-infrared (MIR) spectroscopy probes fundamental molecular vibrations, which arise in the spectral range2,500-25,000 nm. Commercial imaging implementations in the MIR region typically employ Fourier TransformInfrared (FT-IR) interferometers and the range is more commonly presented in wavenumber, 4,000 — 400 cm" . TheMIR absorption bands tend to be relatively narrow and well-resolved; direct spectral interpretation is often possibleby an experienced spectroscopist. MIR spectroscopy can distinguish subtle changes in chemistry and structure, and isoften used for the identification of unknown materials. The absorptions in this spectral range are relatively strong;for this reason, sample presentation is important to limit the amount of material interacting with the incomingradiation in the MIR region. Most data collected in this range is collected in transmission mode through thin sections(-10 micrometres) of material. Water is a very strong absorber of MIR radiation and wet samples often requireadvanced sampling procedures (such as attenuated total reflectance). Commercial instruments include point and linemapping, and imaging. All employ an FT-IR interferometer as wavelength selective element and light source.

For types of MIR microscope, seeMicroscopy#Infrared microscopy.

Atmospheric windows in the infrared

spectrum are also employed to perform

chemical imaging remotely. In these spectral

regions the atmospheric gases (mainly water

and CO ) present low absorption and allow

infrared viewing over kilometer distances.

Target molecules can then be viewed using

the selective absorption/emission processes

described above. An example of the chemical imaging of a simultaneous release of SF and NH is shown in the

image.

Remote chemical imaging of a simultaneous release of SF and NH at 1.5km using

V&\ 3

the FIRST imaging spectrometer

Near-infrared chemical imaging

The analytical near infrared (NIR) region spans the range from approximately 700-2,500 nm. The absorption bandsseen in this spectral range arise from overtones and combination bands of O-H, N-H, C-H and S-H stretching andbending vibrations. Absorption is one to two orders of magnitude smaller in the NIR compared to the MIR; thisphenomenon eliminates the need for extensive sample preparation. Thick and thin samples can be analyzed withoutany sample preparation, it is possible to acquire NIR chemical images through some packaging materials, and thetechnique can be used to examine hydrated samples, within limits. Intact samples can be imaged in transmittance ordiffuse reflectance.

The lineshapes for overtone and combination bands tend to be much broader and more overlapped than for thefundamental bands seen in the MIR. Often, multivariate methods are used to separate spectral signatures of samplecomponents. NIR chemical imaging is particularly useful for performing rapid, reproducible and non-destructive

[22] [231

analyses of known materials . NIR imaging instruments are typically based on one of two platforms: imaging

using a tunable filter and broad band illumination, and line mapping employing an FT-IR interferometer as thewavelength filter and light source.

Raman chemical imaging

The Raman shift chemical imaging spectral range spans from approximately 50 to 4,000 cm" ; the actual spectralrange over which a particular Raman measurement is made is a function of the laser excitation frequency. The basicprinciple behind Raman spectroscopy differs from the MIR and NIR in that the x-axis of the Raman spectrum ismeasured as a function of energy shift (in cm" ) relative to the frequency of the laser used as the source of radiation.Briefly, the Raman spectrum arises from inelastic scattering of incident photons, which requires a change inpolarizability with vibration, as opposed to infrared absorption, which requires a change in dipole moment withvibration. The end result is spectral information that is similar and in many cases complementary to the MIR. The

7

Raman effect is weak - only about one in 10 photons incident to the sample undergoes Raman scattering. Bothorganic and inorganic materials possess a Raman spectrum; they generally produce sharp bands that are chemicallyspecific. Fluorescence is a competing phenomenon and, depending on the sample, can overwhelm the Raman signal,for both bulk spectroscopy and imaging implementations.

Raman chemical imaging requires little or no sample preparation. However, physical sample sectioning may be usedto expose the surface of interest, with care taken to obtain a surface that is as flat as possible. The conditions requiredfor a particular measurement dictate the level of invasiveness of the technique, and samples that are sensitive to highpower laser radiation may be damaged during analysis. It is relatively insensitive to the presence of water in thesample and is therefore useful for imaging samples that contain water such as biological material.

Fluorescence imaging (visible and NIR)

This emission microspectroscopy mode is the most sensitive in both visible and FT-NIR microspectroscopy, and hastherefore numerous biomedical, biotechnological and agricultural applications. There are several powerful, highlyspecific and sensitive fluorescence techniques that are currently in use, or still being developed; among the formerare FLIM, FRAP, FRET and FLIM-FRET; among the latter are NIR fluorescence and probe-sensitivity enhancedNIR fluorescence microspectroscopy and nanospectroscopy techniques (see "Further reading" section).

Sampling and samples

The value of imaging lies in the ability to resolve spatial heterogeneities in solid-state or gel/gel-like samples.Imaging a liquid or even a suspension has limited use as constant sample motion serves to average spatialinformation, unless ultra-fast recording techniques are employed as in fluorescence correlation microspectroscopy orFLIM obsevations where a single molecule may be monitored at extremely high (photon) detection speed.High-throughput experiments (such as imaging multi-well plates) of liquid samples can however provide valuable

information. In this case, the parallel acquisition of thousands of spectra can be used to compare differences betweensamples, rather than the more common implementation of exploring spatial heterogeneity within a single sample.

Similarly, there is no benefit in imaging a truly homogeneous sample, as a single point spectrometer will generatethe same spectral information. Of course the definition of homogeneity is dependent on the spatial resolution of theimaging system employed. For MIR imaging, where wavelengths span from 3-10 micrometres, objects on the orderof 5 micrometres may theoretically be resolved. The sampled areas are limited by current experimentalimplementations because illumination is provided by the interferometer. Raman imaging may be able to resolveparticles less than 1 micrometre in size, but the sample area that can be illuminated is severely limited. With Ramanimaging, it is considered impractical to image large areas and, consequently, large samples. FT-NIRchemical/hyperspectral imaging usually resolves only larger objects (>10 micrometres), and is better suited for large

samples because illumination sources are readily available. However, FT-NIR microspectroscopy was recently

T241reported to be capable of about 1.2 micron (micrometer) resolution in biological samples Furthermore,

two-photon excitation FCS experiments were reported to have attained 15 nanometer resolution on biomembrane

thin films with a special coincidence photon-counting setup.

Detection limit

The concept of the detection limit for chemical imaging is quite different than for bulk spectroscopy, as it dependson the sample itself. Because a bulk spectrum represents an average of the materials present, the spectral signaturesof trace components are simply overwhelmed by dilution. In imaging however, each pixel has a correspondingspectrum. If the physical size of the trace contaminant is on the order of the pixel size imaged on the sample, itsspectral signature will likely be detectable. If however, the trace component is dispersed homogeneously (relative topixel image size) throughout a sample, it will not be detectable. Therefore, detection limits of chemical imagingtechniques are strongly influenced by particle size, the chemical and spatial heterogeneity of the sample, and thespatial resolution of the image.

Data analysis

Data analysis methods for chemical imaging data sets typically employ mathematical algorithms common to singlepoint spectroscopy or to image analysis. The reasoning is that the spectrum acquired by each detector is equivalent toa single point spectrum; therefore pre-processing, chemometrics and pattern recognition techniques are utilized withthe similar goal to separate chemical and physical effects and perform a qualitative or quantitative characterization ofindividual sample components. In the spatial dimension, each chemical image is equivalent to a digital image andstandard image analysis and robust statistical analysis can be used for feature extraction.

• Multispectral image

• Microspectroscopy

• Imaging spectroscopy

1. E. N. Lewis, P. J. Treado, I. W. Levin, Near-Infrared and Raman Spectroscopic Imaging, American Laboratory,06/1994:16(1994)

2. E. N. Lewis, P. J. Treado, R. C. Reeder, G. M. Story, A. E. Dowrey, C. Marcott, I. W. Levin, FTIR spectroscopicimaging using an infrared focal-plane array detector, Analytical Chemistry, 67:3377 (1995)

3. P. Colarusso, L. H. Kidder, I. W. Levin, J. C. Fraser, E. N. Lewis Infrared Spectroscopic Imaging: from Planetaryto Cellular Systems, Applied Spectroscopy, 52 (3):106A (1998)

4. P. J. Treado I. W. Levin, E. N. Lewis, Near-Infrared Spectroscopic Imaging Microscopy of Biological MaterialsUsing an Infrared Focal-Plane Array and an Acousto-Optic Tunable Filter (AOTF), Applied Spectroscopy, 48:5(1994)

5. Hammond, S.V., Clarke, F. C, Near-infrared microspectroscopy. In: Handbook of Vibrational Spectroscopy,Vol. 2, J.M. Chalmers and P.R. Griffiths Eds. John Wiley and Sons, West Sussex, UK, 2002, p.1405-1418

6. L.H. Kidder, A.S. Haka, E.N. Lewis, Instrumentation for FT-IR Imaging. In: Handbook of VibrationalSpectroscopy, Vol. 2, J.M. Chalmers and P.R. Griffiths Eds. John Wiley and Sons, West Sussex, UK, 2002,pp. 1386-1404

7. J. Zhang; A. OGonnor; J. F. Turner II, Cosine Histogram Analysis for Spectral Image DataClassification,Applied Spectroscopy, Volume 58, Number 11, November 2004, pp. 1318-1324(7)

8. J. F. Turner II; J. Zhang; A. O'Connor, A Spectral Identity Mapper for Chemical Image Analysis, AppliedSpectroscopy, Volume 58, Number 11, November 2004, pp. 1308-1317(10)

9. H. R. MORRIS, J. F. TURNER II, B. MUNRO, R. A. RYNTZ, P. J. TREADO, Chemical imaging ofthermoplastic olefin (TPO) surface architecture, Langmuir, 1999, vol. 15, no8, pp. 2961-2972

10. J. F. Turner II, Chemical imaging and spectroscopy using tunable filters: Instrumentation, methodology, andmultivariate analysis, Thesis (PhD). UNIVERSITY OF PITTSBURGH, Source DAI-B 59/09, p. 4782, Mar 1999,286 pages.

11. P. Schwille.(2001). in Fluorescence Correlation Spectroscopy. Theory and applications. R. Rigler & E.S. Elson,eds., p. 360. Springer Verlag: Berlin.

12. Schwille P., Oehlenschlager F. and Walter N. (1996). Analysis of RNA-DNA hybridization kinetics byfluorescence correlation spectroscopy, Biochemistry 35:10182.

13. FLIM I Fluorescence Lifetime Imaging Microscopy: Fluorescence, fluorophore chemical imaging, confocal

[251emission microspectroscopy, FRET, cross-correlation fluorescence microspectroscopy[251

14. FLIM Applications: "FLIM is able to discriminate between fluorescence emanating from different

fluorophores and autoflorescing molecules in a specimen, even if their emission spectra are similar. It is,therefore, ideal for identifying fluorophores in multi-label studies. FLIM can also be used to measure intracellularion concentrations without extensive calibration procedures (for example, Calcium Green) and to obtaininformation about the local environment of a fluorophore based on changes in its lifetime." FLIM is also oftenused in microspectroscopic/chemical imaging, or microscopic, studies to monitor spatial and temporalprotein-protein interactions, properties of membranes and interactions with nucleic acids in living cells.

15. Gadella TW Jr., FRET and FLIM techniques, 33. Imprint: Elsevier, ISBN 978-0-08-054958-3. (2008) 560 pages

16. Langel FD, et al., Multiple protein domains mediate interaction between BcllO and Maltl, J. Biol. Chem.,(2008)283(47):32419-31

17. Clayton AH. , The polarized AB plot for the frequency-domain analysis and representation of fluorophorerotation and resonance energy homotransfer. J Microscopy. (2008) 232(2):306-12

18. Clayton AH, et al., Predominance of activated EGFR higher-order oligomers on the cell surface. GrowthFactors (2008) 20:1

19. Plowman et al., Electrostatic Interactions Positively Regulate K-Ras Nanocluster Formation and Function.Molecular and Cellular Biology (2008) 4377-4385

20. Belanis L, et al., Galectin-1 Is a Novel Structural Component and a Major Regulator of H-Ras Nanoclusters.Molecular Biology of the Cell (2008) 19:1404-1414

21. Van Manen HJ, Refractive index sensing of green fluorescent proteins in living cells using fluorescence lifetimeimaging microscopy. Biophys J. (2008) 94(8):L67-9

22. Van der Krogt GNM, et al., A Comparison of Donor-Acceptor Pairs for Genetically Encoded FRET Sensors:Application to the Epac cAMP Sensor as an Example, PLoS ONE, (2008) 3(4):el916

23. Dai X, et al., Fluorescence intensity and lifetime imaging of free and micellar-encapsulated doxorubicin inliving cells. Nanomedicine. (2008) 4(l):49-56.

• NIR Chemical Imaging in Pharmaceutical Industry

• Pharmaceutical Process Analytical Technology:

• NIR Chemical Imaging for Counterfeit Pharmaceutical Product Analysis

[271

• Chemical Imaging: Potential New Crime Busting Tool

T281

• Applications of Chemical Imaging in Research

References

[2] http://www.malvern.com/LabEng/produc...bliography.htm E. N. Lewis, E. Lee and L. H. Kidder, Combining

Imaging and Spectroscopy: Solving Problems with Near-Infrared Chemical Imaging. Microscopy Today, Volume 12, No. 6, 11/2004.[3] C.L. Evans and X.S. Xie.2008. Coherent Anti-Stokes Raman Scattering Microscopy: Chemical Imaging for Biology and Medicine.,

doi:10.1146/annurev.anchem.l.031207.112754 Annual Review of Analytical Chemistry, 1: 883-909.[4] Diaspro, A., and Robello, M. (1999). Multi-photon Excitation Microscopy to Study Biosystems. European Microscopy and Analysis., 5:5-7.[5] D.S. Mantus and G. H. Morrison. 1991. Chemical imaging in biology and medicine using ion microscopy., Microchimica Acta, 104, (1-6)

January 1991, doi: 10.1007/BF01245536[6] Bagatolli, L.A., and Gratton, E. (2000). Two-photon fluorescence microscopy of coexisting lipid domains in giant unilamellar vesicles of

binary phospholipid mixtures. Biophys J., 78:290-305.[7] Schwille, P., Haupts, U., Maiti, S., and Webb. W.(1999). Molecular dynamics in living cells observed by fluorescence correlation

spectroscopy with one- and two-photon excitation. Biophysical Journal, 77(10):2251-2265.[8] l.Lee, S. C. et al., (2001). One Micrometer Resolution NMR Microscopy. J. Magn. Res., 150: 207-213.[9] Near Infrared Microspectroscopy, Fluorescence Microspectroscopy,Infrared Chemical Imaging and High Resolution Nuclear Magnetic

Resonance Analysis of Soybean Seeds, Somatic Embryos and Single Cells., Baianu, I.C. et al. 2004., In Oil Extraction and Analysis., D.

Luthria, Editor pp.241-273, AOCS Press., Champaign, IL.[10] Single Cancer Cell Detection by Near Infrared Microspectroscopy, Infrared Chemical Imaging and Fluorescence Microspectroscopy.2004.1.

C. Baianu, D. Costescu, N. E. Hofmann and S. S. Korban, q-bio/0407006 (July 2004) (http://arxiv.org/abs/q-bio/0407006)

[II] J. Dubois, G. Sando, E. N. Lewis, Near-Infrared Chemical Imaging, A Valuable Tool for the Pharmaceutical Industry, G.I.T. LaboratoryJournal Europe, No. 1-2, 2007.

[12] Raghavachari, R., Editor. 2001. Near-Infrared Applications in Biotechnology, Marcel-Dekker, New York, NY.

[13] Applications of Novel Techniques to Health Foods, Medical and Agricultural Biotechnology.(June 2004) I. C. Baianu, P. R. Lozano, V. I.

Prisecaru and H. C. Lin q-bio/0406047 (http://arxiv.org/abs/q-bio/0406047)[14] http://www.spectroscopyeurope.com/NIR_14_3.pdf[15] http://www.fda.gov/cder/OPS/PAT.htm[16] Eigen, M., and Rigler, R. (1994). Sorting single molecules: Applications to diagnostics and evolutionary biotechnology, Proc. Natl. Acad.

Sci. USA 91:5740.[17] Rigler R. and Widengren J. (1990). Ultrasensitive detection of single molecules by fluorescence correlation spectroscopy, BioScience (Ed.

Klinge & Owman) p. 180.[18] Single Cancer Cell Detection by Near Infrared Microspectroscopy, Infrared Chemical Imaging and Fluorescence Microspectroscopy.2004.1.

C. Baianu, D. Costescu, N. E. Hofmann, S. S. Korban and et al., q-bio/0407006 (July 2004) (http://arxiv.org/abs/q-bio/0407006)[19] Oehlenschlager F., Schwille P. and Eigen M. (1996). Detection of HIV-1 RNA by nucleic acid sequence-based amplification combined with

fluorescence correlation spectroscopy, Proc. Natl. Acad. Sci. USA 93:1281.[20] Near Infrared Microspectroscopy, Fluorescence Microspectroscopy,Infrared Chemical Imaging and High Resolution Nuclear Magnetic

Resonance Analysis of Soybean Seeds, Somatic Embryos and Single Cells., Baianu, I.C. et al. 2004., In Oil Extraction and Analysis., D.

Luthria, Editor pp.241-273, AOCS Press., Champaign, IL.[21] M. Chamberland, V. Farley, A. Vallieres, L. Belhumeur, A. Villemaire, J. Giroux et J. Legault, High-Performance Field-Portable Imaging

Radiometric Spectrometer Technology For Hyperspectral imaging Applications, Proc. SPIE 5994, 59940N, September 2005.[22] Novel Techniques for Microspectroscopy and Chemical Imaging Analysis of Soybean Seeds and Embryos.(2002). Baianu, I.C, Costescu,

D.M., and You, T. Soy2002 Conference, Urbana, Illinois.[23] Near Infrared Microspectroscopy, Chemical Imaging and NMR Analysis of Oil in Developing and Mutagenized Soybean Embryos in

Culture. (2003). Baianu, I.C, Costescu, D.M., Hofmann, N., and Korban, S.S. AOCS Meeting, Analytical Division.[24] Near Infrared Microspectroscopy, Fluorescence Microspectroscopy,Infrared Chemical Imaging and High Resolution Nuclear Magnetic

Resonance Analysis of Soybean Seeds, Somatic Embryos and Single Cells., Baianu, I.C. et al. 2004., In Oil Extraction and Analysis., D.

Luthria, Editor pp.241-273, AOCS Press., Champaign, IL.[25] http://www.nikoninstruments.com/info...php?n=FLIM[26] httpV/www.spectroscopymag.com/spectroscopy/Near-IR+Spectroscopy/NIR-Chemical-Imaging-for-Counterfeit-Pharmaceutica/

ArticleStandard/Article/detail/406629

Chemical imaging 121

[27] http://www. sciencedaily.com/releases/2007/08/070802103435.htm

Spin polarization

Spin polarization is the degree to which the spin, i.e. the intrinsic angular momentum of elementary particles, isaligned with a given direction . This property may pertain to the spin, hence to the magnetic moment, ofconduction electrons in ferromagnetic metals, such as iron, giving rise to spin polarized currents. It may also pertainto beams of particles, produced for particular aims, such as polarized neutron scattering or muon spin spectroscopy.Spin polarization of electrons or of nuclei, often called simply magnetization, is also produced by the application of amagnetic field, thanks to the Curie law and it is used to produce an induction signal in Electron spin resonance (ESRor EPR) and in Nuclear magnetic resonance (NMR).

Spin polarization is also important for spintronics, a branch of electronics. Magnetic semiconductors are beingresearched as possible spintronics materials.

The spin of free electrons is measured either by a LEED image from a clean wolfram-crystal (SPLEED) or

by an electron microscope composed purely of electrostatic lenses and a gold foil as a sample. Back scatteredelectrons are decelerated by annular optics and focused onto a ring shaped electron mulitplier at about 15°. Theposition on the ring is recorded. This whole device is called a Mott-detector. Depending on their spin the electronshave the chance to hit the ring at different positions. 1% of the electrons are scattered in the foil. Of these 1% arecollected by the detector and then about 30% of the electrons hit the detector at the wrong position. Both deviceswork due to spin orbit coupling.

References

[1] J. Kessler (1976). Polarized Electrons. Springer Verlag Berlin Heidelberg, pp. 7—19.

[2] J. Kirschner and R. Feder (1979). "Spin Polarization in Double Diffraction of Low-Energy Electrons from W(001): Experiment and Theory".

Physical Review Letters 42: 1008-1011.[3] M. Kalisvaart, M. R. O'Neill, T. W. Riddle, F. B. Dunning, and G. K. Walters (1977). "Electron-spin polarization in low-energy electron

diffraction from tungsten (001)". Physical Review B 17: 1570-1578.[4] R. Feder (1976). "Spin Polarization in Low-Energy Electron Diffraction from W(001)". Physical Review Letters 36: 598—600.

Polarized Neutron Spectroscopy

Triple-axis spectrometry (TAS, T also resolved as "three", S also resolved as "spectroscopy") is a technique used ininelastic neutron scattering. The instrument is referred to as triple-axis spectrometer (also called TAS). It allowsmeasurement of the scattering function at any point in energy and momentum space physically accessible by thespectrometer.

History

The triple-axis spectrometry method was first developed by Bertram Brockhouse at the NRX research reactor at theChalk River Laboratories in Canada. The first results from the prototype triple-axis spectrometer were published inJanuary 1955 and the first true triple-axis spectrometer was built in 1956. Bertram Brockhouse shared the 1994Nobel prize for Physics for this development, which allowed elementary excitations, such as phonons and magnons,to be observed directly. The Nobel citation was "for pioneering contributions to the development of neutronscattering techniques for studies of condensed matter" and "for the development of neutron spectroscopy".

TAS Instruments in current use

FRM-II Forschungsneutronenquelle Heinz Maier-Leibnitz

• PANDA - a cold neutron triple-axis spectrometer.

• PUMA - a thermal neutron triple-axis spectrometer with multianalyser-detector option.

Institut Laue-Langevin

INI - a hot neutron triple-axis spectrometer.

MiIN3 - a thermal neutron triple-axis spectrometer for tests.

IN8 - a high-flux thermal neutron triple-axis spectrometer.

IN 12 - a cold neutron triple-axis spectrometer.

IN14 - a cold neutron triple-axis spectrometer with polarized neutron capability.

ro]

IN20 - a thermal neutron triple-axis spectrometer with polarized neutron capability.IN22 - a thermal neutron triple-axis spectrometer with polarized neutron capability.D10 - a thermal neutron four-circle diffractometer with a triple-axis energy analysis option.

CEA/Saclay Laboratoire Leon Brillouin

• 1T-1 - a double-focusing thermal neutron triple-axis spectrometer.

• 2T-1 - a thermal neutron triple-axis spectrometer.

ri3i

• 4F-1 - a cold neutron triple-axis spectrometer.

• 4F-2 - a cold neutron triple-axis spectrometer.

NIST Center for Neutron Research

• SPINS - a cold neutron triple-axis spectrometer with polarized neutron capability.

• BT-7 - a thermal neutron triple-axis spectrometer with polarized neutron capability.

BT-9 - a thermal neutron triple-axis spectrometer.

MURR [17] University of Missouri Research Reactor

• Triax - a thermal neutron triple-axis spectrometer.

ri9i

• Nobelprize.org page for the 1994 Nobel Prize for Physics

References

Polarized Muon Spectroscopy

Muon spin spectroscopy is an experimental technique based on the implantation of spin polarized muons in matterand on the detection of the influence of the atomic, molecular or crystalline surroundings on their spin motion. Themotion of the muon spin is due to the magnetic field experienced by the particle and may provide information on itslocal environment in a very similar way to other magnetic resonance techniques, such as electron spin resonance(ESR or EPR) and, more closely, nuclear magnetic resonance (NMR).

Acronym

In analogy with the acronyms for these previously established spectroscopies, the muon spin spectroscopy is alsoknown as |jSR, which stands for muon spin rotation, or relaxation, or resonance, depending respectively on whetherthe muon spin motion is predominantly a rotation (more precisely a precession around a still magnetic field), or arelaxation towards an equilibrium direction, or, again, a more complex dynamics dictated by the addition of shortradio frequency pulses.

How it works

The time scale on which the spin motion may be exploited is that of the muon decay, i.e. a few mean lifetimes, eachroughly 2.2 ps (2.2 millionths of a second). Both the production of muon beams with nearly perfect alignment of thespin to the beam direction (what was referred to above as spin polarization and caused by the spontaneous symmetrybreaking), and the ability to detect the muon spin direction at the instant of the muon decay rely on the violation ofparity, which takes place whenever weak forces are at play.

In short this means that certain elementary events happen only when including clockwise (or only when includingcounterclockwise) rotations. For instance, the positive muon decays into a positron plus two neutrinos and thepositron is preferentially emitted in the direction of the muon spin. Therefore it would most often see the spin as acounterclockwise rotation while flying away from the decay point.

Spin alignment allows the production of a muon beam with an aligned magnetic moment. Muons are injected intothe material under investigation as short-lived spies [1] sending information from the interior back out to theexperimental apparatus. These muons are able to send a message from inside the crystal about the local magneticfield in their surroundings. After some time (mean lifetime 2.2 |is) these spies decay and emit positrons. A beam ofaligned muons produces asymmetric positron radiation. The asymmetry of positron radiation contains informationabout the direction of local magnetic field in the moment of muon decay. Taking into consideration the initialdirection of muon magnetic moment and the time interval between the moment of injection and moment of muondecay we can calculate the precession frequency (how rapidly the muon's magnetic moment rotates). The frequencyof magnetic moment precession depends on the local magnetic field. Larmor precession is appeared with z-directionmagnetic field and only decay in 2.2 ps. But when x-direction magnetic field is applied in muon, the rate of decay isenhanced by gaussian with depolarization rate.

Since 1987 this method was used to measure internal magnetic fields inside high-temperature superconductors.High-temperature superconductors are Type II superconductors, in which the local magnetic fields inside thesuperconductor depend on the superconducting carrier density—one of the significant parameters of anysuperconductor (see for example the Bardeen—Cooper—Shrieffer theory of superconductors).

Applications

Muon Spin Rotation and Relaxation are mostly performed with positive muons. They are well suited to the study ofmagnetic fields at the atomic scale inside matter, such as those produced by various kinds of magnetism and/orsuperconductivity encountered in compounds occurring in nature or artificially produced by modern materialscience.

The London penetration depth is one of the most important parameters characterizing a superconductor because itsinverse square provides a measure of the density n of Cooper pairs. The dependence of n on temperature andmagnetic field directly indicates the symmetry of the superconducting gap. Muon spin spectroscopy provides a wayto measure the penetration depth, and so has been used to study high-temperature cuprate superconductors since theirdiscovery in 1986.

Other important fields of application of pSR exploit the fact that positive muons capture electrons to form muoniumatoms which behave chemically as light isotopes of the hydrogen atom. This allows investigation of the largestknown "isotope effect" in some of the simplest types of chemical reactions, as well as the early stages of formationof radicals in organic chemicals. Muonium is also studied as an analogue of hydrogen in semiconductors, wherehydrogen is one of the most ubiquitous impurities.

Facilities

|jSR requires a particle accelerator for the production of a muon beam. This is presently achieved at few large scale

facilities in the world: the CMMS[2] continuous source at TRIUMF in Vancouver, Canada; the LMU continuous

misource at the Paul Scherrer Institut (PSI) in Villigen, Switzerland; the ISIS and RIKEN-RAL pulsed sources at the

Rutherford Appleton Laboratory in Chilton, United Kingdom; and the J-PARC facility in Tokai, Japan, where a new

pulsed source is being built to replace that at KEK in Tsukuba, Japan. Muon beams are also available at the

Laboratory of Nuclear Problems, Joint Institute for Nuclear Research (JINR) in Dubna, Russia. The International

Society for uSR Spectroscopy (ISMS ) exists to promote the worldwide advancement of pSR. Membership in the

society is open free of charge to all individuals in academia, government laboratories and industry who have an

interest in the society's goals.

• Muon

• Muonium

• Nuclear magnetic resonance

References

• ISIS Introductory course in pSR

• introduction to pSR

• |jSR Brochure [8] (a 3.2 MB PDF file)

• CMMS [2]: TRIUMF Center for Molecular and Materials Science

• ISIS [9]

Polarized Muon Spectroscopy 126

References

htm

Time-resolved spectroscopy

In physics and physical chemistry, time-resolved spectroscopy is the study of dynamic processes in materials orchemical compounds by means of spectroscopic techniques. Most often, processes are studied that occur afterillumination of a material, but in principle, the technique can be applied to any process which leads to a change inproperties of a material. With the help of pulsed lasers, it is possible to study processes which occur on time scales as

— 14

short as 10 seconds. The rest of the article discusses different types of time-resolved spectroscopy.

Transient-absorption spectroscopy

Transient-absorption spectroscopy is an extension of absorption spectroscopy. Here, the absorbance at a particularwavelength or range of wavelengths of a sample is measured as a function of time after excitation by a flash of light.In a typical experiment, both the light for excitation ('pump') and the light for measuring the absorbance ('probe') aregenerated by a pulsed laser. If the process under study is slow, then the time resolution can be obtained with acontinuous (i.e., not pulsed) probe beam and repeated conventional spectrophotometric techniques.

Examples of processes that can be studied:

• Optical gain spectroscopy of semiconductor laser materials.

• Chemical reactions that are initiated by light (or 'photoinduced chemical reactions');

• The transfer of excitation energy between molecules, parts of molecules, or molecules and their environment;

• The behaviour of electrons that are freed from a molecule or crystalline material.

Other multiple-pulse techniques

Transient spectroscopy as discussed above is a technique that involves two pulses. There are many more techniquesthat employ two or more pulses, such as:

• Photon echoes.

• Four-wave mixing (involves three laser pulses)

The interpretation of experimental data from these techniques is usually much more complicated than intransient-absorption spectroscopy.

Nuclear magnetic resonance and electron spin resonance are often implemented with multiple-pulse techniques,though with radio waves and micro waves instead of visible light.

Time-resolved spectroscopy 127

Time-resolved infrared spectroscopy

Time-resolved infrared (TRIR) spectroscopy also employs a two-pulse, "pump-probe" methodology. The pump pulseis typically in the UV region and is often generated by a high-powered Nd:YAG laser whilst the probe beam is in theinfrared region. This technique currently operates down to the picosecond time regime and surpasses transientabsorption and emission spectroscopy by providing structural information on the excited-state kinetics of both darkand emissive states.

Time-resolved fluorescence spectroscopy

Time-resolved fluorescence spectroscopy is an extension of fluorescence spectroscopy. Here, the fluorescence of asample is monitored as a function of time after excitation by a flash of light. The time resolution can be obtained in anumber of ways, depending on the required sensitivity and time resolution:

• With fast detection electronics (nanoseconds and slower);

• With a streak camera (picoseconds and slower);

• With optical gating (femtoseconds-nanoseconds) - a short laser pulse acts as a gate for the detection offluorescence light; only fluorescence light that arrives at the detector at the same time as the gate pulse isdetected. This technique has the best time resolution, but the efficiency is rather low. An extension of this opticalgating technique is to use a "Kerr gate", which allows the scattered Raman signal to be collected before the(slower) fluorescence signal overwhelms it. This technique can greatly improve the signaknoise ratio of Ramanspectra.

Terahertz spectroscopy

Terahertz frequency radiation for spectroscopy is typically generated in one of three ways:

• time domain terahertz spectroscopy (TDTS), using ultrashort laser pulses

• photomixing, mixing two radiation sources to generate their difference frequency

• Fourier transform spectroscopy, using a blackbody radiation source

128

Applied spectroscopy

Applied spectroscopy is the application of various spectroscopic methods for detection and identification ofdifferent elements/compounds in solving problems in the fields of forensics, medicine, oil industry, atmosphericchemistry, pharmacology, etc.

Spectroscopic methods

Among the more common spectroscopic methods used for analysis is FTIR spectroscopy, where chemical bonds canbe detected through their characteristic infra-red absorption frequencies or wavelengths. UV spectroscopy is usedwhere strong absorption of ultra-violet radiation occurs in a substance. Such groups are known as chromophores andinclude aromatic groups, conjugated system of bonds, carbonyl groups and so on. NMR spectroscopy detectshydrogen atoms in specific environments, and complements both IR and UV spectroscopy. The use of Ramanspectroscopy is growing for more specialist applications.

There are also derivative methods such as infrared microscopy which allows very small areas to be analysed in anoptical microscope.

One method of elemental analysis which is important in forensic analysis is EDX performed in the environmentalscanning electron microscope, or ESEM. The method involves analysis of back-scattered X-rays from the sample asa result of interaction with the electron beam.

Sample preparation

In all three spectroscopic methods, the sample usually needs to be present in solution, which may present problemsduring forensic examination because it necessarily involves sampling solid from the object to be examined.

FTIR: Three types of samples can be analyzed, a solution (KBr), a powder, or a film. A solid film is the easiest andmost straight forward sample type to test.

Analysis of polymers

Many polymer degradation mechanisms can be followed using infra-red spectroscopy, such as UV degradation andoxidation, amongst many other failure modes.

Many polymers are attacked by UV radiation at vulnerable pointsin their chain structures. Thus polypropylene suffers severecracking in sunlight unless anti-oxidants are added. The point ofattack occurs at the tertiary carbon atom present in every repeatunit, causing oxidation and finally chain breakage. Polyethylene isalso susceptible to UV degradation, especially those variantswhich are branched polymers such as LDPE. The branch pointsare tertiary carbon atoms, so polymer degradation starts there andresults in chain cleavage, and embrittlement. In the exampleshown at left, carbonyl groups were readily detected by IR

spectroscopy from a cast thin film. The product was a road cone which had cracked in service, and many similar

cones also failed because an anti-UV additive had not been used.

 \ r / C-0 /

1400 1200 1000

WavG Number (cm-1)

IR spectrum showing carbonyl absorption due to UVdegradation of polyethylene

129

Oxidation

Polymers are susceptible to attack by atmospheric oxygen,especially at elevated temperatures encountered during processingto shape. Many process methods such as extrusion and injectionmoulding involve pumping molten polymer into tools, and thehigh temperatures needed for melting may result in oxidationunless precautions are taken. For example, a forearm crutchsuddenly snapped and the user was severely injured in theresulting fall. The crutch had fractured across a polypropyleneinsert within the aluminium tube of the device, and infra-redspectroscopy of the material showed that it had oxidised, possibleas a result of poor moulding.

4000 3500 3000 2500 2000

IR spectrum showing carbonyl absorption due to

oxidative degradation of polypropylene crutch

moulding

Oxidation is usually relatively easy to detect owing to the strong

absorption by the carbonyl group in the spectrum of polyolefins.

Polypropylene has a relatively simple spectrum with few peaks at the carbonyl position (like polyethylene).

Oxidation tends to start at tertiary carbon atoms because free radicals here at more stable, so last longer and are

attacked by oxygen. The carbonyl group can be further oxidised to break the chain, so weakening the material by

lowering the molecular weight, and cracks start to grow in the regions affected.

Ozonolysis

The reaction occurring between double bonds and ozone is known as ozonolysis when one molecule of the gas reactswith the double bond:

RjR3 o3

/=\ ;

R2 R4

R-i R3

R2 R4

The immediate result is formation of an ozonide, which then decomposes rapidly so that the double bond is cleaved.This is the critical step in chain breakage when polymers are attacked. The strength of polymers depends on thechain molecular weight or degree of polymerization, the higher the chain length, the greater the mechanical strength(such as tensile strength). By cleaving the chain, the molecular weight drops rapidly and there comes a point when ithas little strength whatsoever, and a crack forms. Further attack occurs in the freshly exposed crack surfaces and thecrack grows steadily until it completes a circuit and the product separates or fails. In the case of a seal or a tube,failure occurs when the wall of the device is penetrated.

130

 •:.li- |j 40-; ' 3D— | ?n_ & S 10-= JIJ Jl Al I hi _Ci Zr,

EDX spectrum of crack surface

 20- D \5— s 10— a 5- H3 n !■■■ ' ^rrrrrrrr7rr^T.r7^ a i

EDX spectrum of unaffected rubber surface

The carbonyl end groups which are formed are usuallyaldehydes or ketones, which can oxidise further tocarboxylic acids. The net result is a high concentrationof elemental oxygen on the crack surfaces, which canbe detected using Energy-dispersive X-rayspectroscopy in the environmental SEM, or ESEM. Thespectrum at left shows the high oxygen peak comparedwith a constant sulphur peak. The spectrum at rightshows the unaffected elastomer surface spectrum, witha relatively low oxygen peak compared with thesulphur peak. The spectra were obtained during aninvestigation into ozone cracking of diaphragm seals ina semi-conductor fabrication factory.

Absorption spectroscopy

Infrared spectroscopy correlation table

Infrared spectroscopy

Forensic chemistry

Forensic engineering

Forensic polymer engineering

Polymer engineering

Spectroscopy

• Society for Applied Spectroscopy

References

• Forensic Materials Engineering: Case Studies by Peter Rhys Lewis, Colin Gagg, Ken Reynolds, CRC Press(2004).

• Peter R Lewis and Sarah Hainsworth, Fuel Line Failure from stress corrosion cracking, Engineering FailureAnalysis, 13 (2006) 946-962.

• Museum of failed products

• New Forensic course

[l]

The journal Engineering Failure Analysis

[3]

Forensic science and engineering

[4]

Applied spectroscopy

131

References

Amino acids

Amino acids are molecules containing anamine group, a carboxylic acid group and a sidechain that varies between different amino acids.These molecules contain the key elements ofCarbon, Hydrogen, Oxygen, and Nitrogen.These molecules are particularly important inbiochemistry, where this term refers toalpha-amino acids with the general formulaH2NCHRCOOH, where R is an organicsubstituent. In an alpha amino acid, the aminoand carboxylate groups are attached to the samecarbon atom, which is called the a—carbon. Thevarious alpha amino acids differ in which sidechain (R group) is attached to their alphacarbon. These side chains can vary in size fromjust a hydrogen atom in glycine, to a methylgroup in alanine, through to a large heterocyclicgroup in tryptophan.

Amino acids are critical to life, and have manyfunctions in metabolism. One particularlyimportant function is as the building blocks ofproteins, which are linear chains of amino acids.Every protein is chemically defined by thisprimary structure, its unique sequence of aminoacid residues, which in turn define thethree-dimensional structure of the protein. Justas the letters of the alphabet can be combined toform an almost endless variety of words, aminoacids can be linked together in varyingsequences to form a vast variety of proteins.Amino acids are also important in many otherbiological molecules, such as forming parts ofcoenzymes, as in S-adenosylmethionine, or asprecursors for the biosynthesis of moleculessuch as heme. Due to this central role inbiochemistry, amino acids are very important in

Twenty-One Amino Acids

A. Amino Adds with Bemicaly Charged Side ChainsPositive

6, flm-inc Grid's witfr Palar Uncharged Side Chains C Speaal Cases

Serine Threonine Asparagine Glutamine Cysteine 5elenocystelne Glycine Proline

':x'"0 <Thl> A ,Asnt fl [Ght _!_ '""'''ifft ISecl ffi (Glyt<5_ '"'■ £_

D. Amino A;.1.:; n/ith htfdiaphobk SWc Chain

Alanine Isaleucine Leucine Methionine P hen ylaLa nine Tryptophan Tyrosine Valine

The twenty-one amino acids found in eukaryotes, grouped according to theirside chains' pKa's and charge at physiological pH 7.4

nutrition. Amino acids are commonly used in food technology and industry. For example, monosodium glutamate isa common flavor enhancer that gives foods the taste called umami. They are also used in industry. Applicationsinclude the production of biodegradable plastics, drugs and chiral catalysts.

History

The first few amino acids were discovered in the early 1800s. In 1806, the French chemists Louis-Nicolas Vauquelinand Pierre Jean Robiquet isolated a compound in asparagus that proved to be asparagine, the first amino acid to bediscovered. Another amino acid that was discovered in the early 19th century was cystine, in 1810, although

its monomer, cysteine, was discovered much later, in 1884. Glycine and leucine were also discovered around

mistime, in 1820.[7]

General structure

C'OO

In the structure shown at the top of the page, R represents a side chain specific to

each amino acid. The carbon atom next to the carbonyl group is called the a—carbon

and amino acids with a side chain bonded to this carbon are referred to as alpha , ffiJ^ -„

amino acids. These are the most common form found in nature. In the alpha amino ' i

T81 ft I 3

acids, the a—carbon is a chiral carbon atom, with the exception of glycine. In /tT

amino acids that have a carbon chain attached to the a—carbon (such as lysine,

[9]

y I i

shown to the right) the carbons are labeled in order as a, |3, y, 8, and so on. In CHa

some amino acids, the amine group is attached to the (3 or y-carbon, and these are § | ^

therefore referred to as beta or gamma amino acids. v-Hj

5 I flAmino acids are usually classified by the properties of their side chain into four £TH

groups. The side chain can make an amino acid a weak acid or a weak base, and a I

roi ^^ |

hydrophile if the side chain is polar or a hydrophobe if it is nonpolar. The Nil-

chemical structures of the twenty-two standard amino acids, along with their

Lysine with the carbon atoms in

chemical properties, are described more fully in the article on these proteinogenic the side chain |abeie(j

amino acids.

The phrase "branched-chain amino acids" or BCAA refers to the amino acids having aliphatic side chains that arenon-linear; these are leucine, isoleucine, and valine. Proline is the only proteinogenic amino acid whose side grouplinks to the a-amino group and, thus, is also the only proteinogenic amino acid containing a secondary amine at thisposition. Chemically, proline is therefore an imino acid since it lacks a primary amino group, although it is stillclassed as an amino acid in the current biochemical nomenclature, and may also be called an "N-alkylatedalpha-amino acid".

Isomerism

Of the standard a-amino acids, all but glycine can exist in either of twooptical isomers, called L or D amino acids, which are mirror images ofeach other (see also Chirality). While L-amino acids represent all of theamino acids found in proteins during translation in the ribosome,D-amino acids are found in some proteins produced by enzymeposttranslational modification after translation and translocation to theendoplasmic reticulum, as in exotic sea-dwelling organisms such as

The two optical isomers of alanine, D-Alanine ., [131 „. , , , „ .,

cone snails. They are also abundant components of the

and L-Alanine

133

peptidoglycan cell walls of bacteria. and D-serine may act as a neurotransmitter in the brain. The L and Dconvention for amino acid configuration refers not to the optical activity of the amino acid itself, but rather to theoptical activity of the isomer of glyceraldehyde from which that amino acid can theoretically be synthesized(D-glyceraldehyde is dextrorotary; L-glyceraldehyde is levorotary). Alternatively, the (S) and (R) designators areused to indicate the absolute stereochemistry. Almost all of the amino acids in proteins are (S) at the a carbon, withcysteine being (R) and glycine non-chiral. Cysteine is unusual since it has a sulfur atom at the first position in itsside-chain, which has a larger atomic mass than the groups attached to the a-carbon in the other standard aminoacids, thus the (R) instead of (S).

Zwitterions

Amino acids have both amine andcarboxylic acid functional groups andare therefore both an acid and a base at

ro]

the same time. At a certain pH knownas the isoelectric point an amino acidhas no overall charge, since the numberof protonated ammonium groups(positive charges) and deprotonatedcarboxylate groups (negative charges)are equal. The amino acids all havedifferent isoelectric points. The ions produced at the isoelectric point have both positive and negative charges and are

„ [18]

 0 H © H H2N- R H3N+ R X)

An amino acid in its (1) unionized and (2) zwitterionic forms

[19]

known as a zwitterion, which comes from the German word Zwitter meaning "hermaphrodite" or "hybridAmino acids can exist as zwitterions in solids and in polar solutions such as water, but not in the gas phase.1Zwitterions have minimal solubility at their isolectric point and an amino acid can be isolated by precipitating it fromwater by adjusting the pH to its particular isolectric point.

Occurrence and functions in biochemistry

Standard amino acids

Amino acids are the structural units thatmake up proteins. They join together toform short polymer chains called peptides orlonger chains called either polypeptides orproteins. These polymers are linear andunbranched, with each amino acid withinthe chain attached to two neighbouringamino acids. The process of making proteinsis called translation and involves thestep-by-step addition of amino acids to agrowing protein chain by a ribozyme that is

Amino Acid

A polypeptide is an unbranched chain of amino acids.

called a ribosome. The order in which the

amino acids are added is read through the genetic code from an mRNA template, which is a RNA copy of one of the

organism's genes

Twenty-two amino acids are naturally incorporated into polypeptides and are called proteinogenic or standard amino

ro]

acids. Of these twenty-two, twenty are directly encoded by the universal genetic code. The remaining two,

134

selenocysteine and pyrrolysine, are incorporated into proteins by unique synthetic mechanisms. Selenocysteine is

incorporated when the mRNA being translated includes a SECIS element, which causes the UGA codon to encode

T211selenocysteine instead of a stop codon. Pyrrolysine is used by some methanogenic archaea in enzymes that they

[221use to produce methane. It is coded for with the codon UAG, which is normally a stop codon in other organisms.

HSe

Non-standard amino acids

Aside from the twenty-two standard amino acids, there are a vast

number of "non-standard" amino acids. These non-standard amino

acids found in proteins are formed by post-translational modification,

which is modification after translation in protein synthesis. These

modifications are often essential for the function or regulation of a

protein; for example, the carboxylation of glutamate allows for better

[231binding of calcium cations, and the hydroxylation of proline is

T241critical for maintaining connective tissues. Another example is the

formation of hypusine in the translation initiation factor EIF5A,

T251through modification of a lysine residue. Such modifications can

also determine the localization of the protein, e.g., the addition of long hydrophobic groups can cause a protein to

bind to a phospholipid membrane

HoN

The amino acid selenocysteine

[26]

C^H,

Haca

►H3N COO

+H,N

cph,

H

if \

al

Examples of nonstandard amino acids that are notfound in proteins include lanthionine,2-aminoisobutyric acid, dehydroalanine and theneurotransmitter gamma-aminobutyric acid.

Nonstandard amino acids often occur as intermediatesin the metabolic pathways for standard amino acids —for example ornithine and citrulline occur in the urea

T271

cycle, part of amino acid catabolism (see below). Arare exception to the dominance of a-amino acids inbiology is the p-amino acid beta alanine(3-aminopropanoic acid), which is used in plants and microorganisms in the synthesis of pantothenic acid (vitamin

COO

L-ot alanine ^-alanine

|3-alanine and its a-alanine isomer

B5), a component of coenzyme A

[28]

In human nutrition

When taken up into the human body from the diet, the twenty two standard amino acids are either used to synthesize

[29]proteins and other biomolecules or oxidized to urea and carbon dioxide as a source of energy. The oxidation

pathway starts with the removal of the amino group by a transaminase, the amino group is then fed into the urea

cycle. The other product of transamidation is a keto acid that enters the citric acid cycle. Glucogenic amino acids

nilcan also be converted into glucose, through gluconeogenesis.

Pyrrolysine trait is restricted to several microbes, and only one organism has both Pyl and Sec. Of the twenty-twostandard amino acids, eight are called essential amino acids because the human body cannot synthesize them from

[32]

other compounds at the level needed for normal growth, so they must be obtained from food. However, thesituation is quite complicated since cysteine, taurine, tyrosine, histidine and arginine are semiessential amino acids inchildren, because the metabolic pathways that synthesize these amino acids are not fully developed. The

amounts required also depend on the age and health of the individual, so it is hard to make general statements aboutthe dietary requirement for some amino acids.

135

 Essential Nonessential Isoleucine Alanine Leucine Asparagine Lysine Aspartic Acid Methionine Cysteine* Phenylalanine Glutamic Acid Threonine Glutamine* Tryptophan Glycine* Valine Proline* Selenocysteine* Serine* Tyrosine* Arginine* Histidine*

(*) Essential only in certain cases

[35] [36]

Non-protein functions

In humans, non-protein amino acids also have important roles as metabolic intermediates, such as in the biosynthesisof the neurotransmitter gamma-aminobutyric acid. Many amino acids are used to synthesize other molecules, forexample:

Tryptophan is a precursor of the neurotransmitter serotoninGlycine is a precursor of porphyrins such as heme

[37]

[38]

Arginine is a precursor of nitric oxide

[39]

Ornithine and S-adenosylmethionine are precursors of poly amines

[40]

[41]

• Aspartate, glycine and glutamine are precursors of nucleotides.

• Phenylalanine is a precursor of various phenylpropanoids which are important in plant metabolism.

However, not all of the functions of other abundant non-standard amino acids are known, for example taurine is amajor amino acid in muscle and brain tissues, but although many functions have been proposed, its precise role in

[421

the body has not been determined.

[43]

Some non-standard amino acids are used as defenses against herbivores in plants. For example canavanine is an

[441

analogue of arginine that is found in many legumes, and in particularly large amounts in Canavalia gladiata

[451

(sword bean). This amino acid protects the plants from predators such as insects and can cause illness in people ifsome types of legumes are eaten without processing. The non-protein amino acid mimosine is found in other

[471

species of legume, particularly Leucaena leucocephala. This compound is an analogue of tyrosine and can poisonanimals that graze on these plants.

Uses in technology

Amino acids are used for a variety of applications in industry but their main use is as additives to animal feed. This isnecessary since many of the bulk components of these feeds, such as soybeans, either have low levels or lack someof the essential amino acids: lysine, methionine, threonine, and tryptophan are most important in the production of

these feeds. The food industry is also a major consumer of amino acids, particularly glutamic acid, which is used

[491as a flavor enhancer, and Aspartame (aspartyl-phenylalanine-1-methyl ester) as a low-calorie artificial

136

sweetener. The remaining production of amino acids is used in the synthesis of drugs and cosmetics.

 Amino acid derivative Pharmaceutical application 5-HTP (5-hydroxytryptophan) Experimental treatment for depression. L-DOPA (L-dihydroxyphenylalanine) [52]Treatment for Parkinsonism. Eflornithine Drug that inhibits ornithine decarboxylase and is used in the treatment of sleeping sickness [53]

Chemical building blocks

Amino acids are important as low-cost feedstocks. These compounds are used in chiral pool synthesis as

[541

enantiomerically-pure building blocks.

Amino acids have been investigated as precursors chiral catalysts, e.g. for asymmetric hydrogenation reactions,although no commercial applications exist.

Amino acids are under development as components of a range of biodegradable polymers. These materials haveapplications as environmentally-friendly packaging and in medicine in drug delivery and the construction ofprosthetic implants. These polymers include polypeptides, polyamides, polyesters, poly sulfides and polyurethaneswith amino acids either forming part of their main chains or bonded as side chains. These modifications alter thephysical properties and reactivities of the polymers. An interesting example of such materials is poly aspartate, a

[571

water-soluble biodegradable polymer that may have applications in disposable diapers and agriculture. Due to itssolubility and ability to chelate metal ions, polyaspartate is also being used as a biodegradeable anti-scaling agentand a corrosion inhibitor. In addition, the aromatic amino acid tyrosine is being developed as a possible

replacement for toxic phenols such as bisphenol A in the manufacture of polycarbonates.

Reactions

As amino acids have both a primary amine group and a primary carboxyl group, these chemicals can undergo mostof the reactions associated with these functional groups. These include nucleophilic addition, amide bond formationand imine formation for the amine group and esterification, amide bond formation and decarboxylation for thecarboxylic acid group. The multiple side chains of amino acids can also undergo chemical reactions. The typesof these reactions are determined by the groups on these side chains and are therefore different between the varioustypes of amino acid.

KCN

0

RAH NHzCI

NH2

H+

NH:

N

O

OH

The Strecker amino acid synthesis

Chemical synthesis

Several methods exist to synthesizeamino acids. One of the oldestmethods, begins with the brominationat the a-carbon of a carboxyic acid.Nucleophilic substitution withammonia then converts the alkyl bromide to the amino acid.LUJJ Alternatively, the Strecker amino acid synthesisinvolves the treatment of an aldehyde with potassium cyanide and ammonia, this produces an a-amino nitrile as anintermediate. Hydrolysis of the nitrile in acid then yields a a-amino acid. Using ammonia or ammonium salts inthis reaction gives unsubstituted amino acids, while substituting primary and secondary amines will yield substituted

amino acids. Likewise, using ketones, instead of aldehydes, gives a,a-disubstituted amino acids. The classicalsynthesis gives racemic mixtures of a-amino acids as products, but several alternative procedures using asymmetric

[63]

137

Amino acid (1)

Amino acid (2)

auxiliaries or asymmetric catalysts have been developed.

Currently the most adopted method is an automated synthesis on a solid support (e.g. polystyrene beads), usingprotecting groups (e.g. Fmoc and t-Boc) and activating groups (e.g. DCC and DIC).

Peptide bond formation

As both the amine and carboxylic acidgroups of amino acids can react toform amide bonds, one amino acidmolecule can react with another andbecome joined through an amidelinkage. This polymerization of aminoacids is what creates proteins. Thiscondensation reaction yields the newlyformed peptide bond and a molecule ofwater. In cells, this reaction does notoccur directly; instead the amino acidis first activated by attachment to atransfer RNA molecule through anester bond. This aminoacyl-tRNA isproduced in an ATP-dependentreaction carried out by an aminoacylfRNA synthetase.[71] This

aminoacyl-tRNA is then a substrate forthe ribosome, which catalyzes theattack of the amino group of the elongatinproteins made by ribosomes are synthesized

▼ H

Peptide bond

WaterDipeptide

The condensation of two amino acids to form a peptide bond

T721g protein chain on the ester bond. As a result of this mechanism, all

starting at their N-terminus and moving towards their C-terminus.

However, not all peptide bonds are formed in this way. In a few cases, peptides are synthesized by specific enzymes.For example, the tripeptide glutathione is an essential part of the defenses of cells against oxidative stress. Thispeptide is synthesized in two steps from free amino acids. In the first step gamma-glutamylcysteine synthetasecondenses cysteine and glutamic acid through a peptide bond formed between the side-chain carboxyl of the

glutamate (the gamma carbon of this side chain) and the amino group of the cysteine. This dipeptide is then

T741condensed with glycine by glutathione synthetase to form glutathione.

In chemistry, peptides are synthesized by a variety of reactions. One of the most used in solid-phase peptide

synthesis, which uses the aromatic oxime derivatives of amino acids as activated units. These are added in sequence

[751onto the growing peptide chain, which is attached to a solid resin support. The ability to easily synthesize vast

numbers of different peptides by varying the types and order of amino acids (using combinatorial chemistry) has

made peptide synthesis particularly important in creating libraries of peptides for use in drug discovery through

high-throughput screening

[76]

Biosynthesis and catabolism

In plants, nitrogen is first assimilated into organic compounds in the form of glutamate, formed from

alpha-ketoglutarate and ammonia in the mitochondrion. In order to form other amino acids, the plant uses

transaminases to move the amino group to another alpha-keto carboxylic acid. For example, aspartate

[77]aminotransferase converts glutamate and oxaloacetate to alpha-ketoglutarate and aspartate. Other organisms use

transaminases for amino acid synthesis too. Transaminases are also involved in breaking down amino acids.

Degrading an amino acid often involves moving its amino group to alpha-ketoglutarate, forming glutamate. In manyvertebrates, the amino group is then removed through the urea cycle and is excreted in the form of urea. However,amino acid degradation can produce uric acid or ammonia instead. For example, serine dehydratase converts serineto pyruvate and ammonia.

Nonstandard amino acids are usually formed through modifications to standard amino acids. For example,homocysteine is formed through the transsulfuration pathway or by the demethylation of methionine via the

[421

intermediate metabolite S-adenosyl methionine, while hydroxyproline is made by a posttranslational modificationof proline.

Microorganisms and plants can synthesize many uncommon amino acids. For example, some microbes make2-aminoisobutyric acid and lanthionine, which is a sulfide-bridged derivative of alanine. Both of these amino acidsare found in peptidic lantibiotics such as alamethicin. While in plants, 1-aminocyclopropane-l-carboxylic acid is

roil

a small disubstituted cyclic amino acid that is a key intermediate in the production of the plant hormone ethylene.

Hydrophilic and hydrophobic amino acids

rsiDepending on the polarity of the side chain, amino acids vary in their hydrophilic or hydrophobic character. These

properties are important in protein structure and protein—protein interactions. The importance of the physical

properties of the side chains comes from the influence this has on the amino acid residues' interactions with other

structures, both within a single protein and between proteins. The distribution of hydrophilic and hydrophobic amino

acids determines the tertiary structure of the protein, and their physical location on the outside structure of the

ro]

proteins influences their quaternary structure.

For example, soluble proteins have surfaces rich with polar amino acids like serine and threonine, while integralmembrane proteins tend to have outer rings of hydrophobic amino acids that anchor them into the lipid bilayer. Inthe case part-way between these two extremes, peripheral membrane proteins have a patch of hydrophobic aminoacids on their surface that locks onto the membrane. Similarly, proteins that have to bind to positively-chargedmolecules have surfaces rich with negatively charged amino acids like glutamate and aspartate, while proteinsbinding to negatively-charged molecules have surfaces rich with positively charged chains like lysine and arginine.Recently a new scale of hydrophobicity based on the free energy of hydrophobic association has been proposed.

The hydrophilic and hydrophobic interactions of proteins are not always the result of the properties of their aminoacid sidechains. This is because a range of posttranslational modifications can attach other chemical groups to theamino acids in proteins. For example, these modifications can produce hydrophobic lipoproteins, or hydrophilicglycoproteins. These type of modification allow the reversible targeting of a protein to a membrane. For example,the addition and removal of the fatty acid palmitic acid to cysteine residues in some signaling proteins causes the

roc]

proteins to attach and then detach from cell membranes.

Table of standard amino acid abbreviations and side chain properties

139

 Amino Acid 3-Letter[86] 1-Letter[86] Side chaini •. [8fi]polarity Side chain charge(phW8* Hydropathyindex AbsorbanceI („m)[88]max e at X (xlO-3M-cZ-V881 Alanine Ala A nonpolar neutral 1.8 Arginine Arg R polar positive -4.5 Asparagine Asn N polar neutral -3.5 Aspartic acid Asp D polar negative -3.5 Cysteine Cys C nonpolar neutral 2.5 250 0.3 Glutamic acid Glu E polar negative -3.5 Glutamine Gin Q polar neutral -3.5 Glycine Gly G nonpolar neutral -0.4 Histidine His H polar positive(10%),neutral(90%) -3.2 211 5.9 Isoleucine He I nonpolar neutral 4.5 Leucine Leu L nonpolar neutral 3.8 Lysine Lys K polar positive -3.9 Methionine Met M nonpolar neutral 1.9 Phenylalanine Phe F nonpolar neutral 2.8 257, 206, 188 0.2, 9.3, 60.0 Proline Pro P nonpolar neutral -1.6 Serine Ser S polar neutral -0.8 Threonine Thr T polar neutral -0.7 Tryptophan Trp W nonpolar neutral -0.9 280,219 5.6, 47.0 Tyrosine Tyr Y polar neutral -1.3 274, 222, 193 1.4,8.0,48.0 Valine Val V nonpolar neutral 4.2

In addition to the specific amino acid codes, placeholders are used in cases where chemical or crystallographicanalysis of a peptide or protein can not conclusively determine the identity of a residue.

Ambiguous Amino Acids

Asparagine or aspartic acid

Glutamine or glutamic acidLeucine or Isoleucine

 3-Letter 1-Letter Asx B Glx Z Xle J

Unspecified or unknown amino acid Xaa

Unk is sometimes used instead of Xaa, but is less standard.

Additionally, many non-standard amino acids have a specific code. For example, several peptide drugs, such asBortezomib or MG132 are artificially synthesized and retain their protecting groups, which have specific codes.Bortezomib is Pyz-Phe-boroLeu and MG132 is Z-Leu-Leu-Leu-al. Additionally, To aid in the analysis of proteinstructure, photocrosslinking amino acids are available. These include photoleucine (pLeu) and photomethionine

(pMet)

[891

Amino acid dating

Beta amino acid

Degron

Glucogenic amino acid

Homochirality

Leucines

Proteinogenic amino acid (including chemical structures)

Table of codons, 3-nucleotide sequences that encode each amino acid

• Doolittle, R.F. (1989) Redundancies in protein sequences. In Predictions of Protein Structure and the Principlesof Protein Conformation (Fasman, G.D. ed) Plenum Press, New York, pp. 599—623

• David L. Nelson and Michael M. Cox, Lehninger Principles of Biochemistry, 3rd edition, 2000, Worth Publishers,ISBN 1-57259-153-6

• Meierhenrich, U.J.: Amino acids and the asymmetry of life, Springer-Verlag, Berlin, New York, 2008. ISBN978-3-540-76885-2

• Morelli, Robert J. "Studies of amino acid absorption from the small intestine." San Francisco: Morelli, 1952.

• Amino acids overview physical-chemistry properties, 3D structures, etc

• List of Standard Amino Acids The Detailed PDF List of Standard Amino Acids (including 3D depictions)

[92]

• Nomenclature and Symbolism for Amino Acids and Peptides IUPAC-IUB Joint Commission on Biochemical

[93]Molecular Expressions: The Amino Acid Collection — Has detailed information and microscopy photographs

[94]• Amino acid properties — Properties of the amino acids (a tool aimed mostly at molecular geneticists trying to

Nomenclature (JCBN)

Molecular Expressi

of each amino acid

Amino acid propen

understand the meaning of mutations)

[95]

• Synthesis of Amino Acids and Derivatives

• Learn the 20 proteinogenic amino acids online

[97]

• The origin of the single-letter code for the amino acids

• Amino acid solution's pH, titration and isoelectric point calculation free spreadsheet

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144

Proteins

This

article is part of the series on:Gene expression

a Molecular biology topic {portal)(Glossary)

Introduction to Genetics

General flow: DNA > RNA > Protein

special transfers (RNA > RNA,RNA > DNA, Protein > Protein)

Genetic code

Transcription

Transcription (Transcription factors,RNA Polymerase,promoter) Prokaryotic / Archaeal / Eukaryotic

post-transcriptional modification(hnRNA,Splicing)

Translation

Translation (Ribosome,tRNA) Prokaryotic / Archaeal / Eukaryotic

post-translational modification

{functional groups, peptides,

structural changes)

gene regulation

epigenetic regulation{Genomic imprinting)

transcriptional regulation

post-transcriptional regulation

{sequestration,

alternative splicing,miRNA)

translational regulation

post-translational regulation(reversible irreversible)

[1] ,- [2]ask a question , edit

145

A representation of the 3D structure of myoglobin

showing coloured alpha helices. This protein was the

first to have its structure solved by X-ray

crystallography.

Proteins (also known as polypeptides) are organic compoundsmade of amino acids arranged in a linear chain and folded into aglobular form. The amino acids in a polymer are joined togetherby the peptide bonds between the carboxyl and amino groups ofadjacent amino acid residues. The sequence of amino acids in aprotein is defined by the sequence of a gene, which is encoded inthe genetic code. In general, the genetic code specifies 20standard amino acids; however, in certain organisms the geneticcode can include selenocysteine—and in certainarchaea—pyrrolysine. Shortly after or even during synthesis, theresidues in a protein are often chemically modified bypost-translational modification, which alters the physical andchemical properties, folding, stability, activity, and ultimately, thefunction of the proteins. Proteins can also work together to achievea particular function, and they often associate to form stablecomplexes

[4]

Like other biological macromolecules such as polysaccharides andnucleic acids, proteins are essential parts of organisms andparticipate in virtually every process within cells. Many proteins are enzymes that catalyze biochemical reactionsand are vital to metabolism. Proteins also have structural or mechanical functions, such as actin and myosin inmuscle and the proteins in the cytoskeleton, which form a system of scaffolding that maintains cell shape. Otherproteins are important in cell signaling, immune responses, cell adhesion, and the cell cycle. Proteins are alsonecessary in animals' diets, since animals cannot synthesize all the amino acids they need and must obtain essentialamino acids from food. Through the process of digestion, animals break down ingested protein into free amino acidsthat are then used in metabolism.

Proteins were first described by the Dutch chemist Gerhardus Johannes Mulder and named by the Swedish chemistJons Jakob Berzelius in 1838. The central role of proteins in living organisms was however not fully appreciateduntil 1926, when James B. Sumner showed that the enzyme urease was a protein. The first protein to be sequencedwas insulin, by Frederick Sanger, who won the Nobel Prize for this achievement in 1958. The first protein structuresto be solved were hemoglobin and myoglobin, by Max Perutz and Sir John Cowdery Kendrew, respectively, in1958. The three-dimensional structures of both proteins were first determined by x-ray diffraction analysis;

Perutz and Kendrew shared the 1962 Nobel Prize in Chemistry for these discoveries. Proteins may be purified fromother cellular components using a variety of techniques such as ultracentrifugation, precipitation, electrophoresis,and chromatography; the advent of genetic engineering has made possible a number of methods to facilitatepurification. Methods commonly used to study protein structure and function include immunohistochemistry,site-directed mutagenesis, and mass spectrometry.

Biochemistry

Most proteins are linear polymers built fromseries of up to 20 different L-a-amino acids.All amino acids possess common structuralfeatures, including an a-carbon to which anamino group, a carboxyl group, and a

w

£tt^\A

£tt^\A

/ \

Resonance structures of the peptide bond that links individual amino acids to forma protein polymer.

146

variable side chain are bonded. Only proline differs from this basic structure as it contains an unusual ring to the

rsiN-end amine group, which forces the CO—NH amide moiety into a fixed conformation. The side chains of the

standard amino acids, detailed in the list of standard amino acids, have a great variety of chemical structures and

properties; it is the combined effect of all of the amino acid side chains in a protein that ultimately determines its

three-dimensional structure and its chemical reactivity

[9]

o

R

V

n

Chemical structure of the peptide bond (left) and a peptide bond between leucine and threonine (right).

The amino acids in a polypeptide chain are linked by peptide bonds. Once linked in the protein chain, an individualamino acid is called a residue, and the linked series of carbon, nitrogen, and oxygen atoms are known as the mainchain or protein backbone. The peptide bond has two resonance forms that contribute some double-bondcharacter and inhibit rotation around its axis, so that the carbons are roughly coplanar. The other two dihedral anglesin the peptide bond determine the local shape assumed by the protein backbone. The end of the protein with a freecarboxyl group is known as the C-terminus or carboxy terminus, whereas the end with a free amino group is knownas the N-terminus or amino terminus.

The words protein, polypeptide, and peptide are a little ambiguous and can overlap in meaning. Protein is generallyused to refer to the complete biological molecule in a stable conformation, whereas peptide is generally reserved fora short amino acid oligomers often lacking a stable three-dimensional structure. However, the boundary between thetwo is not well defined and usually lies near 20—30 residues. Polypeptide can refer to any single linear chain ofamino acids, usually regardless of length, but often implies an absence of a defined conformation.

Synthesis

GTGCATCTGACTCCTGAGGAGAAGCACGTAGACTGAGGACTCCTCTTC

I

GUGCAUCUGACUCCUGAGGAGAAG

TrTTTTTT

v H L

E E K

. DNA

(transcription). RNA

(translation)

protein

The DNA sequence of a gene encodes the amino acid sequence of a protein.

Proteins are assembled from amino acidsusing information encoded in genes. Eachprotein has its own unique amino acidsequence that is specified by the nucleotidesequence of the gene encoding this protein.The genetic code is a set of three-nucleotidesets called codons and each three-nucleotidecombination designates an amino acid, forexample AUG (adenine-uracil-guanine) isthe code for methionine. Because DNAcontains four nucleotides, the total number of possible codons is 64; hence, there is some redundancy in the genetic

ri3i

code, with some amino acids specified by more than one codon. Genes encoded in DNA are first transcribed intopre-messenger RNA (mRNA) by proteins such as RNA polymerase. Most organisms then process the pre-mRNA(also known as a primary transcript) using various forms of post-transcriptional modification to form the maturemRNA, which is then used as a template for protein synthesis by the ribosome. In prokaryotes the mRNA may eitherbe used as soon as it is produced, or be bound by a ribosome after having moved away from the nucleoid. In contrast,eukaryotes make mRNA in the cell nucleus and then translocate it across the nuclear membrane into the cytoplasm,where protein synthesis then takes place. The rate of protein synthesis is higher in prokaryotes than eukaryotes andcan reach up to 20 amino acids per second.

147

The process of synthesizing a protein from an mRNA template is known as translation. The mRNA is loaded ontothe ribosome and is read three nucleotides at a time by matching each codon to its base pairing anticodon located ona transfer RNA molecule, which carries the amino acid corresponding to the codon it recognizes. The enzymeaminoacyl tRNA synthetase "charges" the tRNA molecules with the correct amino acids. The growing polypeptide is

ri3i

often termed the nascent chain. Proteins are always biosynthesized from N-terminus to C-terminus.

The size of a synthesized protein can be measured by the number of amino acids it contains and by its total

molecular mass, which is normally reported in units of daltons (synonymous with atomic mass units), or the

ri2iderivative unit kilodalton (kDa). Yeast proteins are on average 466 amino acids long and 53 kDa in mass. The

largest known proteins are the titins, a component of the muscle sarcomere, with a molecular mass of almost 3,000

kDa and a total length of almost 27,000 amino acids

[15]

Chemical synthesis

Short proteins can also be synthesized chemically by a family of methods known as peptide synthesis, which rely onorganic synthesis techniques such as chemical ligation to produce peptides in high yield. Chemical synthesisallows for the introduction of non-natural amino acids into polypeptide chains, such as attachment of fluorescent

ri7i

probes to amino acid side chains. These methods are useful in laboratory biochemistry and cell biology, thoughgenerally not for commercial applications. Chemical synthesis is inefficient for polypeptides longer than about 300

amino acids, and the synthesized proteins may not readily assume their native tertiary structure. Most chemical

n risynthesis methods proceed from C-terminus to N-terminus, opposite the biological reaction.

Structure of proteins

Most proteins fold into unique3-dimensional structures. The shapeinto which a protein naturally folds isknown as its native conformation.Although many proteins can foldunassisted, simply through thechemical properties of their aminoacids, others require the aid ofmolecular chaperones to fold into theirnative states. Biochemists often

refer to four distinct aspects of aprotein's structure:

• Primary structure: the amino acidsequence.

• Secondary structure: regularly repeating local structures stabilized by hydrogen bonds. The most commonexamples are the alpha helix, beta sheet and turns. Because secondary structures are local, many regions ofdifferent secondary structure can be present in the same protein molecule.

• Tertiary structure: the overall shape of a single protein molecule; the spatial relationship of the secondarystructures to one another. Tertiary structure is generally stabilized by nonlocal interactions, most commonly theformation of a hydrophobic core, but also through salt bridges, hydrogen bonds, disulfide bonds, and evenpost-translational modifications. The term "tertiary structure" is often used as synonymous with the term fold. TheTertiary structure is what controls the basic function of the protein.

• Quaternary structure: the structure formed by several protein molecules (polypeptide chains), usually calledprotein subunits in this context, which function as a single protein complex.

Three possible representations of the three-dimensional structure of the protein triose

phosphate isomerase. Left: all-atom representation colored by atom type. Middle:

Simplified representation illustrating the backbone conformation, colored by secondary

structure. Right: Solvent-accessible surface representation colored by residue type (acidic

residues red, basic residues blue, polar residues green, nonpolar residues white).

148

[22]

Proteins are not entirely rigid molecules. In addition to these levels of structure, proteins may shift between several

related structures while they perform their functions. In the context of these functional rearrangements, these tertiary

or quaternary structures are usually referred to as "conformations", and transitions between them are called

conformational changes. Such changes are often induced by the binding of a substrate molecule to an enzyme's

active site, or the physical region of the protein that participates in chemical catalysis. In solution proteins also

pundergo variation in structure through thermal vibration and the collision with other molecules.

Proteins can be informally divided intothree main classes, which correlatewith typical tertiary structures:globular proteins, fibrous proteins, andmembrane proteins. Almost allglobular proteins are soluble and manyare enzymes. Fibrous proteins are oftenstructural, such as collagen, the majorcomponent of connective tissue, orkeratin, the protein component of hairand nails. Membrane proteins often serve as receptors or provide channels for polar or charged molecules to pass

Molecular surface of several proteins showing their comparative sizes. From left to right

are: immunoglobulin G (IgG, an antibody), hemoglobin, insulin (a hormone), adenylate

kinase (an enzyme), and glutamine synthetase (an enzyme).

through the cell membrane

[23]

A special case of intramolecular hydrogen bonds within proteins, poorly shielded from water attack and hence

promoting their own dehydration, are called dehydrons

[24]

Structure determination

Discovering the tertiary structure of a protein, or the quaternary structure of its complexes, can provide important

clues about how the protein performs its function. Common experimental methods of structure determination include

X-ray crystallography and NMR spectroscopy, both of which can produce information at atomic resolution. Dual

polarisation interferometry is a quantitative analytical method for measuring the overall protein conformation and

conformational changes due to interactions or other stimulus. Circular dichroism is another laboratory technique for

determining internal beta sheet/ helical composition of proteins. Cryoelectron microscopy is used to produce

[251lower-resolution structural information about very large protein complexes, including assembled viruses; a

variant known as electron crystallography can also produce high-resolution information in some cases , especially

for two-dimensional crystals of membrane proteins. Solved structures are usually deposited in the Protein Data

Bank (PDB), a freely available resource from which structural data about thousands of proteins can be obtained in

the form of Cartesian coordinates for each atom in the protein

[27]

Many more gene sequences are known than protein structures. Further, the set of solved structures is biased towardproteins that can be easily subjected to the conditions required in X-ray crystallography, one of the major structuredetermination methods. In particular, globular proteins are comparatively easy to crystallize in preparation for X-ray

["981

crystallography. Membrane proteins, by contrast, are difficult to crystallize and are underrepresented in the PDB.Structural genomics initiatives have attempted to remedy these deficiencies by systematically solving representativestructures of major fold classes. Protein structure prediction methods attempt to provide a means of generating aplausible structure for proteins whose structures have not been experimentally determined.

149

Cellular functions

Proteins are the chief actors within the cell, said to be carrying out the duties specified by the information encoded in

ri2igenes. With the exception of certain types of RNA, most other biological molecules are relatively inert elements

upon which proteins act. Proteins make up half the dry weight of an Escherichia coli cell, whereas other

macromolecules such as DNA and RNA make up only 3% and 20%, respectivelyin a particular cell or cell type is known as its proteome.

The chief characteristic of proteins thatalso allows their diverse set offunctions is their ability to bind othermolecules specifically and tightly. Theregion of the protein responsible forbinding another molecule is known asthe binding site and is often adepression or "pocket" on themolecular surface. This binding abilityis mediated by the tertiary structure ofthe protein, which defines the bindingsite pocket, and by the chemicalproperties of the surrounding aminoacids' side chains. Protein binding canbe extraordinarily tight and specific;for example, the ribonuclease inhibitorprotein binds to human angiogenin

[29]

The set of proteins expressed

The enzyme hexokinase is shown as a simple ball-and-stick molecular model. To scale inthe top right-hand corner are two of its substrates, ATP and glucose.

-15

with a sub-femtomolar dissociation constant (<10~ M) but does not bind at all to its amphibian homolog onconase(>1 M). Extremely minor chemical changes such as the addition of a single methyl group to a binding partner cansometimes suffice to nearly eliminate binding; for example, the aminoacyl tRNA synthetase specific to the amino

acid valine discriminates against the very similar side chain of the amino acid isoleucine

[30]

Proteins can bind to other proteins as well as to small-molecule substrates. When proteins bind specifically to othercopies of the same molecule, they can oligomerize to form fibrils; this process occurs often in structural proteins thatconsist of globular monomers that self-associate to form rigid fibers. Protein—protein interactions also regulateenzymatic activity, control progression through the cell cycle, and allow the assembly of large protein complexesthat carry out many closely related reactions with a common biological function. Proteins can also bind to, or evenbe integrated into, cell membranes. The ability of binding partners to induce conformational changes in proteins

[31]

allows the construction of enormously complex signaling networks. Importantly, as interactions between proteinsare reversible, and depend heavily on the availability of different groups of partner proteins to form aggregates thatare capable to carry out discrete sets of function, study of the interactions between specific proteins is a key tounderstand important aspects of cellular function, and ultimately the properties that distinguish particular cell

[32] [33]

types

Enzymes

The best-known role of proteins in the cell is as enzymes, which catalyze chemical reactions. Enzymes are usuallyhighly specific and accelerate only one or a few chemical reactions. Enzymes carry out most of the reactionsinvolved in metabolism, as well as manipulating DNA in processes such as DNA replication, DNA repair, and

transcription. Some enzymes act on other proteins to add or remove chemical groups in a process known as

[34]post-translational modification. About 4,000 reactions are known to be catalyzed by enzymes. The rate

17

acceleration conferred by enzymatic catalysis is often enormous — as much as 10 -fold increase in rate over the

150

uncatalyzed reaction in the case of orotate decarboxylase (78 million years without the enzyme, 18 milliseconds withthe enzyme).

The molecules bound and acted upon by enzymes are called substrates. Although enzymes can consist of hundredsof amino acids, it is usually only a small fraction of the residues that come in contact with the substrate, and an even

smaller fraction — 3 to 4 residues on average — that are directly involved in catalysisthat binds the substrate and contains the catalytic residues is known as the active site.

[36]

The region of the enzyme

Cell signaling and ligand binding

Many proteins are involved in the process of cell signaling and signaltransduction. Some proteins, such as insulin, are extracellular proteinsthat transmit a signal from the cell in which they were synthesized toother cells in distant tissues. Others are membrane proteins that act asreceptors whose main function is to bind a signaling molecule andinduce a biochemical response in the cell. Many receptors have abinding site exposed on the cell surface and an effector domain withinthe cell, which may have enzymatic activity or may undergo aconformational change detected by other proteins within the cell

[37]

Antibodies are protein components of adaptive immune system whosemain function is to bind antigens, or foreign substances in the body,and target them for destruction. Antibodies can be secreted into theextracellular environment or anchored in the membranes of specializedB cells known as plasma cells. Whereas enzymes are limited in theirbinding affinity for their substrates by the necessity of conducting theirreaction, antibodies have no such constraints. An antibody's bindingaffinity to its target is extraordinarily high

[38]

Ribbon diagram of a mouse antibody againstcholera that binds a carbohydrate antigen

Many ligand transport proteins bind particular small biomolecules and

transport them to other locations in the body of a multicellular

organism. These proteins must have a high binding affinity when their ligand is present in high concentrations, but

must also release the ligand when it is present at low concentrations in the target tissues. The canonical example of a

ligand-binding protein is haemoglobin, which transports oxygen from the lungs to other organs and tissues in all

[39]vertebrates and has close homologs in every biological kingdom. Lectins are sugar-binding proteins which are

highly specific for their sugar moieties. Lectins typically play a role in biological recognition phenomena involving

cells and proteins. Receptors and hormones are highly specific binding proteins.

Transmembrane proteins can also serve as ligand transport proteins that alter the permeability of the cell membraneto small molecules and ions. The membrane alone has a hydrophobic core through which polar or charged moleculescannot diffuse. Membrane proteins contain internal channels that allow such molecules to enter and exit the cell.Many ion channel proteins are specialized to select for only a particular ion; for example, potassium and sodium

channels often discriminate for only one of the two ions

[41]

Structural proteins

Structural proteins confer stiffness and rigidity to otherwise-fluid biological components. Most structural proteins arefibrous proteins; for example, actin and tubulin are globular and soluble as monomers, but polymerize to form long,stiff fibers that comprise the cytoskeleton, which allows the cell to maintain its shape and size. Collagen and elastinare critical components of connective tissue such as cartilage, and keratin is found in hard or filamentous structures

such as hair, nails, feathers, hooves, and some animal shells

[42]

Other proteins that serve structural functions are motor proteins such as myosin, kinesin, and dynein, which arecapable of generating mechanical forces. These proteins are crucial for cellular motility of single celled organismsand the sperm of many multicellular organisms which reproduce sexually. They also generate the forces exerted bycontracting muscles.

Methods of study

As some of the most commonly studied biological molecules, the activities and structures of proteins are examinedboth in vitro and in vivo. In vitro studies of purified proteins in controlled environments are useful for learning how aprotein carries out its function: for example, enzyme kinetics studies explore the chemical mechanism of an enzyme'scatalytic activity and its relative affinity for various possible substrate molecules. By contrast, in vivo experiments onproteins' activities within cells or even within whole organisms can provide complementary information about wherea protein functions and how it is regulated.

Protein purification

In order to perform in vitro analysis, a protein must be purified away from other cellular components. This processusually begins with cell lysis, in which a cell's membrane is disrupted and its internal contents released into asolution known as a crude lysate. The resulting mixture can be purified using ultracentrifugation, which fractionatesthe various cellular components into fractions containing soluble proteins; membrane lipids and proteins; cellularorganelles, and nucleic acids. Precipitation by a method known as salting out can concentrate the proteins from this

lysate. Various types of chromatography are then used to isolate the protein or proteins of interest based on

T441properties such as molecular weight, net charge and binding affinity. The level of purification can be monitored

using various types of gel electrophoresis if the desired protein's molecular weight and isoelectric point are known,

by spectroscopy if the protein has distinguishable spectroscopic features, or by enzyme assays if the protein has

[451enzymatic activity. Additionally, proteins can be isolated according their charge using electrofocusing.

For natural proteins, a series of purification steps may be necessary to obtain protein sufficiently pure for laboratoryapplications. To simplify this process, genetic engineering is often used to add chemical features to proteins thatmake them easier to purify without affecting their structure or activity. Here, a "tag" consisting of a specific aminoacid sequence, often a series of histidine residues (a "His-tag"), is attached to one terminus of the protein. As a result,when the lysate is passed over a chromatography column containing nickel, the histidine residues ligate the nickeland attach to the column while the untagged components of the lysate pass unimpeded. A number of different tagshave been developed to help researchers purify specific proteins from complex mixtures.

152

Cellular localization

The study of proteins in vivo is often concernedwith the synthesis and localization of the proteinwithin the cell. Although many intracellularproteins are synthesized in the cytoplasm andmembrane-bound or secreted proteins in theendoplasmic reticulum, the specifics of howproteins are targeted to specific organelles orcellular structures is often unclear. A usefultechnique for assessing cellular localization usesgenetic engineering to express in a cell a fusionprotein or chimera consisting of the natural

protein of interest linked to a "reporter" such as

1471green fluorescent protein (GFP). The fused

protein's position within the cell can be cleanly

and efficiently visualized using microscopy,

as shown in the figure opposite.

Other methods for elucidating the cellular

location of proteins requires the use of known

compartmental markers for regions such as the

ER, the Golgi, lysosomes/vacuoles,

mitochondria, chloroplasts, plasma membrane,

etc. With the use of fluorescently-tagged

versions of these markers or of antibodies to

known markers, it becomes much simpler to

identify the localization of a protein of interest.

For example, indirect immunofluorescence will allow for fluorescence colocalization and demonstration of location.

Fluorescent dyes are used to label cellular compartments for a similar purpose.

Other possibilities exist, as well. For example, immunohistochemistry usually utilizes an antibody to one or moreproteins of interest that are conjugated to enzymes yielding either luminescent or chromogenic signals that can becompared between samples, allowing for localization information. Another applicable technique is cofractionation insucrose (or other material) gradients using isopycnic centrifugation. While this technique does not provecolocalization of a compartment of known density and the protein of interest, it does increase the likelihood, and ismore amenable to large-scale studies.

Finally, the gold-standard method of cellular localization is immunoelectron microscopy. This technique also uses anantibody to the protein of interest, along with classical electron microscopy techniques. The sample is prepared fornormal electron microscopic examination, and then treated with an antibody to the protein of interest that isconjugated to an extremely electro-dense material, usually gold. This allows for the localization of bothultrastructural details as well as the protein of interest.

Through another genetic engineering application known as site-directed mutagenesis, researchers can alter theprotein sequence and hence its structure, cellular localization, and susceptibility to regulation. This technique even

T521

allows the incorporation of unnatural amino acids into proteins, using modified tRNAs, and may allow the

[531rational design of new proteins with novel properties.

wtth friendlv oermission of Jeremv Simoson and Rainer PeoDerkokProteins in different cellular compartments and structures tagged with greenfluorescent protein) (here, white).

Proteomics and bioinformatics

The total complement of proteins present at a time in a cell or cell type is known as its proteome, and the study ofsuch large-scale data sets defines the field of proteomics, named by analogy to the related field of genomics. Keyexperimental techniques in proteomics include 2D electrophoresis, which allows the separation of a large numberof proteins, mass spectrometry, which allows rapid high-throughput identification of proteins and sequencing ofpeptides (most often after in-gel digestion), protein microarrays, which allow the detection of the relative levelsof a large number of proteins present in a cell, and two-hybrid screening, which allows the systematic exploration of

T571

protein—protein interactions. The total complement of biologically possible such interactions is known as the

reel

interactome. A systematic attempt to determine the structures of proteins representing every possible fold isknown as structural genomics.

The large amount of genomic and proteomic data available for a variety of organisms, including the human genome,allows researchers to efficiently identify homologous proteins in distantly related organisms by sequence alignment.Sequence profiling tools can perform more specific sequence manipulations such as restriction enzyme maps, openreading frame analyses for nucleotide sequences, and secondary structure prediction. From this data phylogenetictrees can be constructed and evolutionary hypotheses developed using special software like ClustalW regarding theancestry of modern organisms and the genes they express. The field of bioinformatics seeks to assemble, annotate,and analyze genomic and proteomic data, applying computational techniques to biological problems such as genefinding and cladistics.

Structure prediction and simulation

Complementary to the field of structural genomics, protein structure prediction seeks to develop efficient ways toprovide plausible models for proteins whose structures have not yet been determined experimentally . The mostsuccessful type of structure prediction, known as homology modeling, relies on the existence of a "template"structure with sequence similarity to the protein being modeled; structural genomics' goal is to provide sufficientrepresentation in solved structures to model most of those that remain. Although producing accurate modelsremains a challenge when only distantly related template structures are available, it has been suggested that sequencealignment is the bottleneck in this process, as quite accurate models can be produced if a "perfect" sequencealignment is known. Many structure prediction methods have served to inform the emerging field of proteinengineering, in which novel protein folds have already been designed. A more complex computational problem isthe prediction of intermolecular interactions, such as in molecular docking and protein—protein interactionprediction.

The processes of protein folding and binding can be simulated using such technique as molecular mechanics, inparticular, molecular dynamics and Monte Carlo, which increasingly take advantage of parallel and distributedcomputing (Folding@Home project ; molecular modeling on GPU). The folding of small alpha-helical proteindomains such as the villin headpiece and the HIV accessory protein have been successfully simulated in silico,and hybrid methods that combine standard molecular dynamics with quantum mechanics calculations have allowedexploration of the electronic states of rhodopsins.

Nutrition

Most microorganisms and plants can biosynthesize all 20 standard amino acids, while animals (including humans)

[291must obtain some of the amino acids from the diet. The amino acids that an organism cannot synthesize on its

own are referred to as essential amino acids. Key enzymes that synthesize certain amino acids are not present in

animals — such as aspartokinase, which catalyzes the first step in the synthesis of lysine, methionine, and threonine

from aspartate. If amino acids are present in the environment, microorganisms can conserve energy by taking up the

amino acids from their surroundings and downregulating their biosynthetic pathways.

In animals, amino acids are obtained through the consumption of foods containing protein. Ingested proteins are thenbroken down into amino acids through digestion, which typically involves denaturation of the protein throughexposure to acid and hydrolysis by enzymes called proteases. Some ingested amino acids are used for proteinbiosynthesis, while others are converted to glucose through gluconeogenesis, or fed into the citric acid cycle. Thisuse of protein as a fuel is particularly important under starvation conditions as it allows the body's own proteins to beused to support life, particularly those found in muscle. Amino acids are also an important dietary source ofnitrogen.

History and etymology

Proteins were recognized as a distinct class of biological molecules in the eighteenth century by Antoine Fourcroyand others, distinguished by the molecules' ability to coagulate or flocculate under treatments with heat or acid.Noted examples at the time included albumin from egg whites, blood serum albumin, fibrin, and wheat gluten. Dutchchemist Gerhardus Johannes Mulder carried out elemental analysis of common proteins and found that nearly allproteins had the same empirical formula, C,„„H,„N,-„0,,,„P,S,. He came to the erroneous conclusion that they

r r 400 620 100 120 1 1 J

might be composed of a single type of (very large) molecule. The term "protein" to describe these molecules wasproposed in 1838 by Mulder's associate Jons Jakob Berzelius; protein is derived from the Greek word xpmxeloc,

T711 T721

(proteios), meaning "primary" , "in the lead", or "standing in front". Mulder went on to identify the products ofprotein degradation such as the amino acid leucine for which he found a (nearly correct) molecular weight of 131Da.[70]

The difficulty in purifying proteins in large quantities made them very difficult for early protein biochemists tostudy. Hence, early studies focused on proteins that could be purified in large quantities, e.g., those of blood, eggwhite, various toxins, and digestive/metabolic enzymes obtained from slaughterhouses. In the 1950s, the ArmourHot Dog Co. purified 1 kg of pure bovine pancreatic ribonuclease A and made it freely available to scientists; thisgesture helped ribonuclease A become a major target for biochemical study for the following decades.

Linus Pauling is credited with the successful prediction of regular protein secondary structures based on hydrogen

T731 T741

bonding, an idea first put forth by William Astbury in 1933. Later work by Walter Kauzmann on denaturation,

based partly on previous studies by Kaj Linderstr0m-Lang, contributed an understanding of protein folding

and structure mediated by hydrophobic interactions. In 1949 Fred Sanger correctly determined the amino acid

sequence of insulin, thus conclusively demonstrating that proteins consisted of linear polymers of amino acids rather

T771than branched chains, colloids, or cyclols. The first atomic-resolution structures of proteins were solved by X-ray

crystallography in the 1960s and by NMR in the 1980s. As of 2009, the Protein Data Bank has over 55,000

T7R1

atomic-resolution structures of proteins. In more recent times, cryo-electron microscopy of large macromolecularassemblies and computational protein structure prediction of small protein domains are two methodsapproaching atomic resolution.

Expression cloning

Intein

List of proteins

List of recombinant proteins

Prion

Protein design

Protein dynamics

Protein structure prediction software

Proteopathy

Proteopedia

• Cdx protein family

References

• Branden C, Tooze J. (1999). Introduction to Protein Structure. New York: Garland Pub. ISBN 0-8153-2305-0.

• Murray RF, Harper HW, Granner DK, Mayes PA, Rodwell VW. (2006). Harper's Illustrated Biochemistry. NewYork: Lange Medical Books/McGraw-Hill. ISBN 0-07-146197-3.

• Van Holde KE, Mathews CK. (1996). Biochemistry. Menlo Park, Calif: Benjamin/Cummings Pub. Co., Inc.ISBN 0-8053-3931-0.

• Jorg von Hagen, VCH-Wiley 2008 Proteomics Sample Preparation. ISBN 978-3-527-31796-7

[81 ]

• Protein Songs (Stuart Mitchell — DNA Music Project) , 'When a "tape" of mRNA passes through the "playinghead" of a ribosome, the "notes" produced are amino acids and the pieces of music they make up are proteins.'

Databases and projects

rs2i

• Comparative Toxicogenomics Database curates protein—chemical interactions, as well as

gene/protein—disease relationships and chemical-disease relationships.

• Bioinformatic Harvester A Meta search engine (29 databases) for gene and protein information.

• The Protein Databank (see also PDB Molecule of the Month , presenting short accounts on selectedproteins from the PDB)

• Proteopedia — Life in 3D : rotatable, zoomable 3D model with wiki annotations for every known protein

molecular structure.

al Prote

[88]

rs7i• UniProt the Universal Protein Resource

• The Protein Naming Utility

• Human Protein Atlas

• NCBI Entrez Protein database

• NCBI Protein Structure database [91]

[92]

• Human Protein Reference Database

• Human Proteinpedia

[94]

• Folding©Home (Stanford University)

Tutorials and educational websites

[95]

• "An Introduction to Proteins" from HOPES (Huntington's Disease Outreach Project for Education at Stanford)

• Proteins: Biogenesis to Degradation — The Virtual Library of Biochemistry and Cell Biology

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[81] http

[82] http

[83] http

[84] http

[85] http

[86] http

[87] http

[88] http

[89] http

[90] http

[91] http

[92] http

[93] http

[94] http

[95] http

[96] http

//www. tjmitchell.com/stuart/dna.html

//ctd.mdibl.org/

//harvester.fzk.de

//www.rcsb.org

//www.rcsb.org/pdb/static.do ?p=education_discussion/molecule_of_the_month/index.html

//www.proteopedia.org

//www.expasy.uniprot.org

//www.jcvi.org/pn-utility

//w w w. pro teinatlas. org

//www. ncbi.nlm. nih. go v/sites/entrez?db=protein

//www. ncbi.nlm. nih. go v/sites/entrez?db=structure

//www.hprd.org/

//www.humanproteinpedia.org/

//folding, stanford.edu/

//hopes.stanford.edu/basics/proteins/pO.html

//www.biochemweb.org/proteins.shtml

159

Protein structure

Proteins are an important class of biological macromolecules present in all biological organisms, made up of suchelements as carbon, hydrogen, nitrogen, oxygen, and sulphur. All proteins are polymers of amino acids. According totheir physical size, proteins are nanoparticles (definition: 1-100 nm). The polymers, also known as polypeptides,consist of a sequence of 20 different L-a-amino acids, also referred to as residues. For chains under 40 residues theterm peptide is frequently used instead of protein. To be able to perform their biological function, proteins fold intoone or more specific spatial conformations, driven by a number of noncovalent interactions such as hydrogenbonding, ionic interactions, Van Der Waals forces and hydrophobic packing. To understand the functions of proteinsat a molecular level, it is often necessary to determine their three dimensional structure. This is the topic of thescientific field of structural biology, that employs techniques such as X-ray crystallography, NMR spectroscopy,andDual Polarisation Interferometry to determine the structure of proteins.

A number of residues is necessary to perform a particular biochemical function, and around 40-50 residues appearsto be the lower limit for a functional domain size. Protein sizes range from this lower limit to several thousandresidues in multi-functional or structural proteins. However, the current estimate for the average protein length isaround 300 residues. Very large aggregates can be formed from protein subunits, for example many thousand actinmolecules assemble into a microfilament.

Levels of protein structure

Primary protein emicnire

is sequence of s chain oT amino asids

Amino Acids

Alpha helix

Biochemistry refers to four distinct aspects of aprotein's structure:

Primary structure

the amino acid sequence of the peptide chains.

Secondary structure

highly regular sub-structures (alpha helix andstrands of beta pleated sheet), which are locallydefined, meaning that there can be manydifferent secondary motifs present in one singleprotein molecule.

Tertiary structure

three-dimensional structure of a single proteinmolecule; a spatial arrangement of the secondarystructures. It also describes the completely foldedand compacted polypeptide chain.

Quaternary structure

complex of several protein molecules orpolypeptide chains, usually called proteinsubunits in this context, which function as part ofthe larger assembly or protein complex.

In addition to these levels of structure, a protein mayshift between several similar structures in performing its biological function. This process is also reversible. In thecontext of these functional rearrangements, these tertiary or quaternary structures are usually referred to as chemicalconformation, and transitions between them are called conformational changes.

Secondary protein auijclijre

occurs, when ma sequence of amino acirjsare linked by hydrogen tends

Pleated sheet

Tertiary protein structure

occursiwhsn certain attractions are pre&embetween alpha helcsa end pleated Shasta.

°- Alpha heJix

Quaternary protein structure

ib a protein consisting of more man oneamino end chain

Protein structure, from primary to quaternary structure.

The primary structure is held together by covalent or peptide bonds, which are made during the process of proteinbiosynthesis or translation. These peptide bonds provide rigidity to the protein. The two ends of the amino acid chainare referred to as the C-terminal end or carboxyl terminus (C-terminus) and the N-terminal end or amino terminus(N-terminus) based on the nature of the free group on each extremity.

The various types of secondary structure are defined by their patterns of hydrogen bonds between the main-chainpeptide groups. However, these hydrogen bonds are generally not stable by themselves, since the water-amidehydrogen bond is generally more favorable than the amide-amide hydrogen bond. Thus, secondary structure is stableonly when the local concentration of water is sufficiently low, e.g., in the molten globule or fully folded states.

Similarly, the formation of molten globules and tertiary structure is driven mainly by structurally non-specificinteractions, such as the rough propensities of the amino acids and hydrophobic interactions. However, the tertiarystructure is fixed only when the parts of a protein domain are locked into place by structurally specific interactions,such as ionic interactions (salt bridges), hydrogen bonds, and the tight packing of side chains. The tertiary structureof extracellular proteins can also be stabilized by disulfide bonds, which reduce the entropy of the unfolded state;disulfide bonds are extremely rare in cytosolic proteins, since the cytosol is generally a reducing environment.

Primary structure

The sequence of the different amino acids is called the primary structure of the peptide or protein. Counting ofresidues always starts at the N-terminal end (NH -group), which is the end where the amino group is involved in apeptide bond. The primary structure of a protein is determined by the gene corresponding to the protein. A specificsequence of nucleotides in DNA is transcribed into mRNA, which is read by the ribosome in a process calledtranslation. The sequence of a protein is unique to that protein, and defines the structure and function of the protein.The sequence of a protein can be determined by methods such as Edman degradation or tandem mass spectrometry.Often however, it is read directly from the sequence of the gene using the genetic code. Post-translationalmodifications such as disulfide formation, phosphorylations and glycosylations are usually also considered a part ofthe primary structure, and cannot be read from the gene.

Secondary structure

Left: Ca atom trace. Right: Secondary structure cartoon ("ribbon")

By building models of peptides using known information about bond lengths and angles, the first elements ofsecondary structure, the alpha helix and the beta sheet, were suggested in 1951 by Linus Pauling and coworkers.Each of these two secondary structure elements have a regular geometry, meaning they are constrained to specificvalues of the dihedral angles t|> and ep. Thus they can be found in a specific region of the Ramachandran plot. Boththe alpha helix and the beta-sheet represent a way of saturating all the hydrogen bond donors and acceptors in thepeptide backbone. These secondary structure elements only depend on properties of the polypeptide main chain,explaining why they occur in all proteins. The part of the protein that is not in a regular secondary structure is said tobe a "non-regular structure" (not to be mixed with random coil, an unfolded polypeptide chain lacking any fixedthree-dimensional structure). Some more representations of the same helix are shown at right.

Supersecondary structure

The elements of secondary structure are usually folded into a compact shape using a variety of loops and turns.Secondary structures are bonded by hydrogen bond to form supersecondary structures like Greek key. SeeSupersecondary structure for a detailed example. It is also suggested by many scientists that th secondary structureconsists only of the amino acid sequence.

Tertiary structure

The elements of secondary structure are usually folded into a compact shape using a variety of loops and turns. Theformation of tertiary structure is usually driven by the burial of hydrophobic residues, but other interactions such ashydrogen bonding, ionic interactions and disulfide bonds can also stabilize the tertiary structure. The tertiarystructure encompasses all the noncovalent interactions that are not considered secondary structure, and is whatdefines the overall fold of the protein, and is usually indispensable for the function of the protein.

Quaternary structure

The quaternary structure is the interaction between several chains of peptide bonds. The individual chains are calledsubunits. The individual subunits are usually not covalently connected, but might be connected by a disulfide bond.Not all proteins have quaternary structure, since they might be functional as monomers. The quaternary structure isstabilized by the same range of interactions as the tertiary structure. Complexes of two or more polypeptides (i.e.multiple subunits) are called multimers. Specifically it would be called a dimer if it contains two subunits, a trimer ifit contains three subunits, and a tetramer if it contains four subunits. The subunits are usually related to one anotherby symmetry axes, such as a 2-fold axis in a dimer. Multimers made up of identical subunits may be referred to witha prefix of "homo-" (e.g. a homotetramer) and those made up of different subunits may be referred to with a prefix of"hetero-" (e.g. a heterotetramer, such as the two alpha and two beta chains of hemoglobin).

162

Structure of the amino acids

An oc-amino acid consists of a part that is present in allthe amino acid types, and a side chain that is unique toeach type of residue. The C atom is bound to 4

a

different atoms: a hydrogen atom (the H is omitted inthe diagram), an amino group nitrogen, a carboxylgroup carbon, and a side chain carbon specific for thistype of amino acid. An exception from this rule isproline, where the hydrogen atom is replaced by a bondto the side chain. Because the carbon atom is bound tofour different groups it is chiral, however only one ofthe isomers occur in biological proteins. Glycinehowever, is not chiral since its side chain is a hydrogenatom. A simple mnemonic for correct L-form is"CORN": when the C atom is viewed with the H in

a

front, the residues read "CO-R-N" in a clockwisedirection.

R

C

a

,0-H

\

H-N

H

C

O

An a-amino acid

' CORN'

The side chain determines the chemical properties of thea-amino acid and may be any one of the 20 differentside chains:

The 20 naturally occurring amino acids can be dividedinto several groups based on their chemical properties.Important factors are charge,

hydrophobicity/hydrophilicity, size and functionalgroups. The nature of the interaction of the different sidechains with the aqueous environment plays a major rolein molding protein structure. Hydrophobic side chainstends to be buried in the middle of the protein, whereashydrophilic side chains are exposed to the solvent.

Examples of hydrophobic residues are: Leucine,isoleucine, phenylalanine, and valine, and to a lesserextent tyrosine, alanine and tryptophan. The charge ofthe side chains plays an important role in proteinstructures, since ion bonding can stabilize proteinsstructures, and an unpaired charge in the middle of aprotein can disrupt structures. Charged residues are strongly hydrophilic, and are usually found on the out side ofproteins. Positively charged side chains are found in lysine and arginine, and in some cases in histidine. Negativecharges are found in glutamate and aspartate. The rest of the amino acids have smaller generally hydrophilic sidechains with various functional groups. Serine and threonine have hydroxyl groups, and aspargine and glutamine haveamide groups. Some amino acids have special properties such as cysteine, that can form covalent disulfide bonds toother cysteines, proline that is cyclical, and glycine that is small, and more flexible than the other amino acids.

CO-R-N rule

163

The peptide bond (amide bond)

Two amino acids can be combined in acondensation reaction. By repeating thisreaction, long chains of residues (aminoacids in a peptide bond) can be generated.This reaction is catalysed by the ribosome ina process known as translation. The peptidebond is in fact planar due to thederealization of the electrons from thedouble bond. The rigid peptide dihedralangle, to (the bond between C and N) isalways close to 180 degrees. The dihedralangles phi cp (the bond between N and Ca)and psi op (the bond between Ca and C ) canhave a certain range of possible values.These angles are the degrees of freedom of aprotein, they control the protein's threedimensional structure. They are restrainedby geometry to allowed ranges typical forparticular secondary structure elements, andrepresented in a Ramachandran plot. A fewimportant bond lengths are given in the tablebelow.

 R R' H- -N ^H 0 yO-HTwo imino acids N' ^1 O'H

R

H-NH

H

O'

/Ny c;

r\

o

R'

Bond angles for i|> and a>

 Peptide bond Average length Singlebond Average length Hydrogen bond Average(+30) Ca-C 153 pm C-C 154 pm OH — O-H 280 pm C-N 133 pm C-N 148 pm N-H — 0=C 290 pm N-Ca 146 pm c-o 143 pm O-H — 0=C 280 pm

Side-chain conformation and Rotamers

The atoms along the side chain are named with Greek letters in Greek alphabetical order: a, |3, y, 6, e, and so on. C

refers to the carbon atom of the backbone closest to the carbonyl group of that amino acid, C the second closest and

Pso on. The C is part of the backbone, while C and atoms further out comprise the side chain. The dihedral angles

around the bonds between these atoms are named y\, yl, x3, etc. The dihedral angle of the first movable atom of the

side chain, 7> defined as N-C a-C j3 - X'Y, is named %1. Most side chains can be in different conformations

called gauche(-), trans, and gauche(+). Side chains generally tend to try to come into a staggered conformation

around yl, driven by the minimization of the overlap between the electron orbitals of substituent atoms.

The diversity of side-chain conformations is often expressed in rotamer libraries. A rotamer library is a collection of

rotamers for each residue type in proteins with side-chain degrees of freedom. Rotamer libraries usually contain

information about both conformation and frequency of a certain conformation. Often libraries will also contain

information about the variance about dihedral angle means or modes, which can be used in sampling

[4]

Side-chain dihedral angles are not evenly distributed, but for most side chain types, the X angles occur in tightclusters around certain values. Rotamer libraries therefore are usually derived from statistical analysis of side-chainconformations in known structures of proteins by clustering observed conformations or by dividing dihedral anglespace into bins, and determining an average conformation in each bin. This division is usually on physical-chemicalgrounds, as in the divisions for rotation about sp3-sp3 bonds into three 120° bins centered on each staggeredconformation (60°, 180°, -60°).

Rotamer libraries can be backbone-independent, secondary-structure-dependent, or backbone-dependent. Thedistinctions are made depending on whether the dihedral angles for the rotamers and/or their frequencies depend onthe local backbone conformation or not. Backbone-independent rotamer libraries make no reference to backboneconformation, and are calculated from all available side chains of a certain type. Secondary-structure-dependentlibraries present different dihedral angles and/or rotamer frequencies for a -helix, (3 -sheet, or coil secondarystructures. Backbone-dependent rotamer libraries present conformations and/or frequencies dependent on the localbackbone conformation as defined by the backbone dihedral angles (f) and if} , regardless of secondary structure.Finally, a variant on backbone-dependent rotamer libraries exists in the form of position-specific rotamers, thosedefined by a fragment usually of 5 amino acids in length, where the central residue's side chain conformation isexamined.

Domains, motifs, and folds in protein structure

Many proteins are organized into several units. A structural domain is an element of the protein's overall structurethat is self-stabilizing and often folds independently of the rest of the protein chain. Many domains are not unique tothe protein products of one gene or one gene family but instead appear in a variety of proteins. Domains often arenamed and singled out because they figure prominently in the biological function of the protein they belong to; forexample, the "calcium-binding domain of calmodulin". Because they are self-stabilizing, domains can be "swapped"by genetic engineering between one protein and another to make chimeras. A motif in this sense refers to a smallspecific combination of secondary structural elements (such as helix-turn-helix). These elements are often calledsupersecondary structures. Fold refers to a global type of arrangement, like helix bundle or beta-barrel. Structuremotifs usually consist of just a few elements, e.g. the 'helix-turn-helix' has just three. Note that while the spatialsequence of elements is the same in all instances of a motif, they may be encoded in any order within the underlyinggene. Protein structural motifs often include loops of variable length and unspecified structure, which in effect createthe "slack" necessary to bring together in space two elements that are not encoded by immediately adjacent DNAsequences in a gene. Note also that even when two genes encode secondary structural elements of a motif in thesame order, nevertheless they may specify somewhat different sequences of amino acids. This is true not onlybecause of the complicated relationship between tertiary and primary structure, but because the size of the elementsvaries from one protein and the next. Despite the fact that there are about 100,000 different proteins expressed ineukaryotic systems, there are much fewer different domains, structural motifs and folds. This is partly a consequenceof evolution, since genes or parts of genes can be doubled or moved around within the genome. This means that, forexample, a protein domain might be moved from one protein to another thus giving the protein a new function.Because of these mechanisms pathways and mechanisms tends to be reused in several different proteins.

165

Protein folding

An unfolded polypeptide folds into its characteristic three-dimensional structure from random coil.

Protein structure determination

Around 90% of the protein structures available in the Protein Data Bank have been determined by X-raycrystallography. This method allows one to measure the 3D density distribution of electrons in the protein (in thecrystallized state) and thereby infer the 3D coordinates of all the atoms to be determined to a certain resolution.Roughly 9% of the known protein structures have been obtained by Nuclear Magnetic Resonance techniques, whichcan also be used to determine secondary structure. Note that aspects of the secondary structure as whole can bedetermined via other biochemical techniques such as circular dichroism or dual polarisation interferometry.Secondary structure can also be predicted with a high degree of accuracy (see next section). Cryo-electronmicroscopy has recently become a means of determining protein structures to high resolution (less than 5 angstromsor 0.5 nanometer) and is anticipated to increase in power as a tool for high resolution work in the next decade. Thistechnique is still a valuable resource for researchers working with very large protein complexes such as virus coatproteins and amyloid fibers.

Resolution

(A)

A rough guide to the resolution of protein structures

Meaning

>4.03.0-4.0

Individual coordinates meaningless

Fold possibly correct, but errors are very likely. Many sidechains placed with wrong rotamer.

2.5-3.0

2.0-2.5

Fold likely correct except that some surface loops might be mismodelled. Several long, thin sidechains (lys, glu, gin, etc) and smallsidechains (ser, val, thr, etc) likely to have wrong rotamers.

As 2.5 - 3.0, but number of sidechains in wrong rotamer is considerably less. Many small errors can normally be detected. Foldnormally correct and number of errors in surface loops is small. Water molecules and small ligands become visible.

1.5-2.0

0.5 - 1.5

Few residues have wrong rotamer. Many small errors can normally be detected. Folds are extremely rarely incorrect, even in surfaceloops.

In general, structures have almost no errors at this resolution. Rotamer libraries and geometry studies are made from these structures.

Structure classification

Protein structures can be classified based on their similarity or a common evolutionary origin. SCOP and CATHdatabases provide two different structural classifications of proteins.

Computational prediction of protein structure

The generation of a protein sequence is much simpler than the generation of a protein structure. However, thestructure of a protein gives much more insight in the function of the protein than its sequence. Therefore, a numberof methods for the computational prediction of protein structure from its sequence have been proposed. Ab initioprediction methods use just the sequence of the protein. Threading uses existing protein structures. HomologyModeling to build a reliable 3D model for a protein of unknown structure from one or more related proteins ofknown structure. The recent progress and challenges in protein structure prediction was reviewed by Zhang

Protein structure related software

There are software to aid researchers working on, often overlapping, different aspects of protein structure. The mostbasic functionality is providing structure visualization. Analysis of protein structure can be facilitated by softwarethat aligns structures. In the absence of existing structures for a given protein sequence, there are methods to predictor to model the structure of such sequences based on known protein structures. And given models of known orpredicted structures, one can use software to verify them for errors, predict protein conformational changes, orpredict substrate binding sites.

• Protein dynamics

• Chiang YS, Gelfand TI, Kister AE, Gelfand IM (2007). "New classification of supersecondary structures ofsandwich-like proteins uncovers strict patterns of strand assemblage.". Proteins. 68 (4): 915—921.doi:10.1002/prot.21473. PMID 17557333.

• Habeck M, Nilges M, Rieping W (2005). "Bayesian inference applied to macromolecular structure determination"

. Physical review. E, Statistical, nonlinear, and soft matter physics 72 (3 Pt 1): 031912. PMID 16241487.(Bayesian computational methods for the structure determination from NMR data)

• SSS Database — super-secondary structure protein database

• SPROUTS [10] (Structural Prediction for pRotein folding UTility System)

• ProSA-web — a web service for the recognition of errors in experimentally or theoretically determinedprotein structures

ri2i

• NQ-Flipper — checks for unfavorable rotamers of Asn and Gin residues in protein structures

ri3i

• WHAT IF servers — checks nearly 200 aspects of protein structure, like packing, geometry, unfavourable

rotamers in general of for Asn, Gin, and His especially, strange water molecules, backbone conformations, atomnomenclature, symmetry parameters, etc.

ri4i

• Bioinformatics course — an interactive, fully free, course explaining many of the aspects discussed in thiswiki entry.

References

[1] Brocchieri L, Karlin S (2005-06-10). "Protein length in eukaryotic and prokaryotic proteomes" (http://www.pubmedcentral.nih.gov/

articlerender.fcgi?tool=pmcentrez&artid=1150220). Nucleic Acids Research 33 (10): 3390-3400. doi: 10.1093/nar/gki615. PMID 15951512.

PMC 1150220.[2] Pauling L, Corey RB, Branson HR (1951). "The structure of proteins; two hydrogen-bonded helical configurations of the polypeptide chain"

(http://www.pubmedcentral.nih.gov/art...&artid=1063337). Proc Natl Acad Sci USA 37 (4): 205—211.

doi:10.1073/pnas.37.4.205. PMID 14816373. PMC 1063337.[3] Chiang YS, Gelfand TI, Kister AE, Gelfand IM (2007). "New classification of supersecondary structures of sandwich-like proteins uncovers

strict patterns of strand assemblage.". Proteins. 68 (4): 915-921. doi:10.1002/prot.21473. PMID 17557333.[4] Dunbrack, RL (2002). "Rotamer Libraries in the 21st Century". Curr. Opin. Struct. Biol. 12 (4): 431-440.

doi:10.1016/S0959-440X(02)00344-5. PMID 12163064.[5] Richardson Rotamer Libraries (http://pibs.duke.edu/databases/rotamer.php)[6] Dunbrack Rotamer Libraries (http://dunbrack.fccc.edu/bbdep)[7] Zhang Y (2008). "Progress and challenges in protein structure prediction" (http://www.pubmedcentral.nih.gov/articlerender.

fcgi?tool=pmcentrez&artid=2680823). Curr Opin Struct Biol 18 (3): 342-348. doi:10.1016/j.sbi.2008.02.004. Entrez Pubmed 18436442

(http://www.ncbi.nlm.nih.gov/entrez/q..._uids=l8436442). PMID 18436442.

PMC 2680823.

Protein structure

167

[9] http://binfs.umdnj .edu/sssdb/

Protein folding

Protein folding is the physical process bywhich a polypeptide folds into itscharacteristic and functional

three-dimensional structure from randomcoil. Each protein exists as an unfoldedpolypeptide or random coil when translatedfrom a sequence of mRNA to a linear chainof amino acids. This polypeptide lacks anydeveloped three-dimensional structure (theleft hand side of the neighboring figure).Amino acids interact with each other toproduce a well-defined three dimensional structure, the folded protein (the right hand side of the figure), known as

[2]

the native state. The resulting three-dimensional structure is determined by the amino acid sequence.

[3]

For many proteins the correct three dimensional structure is essential to function. Failure to fold into the intendedshape usually produces inactive proteins with different properties including toxic prions. Several neurodegenerative

Protein before and after folding.

and other diseases are believed to result from the accumulation of misfolded (incorrectly folded) proteins

[4]

168

Known facts

Relationship between folding and amino acid sequence

The amino-acid sequence (or primarystructure) of a protein defines its nativeconformation. A protein molecule foldsspontaneously during or after synthesis.While these macromolecules may beregarded as "folding themselves", theprocess also depends on the solvent (wateror lipid bilayer), the concentration of salts,the temperature, and the presence ofmolecular chaperones.

Folded proteins usually have a hydrophobiccore in which side chain packing stabilizesthe folded state, and charged or polar sidechains occupy the solvent-exposed surfacewhere they interact with surrounding water.Minimizing the number of hydrophobicside-chains exposed to water is an importantdriving force behind the folding process.Formation of intramolecular hydrogen

bonds provides another important

[71contribution to protein stability. The strength of hydrogen bonds depends on their environment, thus H-bonds

enveloped in a hydrophobic core contribute more than H-bonds exposed to the aqueous environment to the stability

Illustration of the main driving force behind protein structure formation. In the

compact fold (to the right), the hydrophobic amino acids (shown as black spheres)

are in general shielded from the solvent.

of the native state

[81

In the seminal research work published nearly four decades ago, C.B. Anfinsen hypothesized that "information

191dictating the native fold of protein domains is encoded in their amino acid sequence" . However, with the

explosive amount of protein sequence, structure, and fold data generated since the time of Anfinsen during the omics

era, the emerging picture of the protein universe has challenged Anfinsen's dogma, for it has become evident that

numerous protein folds have incredible sequence diversity with no consistent "fold code" .In support of this

observation, recent studies have shown that proteins with as low as 1-2% sequence identity may still adopt the same

native fold, thus defying any tangible encoding of fold-dictating information into protein sequence . The pursuit

of the elusive "fold code" has resulted in little more than patterns of amino acid sequence conservations specific to

certain proteins, but no finding has been compelling enough to generalize universally or to utilize for biological

applications

In a recent study, scientists from Harvard-MIT have shown that, despite the enormous diversity within protein foldsat the level of 1-dimensional amino acid sequence, nature has encoded fold-conserved information at higher

dimensions of protein space such as the 2-D (protein contact maps) or 3-D (structure), that are known to be more

[131intricately related to protein folding phenomena . The study published in PLoS ONE illuminated latent

fold-conserved information from higher dimensional protein space using network theory approaches. By examining

the entire protein universe on a fold-by-fold basis, the study revealed that atomic interaction networks in the

solvent-unexposed core of protein domains are fold-conserved and unique to each protein's native fold, thus

appearing to be the encoded "signature" of protein domains. This study hence uncoverd that the protein fold code is a

"network phenomena" in addition to a sequence and structural phenomena as commonly presumed. The discovery of

such a protein folding code also confirms Anfinsens Dogma by proving that a significant portion of the fold-dictating

information is encoded by the atomic interaction network in the solvent-unexposed core of protein domains.

The process of folding in vivo often begins co-translationally, so that the N-terminus of the protein begins to foldwhile the C-terminal portion of the protein is still being synthesized by the ribosome. Specialized proteins called

ri4i

chaperones assist in the folding of other proteins. A well studied example is the bacterial GroEL system, whichassists in the folding of globular proteins. In eukaryotic organisms chaperones are known as heat shock proteins.Although most globular proteins are able to assume their native state unassisted, chaperone-assisted folding is oftennecessary in the crowded intracellular environment to prevent aggregation; chaperones are also used to preventmisfolding and aggregation which may occur as a consequence of exposure to heat or other changes in the cellularenvironment.

For the most part, scientists have been able to study many identical molecules folding together en masse. At thecoarsest level, it appears that in transitioning to the native state, a given amino acid sequence takes on roughly thesame route and proceeds through roughly the same intermediates and transition states. Often folding involves firstthe establishment of regular secondary and supersecondary structures, particularly alpha helices and beta sheets, andafterwards tertiary structure. Formation of quaternary structure usually involves the "assembly" or "coassembly" ofsubunits that have already folded. The regular alpha helix and beta sheet structures fold rapidly because they arestabilized by intramolecular hydrogen bonds, as was first characterized by Linus Pauling. Protein folding mayinvolve covalent bonding in the form of disulfide bridges formed between two cysteine residues or the formation ofmetal clusters. Shortly before settling into their more energetically favourable native conformation, molecules maypass through an intermediate "molten globule" state.

The essential fact of folding, however, remains that the amino acid sequence of each protein contains the informationthat specifies both the native structure and the pathway to attain that state. This is not to say that nearly identicalamino acid sequences always fold similarly. Conformations differ based on environmental factors as well; similarproteins fold differently based on where they are found. Folding is a spontaneous process independent of energyinputs from nucleoside triphosphates. The passage of the folded state is mainly guided by hydrophobic interactions,formation of intramolecular hydrogen bonds, and van der Waals forces, and it is opposed by conformational entropy.

Disruption of the native state

Under some conditions proteins will not fold into their biochemically functional forms. Temperatures above orbelow the range that cells tend to live in will cause thermally unstable proteins to unfold or "denature" (this is whyboiling makes an egg white turn opaque). High concentrations of solutes, extremes of pH, mechanical forces, and thepresence of chemical denaturants can do the same. Protein thermal stability is far from constant, however. Forexample, hyperthermophilic bacteria have been found that grow at temperatures as high as 122°C, which ofcourse requires that their full complement of vital proteins and protein assemblies be stable at that temperature orabove.

A fully denatured protein lacks both tertiary and secondary structure, and exists as a so-called random coil. Under

ri7icertain conditions some proteins can refold; however, in many cases denaturation is irreversible. Cells sometimes

protect their proteins against the denaturing influence of heat with enzymes known as chaperones or heat shock

proteins, which assist other proteins both in folding and in remaining folded. Some proteins never fold in cells at all

except with the assistance of chaperone molecules, which either isolate individual proteins so that their folding is not

interrupted by interactions with other proteins or help to unfold misfolded proteins, giving them a second chance to

refold properly. This function is crucial to prevent the risk of precipitation into insoluble amorphous aggregates.

Incorrect protein folding and neurodegenerative disease

Aggregated proteins are associated with prion-related illnesses such as Creutzfeldt-Jakob disease, bovine spongiformencephalopathy (mad cow disease), amyloid-related illnesses such as Alzheimer's Disease and familial amyloidcardiomyopathy or polyneuropathy, as well as intracytoplasmic aggregation diseases such as Huntington's andParkinson's disease. These age onset degenerative diseases are associated with the multimerization of

misfolded proteins into insoluble, extracellular aggregates and/or intracellular inclusions including cross-beta sheetamyloid fibrils; it is not clear whether the aggregates are the cause or merely a reflection of the loss of proteinhomeostasis, the balance between synthesis, folding, aggregation and protein turnover. Misfolding and excessivedegradation instead of folding and function leads to a number of proteopathy diseases such as antitrypsin-associatedEmphysema, cystic fibrosis and the lysosomal storage diseases, where loss of function is the origin of the disorder.While protein replacement therapy has historically been used to correct the latter disorders, an emerging approach isto use pharmaceutical chaperones to fold mutated proteins to render them functional.

The Levinthal paradox and Kinetics

ri9i

The Levinthal paradox observes that if a protein were to fold by sequentially sampling all possible conformations,it would take an astronomical amount of time to do so, even if the conformations were sampled at a rapid rate (on thenanosecond or picosecond scale). Based upon the observation that proteins fold much faster than this, Levinthal thenproposed that a random conformational search does not occur, and the protein must, therefore, fold through a seriesof meta-stable intermediate states.

The duration of the folding process varies dramatically depending on the protein of interest. When studied outsidethe cell, the slowest folding proteins require many minutes or hours to fold primarily due to proline isomerization,and must pass through a number of intermediate states, like checkpoints, before the process is complete. On theother hand, very small single-domain proteins with lengths of up to a hundred amino acids typically fold in a singlestep. Time scales of millisecwithin a few microseconds.

T211step. Time scales of milliseconds are the norm and the very fastest known protein folding reactions are complete

Energy landscape theory of protein folding

The protein folding phenomenon was largely an experimental endeavor until the formulation of energy landscapetheory by Joseph Bryngelson and Peter Wolynes in the late 1980s and early 1990s. This approach introduced theprinciple of minimal frustration, which asserts that evolution has selected the amino acid sequences of naturalproteins so that interactions between side chains largely favor the molecule's acquisition of the folded state.Interactions that do not favor folding are selected against, although some residual frustration is expected to exist. Aconsequence of these evolutionarily selected sequences is that proteins are generally thought to have globally"funneled energy landscapes" (coined by Jose Onuchic[reference needed]) that are largely directed towards thenative state. This "folding funnel" landscape allows the protein to fold to the native state through any of a largenumber of pathways and intermediates, rather than being restricted to a single mechanism. The theory is supportedby both computational simulations of model proteins and numerous experimental studies, and it has been used toimprove methods for protein structure prediction and design [reference needed]. The description of protein foldingby the leveling free-energy landscape is also consistent with the 2n law of thermodynamics.

Techniques for studying protein foldingCircular dichroism

Circular dichroism is one of the most general and basic tools to study protein folding. Circular dichroismspectroscopy measures the absorption of circularly polarized light. In proteins, structures such as alpha helicies andbeta sheets are chiral, and thus absorb such light. The absorption of this light acts as a marker of the degree offoldedness of the protein ensemble. This technique can be used to measure equilibrium unfolding of the protein bymeasuring the change in this absorption as a function of denaturant concentration or temperature. A denaturant meltmeasures the free energy of unfolding as well as the protein's m value, or denaturant dependence. A temperature meltmeasures the melting temperature (T ) of the protein. This type of spectroscopy can also be combined withfast-mixing devices, such as stopped flow, to measure protein folding kinetics and to generate chevron plots.

Vibrational circular dichroism of proteins

The more recent developments of vibrational circular dichroism (VCD) techniques for proteins, currently involvingFourier transform (FFT) instruments, provide powerful means for determining protein conformations in solutioneven for very large protein molecules. Such VCD studies of proteins are often combined with X-ray diffraction ofprotein crystals, FT-IR data for protein solutions in heavy water (DO), or ab initio quantum computations to provideunambiguous structural assignments that are unobtainable from CD.

Modern studies of folding with high time resolution

The study of protein folding has been greatly advanced in recent years by the development of fast, time-resolved

techniques. These are experimental methods for rapidly triggering the folding of a sample of unfolded protein, and

T241then observing the resulting dynamics. Fast techniques in widespread use include neutron scattering , ultrafast

mixing of solutions, photochemical methods, and laser temperature jump spectroscopy. Among the many scientists

who have contributed to the development of these techniques are Jeremy Cook, Heinrich Roder, Harry Gray, Martin

Gruebele, Brian Dyer, William Eaton, Sheena Radford, Chris Dobson, Sir Alan R. Fersht and Bengt Nolting.

Computational prediction of protein tertiary structure

De novo or ab initio techniques for computational protein structure prediction is related to, but strictly distinct from,studies involving protein folding. Molecular Dynamics (MD) is an important tool for studying protein folding anddynamics in silico. Because of computational cost, ab initio MD folding simulations with explicit water are limitedto peptides and very small proteins . MD simulations of larger proteins remain restricted to dynamics of the

experimental structure or its high-temperature unfolding. In order to simulate long time folding processes (beyondabout 1 microsecond), like folding of small-size proteins (about 50 residues) or larger, some approximations orsimplifications in protein models need to be introduced. An approach using reduced protein representation

(pseudo-atoms representing groups of atoms are defined) and statistical potential is not only useful in protein

T271structure prediction, but is also capable of reproducing the folding pathways.

There are distributed computing projects which use idle CPU or GPU time of personal computers to solve problemssuch as protein folding or prediction of protein structure. People can run these programs on their computer orPlayStation 3 to support them. See links below (for example Folding@Home) to get information about how toparticipate in these projects.

Experimental techniques of protein structure determination

Folded structures of proteins are routinely determined by X-ray crystallography and NMR.

Anfinsen's dogma

1281

Harvard-MIT Scientists Discover the Protein Folding Code and demonstrate this is a Network phenomenon

Chevron plot

Denaturation (biochemistry)

Denaturation midpoint

Downhill folding

Folding (chemistry)

Foldit computer game

Protein design

Protein dynamics

Protein Misfolding Cyclic Amplification

Protein structure prediction

Protein structure prediction software

Rosetta@home

Software for molecular mechanics modeling

[291

• Foldit - Folding Protein Game

• Folding® Home

• Rosetta@Home [31]

References

[1] Alberts, Bruce; Alexander Johnson, Julian Lewis, Martin Raff, Keith Roberts, and Peter Walters (2002). "The Shape and Structure of

AND+372270[uid]&rid=mboc4.section.388). Molecular Biology of the Cell; Fourth Edition. New York and London: Garland Science.

ISBN 0-8153-3218-1..[2] Anfinsen, C. (1972). "The formation and stabilization of protein structure" (http://www.pubmedcentral.nih.gov/articlerender.

fcgi?tool=pmcentrez&artid=l 173893). Biochem. J. 128 (4): 737^9. PMID 4565129. PMC 1173893.[3] Jeremy M. Berg, John L. Tymoczko, Lubert Stryer; Web content by Neil D. Clarke (2002). "3. Protein Structure and Function" (http://www.

ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Search&db=books&doptcmdl=GenBookHL&term=stryer[book]+AND+215168[uid]&

rid=stryer.chapter.280). Biochemistry. San Francisco: W. H. Freeman. ISBN 0-7167-4684-0..[4] Dennis J. Selkoe (2003). "Folding proteins in fatal ways" (http://www.nature.com/nature/journal...ture02264.html).

Nature 426: pp. 900-904. doi:10.1038/nature02264. PMID 14685251. .[5] van den Berg, B., Wain, R., Dobson, C. M., Ellis R. J. (August 2000). "Macromolecular crowding perturbs protein refolding kinetics:

implications for folding inside the cell" (http://www.pubmedcentral.nih.gov/art...z&artid=306593). EMBO J.

19 (15): 3870-5. doi: 10.1093/emboj/19.15.3870. PMID 10921869. PMC 306593.[6] Pace, C, Shirley, B., McNutt, M., Gajiwala, K. (1 January 1996). "Forces contributing to the conformational stability of proteins" (http://

www.fasebj.org/cgi/reprint/10/1/75). FASEB J. 10 (1): 75-83. PMID 8566551. .[7] Rose, G., Fleming, P., Banavar, J., Maritan, A. (2006). "A backbone-based theory of protein folding" (http://www.pubmedcentral.nih.gov/

articlerender.fcgi?tool=pmcentrez&artid=1636505). Proc. Natl. Acad. Sci. U.S.A. 103 (45): 16623-33. doi:10.1073/pnas.0606843103.

PMID 17075053. PMC 1636505.[8] Deechongkit, S., Nguyen, H., Dawson, P. E., Gruebele, M., Kelly, J. W. (2004). "Context Dependent Contributions of Backbone H-Bonding

to [5-Sheet Folding Energetics" (http://www.pubmedcentral.nih.gov/art...&artid=1636505). Nature 403 (45):

101-5. doi:10.1073/pnas.0606843103. PMID 17075053. PMC 1636505.

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[9] Anfinsen CB. (20 July 1973). "Principles that Govern the Folding of Protein Chains" (http://www.sciencemag.org/cgi/pdf_extract/181/

4096/223). Science. 181 (96): 223-230. doi:10.1126/science.l81.4096.223. PMID4124164..[10] Govindarajan S, Recabarren R, Goldstein RA. (17 Sep 1999). "Estimating the total number of protein folds." (http://www3.interscience.

wiley.com/journal/65000323/abstract). Proteins. 35 (4): 408-414.

doi:10.1002/(SICI)1097-0134(19990601)35:4<408::AID-PROT4>3.0.CO;2-A. PMID 10382668. .[11] Mirny, L. A., Abkevich, V. I. & Shakhnovich, E. I. (28 Apr 1998). "How evolution makes proteins fold quickly." (http://www.pnas.org/

content/95/9/4976.abstract). Proc Natl Acad Sci U S A. 95 (9): 4976^981. doi:10.1073/pnas.95.9.4976. PMID 9560213. PMC 20198..[12] S Rackovsky. (15 Jan 1993). "On the nature of the protein folding code." (http://www.pnas.Org/content/90/2/644.abstract). Proc Natl

AcadSciUSA. 90 (2): 644-648. doi:10.1073/pnas.90.2.644. PMID 8421700. PMC45720..[13] Venkataramanan Soundararajan, Rahul Raman, S. Raguram, V. Sasisekharan, Ram Sasisekharan (2010). "Atomic Interaction Networks in

the Core of Protein Domains and Their Native Folds" (http://www.pubmedcentral.nih.gov/art...ool=pmcentrez&

artid=2826414). PLoS ONE 5 (2): e9391. doi:10.1371/journal.pone.0009391. PMID 20186337. PMC 2826414.[14] Lee, S., Tsai, F. (2005). "Molecular chaperones in protein quality control" (http://www.jbmb.or.kr/fulltext/jbmb/view.php?vol=38&

page=259). J. Biochem. Mol. Biol. 38 (3): 259-65. PMID 15943899. .[15] Alexander, P. A., He Y., Chen, Y., Orban, J., Bryan, P. N. (2007). "The design and characterization of two proteins with 88% sequence

identity but different structure and function" (http://www.pubmedcentral.nih.gov/art...&artid=1906725).

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(2008). "Cell proliferation at 122°C and isotopically heavy CH4 production by a hyperthermophilic methanogen under high-pressure

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fasebj.org/cgi/reprint/10/1/27). FASEB J. 10 (1): 27-34. PMID 8566543. .[18] Chiti, F.; Dobson, C. (2006). "Protein misfolding, functional amyloid, and human disease.". Annual review of biochemistry 75: 333—366.

doi:10.1146/annurev.biochem.75.101304.123901. PMID 16756495.[19] C. Levinthal (1968). "Are there pathways for protein folding?" (http://www.biochem.wisc.edu/courses/...em704/Reading/

Levinthall968.pdf). J. Chim. Phys. 65: 44-5..[20] Kim, P. S., Baldwin, R. L. (1990). "Intermediates in the folding reactions of small proteins". Annu. Rev. Biochem. 59: 631—60.

doi:10.1146/annurev.bi.59.070190.003215. PMID 2197986.[21] Jackson S. E. (August 1998). "How do small single-domain proteins fold?" (http://biomednet.com/elecref/13590278003R0081). Fold Des

3 (4): R81-91. doi:10.1016/S1359-0278(98)00033-9. PMID 9710577. .[22] Kubelka, J., Hofrichter, J., Eaton, W. A. (February 2004). "The protein folding 'speed limit'". Curr. Opin. Struct. Biol. 14 (1): 76—88.

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alpha-lactalbuminC". JMolBioliU (4): 865-873. doi:10.1006/jmbi.2001.5006. PMID 11575938.[25] "Fragment-based Protein Folding Simulations" (http://www.cs.ucl.ac.Uk/staff/d.jones/t42morph.html)..[26] "Protein folding" (http://www.biomolecular-modeling.com...n-folding.html) (by Molecular Dynamics). .[27] Kmiecik, S., and Kolinski, A. (2007). "Characterization of protein-folding pathways by reduced-space modeling" (http://www.

pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=1941469). Proc. Natl. Acad. Sci. U.S.A. 104 (30): 12330—5.

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Protein dynamics

A protein domain is a part of protein sequence andstructure that can evolve, function, and existindependently of the rest of the protein chain. Eachdomain forms a compact three-dimensional structureand often can be independently stable and folded.Many proteins consist of several structural domains.One domain may appear in a variety of evolutionarilyrelated proteins. Domains vary in length from betweenabout 25 amino acids up to 500 amino acids in length.The shortest domains such as zinc fingers are stabilizedby metal ions or disulfide bridges. Domains often formfunctional units, such as the calcium-binding EF handdomain of calmodulin. Because they are self-stable,domains can be "swapped" by genetic engineeringbetween one protein and another to make chimericproteins.

Background

The concept of the domain was first proposed in 1973by Wetlaufer after X-ray crystallographic studies of henlysozyme and papain and by limited proteolysis

[4] [5]

Pyruvate kinase, a protein from three domains (PDB lpkn )

studies of immunoglobulins . Wetlaufer defined

domains as stable units of protein structure that could fold autonomously. In the past domains have been described as

units of:

compact structurefunction and evolution1

[8]

[7]

• folding

Each definition is valid and will often overlap, i.e. a compact structural domain that is found amongst diverseproteins is likely to fold independently within its structural environment. Nature often brings several domainstogether to form multidomain and multifunctional proteins with a vast number of possibilities . In a multidomainprotein, each domain may fulfil its own function independently, or in a concerted manner with its neighbours.Domains can either serve as modules for building up large assemblies such as virus particles or muscle fibres, or canprovide specific catalytic or binding sites as found in enzymes or regulatory proteins.

An appropriate example is pyruvate kinase, a glycolytic enzyme that plays an important role in regulating the fluxfrom fructose-1,6-biphosphate to pyruvate. It contains an all-|3 regulatory domain, an a/p-substrate binding domainand an a/p-nucleotide binding domain, connected by several polypeptide linkers (see figure, right). Each domainin this protein occurs in diverse sets of protein families.

The central a/p-barrel substrate binding domain is one of the most common enzyme folds. It is seen in manydifferent enzyme families catalysing completely unrelated reactions . The a/p-barrel is commonly called the TIMbarrel named after triose phosphate isomerase, which was the first such structure to be solved . It is currentlyclassified into 26 homologous families in the CATH domain database . The TIM barrel is formed from a

sequence of p-a-p motifs closed by the first and last strand hydrogen bonding together, forming an eight stranded

barrel. There is debate about the evolutionary origin of this domain. One study has suggested that a single ancestral

ri4ienzyme could have diverged into several families , while another suggests that a stable TIM-barrel structure has

evolved through convergent evolution

The TIM-barrel in pyruvate kinase is 'discontinuous', meaning that more than one segment of the polypeptide isrequired to form the domain. This is likely to be the result of the insertion of one domain into another during theprotein's evolution. It has been shown from known structures that about a quarter of structural domains arediscontinuous. The inserted p-barrel regulatory domain is 'continuous', made up of a single stretch of

polypeptide.

Covalent association of two domains represents a functional and structural advantage since there is an increase in

no]

stability when compared with the same structures non-covalently associated . Other, advantages are the

protection of intermediates within inter-domain enzymatic clefts that may otherwise be unstable in aqueous

environments, and a fixed stoichiometric ratio of the enzymatic activity necessary for a sequential set of reactions

[19]

Domains are units of protein structurePrimary structure

The primary structure (string of amino acids) of a protein encodes its uniquely folded 3D conformation. The mostimportant factor governing the folding of a protein into 3D structure is the distribution of polar and non-polar sidechains. Folding is driven by the burial of hydrophobic side chains into the interior of the molecule so to avoidcontact with the aqueous environment.

Sequence alignment is an important tool for determining domains.

Secondary structure

Generally proteins have a core of hydrophobic residues surrounded by a shell of hydrophilic residues. Since thepeptide bonds themselves are polar they are neutralised by hydrogen bonding with each other when in thehydrophobic environment. This gives rise to regions of the polypeptide that form regular 3D structural patternscalled 'secondary structure'. There are two main types of secondary structure:

• a-helices

• p-sheet

Secondary structure motifs

Some simple combinations of secondary structure elements have been found to frequently occur in protein structureand are referred to as 'super-secondary structure' or motifs. For example, the p-hairpin motif consists of two adjacentantiparallel p-strands joined by a small loop. It is present in most antiparallel p structures both as an isolated ribbonand as part of more complex p-sheets. Another common super-secondary structure is the P-a-P motif, which isfrequently used to connect two parallel p-strands. The central a-helix connects the C-termini of the first strand to theN-termini of the second strand, packing its side chains against the p-sheet and therefore shielding the hydrophobicresidues of the p-strands from the surface.

Tertiary structure

Several motifs pack together to form compact, local, semi-independent units called domains. The overall 3Dstructure of the polypeptide chain is referred to as the protein's 'tertiary structure'. Domains are the fundamental unitsof tertiary structure, each domain containing an individual hydrophobic core built from secondary structural unitsconnected by loop regions. The packing of the polypeptide is usually much tighter in the interior than the exterior of

T221

the domain producing a solid-like core and a fluid-like surface. In fact, core residues are often conserved in aprotein family, whereas the residues in loops are less conserved, unless they are involved in the protein's function.Protein tertiary structure can be divided into four main classes based on the secondary structural content of thedomain.

• All-a domains have a domain core built exclusively from cc-helices. This class is dominated by small folds, manyof which form a simple bundle with helices running up and down.

• All-p domains have a core comprising of antiparallel p-sheets, usually two sheets packed against each other.

Various patterns can be identified in the arrangement of the strands, often giving rise to the identification of

T241recurring motifs, for example the Greek key motif.

• a+p domains are a mixture of all-a and all-p motifs. Classification of proteins into this class is difficult because

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of overlaps to the other three classes and therefore is not used in the CATH domain database.

• a/p domains are made from a combination of p-a-p motifs that predominantly form a parallel p-sheet surroundedby amphipathic a-helices. The secondary structures are arranged in layers or barrels.

Structural alignment is an important tool for determining domains.

Domains have limits on size

T251Domains have limits on size. The size of individual structural domains varies from 36 residues in E-selectin to

692 residues in lipoxygenase-1, but the majority, 90%, have less than 200 residues with an average of

approximately 100 residues. Very short domains, less than 40 residues, are often stabilised by metal ions or

rofil

disulfide bonds. Larger domains, greater than 300 residues, are likely to consist of multiple hydrophobic cores.

Relationship between primary and tertiary structureModules

[291Nature is a tinkerer and not an inventor, new sequences are adapted from pre-existing sequences rather than

invented. Domains are the common material used by nature to generate new sequences, they can be thought of as

genetically mobile units, referred to as 'modules'. Often, the C and N termini of domains are close together in space,

allowing them to easily be "slotted into" parent structures during the process of evolution. Many domain families are

found in all three forms of life, Archaea, Bacteria and Eukarya. Domains that are repeatedly found in diverse

proteins are often referred to as modules, examples can be found among extracellular proteins associated with

clotting, fibrinolysis, complement, the extracellular matrix, cell surface adhesion molecules and cytokine

[30]

receptors.

Protein families

Molecular evolution gives rise to families of related proteins with similar sequence and structure. However, sequencesimilarities can be extremely low between proteins that share the same structure. Protein structures may be similarbecause proteins have diverged from a common ancestor. Alternatively, some folds may be more favored than othersas they represent stable arrangements of secondary structures and some proteins may converge towards these foldsover the course of evolution . There are currently about 45,000 experimentally determined protein 3D structuresdeposited within the Protein Data Bank (PDB). However this set contains a lot of identical or very similarstructures. All proteins should be classified to structural families to understand their evolutionary relationships.

Structural comparisons are best achieved at the domain level. For this reason many algorithms have been developedto automatically assign domains in proteins with known 3D structure, see 'Domain definition from structuralco-ordinates'.

Super-folds

The CATH domain database classifies domains into approximately 800 fold families, ten of these folds are highly

populated and are referred to as 'super-folds'. Super-folds are defined as folds for which there are at least three

T321structures without significant sequence similarity. The most populated is the a/p-barrel super-fold as described

previously.

Multidomain proteins

The majority of genomic proteins, two-thirds in unicellular organisms and more than 80% in metazoa, are

[33]multidomain proteins created as a result of gene duplication events. Many domains in multidomain structures

could have once existed as independent proteins. More and more domains in eukaryotic multidomain proteins can be

found as independent proteins in prokaryotes. For example, vertebrates have a multi-enzyme polypeptide

containing the GAR synthetase, AIR synthetase and GAR transformylase modules (GARs-AIRs-GARt; GAR:

glycinamide ribonucleotide synthetase/transferase; AIR: aminoimidazole ribonucleotide synthetase). In insects, the

polypeptide appears as GARs-(AIRs)2-GARt, in yeast GARs-AIRs is encoded separately from GARt, and in

T351bacteria each domain is encoded separately.

Origin

Multidomain proteins are likely to have emerged from a selective pressure during evolution to create new functions.Various proteins have diverged from common ancestors by different combinations and associations of domains.Modular units frequently move about, within and between biological systems through mechanisms of geneticshuffling:

• transposition of mobile elements including horizontal transfers (between species);

• gross rearrangements such as inversions, translocations, deletions and duplications;

• homologous recombination;

• slippage of DNA polymerase during replication.

Difference in proliferation

It is likely that all these and organisms. For example, the ABC transporter domain constitutes one of the largest

[35]domain families that appear in all organisms. Many other families that appear in all organisms show much less

proliferation. These include metabolic enzymes and components of translational apparatus.

Types of organisation

T371The simplest multidomain organisation seen in proteins is that of a single domain repeated in tandem. The

domains may interact with each other or remain isolated, like beads on string. The giant 30,000 residue muscle

T3R1

protein titin comprises about 120 fibronectin-III-type and Ig-type domains. In the serine proteases, a gene

[39]duplication event has led to the formation of a two p-barrel domain enzyme. The repeats have diverged so widely

that there is no obvious sequence similarity between them. The active site is located at a cleft between the two

p-barrel domains, in which functionally important residues are contributed from each domain. Genetically

engineered mutants of the chymotrypsin serine protease were shown to have some proteinase activity even though

their active site residues were abolished and it has therefore been postulated that the duplication event enhanced the

<•■ •<• [39]enzyme s activity.

Connectivity

Modules frequently display different connectivity relationships, as illustrated by the kinesins and ABC transporters.The kinesin motor domain can be at either end of a polypeptide chain that includes a coiled-coil region and a cargodomain. ABC transporters are built with up to four domains consisting of two unrelated modules, ATP-bindingcassette and an integral membrane module, arranged in various combinations.

Domain insertion

Not only do domains recombine, but there are many examples of a domain having been inserted into another.Sequence or structural similarities to other domains demonstrate that homologues of inserted and parent domains canexist independently. An example is that of the 'fingers' inserted into the 'palm' domain within the polymerases of thePol I family.[41]

Difference between structural and evolutionary domain

Since a domain can be inserted into another, there should always be at least one continuous domain in a multidomainprotein. This is the main difference between definitions of structural domains and evolutionary/functional domains.An evolutionary domain will be limited to one or two connections between domains, whereas structural domains canhave unlimited connections, within a given criterion of the existence of a common core. Several structural domainscould be assigned to an evolutionary domain.

Domains are autonomous folding unitsFolding

History

Protein folding - the unsolved problem

Since the seminal work of Anfinsen over forty years ago, the goal to completely understand the mechanismby which a polypeptide rapidly folds into its stable native conformation remains elusive. Many experimentalfolding studies have contributed much to our understanding, but the principles that govern protein folding arestill based on those discovered in the very first studies of folding. Anfinsen showed that the native state of aprotein is thermodynamically stable, the conformation being at a global minimum of its free energy.

Folding pathway

Folding is a directed search of conformational space allowing the protein to fold on a biologically feasible time scale.

The Levinthal paradox states that if an averaged sized protein would sample all possible conformations before

T421finding the one with the lowest energy, the whole process would take billions of years. Proteins typically fold

within 0.1 and 1000 seconds, therefore the protein folding process must be directed some way through a specific

folding pathway. The forces that direct this search are likely to be a combination of local and global influences

whose effects are felt at various stages of the reaction.

Advances in experimental and theoretical studies have shown that folding can be viewed in terms of energy

[44] [451

landscapes, where folding kinetics is considered as a progressive organisation of an ensemble of partially

folded structures through which a protein passes on its way to the folded structure. This has been described in termsof a folding funnel, in which an unfolded protein has a large number of conformational states available and there arefewer states available to the folded protein. A funnel implies that for protein folding there is a decrease in energy andloss of entropy with increasing tertiary structure formation. The local roughness of the funnel reflects kinetic traps,corresponding to the accumulation of misfolded intermediates. A folding chain progresses toward lower intra-chainfree-energies by increasing its compactness. The chains conformational options become increasingly narrowed

ultimately toward one native structure.

Advantage of domains in protein folding

The organisation of large proteins by structural domains represents an advantage for protein folding, with eachdomain being able to individually fold, accelerating the folding process and reducing a potentially large combinationof residue interactions. Furthermore, given the observed random distribution of hydrophobic residues in proteins,domain formation appears to be the optimal solution for a large protein to bury its hydrophobic residues whilekeeping the hydrophilic residues at the surface.

However, the role of inter-domain interactions in protein folding and in energetics of stabilisation of the native

structure, probably differs for each protein. In T4 lysozyme, the influence of one domain on the other is so strong

that the entire molecule is resistant to proteolytic cleavage. In this case, folding is a sequential process where the

C-terminal domain is required to fold independently in an early step, and the other domain requires the presence of

[49]the folded C-terminal domain for folding and stabilisation.

It has been found that the folding of an isolated domain can take place at the same rate or sometimes faster than thatof the integrated domain. Suggesting that unfavourable interactions with the rest of the protein can occur duringfolding. Several arguments suggest that the slowest step in the folding of large proteins is the pairing of the folded

no]

domains. This is either because the domains are not folded entirely correctly or because the small adjustmentsrequired for their interaction are energetically unfavourable, such as the removal of water from the domaininterface.

Domains and quaternary structureAbout quaternary structures

Many proteins have a quaternary structure, which consists of several polypeptide chains that associate into anoligomeric molecule. Each polypeptide chain in such a protein is called a subunit. Hemoglobin, for example, consistsof two a and two p subunits. Each of the four chains has an all-a globin fold with a heme pocket.

Domain swapping

T521

Domain swapping is a mechanism for forming oligomeric assemblies. . In domain swapping, a secondary ortertiary element of a monomeric protein is replaced by the same element of another protein. Domain swapping can

range from secondary structure elements to whole structural domains. It also represents a model of evolution for

T531functional adaptation by oligomerisation, e.g. oligomeric enzymes that have their active site at subunit interfaces.

Domains and protein flexibility

The presence of multiple domains in proteins gives rise to a great deal of flexibility and mobility, leading to proteindomain dynamics. Domain motions can be inferred by comparing structures of a protein in different environments,

[541

or directly observed using spectra measured by neutron spin echo spectroscopy. One of the largest observeddomain motions is the "swivelling' mechanism in pyruvate phosphate dikinase. The phosphoinositide domain swivelsbetween two states in order to bring a phosphate group from the active site of the nucleotide binding domain to thatof the phosphoenolpyruvate/pyruvate domain. The phosphate group is moved over a distance of 45A involving adomain motion of about 100 degrees around a single residue. Domain motions are important for:

• catalysis;

• regulatory activity;

• transport of metabolites;

• formation of protein assemblies; and

• cellular locomotion.

In enzymes, the closure of one domain onto another captures a substrate by an induced fit, allowing the reaction totake place in a controlled way. A detailed analysis by Gerstein led to the classification of two basic types of domainmotion; hinge and shear. Only a relatively small portion of the chain, namely the inter-domain linker and sidechains undergo significant conformational changes upon domain rearrangement.

Hinges by secondary structures

rcon

A study by Hayward found that the termini of a-helices and p-sheets form hinges in a large number of cases.Many hinges were found to involve two secondary structure elements acting like hinges of a door, allowing anopening and closing motion to occur. This can arise when two neighbouring strands within a p-sheet situated in onedomain, diverge apart as they join the other domain. The two resulting termini then form the bending regionsbetween the two domains, a-helices that preserve their hydrogen bonding network when bent are found to behave as

rco]

mechanical hinges, storing "elastic energy' that drives the closure of domains for rapid capture of a substrate.

Helical to extended conformation

The interconversion of helical and extended conformations at the site of a domain boundary is not uncommon. Incalmodulin, torsion angles change for five residues in the middle of a domain linking a-helix. The helix is split intotwo, almost perpendicular, smaller helices separated by four residues of an extended strand.

Shear motions

Shear motions involve a small sliding movement of domain interfaces, controlled by the amino acid side chainswithin the interface. Proteins displaying shear motions often have a layered architecture: stacking of secondarystructures. The interdomain linker has merely the role of keeping the domains in close proximity.

Domain definition from structural co-ordinates

The importance of domains as structural building blocks and elements of evolution has brought about manyautomated methods for their identification and classification in proteins of known structure. Automatic proceduresfor reliable domain assignment is essential for the generation of the domain databases, especially as the number ofprotein structures is increasing. Although the boundaries of a domain can be determined by visual inspection,construction of an automated method is not straightforward. Problems occur when faced with domains that arediscontinuous or highly associated. The fact that there is no standard definition of what a domain really is hasmeant that domain assignments have varied enormously, with each researcher using a unique set of criteria.

A structural domain is a compact, globular sub-structure with more interactions within it than with the rest of theprotein. Therefore, a structural domain can be determined by two visual characteristics; its compactness and itsextent of isolation. Measures of local compactness in proteins have been used in many of the early methods of

a ■ ■ J64] [65] [66] [67] . . , ,., ., , [26] [68] [69] [70] [71]

domain assignment and in several of the more recent methods.

Considering proteins as small segments

One of the first algorithms used a Ca-Ca distance map together with a hierarchical clustering routine thatconsidered proteins as several small segments, 10 residues in length. The initial segments were clustered one afteranother based on inter-segment distances; segments with the shortest distances were clustered and considered assingle segments thereafter. The stepwise clustering finally included the full protein. Go also exploited the fact thatinter-domain distances are normally larger than intra-domain distances; all possible Ca-Ca distances wererepresented as diagonal plots in which there were distinct patterns for helices, extended strands and combinations ofsecondary structures.

Sowdhamini and Blundell's method

The method by Sowdhamini and Blundell clusters secondary structures in a protein based on their Ca-Ca distancesand identifies domains from the pattern in their dendrograms. As the procedure does not consider the protein as acontinuous chain of amino acids there are no problems in treating discontinuous domains. Specific nodes in thesedendrograms are identified as tertiary structural clusters of the protein, these include both super-secondary structuresand domains. The DOMAK algorithm is used to create the 3Dee domain database. It calculates a 'split value' fromthe number of each type of contact when the protein is divided arbitrarily into two parts. This split value is largewhen the two parts of the structure are distinct.

Method of Wodak and Janin

T721The method of Wodak and Janin was based on the calculated interface areas between two chain segments

repeatedly cleaved at various residue positions. Interface areas were calculated by comparing surface areas of the

cleaved segments with that of the native structure. Potential domain boundaries can be identified at a site where the

interface area was at a minimum.

Other methods have used measures of solvent accessibility to calculate compactness.

PUU algorithm

ri7i

The PUU algorithm incorporates a harmonic model used to approximate inter-domain dynamics. The underlyingphysical concept is that many rigid interactions will occur within each domain and loose interactions will occurbetween domains. This algorithm is used to define domains in the FSSP domain database.

DETECTIVE

Swindells (1995) developed a method, DETECTIVE, for identification of domains in protein structures based on theidea that domains have a hydrophobic interior. Deficiencies were found to occur when hydrophobic cores fromdifferent domains continue through the interface region.

RigidFinder

T751RigidFinder is a novel method for identification of protein rigid blocks (domains and loops) from two different

conformations. Rigid blocks are defined as blocks where all inter residue distances are conserved across

conformations.

PiSQRD

The PiSQRD web-server allows users to optimally subdivide single-chain or multimeric proteins into domains

T771 T7S1 -

that behave approximately as rigid units in the course of protein structural fluctuations . The best rigid-body

decomposition is found using the lowest-energy collective modes of the system. By default the latter are calculatedthrough an elastic network model, or can be uploaded by the user.

Example domains

named after the p-catenin-like Armadillo protein of the fruit fly Drosophila.

Basic Leucine zipper domain (bZIP domain)

is found in many DNA-binding eukaryotic proteins. One part of the domain contains a region that mediatessequence-specific DNA-binding properties and the Leucine zipper that is required for the dimerization of twoDNA-binding regions. The DNA-binding region comprises a number of basic aminoacids such as arginine andlysine

Cadherins function as Ca -dependent cell-cell adhesion proteins. Cadherin domains are extracellular regionswhich mediate cell-to-cell homophilic binding between cadherins on the surface of adjacent cells.

Death effector domain (DED)

allows protein-protein binding by homotypic interactions (DED-DED). Caspase proteases trigger apoptosis viaproteolytic cascades. Pro-Caspase-8 and pro-caspase-9 bind to specific adaptor molecules via DED domainsand this leads to autoactivation of caspases.

EF hand

a helix-turn-helix structural motif found in each structural domain of the signaling protein calmodulin and inthe muscle protein troponin-C.

Immunoglobulin-like domains

[79]are found in proteins of the immunoglobulin superfamily (IgSF). They contain about 70-110 amino acids

and are classified into different categories (IgV, IgCl, IgC2 and Igl) according to their size and function. They

possess a characteristic fold in which two beta sheets form a "sandwich" that is stabilized by interactions

between conserved cysteines and other charged amino acids. They are important for protein-to-protein

interactions in processes of cell adhesion, cell activation, and molecular recognition. These domains are

commonly found in molecules with roles in the immune system.

Phosphotyrosine-binding domain (PTB)

PTB domains usually bind to phosphorylated tyrosine residues. They are often found in signal transductionproteins. PTB-domain binding specificity is determined by residues to the amino-terminal side of thephosphotyrosine. Examples: the PTB domains of both SHC and IRS-1 bind to a NPXpY sequence.PTB-containing proteins such as SHC and IRS-1 are important for insulin responses of human cells.

Pleckstrin homology domain (PH)

PH domains bind phosphoinositides with high affinity. Specificity for PtdIns(3)P, PtdIns(4)P, PtdIns(3,4)P2,PtdIns(4,5)P2, and PtdIns(3,4,5)P3 have all been observed. Given the fact that phosphoinositides aresequestered to various cell membranes (due to their long lipophilic tail) the PH domains usually causesrecruitment of the protein in question to a membrane where the protein can exert a certain function in cellsignalling, cytoskeletal reorganization or membrane trafficking.

Src homology 2 domain (SH2)

SH2 domains are often found in signal transduction proteins. SH2 domains confer binding to phosphorylatedtyrosine (pTyr). Named after the phosphotyrosine binding domain of the src viral oncogene, which is itself atyrosine kinase. See also: SH3 domain.

Zinc finger DNA binding domain (ZnF_GATA)

ZnF_GATA domain-containing proteins are typically transcription factors that usually bind to the DNAsequence [AT] GAT A [AG] of promoters.

The preceding text and figures originate from "Predicting Structural Domains in Proteins" George RA, 2002.

Amino acid

Binding domain

CATH

Conserved domains

Motif domain

Eukaryotic Linear Motif

Protein

Protein structure

Protein structure prediction

Protein structure prediction software

Protein family

Structural biology

Structural Classification of Proteins (SCOP)

Structural domain databases

3Dee[80]

CATH [81]

DALI[82]

SCOP [83]

Pawson Lab - Protein interaction domains

roc]

Nash Lab - Protein interaction domains in Signal TransductionDefinition and assignment of structural domains in proteins

Sequence domain databases

'ro[f

[88]

InterPro

Pfam

[90]

PROSITE [89]

ProDom

[91]

[92]

SMART [91]

NCBI Conserved Domain Database

[93]SUPERFAMILY Library of HMMs representing superfamilies and database of (superfamily and family)

annotations for all completely sequenced organisms

[941• The Protein Families (Pfam) database clan browser provides easy access to information about protein

structural domains. A clan contains two or more Pfam families that have arisen from a single evolutionary origin.

Key papers

Bastian, H. C. (1872). The beginnings of life: being some account of the nature, modes of origin and

transformation of lower organisms. Macmillan and Co., England.

Berman HM et al. (2000). "The Protein Data Bank" [95]. Nucleic Acids Res 28 (1): 235-42.

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Branden, C.-I. and Tooze, J. (1991). Introduction to protein structure. Garland, New York.

Chothia C. (1992). "Proteins. One thousand families for the molecular biologist". Nature 357 (6379): 543—4.

doi:10.1038/357543a0. PMID 1608464.

Das S, Smith TF. (2000). "Identifying nature's protein Lego set". Adv Protein Chem 54: 159—83.

PMID 10829228.

Dietmann S, Park J, Notredame C, Heger A, Lappe M, Holm L. (2001). "A fully automatic evolutionary

classification of protein folds: Dali Domain Dictionary version 3" . Nucleic Acids Res 29 (1): 55—7.

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Dill, Ken A.; Chan, Hue Sun (1997). "From Levinthal to pathways to funnels". Nat Struc Biol 4 (1): 10.

doi:10.1038/nsb0197-10.

Dyson HJ, Sayre JR, Merutka G, Shin HC, Lerner RA, Wright PE. (1992). "Folding of peptide fragments

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Biol226 (3): 819-35. doi:10.1016/0022-2836(92)90634-V. PMID 1507228.

Fersht AR. (1997). "Nucleation mechanisms in protein folding". Curr Opin Struct Biol 7 (1): 3—9.

doi:10.1016/S0959-440X(97)80002-4. PMID 9032066.

George DG, Hunt LT, Barker WC. (1996). "PIR-International Protein Sequence Database". Methods Enzymol

266: 41-59. PMID 8743676.

George, R. A. (2002) "Predicting Structural Domains in Proteins". Thesis, University College London

Go M. (1981). "Correlation of DNA exonic regions with protein structural units in haemoglobin". Nature 291

(5810): 90-2. doi:10.1038/291090a0. PMID 7231530.

Hadley, C and Jones, D.T. (1999). "A systematic comparison of protein structure classifications: SCOP, CATH

and FSSP". Struct Fold Des 7 (9): 1099. doi:10.1016/S0969-2126(99)80177-4.

Hayward S. (1999). "Structural principles governing domain motions in proteins". Proteins 36 (4): 425—35.

doi: 10.1002/(SICI)1097-0134(19990901)36:4<425::AID-PROT6>3.0.CO;2-S (inactive 2010-03-18).

PMID 10450084.

Heringa J, Argos P. (1991). "Side-chain clusters in protein structures and their role in protein folding". J Mol Biol

220 (1): 151-71. doi:10.1016/0022-2836(91)90388-M. PMID 2067014.

Honig B. (1999). "Protein folding: from the levinthal paradox to structure prediction". J Mol Biol 293 (2):

283-93. doi: 10.1006/jmbi. 1999.3006. PMID 10550209.

Kim PS, Baldwin RL. (1990). "Intermediates in the folding reactions of small proteins". Annu Rev Biochem 59

(1): 631-60. doi:10.1146/annurev.bi.59.070190.003215. PMID 2197986.

Larsen TM, Laughlin LT, Holden HM, Rayment I, Reed GH. (1994). "Structure of rabbit muscle pyruvate kinase

complexed with Mn2+, K+, and pyruvate". Biochemistry 33 (20): 6301-9. doi:10.1021/bi00186a033.

PMID 8193145.

Murvai J, Vlahovicek K, Barta E, Cataletto B, Pongor S. (2000). "The SBASE protein domain library, release 7.0:

[971a collection of annotated protein sequence segments" . Nucleic Acids Res 28 (1): 260—2.

doi: 10.1093/nar/28.1.260. PMID 10592241. PMC 102474.

• Murzin AG, Brenner SE, Hubbard T, Chothia C. (1995). "SCOP: a structural classification of proteins databasefor the investigation of sequences and structures". J Mol Biol 247 (4): 536—40.doi:10.1016/S0022-2836(05)80134-2. PMID 7723011.

• Nissen P, Hansen J, Ban N, Moore PB, Steitz TA. (2000). "The structural basis of ribosome activity in peptidebond synthesis". Science 289 (5481): 920-30. doi: 10.1126/science.289.5481.920. PMID 10937990.

• Janin J, Chothia C. (1985). "Domains in proteins: definitions, location, and structural principles". MethodsEnzymol 115: 420-30. PMID 4079796.

• Schultz J, Copley RR, Doerks T, Ponting CP, Bork P. (2000). "SMART: a web-based tool for the study ofgenetically mobile domains" [98]. Nucleic Acids Res 28 (1): 231-4. doi: 10.1093/nar/28.1.231. PMID 10592234.PMC 102444.

• Siddiqui AS, Dengler U, Barton GJ. (2001). "3Dee: a database of protein structural domains". Bioinformatics 17(2): 200-1. doi:10.1093/bioinformatics/17.2.200. PMID 11238081.

• Srinivasarao GY, Yeh LS, Marzec CR, Orcutt BC, Barker WC, Pfeiffer F. (1999). "Database of protein sequencealignments: PIR-ALN" [99]. Nucleic Acids Res 27 (1): 284-5. doi: 10.1093/nar/27.1.284. PMID 9847202.

PMC 148157.

• Tatusov RL et al. (2001). "The COG database: new developments in phylogenetic classification of proteins fromcomplete genomes" [100]. Nucleic Acids Res 29 (1): 22-8. doi:10.1093/nar/29.1.22. PMID 11125040.

PMC 29819.

• Taylor WR, Orengo CA. (1989). "Protein structure alignment". J Mol Biol 208 (1): 1-22.doi: 10.1016/0022-2836(89)90084-3. PMID 2769748.

• Yang AS, Honig B. (1995). "Free energy determinants of secondary structure formation: I. alpha-Helices". J MolBiol 252 (3): 351-65. doi:10.1006/jmbi. 1995.0502. PMID 7563056.

• Yang AS, Honig B. (1995). "Free energy determinants of secondary structure formation: II. Antiparallelbeta-sheets". JMolBiollSl (3): 366-76. doi: 10.1006/jmbi. 1995.0503. PMID 7563057.}

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Nucleic Acids

A nucleic acid is a macromolecule composed of chains of monomeric nucleotides. In biochemistry these moleculescarry genetic information or form structures within cells. The most common nucleic acids are deoxyribonucleic acid(DNA) and ribonucleic acid (RNA). Nucleic acids are universal in living things, as they are found in all cells andviruses. Nucleic acids were first discovered by Friedrich Miescher in 1871.

Artificial nucleic acids include peptide nucleic acid (PNA), Morpholino and locked nucleic acid (LNA), as well asglycol nucleic acid (GNA) and threose nucleic acid (TNA). Each of these is distinguished from naturally-occurringDNA or RNA by changes to the backbone of the molecule.

Chemical structure

The term "nucleic acid" is the generic name for a family of biopolymers, named for their role in the cell nucleus. Itwas later discovered that some nucleic acids are exclusive of the mitochondrion (e.g. Mitochondrial DNA). Themonomers from which nucleic acids are constructed are called nucleotides. Nucleic acids are linear, unbranchedpolymers of nucleotides.

Each nucleotide consists of three components: a nitrogenous heterocyclic base, which is either a purine or apyrimidine; a pentose sugar; and a phosphate group. Nucleic acid types differ in the structure of the sugar in theirnucleotides - DNA contains 2-deoxyribose while RNA contains ribose (where the only difference is the presence of ahydroxyl group). Also, the nitrogenous bases found in the two nucleic acid types are different: adenine, cytosine, andguanine are found in both RNA and DNA, while thymine only occurs in DNA and uracil only occurs in RNA. Otherrare nucleic acid bases can occur, for example inosine in strands of mature transfer RNA.

Nucleic acids are usually either single-stranded or double-stranded, though structures with three or more strands canform. A double-stranded nucleic acid consists of two single-stranded nucleic acids held together by hydrogen bonds,such as in the DNA double helix. In contrast, RNA is usually single-stranded, but any given strand may fold backupon itself to form secondary structure as in tRNA and rRNA. Within cells, DNA is usually double-stranded, thoughsome viruses have single-stranded DNA as their genome. Retroviruses have single-stranded RNA as their genome.

The sugars and phosphates in nucleic acids are connected to each other in an alternating chain, linked by sharedoxygens, forming a phosphodiester bond. In conventional nomenclature, the carbons to which the phosphate groupsattach are the 3' end and the 5' end carbons of the sugar. This gives nucleic acids polarity. The bases extend from aglycosidic linkage to the 1' carbon of the pentose sugar ring. Bases are joined through N-l of pyrimidines and N-9 ofpurines to 1' carbon of ribose through N-p glycosyl bond.

Types of nucleic acidsRibonucleic acid

Ribonucleic acid, or RNA, is a nucleic acid polymer consisting of nucleotide monomers, which plays severalimportant roles in the processes of transcribing genetic information from deoxyribonucleic acid (DNA) into proteins.RNA acts as a messenger between DNA and the protein synthesis complexes known as ribosomes, forms vitalportions of ribosomes, and serves as an essential carrier molecule for amino acids to be used in protein synthesis.The three types of RNA include tRNA (transfer), mRNA (messenger) and rRNA (ribosomal).

Deoxyribonucleic acid

Deoxyribonucleic acid is a nucleic acid that contains the genetic instructions used in the development andfunctioning of all known living organisms. The main role of DNA molecules is the long-term storage of informationand DNA is often compared to a set of blueprints, since it contains the instructions needed to construct othercomponents of cells, such as proteins and RNA molecules. The DNA segments that carry this genetic informationare called genes, but other DNA sequences have structural purposes, or are involved in regulating the use of thisgenetic information.

DNA is made of four types of nucleotides, containing different nucleobases: the pyrimidines cytosine and thymine,and the purines guanine and adenine. The nucleotides are attached to each other in a chain by bonds between theirsugar and phosphate groups, forming a sugar-phosphate backbone. Two of these chains are held together byhydrogen bonding between complementary bases; the chains coil around each other, forming the DNA double helix.

Nucleic acid componentsNucleobases

Nucleobases are heterocyclic aromatic organic compounds containing nitrogen atoms. Nucleobases are the parts ofRNA and DNA involved in base pairing. Cytosine, guanine, adenine, thymine are found predominantly in DNA,while in RNA uracil replaces thymine. These are abbreviated as C, G, A, T, U, respectively.

Nucleobases are complementary, and when forming base pairs, must always join accordingly: cytosine-guanine,adenine-thymine (adenine-uracil when RNA). The strength of the interaction between cytosine and guanine isstronger than between adenine and thymine because the former pair has three hydrogen bonds joining them while thelatter pair have only two. Thus, the higher the GC content of double-stranded DNA, the more stable the moleculeand the higher the melting temperature.

Two main nucleobase classes exist, named for the molecule which forms their skeleton. These are the double-ringedpurines and single-ringed pyrimidines. Adenine and guanine are purines (abbreviated as R), while cytosine, thymine,and uracil are all pyrimidines (abbreviated as Y).

Hypoxanthine and xanthine are mutant forms of adenine and guanine, respectively, created through mutagenpresence, through deamination (replacement of the amine-group with a hydroxyl-group). These are abbreviated HXandX

Nucleosides

Nucleosides are glycosylamines made by attaching a nucleobase (often referred to simply as bases) to a ribose ordeoxyribose (sugar) ring. In short, a nucleoside is a base linked to sugar. The names derive from the nucleobasenames. The nucleosides commonly occurring in DNA and RNA include cytidine, uridine, adenosine, guanosine andthymidine. When a phosphate is added to a nucleoside (by phosphorylated by a specific kinase enzyme), a nucleotideis produced. Nucleoside analogues, such as acyclovir, are sometimes used as antiviral agents.

Nucleic Acids 191

Nucleotides and deoxynucleotides

A nucleotide consists of a nucleoside and one phosphate group. Nucleotides are the monomers of RNA and DNA, aswell as forming the structural units of several important cofactors - CoA, flavin adenine dinucleotide, flavinmononucleotide, adenosine triphosphate and nicotinamide adenine dinucleotide phosphate. In the cell nucleotidesplay important roles in metabolism, and signaling.

Nucleotides are named after the nucleoside on which they are based, in conjunction with the number of phosphatesthey contain, for example:

• Adenine bonded to ribose forms the nucleoside adenosine.

• Adenosine bonded to a phosphate forms adenosine monophosphate.

• As phosphates are added, adenosine diphosphate and adenosine triphosphate are formed, in sequence.

• Nucleic acid methods

• Nucleic acid simulations

References

• Wolfram Saenger, Principles of Nucleic Acid Structure, 1984, Springer-Verlag New York Inc.

• Keith Roberts, Martin Raff, Bruce Alberts, Peter Walter, Julian Lewis and Alexander Johnson, Molecular Biologyof the Cell 4th Edition, Routledge, March, 2002, hardcover, 1616 pages, 7.6 pounds, ISBN 0-8153-3218-1

• Interview with Aaron Klug, Nobel Laureate for structural elucidation of biologically important nucleic-acidprotein complexes provided by the Vega Science Trust.

• Nucleic Acid Research Journal

References

192

DNA

Deoxyribonucleic acid ( 43 /di'Dksl'ralboUnu'klilk 'aesld/Wikipedia:Media helpFile:en-us-Deoxyribonucleic_acid.ogg)

(DNA) is a nucleic acid that contains the genetic instructions usedin the development and functioning of all known living organismsand some viruses. The main role of DNA molecules is thelong-term storage of information. DNA is often compared to a setof blueprints or a recipe, or a code, since it contains the instructionsneeded to construct other components of cells, such as proteins andRNA molecules. The DNA segments that carry this geneticinformation are called genes, but other DNA sequences havestructural purposes, or are involved in regulating the use of thisgenetic information.

Chemically, DNA consists of two long polymers of simple unitscalled nucleotides, with backbones made of sugars and phosphategroups joined by ester bonds. These two strands run in oppositedirections to each other and are therefore anti-parallel. Attached toeach sugar is one of four types of molecules called bases. It is thesequence of these four bases along the backbone that encodesinformation. This information is read using the genetic code, whichspecifies the sequence of the amino acids within proteins. The codeis read by copying stretches of DNA into the related nucleic acidRNA, in a process called transcription.

The structure of part of a DNA double helix

Within cells, DNA is organized into long structures called chromosomes. These chromosomes are duplicated beforecells divide, in a process called DNA replication. Eukaryotic organisms (animals, plants, fungi, and protists) storemost of their DNA inside the cell nucleus and some of their DNA in organelles, such as mitochondria orchloroplasts. In contrast, prokaryotes (bacteria and archaea) store their DNA only in the cytoplasm. Within thechromosomes, chromatin proteins such as histones compact and organize DNA. These compact structures guide theinteractions between DNA and other proteins, helping control which parts of the DNA are transcribed.

193

Properties

DNA is a long polymer made fromrepeating units called nucleotides.

[4]

The DNA chain

is 22 to26 Angstroms wide (2.2 to

2.6 nanometres), and one nucleotide unitis 3.3 A (0.33 nm) long.[5] Although eachindividual repeating unit is very small,DNA polymers can be very largemolecules containing millions ofnucleotides. For instance, the largesthuman chromosome, chromosomenumber 1, is approximately 220 million

Thymine

3' end

OH

base pairs long

[6]

backbone

V-

Cytosine /*"°

Phosphate-deoxyribose"*)^

In living organisms, DNA does notusually exist as a single molecule, but

instead as a pair of molecules that are

T71 rsiheld tightly together. These two

long strands entwine like vines, in the

shape of a double helix. The nucleotide

repeats contain both the segment of the

backbone of the molecule, which holds

the chain together, and a base, which

interacts with the other DNA strand in

the helix. A base linked to a sugar is

called a nucleoside and a base linked to a sugar and one or more phosphate groups is called a nucleotide. If multiple

191nucleotides are linked together, as in DNA, this polymer is called a polynucleotide.

The backbone of the DNA strand is made from alternating phosphate and sugar residues. The sugar in DNA is2-deoxyribose, which is a pentose (five-carbon) sugar. The sugars are joined together by phosphate groups that formphosphodiester bonds between the third and fifth carbon atoms of adjacent sugar rings. These asymmetric bondsmean a strand of DNA has a direction. In a double helix the direction of the nucleotides in one strand is opposite totheir direction in the other strand: the strands are antiparallel. The asymmetric ends of DNA strands are called the 5'(five prime) and 3' (three prime) ends, with the 5' end having a terminal phosphate group and the 3' end a terminalhydroxyl group. One major difference between DNA and RNA is the sugar, with the 2-deoxyribose in DNA being

Guanine 5end

Chemical structure of DNA. Hydrogen bonds shown as dotted lines.

replaced by the alternative pentose sugar ribose in RNA

[8]

DNA

194

The DNA double helix is stabilized by hydrogen bonds betweenthe bases attached to the two strands. The four bases found in DNAare adenine (abbreviated A), cytosine (C), guanine (G) and thymine(T). These four bases are attached to the sugar/phosphate to formthe complete nucleotide, as shown for adenosine monophosphate.

These bases are classified into two types; adenine and guanine arefused five- and six-membered heterocyclic compounds calledpurines, while cytosine and thymine are six-membered rings called

ro]

pyrimidines. A fifth pyrimidine base, called uracil (U), usuallytakes the place of thymine in RNA and differs from thymine bylacking a methyl group on its ring. Uracil is not usually found inDNA, occurring only as a breakdown product of cytosine. Inaddition to RNA and DNA, a large number of artificial nucleic acidanalogues have also been created to study the proprieties of nucleicacids, or for use in biotechnology.

Grooves

Twin helical strands form the DNA backbone. Another doublehelix may be found by tracing the spaces, or grooves, between thestrands. These voids are adjacent to the base pairs and may providea binding site. As the strands are not directly opposite each other,the grooves are unequally sized. One groove, the major groove, is22 A wide and the other, the minor groove, is 12 A wide. Thenarrowness of the minor groove means that the edges of the basesare more accessible in the major groove. As a result, proteins liketranscription factors that can bind to specific sequences in double-stranded DNA usually make contacts to the sides

ri4i

of the bases exposed in the major groove. This situation varies in unusual conformations of DNA within the cell(see below), but the major and minor grooves are always named to reflect the differences in size that would be seenif the DNA is twisted back into the ordinary B form.

A section of DNA. The bases lie horizontally between

the two spiraling strands. Animated version at

File:DNA orbit animated.gif.

Base pairing

Each type of base on one strand forms a bond with just one type of base on the other strand. This is calledcomplementary base pairing. Here, purines form hydrogen bonds to pyrimidines, with A bonding only to T, and Cbonding only to G. This arrangement of two nucleotides binding together across the double helix is called a basepair. As hydrogen bonds are not covalent, they can be broken and rejoined relatively easily. The two strands of DNAin a double helix can therefore be pulled apart like a zipper, either by a mechanical force or high temperature. Asa result of this complementarity, all the information in the double-stranded sequence of a DNA helix is duplicated oneach strand, which is vital in DNA replication. Indeed, this reversible and specific interaction betweencomplementary base pairs is critical for all the functions of DNA in living organisms.

DNA 195

H,0

H 0,

nH H H

w v :» ^ -> >

-H-- i) L N ' h

r\

Guanine H Cytosine

Top, a GC base pair with three hydrogen bonds. Bottom, an AT base pair with two hydrogen bonds. Non-covalent

hydrogen bonds between the pairs are shown as dashed lines.

The two types of base pairs form different numbers of hydrogen bonds, AT forming two hydrogen bonds, and GCforming three hydrogen bonds (see figures, left). DNA with high GC-content is more stable than DNA with lowGC-content, but contrary to popular belief, this is not due to the extra hydrogen bond of a GC base pair but rather thecontribution of stacking interactions (hydrogen bonding merely provides specificity of the pairing, not stability).As a result, it is both the percentage of GC base pairs and the overall length of a DNA double helix that determinethe strength of the association between the two strands of DNA. Long DNA helices with a high GC content have

ri7i

stronger-interacting strands, while short helices with high AT content have weaker-interacting strands. In biology,parts of the DNA double helix that need to separate easily, such as the TATAAT Pribnow box in some promoters,tend to have a high AT content, making the strands easier to pull apart. In the laboratory, the strength of thisinteraction can be measured by finding the temperature required to break the hydrogen bonds, their meltingtemperature (also called T value). When all the base pairs in a DNA double helix melt, the strands separate andexist in solution as two entirely independent molecules. These single-stranded DNA molecules have no single

ri9i

common shape, but some conformations are more stable than others.

Sense and antisense

A DNA sequence is called "sense" if its sequence is the same as that of a messenger RNA copy that is translated intoprotein. The sequence on the opposite strand is called the "antisense" sequence. Both sense and antisensesequences can exist on different parts of the same strand of DNA (i.e. both strands contain both sense and antisensesequences). In both prokaryotes and eukaryotes, antisense RNA sequences are produced, but the functions of theseRNAs are not entirely clear. One proposal is that antisense RNAs are involved in regulating gene expression

To?!

through RNA-RNA base pairing.

A few DNA sequences in prokaryotes and eukaryotes, and more in plasmids and viruses, blur the distinction betweensense and antisense strands by having overlapping genes. In these cases, some DNA sequences do double duty,

encoding one protein when read along one strand, and a second protein when read in the opposite direction along the

T241other strand. In bacteria, this overlap may be involved in the regulation of gene transcription, while in viruses,

[25]overlapping genes increase the amount of information that can be encoded within the small viral genome.

Supercoiling

DNA can be twisted like a rope in a process called DNA supercoiling. With DNA in its "relaxed" state, a strand

usually circles the axis of the double helix once every 10.4 base pairs, but if the DNA is twisted the strands become

more tightly or more loosely wound. If the DNA is twisted in the direction of the helix, this is positive

supercoiling, and the bases are held more tightly together. If they are twisted in the opposite direction, this is

negative supercoiling, and the bases come apart more easily. In nature, most DNA has slight negative supercoiling

[271that is introduced by enzymes called topoisomerases. These enzymes are also needed to relieve the twisting

196

stresses introduced into DNA strands during processes such as transcription and DNA replication

1281

Alternate DNA structures

DNA exists in many possible conformationsthat include A-DNA, B-DNA, and Z-DNAforms, although, only B-DNA and Z-DNAhave been directly observed in functionalorganisms. The conformation that DNAadopts depends on the hydration level, DNAsequence, the amount and direction ofsupercoiling, chemical modifications of thebases, the type and concentration of metalions, as well as the presence of polyamines in

solution

[29]

The first published reports of A-DNA X-ray

diffraction patterns— and also B-DNA used analyses based on Patterson transforms that provided only a limitedamount of structural information for oriented fibers of DNA. An alternate analysis was then proposed by

Wilkins et al, in 1953, for the in vivo B-DNA X-ray diffraction/scattering patterns of highly hydrated DNA fibers in

F321

terms of squares of Bessel functions. In the same journal, Watson and Crick presented their molecular modeling

T71analysis of the DNA X-ray diffraction patterns to suggest that the structure was a double-helix.

T331Although the "B-DNA form' is most common under the conditions found in cells, it is not a well-defined

T341conformation but a family of related DNA conformations that occur at the high hydration levels present in living

cells. Their corresponding X-ray diffraction and scattering patterns are characteristic of molecular paracrystals with a

significant degree of disorder.

Compared to B-DNA, the A-DNA form is a wider right-handed spiral, with a shallow, wide minor groove and anarrower, deeper major groove. The A form occurs under non-physiological conditions in partially dehydratedsamples of DNA, while in the cell it may be produced in hybrid pairings of DNA and RNA strands, as well as in

T371 T3R1

enzyme-DNA complexes. Segments of DNA where the bases have been chemically modified by methylation

may undergo a larger change in conformation and adopt the Z form. Here, the strands turn about the helical axis in a

[391left-handed spiral, the opposite of the more common B form. These unusual structures can be recognized by

specific Z-DNA binding proteins and may be involved in the regulation of transcription

[40]

197

At the ends of the linear chromosomes are

specialized regions of DNA called telomeres. The

main function of these regions is to allow the cell to

replicate chromosome ends using the enzyme

telomerase, as the enzymes that normally replicate

DNA cannot copy the extreme 3' ends of

chromosomes. These specialized chromosome

caps also help protect the DNA ends, and stop the

DNA repair systems in the cell from treating them as

[43]damage to be corrected. In human cells, telomeres

are usually lengths of single-stranded DNA

containing several thousand repeats of a simple

TTAGGG sequence.

[44]

DNA quadruplex formed by telomere repeats. The looped conformation

[41]of the DNA backbone is very different from the typical DNA helix.

These guanine-rich sequences may stabilizechromosome ends by forming structures of stackedsets of four-base units, rather than the usual base

pairs found in other DNA molecules. Here, four guanine bases form a flat plate and these flat four-base units then

1451stack on top of each other, to form a stable G-quadruplex structure. These structures are stabilized by hydrogen

bonding between the edges of the bases and chelation of a metal ion in the centre of each four-base unit. Other

structures can also be formed, with the central set of four bases coming from either a single strand folded around the

bases, or several different parallel strands, each contributing one base to the central structure.

In addition to these stacked structures, telomeres also form large loop structures called telomere loops, or T-loops.Here, the single-stranded DNA curls around in a long circle stabilized by telomere-binding proteins. At the veryend of the T-loop, the single-stranded telomere DNA is held onto a region of double-stranded DNA by the telomerestrand disrupting the double-helical DNA and base pairing to one of the two strands. This triple-stranded structure iscalled a displacement loop or D-loop

[45]

<

Single branch Multiple branches

Branched DNA can form networks containing multiple branches.

Branched DNA

In DNA fraying occurs when non-complementary regions exist at the end of an otherwise complementarydouble-strand of DNA. However, branched DNA can occur if a third strand of DNA is introduced and containsadjoining regions able to hybridize with the frayed regions of the pre-existing double-strand. Although the simplestexample of branched DNA involves only three strands of DNA, complexes involving additional strands and multiplebranches are also possible. Branched DNA can be used in nanotechnology to construct geometric shapes, see thesection on uses in technology below.

DNA

198

Chemical modifications

NH2N

H

cytosine 5-methylcytosine

thymine

Structure of cytosine with and without the 5-methyl group. Deamination converts 5-methylcytosine into thymine.

Base modifications

The expression of genes is influenced by how the DNA is packaged in chromosomes, in a structure called chromatin.Base modifications can be involved in packaging, with regions that have low or no gene expression usuallycontaining high levels of methylation of cytosine bases. For example, cytosine methylation, produces5-methylcytosine, which is important for X-chromosome inactivation. The average level of methylation variesbetween organisms - the worm Caenorhabditis elegans lacks cytosine methylation, while vertebrates have higherlevels, with up to 1% of their DNA containing 5-methylcytosine. Despite the importance of 5-methylcytosine, itcan deaminate to leave a thymine base, methylated cytosines are therefore particularly prone to mutations. Other

T52]

base modifications include adenine methylation in bacteria, the presence of 5-hydroxymethylcytosine in the brain,

and the glycosylation of uracil to produce the "J-base" in kinetoplastids

[53] [54]

Damage

DNA can be damaged by many sorts of mutagens,which change the DNA sequence. Mutagens includeoxidizing agents, alkylating agents and alsohigh-energy electromagnetic radiation such asultraviolet light and X-rays. The type of DNA damageproduced depends on the type of mutagen. Forexample, UV light can damage DNA by producingthymine dimers, which are cross-links betweenpyrimidine bases. On the other hand, oxidants suchas free radicals or hydrogen peroxide produce multipleforms of damage, including base modifications,

[57]

particularly of guanosine, and double-strand breaks.A typical human cell contains about 150,000 bases that

rcoi

have suffered oxidative damage. Of these oxidativelesions, the most dangerous are double-strand breaks,as these are difficult to repair and can produce pointmutations, insertions and deletions from the DNA

sequence, as well as chromosomal translocations

[59]

Many mutagens fit into the space between two adjacentbase pairs, this is called intercalating. Mostintercalators are aromatic and planar molecules, andinclude Ethidium bromide, daunomycin, and

A covalent adduct between benzo[a]pyrene, the major mutagen intobacco smoke, and DNA

DNA 199

doxorubicin. In order for an intercalator to fit between base pairs, the bases must separate, distorting the DNAstrands by unwinding of the double helix. This inhibits both transcription and DNA replication, causing toxicity andmutations. As a result, DNA intercalators are often carcinogens, and Benzo[a]pyrene diol epoxide, acridines,aflatoxin and ethidium bromide are well-known examples. Nevertheless, due to their ability to inhibit

DNA transcription and replication, other similar toxins are also used in chemotherapy to inhibit rapidly growingcancer cells.

Biological functions

DNA usually occurs as linear chromosomes in eukaryotes, and circular chromosomes in prokaryotes. The set ofchromosomes in a cell makes up its genome; the human genome has approximately 3 billion base pairs of DNAarranged into 46 chromosomes. The information carried by DNA is held in the sequence of pieces of DNA calledgenes. Transmission of genetic information in genes is achieved via complementary base pairing. For example, intranscription, when a cell uses the information in a gene, the DNA sequence is copied into a complementary RNAsequence through the attraction between the DNA and the correct RNA nucleotides. Usually, this RNA copy is thenused to make a matching protein sequence in a process called translation which depends on the same interactionbetween RNA nucleotides. Alternatively, a cell may simply copy its genetic information in a process called DNAreplication. The details of these functions are covered in other articles; here we focus on the interactions betweenDNA and other molecules that mediate the function of the genome.

Genes and genomes

Genomic DNA is located in the cell nucleus of eukaryotes, as well as small amounts in mitochondria andchloroplasts. In prokaryotes, the DNA is held within an irregularly shaped body in the cytoplasm called thenucleoid. The genetic information in a genome is held within genes, and the complete set of this information in anorganism is called its genotype. A gene is a unit of heredity and is a region of DNA that influences a particularcharacteristic in an organism. Genes contain an open reading frame that can be transcribed, as well as regulatorysequences such as promoters and enhancers, which control the transcription of the open reading frame.

In many species, only a small fraction of the total sequence of the genome encodes protein. For example, only about1.5% of the human genome consists of protein-coding exons, with over 50% of human DNA consisting ofnon-coding repetitive sequences. The reasons for the presence of so much non-coding DNA in eukaryoticgenomes and the extraordinary differences in genome size, or C-value, among species represent a long-standingpuzzle known as the "C-value enigma." However, DNA sequences that do not code protein may still encodefunctional non-coding RNA molecules, which are involved in the regulation of gene expression.

200

T7 RNA polymerase (blue) producing a mRNA (green) from a DNA template(orange).

Some non-coding DNA sequences playstructural roles in chromosomes. Telomeresand centromeres typically contain fewgenes, but are important for the function andstability of chromosomes. An

abundant form of non-coding DNA inhumans are pseudogenes, which are copiesof genes that have been disabled bymutation. These sequences are usuallyjust molecular fossils, although they canoccasionally serve as raw genetic materialfor the creation of new genes through theprocess of gene duplication anddivergence

[72]

Transcription and translation

A gene is a sequence of DNA that contains genetic information and can influence the phenotype of an organism.Within a gene, the sequence of bases along a DNA strand defines a messenger RNA sequence, which then definesone or more protein sequences. The relationship between the nucleotide sequences of genes and the amino-acidsequences of proteins is determined by the rules of translation, known collectively as the genetic code. The geneticcode consists of three-letter 'words' called codons formed from a sequence of three nucleotides (e.g. ACT, CAG,TTT).

In transcription, the codons of a gene are copied into messenger RNA by RNA polymerase. This RNA copy is thendecoded by a ribosome that reads the RNA sequence by base-pairing the messenger RNA to transfer RNA, whichcarries amino acids. Since there are 4 bases in 3-letter combinations, there are 64 possible codons ( ^3combinations). These encode the twenty standard amino acids, giving most amino acids more than one possiblecodon. There are also three 'stop' or 'nonsense' codons signifying the end of the coding region; these are the TAA,TGA and TAG codons.

Replication

Cell division is essential for anorganism to grow, but when a celldivides it must replicate the DNA in itsgenome so that the two daughter cellshave the same genetic information astheir parent. The double-strandedstructure of DNA provides a simplemechanism for DNA replication. Here,the two strands are separated and theneach strand's complementary DNAsequence is recreated by an enzymecalled DNA polymerase. This enzymemakes the complementary strand by

DNA ligaseDNA Polymerase (Pola)

Topoisomerase

DNA Polymerase (PolS) '

Helitase'Single strand.Binding proteins

DNA replication. The double helix is unwound by a helicase and topoisomerase. Next,

one DNA polymerase produces the leading strand copy. Another DNA polymerase binds

to the lagging strand. This enzyme makes discontinuous segments (called Okazaki

fragments) before DNA ligase joins them together.

finding the correct base through complementary base pairing, and bonding it onto the original strand. As DNApolymerases can only extend a DNA strand in a 5' to 3' direction, different mechanisms are used to copy the

201

T731antiparallel strands of the double helix. In this way, the base on the old strand dictates which base appears on the

new strand, and the cell ends up with a perfect copy of its DNA.

Interactions with proteins

All the functions of DNA depend on interactions with proteins. These protein interactions can be non-specific, or theprotein can bind specifically to a single DNA sequence. Enzymes can also bind to DNA and of these, thepolymerases that copy the DNA base sequence in transcription and DNA replication are particularly important.

DNA-binding proteins

Interaction of DNA with histones (shown in white, top). These proteins' basic amino acids (below left, blue) bind tothe acidic phosphate groups on DNA (below right, red).

Structural proteins that bind DNA are well-understood examples of non-specific DNA-protein interactions. Withinchromosomes, DNA is held in complexes with structural proteins. These proteins organize the DNA into a compactstructure called chromatin. In eukaryotes this structure involves DNA binding to a complex of small basic proteins

[741 [751

called histones, while in prokaryotes multiple types of proteins are involved. The histones form a disk-shaped

complex called a nucleosome, which contains two complete turns of double-stranded DNA wrapped around itssurface. These non-specific interactions are formed through basic residues in the histones making ionic bonds to theacidic sugar-phosphate backbone of the DNA, and are therefore largely independent of the base sequence

[76][77]

Chemical modifications of these basic amino acid residues include methylation, phosphorylation and acetylation.These chemical changes alter the strength of the interaction between the DNA and the histones, making the DNA

[7R]

more or less accessible to transcription factors and changing the rate of transcription. Other non-specific

DNA-binding proteins in chromatin include the high-mobility group proteins, which bind to bent or distorted

[79]DNA. These proteins are important in bending arrays of nucleosomes and arranging them into the larger

structures that make up chromosomes.

A distinct group of DNA-binding proteins are the DNA-binding proteins that specifically bind single-stranded DNA.In humans, replication protein A is the best-understood member of this family and is used in processes where the

[SI]

double helix is separated, including DNA replication, recombination and DNA repair. These binding proteinsseem to stabilize single-stranded DNA and protect it from forming stem-loops or being degraded by nucleases.

DNA

202

In contrast, other proteins have evolved to bind to particular DNAsequences. The most intensively studied of these are the varioustranscription factors, which are proteins that regulate transcription.Each transcription factor binds to one particular set of DNAsequences and activates or inhibits the transcription of genes that havethese sequences close to their promoters. The transcription factors dothis in two ways. Firstly, they can bind the RNA polymeraseresponsible for transcription, either directly or through other mediatorproteins; this locates the polymerase at the promoter and allows it tobegin transcription. Alternatively, transcription factors can bindenzymes that modify the histones at the promoter; this will change theaccessibility of the DNA template to the polymerase

[84]

As these DNA targets can occur throughout an organism's genome,changes in the activity of one type of transcription factor can affect

roc]

thousands of genes. Consequently, these proteins are often the

targets of the signal transduction processes that control responses to

environmental changes or cellular differentiation and development.

The specificity of these transcription factors' interactions with DNA

come from the proteins making multiple contacts to the edges of the

DNA bases, allowing them to "read" the DNA sequence. Most of these base-interactions are made in the major

groove, where the bases are most accessible.

The lambda repressor helix-turn-helix transcription

T821factor bound to its DNA target

The restriction enzyme EcoRV (green) in a complex with its substrate

DNA[87]

DNA-modifying enzymes

Nucleases and ligases

Nucleases are enzymes that cut DNA strands bycatalyzing the hydrolysis of the phosphodiester bonds.Nucleases that hydrolyse nucleotides from the ends ofDNA strands are called exonucleases, whileendonucleases cut within strands. The most frequentlyused nucleases in molecular biology are the restrictionendonucleases, which cut DNA at specific sequences.For instance, the EcoRV enzyme shown to the leftrecognizes the 6-base sequence 5'-GATIATC-3' andmakes a cut at the vertical line. In nature, theseenzymes protect bacteria against phage infection by

[88]

In

digesting the phage DNA when it enters the bacterial cell, acting as part of the restriction modification systemtechnology, these sequence-specific nucleases are used in molecular cloning and DNA fingerprinting.

Enzymes called DNA ligases can rejoin cut or broken DNA strands. Ligases are particularly important in laggingstrand DNA replication, as they join together the short segments of DNA produced at the replication fork into acomplete copy of the DNA template. They are also used in DNA repair and genetic recombination.

DNA 203

Topoisomerases and helicases

Topoisomerases are enzymes with both nuclease and ligase activity. These proteins change the amount of

supercoiling in DNA. Some of these enzymes work by cutting the DNA helix and allowing one section to rotate,

T271thereby reducing its level of supercoiling; the enzyme then seals the DNA break. Other types of these enzymes

are capable of cutting one DNA helix and then passing a second strand of DNA through this break, before rejoining

the helix. Topoisomerases are required for many processes involving DNA, such as DNA replication and

• ♦■ [28]transcription.

Helicases are proteins that are a type of molecular motor. They use the chemical energy in nucleoside triphosphates,predominantly ATP, to break hydrogen bonds between bases and unwind the DNA double helix into singlestrands. These enzymes are essential for most processes where enzymes need to access the DNA bases.

Polymerases

Polymerases are enzymes that synthesize polynucleotide chains from nucleoside triphosphates. The sequence of theirproducts are copies of existing polynucleotide chains - which are called templates. These enzymes function byadding nucleotides onto the 3' hydroxyl group of the previous nucleotide in a DNA strand. Consequently, allpolymerases work in a 5' to 3' direction. In the active site of these enzymes, the incoming nucleoside triphosphatebase-pairs to the template: this allows polymerases to accurately synthesize the complementary strand of theirtemplate. Polymerases are classified according to the type of template that they use.

In DNA replication, a DNA-dependent DNA polymerase makes a copy of a DNA sequence. Accuracy is vital in this

process, so many of these polymerases have a proofreading activity. Here, the polymerase recognizes the occasional

mistakes in the synthesis reaction by the lack of base pairing between the mismatched nucleotides. If a mismatch is

detected, a 3' to 5' exonuclease activity is activated and the incorrect base removed. In most organisms DNA

polymerases function in a large complex called the replisome that contains multiple accessory subunits, such as the

[941DNA clamp or helicases.

RNA-dependent DNA polymerases are a specialized class of polymerases that copy the sequence of an RNA strandinto DNA. They include reverse transcriptase, which is a viral enzyme involved in the infection of cells by

[42] [95]

retroviruses, and telomerase, which is required for the replication of telomeres. Telomerase is an unusual

T431polymerase because it contains its own RNA template as part of its structure.

Transcription is carried out by a DNA-dependent RNA polymerase that copies the sequence of a DNA strand intoRNA. To begin transcribing a gene, the RNA polymerase binds to a sequence of DNA called a promoter andseparates the DNA strands. It then copies the gene sequence into a messenger RNA transcript until it reaches aregion of DNA called the terminator, where it halts and detaches from the DNA. As with human DNA-dependentDNA polymerases, RNA polymerase II, the enzyme that transcribes most of the genes in the human genome,operates as part of a large protein complex with multiple regulatory and accessory subunits.

DNA

204

Genetic recombination

Structure of the Holliday junction intermediate in genetic recombination. The four separate DNA strands are

[97]

coloured red, blue, green and yellow

M

-HHI}-

-[U—H}

C2

Recombination involves the breakage and rejoining of two

chromosomes (M and F) to produce two re-arranged chromosomes

(CI and C2).

A DNA helix usually does not interact with othersegments of DNA, and in human cells the differentchromosomes even occupy separate areas in thenucleus called "chromosome territories". This

physical separation of different chromosomes isimportant for the ability of DNA to function as a stablerepository for information, as one of the few timeschromosomes interact is during chromosomal crossoverwhen they recombine. Chromosomal crossover is whentwo DNA helices break, swap a section and then rejoin.

Recombination allows chromosomes to exchangegenetic information and produces new combinations ofgenes, which increases the efficiency of naturalselection and can be important in the rapid evolution of

[99]

new proteins. Genetic recombination can also be involved in DNA repair, particularly in the cell's response to

double-strand breaks

[100]

The most common form of chromosomal crossover is homologous recombination, where the two chromosomesinvolved share very similar sequences. Non-homologous recombination can be damaging to cells, as it can producechromosomal translocations and genetic abnormalities. The recombination reaction is catalyzed by enzymes knownas recombinases, such as RAD51. The first step in recombination is a double-stranded break either caused by anendonuclease or damage to the DNA. A series of steps catalyzed in part by the recombinase then leads to joiningof the two helices by at least one Holliday junction, in which a segment of a single strand in each helix is annealed tothe complementary strand in the other helix. The Holliday junction is a tetrahedral junction structure that can bemoved along the pair of chromosomes, swapping one strand for another. The recombination reaction is then haltedby cleavage of the junction and re-ligation of the released DNA.

DNA 205

Evolution

DNA contains the genetic information that allows all modern living things to function, grow and reproduce.However, it is unclear how long in the 4-billion-year history of life DNA has performed this function, as it has been

[92] [1041

proposed that the earliest forms of life may have used RNA as their genetic material. RNA may have acted

as the central part of early cell metabolism as it can both transmit genetic information and carry out catalysis as partof ribozymes. This ancient RNA world where nucleic acid would have been used for both catalysis and geneticsmay have influenced the evolution of the current genetic code based on four nucleotide bases. This would occursince the number of different bases in such an organism is a trade-off between a small number of bases increasingreplication accuracy and a large number of bases increasing the catalytic efficiency of ribozymes.

Unfortunately, there is no direct evidence of ancient genetic systems, as recovery of DNA from most fossils isimpossible. This is because DNA will survive in the environment for less than one million years and slowly degradesinto short fragments in solution. Claims for older DNA have been made, most notably a report of the isolation ofa viable bacterium from a salt crystal 250 million years old, but these claims are controversial.

Uses in technologyGenetic engineering

Methods have been developed to purify DNA from organisms, such as phenol-chloroform extraction and manipulateit in the laboratory, such as restriction digests and the polymerase chain reaction. Modern biology and biochemistrymake intensive use of these techniques in recombinant DNA technology. Recombinant DNA is a man-made DNAsequence that has been assembled from other DNA sequences. They can be transformed into organisms in the formof plasmids or in the appropriate format, by using a viral vector. The genetically modified organisms producedcan be used to produce products such as recombinant proteins, used in medical research, or be grown in

. .. [113] [114]

agriculture.

Forensics

Forensic scientists can use DNA in blood, semen, skin, saliva or hair found at a crime scene to identify a matchingDNA of an individual, such as a perpetrator. This process is called genetic fingerprinting, or more accurately, DNAprofiling. In DNA profiling, the lengths of variable sections of repetitive DNA, such as short tandem repeats andminisatellites, are compared between people. This method is usually an extremely reliable technique for identifying amatching DNA. However, identification can be complicated if the scene is contaminated with DNA from severalpeople. DNA profiling was developed in 1984 by British geneticist Sir Alec Jeffreys, and first used in

forensic science to convict Colin Pitchfork in the 1988 Enderby murders case.

People convicted of certain types of crimes may be required to provide a sample of DNA for a database. This hashelped investigators solve old cases where only a DNA sample was obtained from the scene. DNA profiling can alsobe used to identify victims of mass casualty incidents. On the other hand, many convicted people have beenreleased from prison on the basis of DNA techniques, which were not available when a crime had originally beencommitted.

Bioinformatics

Bioinformatics involves the manipulation, searching, and data mining of DNA sequence data. The development oftechniques to store and search DNA sequences have led to widely applied advances in computer science, especiallystring searching algorithms, machine learning and database theory. String searching or matching algorithms,

which find an occurrence of a sequence of letters inside a larger sequence of letters, were developed to search forspecific sequences of nucleotides. In other applications such as text editors, even simple algorithms for this

206

problem usually suffice, but DNA sequences cause these algorithms to exhibit near-worst-case behaviour due to theirsmall number of distinct characters. The related problem of sequence alignment aims to identify homologoussequences and locate the specific mutations that make them distinct. These techniques, especially multiple sequence

ri22i

alignment, are used in studying phylogenetic relationships and protein function. Data sets representing entiregenomes' worth of DNA sequences, such as those produced by the Human Genome Project, are difficult to usewithout annotations, which label the locations of genes and regulatory elements on each chromosome. Regions ofDNA sequence that have the characteristic patterns associated with protein- or RNA-coding genes can be identifiedby gene finding algorithms, which allow researchers to predict the presence of particular gene products in an

ri 231

organism even before they have been isolated experimentally.

DNA nanotechnology

DNA nanotechnology uses the uniquemolecular recognition properties ofDNA and other nucleic acids to createself-assembling branched DNAcomplexes with useful properties.DNA is thus used as a structuralmaterial rather than as a carrier ofbiological information. This has led tothe creation of two-dimensionalperiodic lattices (both tile-based aswell as using the "DNA origami"method) as well as three-dimensionalstructures in the shapes ofpolyhedra. Nanomechanical

devices and algorithmic self-assembly

The DNA structure at left (schematic shown) will self-assemble into the structure

visualized by atomic force microscopy at right. DNA nanotechnology is the field which

seeks to design nanoscale structures using the molecular recognition properties of DNA

molecules. Image from Strong, 2004 (doi: 10.1371/journal.pbio.0020073).

have also been demonstrated, and

these DNA structures have been used to template the arrangement of other molecules such as gold nanoparticles and

strep tavidin proteins.

History and anthropology

Because DNA collects mutations over time, which are then inherited, it contains historical information and by

n 2sicomparing DNA sequences, geneticists can infer the evolutionary history of organisms, their phylogeny. This

field of phylogenetics is a powerful tool in evolutionary biology. If DNA sequences within a species are compared,

population geneticists can learn the history of particular populations. This can be used in studies ranging from

ecological genetics to anthropology; for example, DNA evidence is being used to try to identify the Ten Lost Tribes

oflsrael.[129][130]

DNA has also been used to look at modern family relationships, such as establishing family relationships betweenthe descendants of Sally Hemings and Thomas Jefferson. This usage is closely related to the use of DNA in criminalinvestigations detailed above. Indeed, some criminal investigations have been solved when DNA from crime sceneshas matched relatives of the guilty individual.

207

History of DNA research

DNA was first isolated by the Swiss physician Friedrich Miescher who, in 1869, discovered a microscopic substance

ri32iin the pus of discarded surgical bandages. As it resided in the nuclei of cells, he called it "nuclein". In 1919,

r 1331

Phoebus Levene identified the base, sugar and phosphate nucleotide unit. Levene suggested that DNA consistedof a string of nucleotide units linked together through the phosphate groups. However, Levene thought the chain wasshort and the bases repeated in a fixed order. In 1937 William Astbury produced the first X-ray diffraction patternsthat showed that DNA had a regular structure

[134]

In 1928, Frederick Griffith discovered that traits of the "smooth" form of the Pneumococcus could be transferred tothe "rough" form of the same bacteria by mixing killed "smooth" bacteria with the live "rough" form. Thissystem provided the first clear suggestion that DNA carried genetic information—the Avery-MacLeod-McCartyexperiment—when Oswald Avery, along with coworkers Colin MacLeod and Maclyn McCarty, identified DNA asthe transforming principle in 1943. DNA's role in heredity was confirmed in 1952, when Alfred Hershey and

Martha Chase in the Hershey-Chase experiment showed that DNA is the genetic material of the T2 phage

[137]

DNA

208

Rosalind Franklin

In 1953 James D. Watson and Francis Crick suggested what is now accepted as the first correct double-helix modelof DNA structure in the journal Nature. Their double-helix, molecular model of DNA was then based on a single

ri loi

X-ray diffraction image (labeled as "Photo 51") " taken by Rosalind Franklin and Raymond Gosling in May 1952,as well as the information that the DNA bases were paired—also obtained through private communications fromErwin Chargaff in the previous years. Chargaff s rules played a very important role in establishing double-helixconfigurations for B-DNA as well as A-DNA.

Experimental evidence supporting the Watson and Crick model were published in a series of five articles in the same

ri 39i

issue of Nature. Of these, Franklin and Gosling's paper was the first publication of their own X-ray diffractiondata and original analysis method that partially supported the Watson and Crick model ; this issue also

contained an article on DNA structure by Maurice Wilkins and two of his colleagues, whose analysis and in vivo

B-DNA X-ray patterns also supported the presence in vivo of the double-helical DNA configurations as proposed by

T321Crick and Watson for their double-helix molecular model of DNA in the previous two pages of Nature. In 1962,

after Franklin's death, Watson, Crick, and Wilkins jointly received the Nobel Prize in Physiology or Medicine.

Unfortunately, Nobel rules of the time allowed only living recipients, but a vigorous debate continues on who should

receive credit for the discovery

[142]

In an influential presentation in 1957, Crick laid out the "Central Dogma" of molecular biology, which foretold therelationship between DNA, RNA, and proteins, and articulated the "adaptor hypothesis". Final confirmation ofthe replication mechanism that was implied by the double-helical structure followed in 1958 through the

ri44i

Meselson-Stahl experiment. Further work by Crick and coworkers showed that the genetic code was based onnon-overlapping triplets of bases, called codons, allowing Har Gobind Khorana, Robert W. Holley and MarshallWarren Nirenberg to decipher the genetic code. These findings represent the birth of molecular biology.

Crystallography

DNA microarray

DNA sequencing

Genetic disorder

Junk DNA

Molecular models of DNA

Molecular Structure of Nucleic Acids: A Structure for Deoxyribose Nucleic Acid

Nucleic acid analogues

Nucleic acid methods

Nucleic acid modeling

Nucleic Acid Notations

Paracrystal model and theory

X-ray crystallography

X-ray scattering

Phosphoramidite

Plasmid

Polymerase chain reaction

Proteopedia DNA [146]

Southern blot

Triple-stranded DNA

• Calladine, Chris R.; Drew, Horace R.; Luisi, Ben F. and Travers, Andrew A. (2003). Understanding DNA: themolecule & how it works. Amsterdam: Elsevier Academic Press. ISBN 0-12-155089-3.

• Dennis, Carina; Julie Clayton (2003). 50 years of DNA. Basingstoke: Palgrave Macmillan. ISBN 1-4039-1479-6.

• Judson, Horace Freeland (1996). The eighth day of creation: makers of the revolution in biology. Plainview, N.Y:CSHL Press. ISBN 0-87969-478-5.

• Olby, Robert C. (1994). The path to the double helix: the discovery of DNA. New York: Dover Publications.ISBN 0-486-68117-3., first published in October 1974 by MacMillan, with foreword by Francis Crick;thedefinitive DNA textbook,revised in 1994 with a 9 page postscript.

• Olby, Robert C. (2009). Francis Crick: A Biography. Plainview, N.Y: Cold Spring Harbor Laboratory Press.ISBN 0-87969-798-9.

• Ridley, Matt (2006). Francis Crick: discoverer of the genetic code. [Ashland, OH: Eminent Lives, Atlas Books.ISBN 0-06-082333-X.

• Berry, Andrew; Watson, James D. (2003). DNA: the secret of life. New York: Alfred A. Knopf.ISBN 0-375-41546-7.

• Stent, Gunther Siegmund; Watson, James D. (1980). The double helix: a personal account of the discovery of thestructure of DNA. New York: Norton. ISBN 0-393-95075-1.

DNA 210

• Wilkins, Maurice (2003). The third man of the double helix the autobiography of Maurice Wilkins. Cambridge,Eng: University Press. ISBN 0-19-860665-6.

DNA at the Open Directory Project

DNA binding site prediction on protein

DNA from the Beginning Another DNA Learning Center site on DNA, genes, and heredity from Mendel to

DNA Lab, demonstrates how to extract DNA from wheat using readily available equipment and supplies.

52]FrDNA under electron microscope

Double Helix: 50 years of DNA [155], Nature

DNA coiling to form chromosomesDNA from the Beginningthe human genome project.DNA Lab, demonstrates ho

DNA the Double Helix Game From the official Nobel Prize web site

DNA under electron microscopeDolan DNA Learning CenterDouble Helix: 50 years of DNA [lt

Double Helix 1953—2003 National Centre for Biotechnology Education

Francis Crick and James Watson talking on the BBC in 1962, 1972, and 1974 [157]Genetic Education Modules for Teachers —DNA from the Beginning Study GuideGuide to DNA cloning [159]

Olby R (January 2003). "Quiet debut for the double helix" [160]. Nature 421 (6921): 402-5.doi:10.1038/nature01397. PMID 12540907.PDB Molecule of the Month pdb23_l [161]Rosalind Franklin's contributions to the study of DNA

The Register of Francis Crick Personal Papers 1938 - 2007 at Mandeville Special Collections Library, Geisel

Library, University of California, San Diego

U.S. National DNA Day —watch videos and participate in real-time chat with top scientists"Clue to chemistry of heredity found" . The New York Times. Saturday, June 13, 1953. The first Americannewspaper coverage of the discovery of the DNA structure.• An Introduction to DNA and Chromosomes from HOPES: Huntington's Disease Outreach Project for

Education at Stanford

References

[I] Russell, Peter (2001). [Genetics. New York: Benjamin Cummings. ISBN 0-805-34553-1.

[2] Saenger, Wolfram (1984). Principles of Nucleic Acid Structure. New York: Springer-Verlag. ISBN 0387907629.

[3] Alberts, Bruce; Alexander Johnson, Julian Lewis, Martin Raff, Keith Roberts and Peter Walters (2002). Molecular Biology of the Cell;

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Proc Natl Acad Sci USA 91 (13): 6007-11. doi:10.1073/pnas.91.13.6007. PMID 8016106. PMC 44126. .[116] Weir B, Triggs C, Starling L, Stowell L, Walsh K, Buckleton J (1997). "Interpreting DNA mixtures". J Forensic Sci 42 (2): 213-22.

PMID 9068179.[117] Jeffreys A, Wilson V, Thein S (1985). "Individual-specific 'fingerprints' of human DNA". Nature 316 (6023): 76-9. doi:10.1038/316076a0.

PMID 2989708.[118] Colin Pitchfork — first murder conviction on DNA evidence also clears the prime suspect (http://www.forensic.gov.uk/forensic_t/

inside/news/list_casefiles.php?case=l) Forensic Science Service Accessed 23 December 2006[119] "DNA Identification in Mass Fatality Incidents" (http://massfatality.dna.gov/Introduction/). National Institute of Justice. September

2006. .[120] Baldi, Pierre; Brunak, Soren (2001). Bioinformatics: The Machine Learning Approach. MIT Press. ISBN 978-0-262-02506-5.

OCLC 45951728..[121] Gusfield, Dan. Algorithms on Strings, Trees, and Sequences: Computer Science and Computational Biology. Cambridge University Press,

15 January 1997. ISBN 978-0-521-58519-4.[122] Sjolander K (2004). "Phylogenomic inference of protein molecular function: advances and challenges" (http://bioinformatics.

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Press. ISBN 0879697121. OCLC 55106399.[124] Rothemund PW (March 2006). "Folding DNA to create nanoscale shapes and patterns". Nature 440 (7082): 297-302.

doi:10.1038/nature04586. PMID 16541064.[125] Andersen ES, Dong M, Nielsen MM (May 2009). "Self-assembly of a nanoscale DNA box with a controllable lid". Nature 459 (7243):

73-6. doi:10.1038/nature07971. PMID 19424153.

DNA 215

[126] Ishitsuka Y, Ha T (May 2009). "DNA nanotechnology: a nanomachine goes live". Nat Nanotechnol 4 (5): 281—2.

doi:10.1038/nnano.2009.101. PMID 19421208.[127] Aldaye FA, Palmer AL, Sleiman HF (September 2008). "Assembling materials with DNA as the guide". Science 321 (5897): 1795-9.

doi:10.1126/science.ll54533. PMID 18818351.[128] Wray G; Martindale, Mark Q. (2002). "Dating branches on the tree of life using DNA" (http://genomebiology.eom/1465-6906/3/

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565-81. doi:10.1007/s00439-007-0433-0. PMID 17901982.[133] Levene P, (1 December 1919). "The structure of yeast nucleic acid" (http://www.jbc.Org/cgi/reprint/40/2/415). J Biol Chem 40 (2):

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mmbr.asm.org/cgi/pmidlookup?view=long&pmid=7968924). Microbiol. Rev. 58 (3): 563-602. PMID 7968924. PMC 372978..[136] Avery O, MacLeod C, McCarty M (1944). "Studies on the chemical nature of the substance inducing transformation of pneumococcal

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pictures/sci9.001.5.html) was obtained by Rosalind Franklin and Raymond Gosling in May 1952 at high hydration levels of DNA and it has

been labeled as "Photo 51"[139] Nature Archives Double Helix of DNA: 50 Years (http://www.nature.com/nature/dna50/archive.html)[140] Original X-ray diffraction image (http://osulibrary.oregonstate.edu/sp...lin-typeBphoto.

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Accessed 22 December 06[146] http://proteopedia.org/wiki/index.php/DNA

DNA

216

Molecular models of DNA

Molecular models of DNA structures are representations of the molecular geometry andtopology of Deoxyribonucleic acid (DNA) molecules using one of several means, with theaim of simplifying and presenting the essential, physical and chemical, properties of DNAmolecular structures either in vivo or in vitro. These representations include closely packedspheres (CPK models) made of plastic, metal wires for 'skeletal models', graphiccomputations and animations by computers, artistic rendering. Computer molecular modelsalso allow animations and molecular dynamics simulations that are very important forunderstanding how DNA functions in vivo.

The more advanced, computer-based molecular models of DNA involve molecular dynamics

simulations as well as quantum mechanical computations of vibro-rotations, delocalized

molecular orbitals (MOs), electric dipole moments, hydrogen-bonding, and so on. DNA

molecular dynamics modeling involves simulations of DNA molecular geometry and

topology changes with time as a result of both intra- and inter- molecular interactions of

DNA. Whereas molecular models of Deoxyribonucleic acid (DNA) molecules such as

closely packed spheres (CPK models) made of plastic or metal wires for 'skeletal models' are

useful representations of static DNA structures, their usefulness is very limited for

representing complex DNA dynamics. Computer molecular modeling allows both animations and molecular

dynamics simulations that are very important for understanding how DNA functions in vivo.

Spinning DNAgeneric model.

History

Double HelixDiscovery

William AstburyOswald AveryFrancis CrickErwin ChargaffMax DelbrUckJerry DonohueRosalind FranklinRaymond GoslingPhoebus Levene

Linus PaulingSir John RandallErwin SchrodingerAlex StokesJames WatsonMaurice WilkinsHerbert Wilson

From the very early stages of structural studies of DNA by X-ray diffraction and biochemical means, molecularmodels such as the Watson-Crick double-helix model were successfully employed to solve the 'puzzle' of DNAstructure, and also find how the latter relates to its key functions in living cells. The first high quality X-raydiffraction patterns of A-DNA were reported by Rosalind Franklin and Raymond Gosling in 1953 . The firstcalculations of the Fourier transform of an atomic helix were reported one year earlier by Cochran, Crick and Vand, and were followed in 1953 by the computation of the Fourier transform of a coiled-coil by Crick .

Structural information is generated from X-ray diffraction studies of oriented DNA fibers with the help of molecularmodels of DNA that are combined with crystallographic and mathematical analysis of the X-ray patterns.

T41The first reports of a double-helix molecular model of B-DNA structure were made by Watson and Crick in 1953

. Last-but-not-least, Maurice F. Wilkins, A. Stokes and H.R. Wilson, reported the first X-ray patterns of in vivo

B-DNA in partially oriented salmon sperm heads . The development of the first correct double-helix molecular

model of DNA by Crick and Watson may not have been possible without the biochemical evidence for the

nucleotide base-pairing ([A—T]; [C—G]), or Chargaffs rules .Although such initial studies of

DNA structures with the help of molecular models were essentially static, their consequences for explaining the in

vivo functions of DNA were significant in the areas of protein biosynthesis and the quasi-universality of the genetic

code. Epigenetic transformation studies of DNA in vivo were however much slower to develop in spite of their

importance for embryology, morphogenesis and cancer research. Such chemical dynamics and biochemical reactions

of DNA are much more complex than the molecular dynamics of DNA physical interactions with water, ions and

proteins/enzymes in living cells.

Importance

An old standing dynamic problem is how DNA "self-replication" takes place in living cells that should involvetransient uncoiling of supercoiled DNA fibers. Although DNA consists of relatively rigid, very large elongatedbiopolymer molecules called "fibers" or chains (that are made of repeating nucleotide units of four basic types,attached to deoxyribose and phosphate groups), its molecular structure in vivo undergoes dynamic configurationchanges that involve dynamically attached water molecules and ions. Supercoiling, packing with histones inchromosome structures, and other such supramolecular aspects also involve in vivo DNA topology which is evenmore complex than DNA molecular geometry, thus turning molecular modeling of DNA into an especiallychallenging problem for both molecular biologists and biotechnologists. Like other large molecules and biopolymers,DNA often exists in multiple stable geometries (that is, it exhibits conformational isomerism) and configurational,quantum states which are close to each other in energy on the potential energy surface of the DNA molecule.

218

Such varying molecular geometries can also be computed, at least inprinciple, by employing ab initio quantum chemistry methods that canattain high accuracy for small molecules, although claims thatacceptable accuracy can be also achieved for polynucleotides, as wellas DNA conformations, were recently made on the basis of VCDspectral data. Such quantum geometries define an important class of abinitio molecular models of DNA whose exploration has barely startedespecially in connection with results obtained by VCD in solutions.More detailed comparisons with such ab initio quantum computationsare in principle obtainable through 2D-FT NMR spectroscopy andrelaxation studies of polynucleotide solutions or specifically labeled DNA, as for example with deuterium labels.

In an interesting twist of roles, the DNA molecule itself was proposed to be utilized for quantum computing. BothDNA nanostructures as well as DNA 'computing' biochips have been built (see biochip image at left).

DNA computing biochip:3D

Examples of DNA molecular models

Animated molecular models allow one to visually explore the three-dimensional (3D) structure of DNA. Onevisualization of DNA model is a space-filling, or CPK, model. Another is a wire, or skeletal type.

The hydrogen bonding dynamics and proton exchange is very different by many orders of magnitude between thetwo systems of fully hydrated DNA and water molecules in ice. Thus, the DNA dynamics is complex, involvingnanosecond and several tens of picosecond time scales, whereas that of liquid ice is on the picosecond time scale,and that of proton exchange in ice is on the millisecond time scale; the proton exchange rates in DNA and attachedproteins may vary from picosecond to nanosecond, minutes or years, depending on the exact locations of theexchanged protons in the large biopolymers.

A simple harmonic oscillator 'vibration' is only an oversimplified dynamic representation of the longitudinalvibrations of the DNA intertwined helices which were found to be anharmonic rather than harmonic as oftenassumed in quantum dynamic simulations of DNA.

DNA Spacefilling molecular model

Paracrystalline lattice models of B-DNA structures

A paracrystalline lattice, or paracrystal, is a molecular or atomic lattice with significant amounts (e.g., larger than afew percent) of partial disordering of molecular arranegements. Limiting cases of the paracrystal model arenanostructures, such as glasses, liquids, etc., that may possess only local ordering and no global order. Liquidcrystals also have paracrystalline rather than crystalline structures.

Highly hydrated B-DNA occurs naturally in living cells in such a paracrystalline state, which is a dynamic one inspite of the relatively rigid DNA double-helix stabilized by parallel hydrogen bonds between the nucleotidebase-pairs in the two complementary, helical DNA chains (see figures). For simplicity most DNA molecular modelsommit both water and ions dynamically bound to B-DNA, and are thus less useful for understanding the dynamicbehaviors of B-DNA in vivo. The physical and mathematical analysis of X-ray and spectroscopic data for

paracrystalline B-DNA is therefore much more complicated than that of crystalline, A-DNA X-ray diffractionpatterns. The paracrystal model is also important for DNA technological applications such as DNA nanotechnology.

Novel techniques that combine X-ray diffraction of DNA with X-ray microscopy in hydrated living cells are now;o

]).

also being developed (see, for example, "Application of X-ray microscopy in the analysis of living hydrated cells"

[15],

Genomic and biotechnology applications of DNA molecular modeling

There are various uses of DNA molecular modeling in Genomics and Biotechnology research applications, fromDNA repair to PCR and DNA nanostructures. Two-dimensional DNA junction arrays have been visualized byAtomic force microscopy.

Quadruplex DNA may be involved in certain cancers

DNA structure

X-ray scattering

Neutron scattering

Crystallography

Crystal lattices

2D-FT NMRI and Spectroscopy

List of nucleic acid simulation software

Sirius visualization software

X-ray microscopy

QMC@Home

Sir Lawrence Bragg, FRS

Spectroscopy

• Vibrational circular dichroism (VCD)

• FT-NMR[20] [21]

• NMR Atlas-database [22]

T231

• mmcif downloadable coordinate files of nucleic acids in solution from 2D-FT NMR data

• NMR constraints files for NAs in PDB format

[25]

NMR microscopyMicrowave spectroscopyFT-IR

FT-NIR[26] [27] [28]

Spectral, Hyperspectral, and Chemical imaging)

Raman spectroscopy/microscopy and CARS

Fluorescence correlation spectroscopy , Fluorescence cross-correlation

a ddetI42! [43] [44]

spectroscopy and FRETConfocal microscopy

• Applications of Novel Techniques to Health Foods, Medical and Agricultural Biotechnology .(June 2004) I. C.Baianu, P. R. Lozano, V. I. Prisecaru and H. C. Lin., q-bio/0406047.

• F. Bessel, Untersuchung des Theils der planetarischen Storungen, Berlin Abhandlungen (1824), article 14.

• Sir Lawrence Bragg, FRS. The Crystalline State, A General survey. London: G. Bells and Sons, Ltd., vols. 1 and2., 1966., 2024 pages.

• Cantor, C. R. and Schimmel, P.R. Biophysical Chemistry, Parts I and II., San Franscisco: W.H. Freeman and Co.1980. 1,800 pages.

• Voet, D. and J.G. Voet. Biochemistry, 2nd Edn., New York, Toronto, Singapore: John Wiley & Sons, Inc., 1995,ISBN0-471-58651-X., 1361 pages.

• Watson, G. N. A Treatise on the Theory of Bessel Functions., (1995) Cambridge University Press. ISBN0-521-48391-3.

• Watson, James D. Molecular Biology of the Gene. New York and Amsterdam: W.A. Benjamin, Inc. 1965., 494pages.

• Wentworth, W.E. Physical Chemistry. A short course., Maiden (Mass.): Blackwell Science, Inc. 2000.

• Herbert R. Wilson, FRS. Diffraction of X-rays by proteins, Nucleic Acids and Viruses., London: Edward Arnold(Publishers) Ltd. 1966.

• Kurt Wuthrich. NMR of Proteins and Nucleic Acids., New York, Brisbane,Chicester, Toronto, Singapore: J.Wiley & Sons. 1986., 292 pages.

• Robinson, Bruche H.; Seeman, Nadrian C. (August 1987). "The Design of a Biochip: A Self-AssemblingMolecular-Scale Memory Device". Protein Engineering 1 (4): 295-300. ISSN 0269-2139. Link [45]

• Rothemund, Paul W. K.; Ekani-Nkodo, Axel; Papadakis, Nick; Kumar, Ashish; Fygenson, Deborah Kuchnir &Winfree, Erik (22 December 2004). "Design and Characterization of Programmable DNA Nanotubes". Journal ofthe American Chemical Society 126 (50): 16344-16352. doi:10.1021/ja0443191. ISSN 0002-7863.

• Keren, K; Kinneret Keren, Rotem S. Berman, Evgeny Buchstab, Uri Sivan, Erez Braun (November 2003)."DNA-Templated Carbon Nanotube Field-Effect Transistor" [46]. Science 302 (6549): 1380-1382.

doi: 10.1126/science. 1091022. ISSN 1095-9203.

• Zheng, Jiwen; Constantinou, Pamela E.; Micheel, Christine; Alivisatos, A. Paul; Kiehl, Richard A. & SeemanNadrian C. (2006). "2D Nanoparticle Arrays Show the Organizational Power of Robust DNA Motifs". NanoLetters 6: 1502-1504. doi:10.1021/nl060994c. ISSN 1530-6984.

• Cohen, Justin D.; Sadowski, John P.; Dervan, Peter B. (2007). "Addressing Single Molecules on DNANanostructures". Angewandte Chemie 46 (42): 7956-7959. doi:10.1002/anie.200702767. ISSN 0570-0833.

• Constantinou, Pamela E.; Wang, Tong; Kopatsch, Jens; Israel, Lisa B.; Zhang, Xiaoping; Ding, Baoquan;Sherman, William B.; Wang, Xing; Zheng, Jianping; Sha, Ruojie & Seeman, Nadrian C. (2006). "Doublecohesion in structural DNA nanotechnology". Organic and Biomolecular Chemistry 4: 3414—3419.doi:10.1039/b605212f.

• Hallin PF, David Ussery D (2004). "CBS Genome Atlas Database: A dynamic storage for bioinformatic resultsand DNA sequence data". Bioinformatics 20: 3682—3686.

• Zhang CT, Zhang R, Ou HY (2003). "The Z curve database: a graphic representation of genome sequences".Bioinformatics 19 (5): 593-599. doi:10.1093/bioinformatics/btg041

• DNA the Double Helix Game From the official Nobel Prize web site

• MDDNA: Structural Bioinformatics of DNA [47]

• Double Helix 1953—2003 National Centre for Biotechnology Education

• DNAlive: a web interface to compute DNA physical properties . Also allows cross-linking of the results with

the UCSC Genome browser and DNA dynamics.

[491

• DiProDB: Dinucleotide Property Database . The database is designed to collect and analyse thermodynamic,

structural and other dinucleotide properties.

• Further details of mathematical and molecular analysis of DNA structure based on X-ray data

• Bessel functions corresponding to Fourier transforms of atomic or molecular helices.

• Application of X-ray microscopy in analysis of living hydrated cells

T521

• overview of STM/AFM/SNOM principles with educative videos

Databases for DNA molecular models and sequencesX-ray diffraction

• NDB ID: UD0017 Database [17]

• X-ray Atlas -database

T541

• PDB files of coordinates for nucleic acid structures from X-ray diffraction by NA (incl. DNA) crystals

• Structure factors dowloadable files in CIF formatNeutron scattering

• ISIS neutron source: ISIS pulsed neutron source:A world centre for science with neutrons & muons at Harwell,near Oxford, UK.

X-ray microscopy

• Application of XElectron microscopy

• DNA under electron microscope

Application of X-ray microscopy in the analysis of living hydrated cells

Genomic and structural databases

— contains examples of base skews.

[58]

T571• CBS Genome Atlas Database —contains examples of base skews.

• The Z curve database of genomes — a 3-dimensional visualization and analysis tool of genomes

• DNA and other nucleic acids' molecular models: Coordinate files of nucleic acids molecular structure models inPDB and CIF formats [59]

Atomic force microscopy

• How SPM Works [60]

• SPM Image Gallery - AFM STM SEM MFM NSOM and more. [61]

References

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[20] (http://www.jonathanpmiller.com/Karplus.html)- obtaining dihedral angles from J coupling constants[21] (http://www.spectroscopynow.com/FCKed...e/specNOW/HTML filesZGeneral_Karplus_Calculator.htm) Another

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[50] http

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[53] http

[54] http

[55] http

[56] http

[57] http

[58] http

[59] http

[60] http

[61] http

//www.fretimaging.org/mcnamaraintro.html FRET imaging introduction

//peds.oxfordjournals.org/cgi/content/abstract/1/4/295

//www.sciencemag.org/cgi/content/abstract/sci;302/5649/1380

//humphry.chem.wesleyan.edu:8080/MDDNA/

//mmb.pcb.ub.es/DNAlive

//diprodb.fli-leibniz.de

//planetphysics.org/encyclopedia/BesselFunctionsApplicationsToDiffrac tionByHelicalStructures.html

//planetphysics.org/?op=getobj&from=objects&name=BesselFunctionsAndTheirApplicationsToDiffractionByHelicalStructures

//www.ntmdt.ru/SPM-Techniques/Principles/

//ndbserver.rutgers.edu/atlas/xray/index.html

//ndbserver.rutgers.edu/ftp/NDB/coordinates/na-biol/

//ndbserver.rutgers.edu/ftp/NDB/structure-factors/

//www.isis.rl.ac.uk/

//www.cbs.dtu.dk/services/GenomeAtlas/

//tubic.tju.edu.cn/zcurve/

//ndbserver.rutgers.edu/ftp/NDB/models/

//www.parkafm.com/New_html/resources/01general.php

//www.rhk-tech.com/results/showcase.php

DNA structure

The structure of DNA shows a variety of forms, both double-stranded and single-stranded. The mechanicalproperties of DNA, which are directly related to its structure, are a significant problem for cells. Every process whichbinds or reads DNA is able to use or modify the mechanical properties of DNA for purposes of recognition,packaging and modification. The extreme length (a chromosome may contain a 10 cm long DNA strand), relativerigidity and helical structure of DNA has led to the evolution of histones and of enzymes such as topoisomerases andhelicases to manage a cell's DNA. The properties of DNA are closely related to its molecular structure and sequence,particularly the weakness of the hydrogen bonds and electronic interactions that hold strands of DNA togethercompared to the strength of the bonds within each strand.

Experimental techniques which can directly measure the mechanical properties of DNA are relatively new, andhigh-resolution visualization in solution is often difficult. Nevertheless, scientists have uncovered large amount ofdata on the mechanical properties of this polymer, and the implications of DNA's mechanical properties on cellularprocesses is a topic of active current research.

The DNA found in many cells can be macroscopic in length - a few centimetres long for each human chromosome.Consequently, cells must compact or "package" DNA to carry it within them. In eukaryotes this is carried byspool-like proteins known as histones, around which DNA winds. It is the further compaction of this DNA-proteincomplex which produces the well known mitotic eukaryotic chromosomes.

Structure determination

DNA structures can be determined using either nuclear magnetic resonance spectroscopy or X-ray crystallography.The first published reports of A-DNA X-ray diffraction patterns— and also B-DNA—employed analyses based onPatterson transforms that provided only a limited amount of structural information for oriented fibers of DNAisolated from calf thymus. An alternate analysis was then proposed by Wilkins et al. in 1953 for B-DNA X-ray

diffraction/scattering patterns of hydrated, bacterial oriented DNA fibers and trout sperm heads in terms of squaresof Bessel functions. Although the "B-DNA form' is most common under the conditions found in cells, it is not awell-defined conformation but a family or fuzzy set of DNA-conformations that occur at the high hydration levelspresent in a wide variety of living cells. Their corresponding X-ray diffraction & scattering patterns arecharacteristic of molecular paracrystals with a significant degree of disorder (>20%) , and concomitantly the

structure is not tractable using only the standard analysis.

ro]

On the other hand, the standard analysis, involving only Fourier transforms of Bessel functions and DNAmolecular models, is still routinely employed for the analysis of A-DNA and Z-DNA X-ray diffraction patterns.

Base pair geometry

The geometry of a base, or base pair step can be characterized by 6 coordinates: Shift, Slide, Rise, Tilt, Roll, andTwist. These values precisely define the location and orientation in space of every base or base pair in a DNAmolecule relative to its predecessor along the axis of the helix. Together, they characterize the helical structure of themolecule. In regions of DNA where the "normal" structure is disrupted the change in these values can be used todescribe such disruption.

For each base pair, considered relative to its predecessor :

• Shear

• Stretch

• Stagger

• Buckle

Propeller twist: Rotation of one base with respect to the other in the same base pair.

Opening

Shift: displacement along an axis in the base-pair plane perpendicular to the first, directed from the minor to themajor groove.

Slide: displacement along an axis in the plane of the base pair directed from one strand to the other.

Rise: displacement along the helix axis.

Tilt: rotation around this axis.

Roll: rotation around this axis.

Twist: rotation around the helix axis.

x-displacement

y-displacement

inclination

tip

pitch: the number of base pairs per complete turn of the helix

Rise and twist determine the handedness and pitch of the helix. The other coordinates, by contrast, can be zero. Slideand shift are typically small in B-DNA, but are substantial in A- and Z-DNA. Roll and tilt make successive basepairs less parallel, and are typically small. A diagram of these coordinates can be found in 3DNA website.

Note that "tilt" has often been used differently in the scientific literature, referring to the deviation of the first,inter-strand base-pair axis from perpendicularity to the helix axis. This corresponds to slide between a succession ofbase pairs, and in helix-based coordinates is properly termed "inclination".

DNA helix geometries

Three DNA conformations are believed to be found in nature, A-DNA, B-DNA, and Z-DNA. The "B" formdescribed by James D. Watson and Francis Crick is believed to predominate in cells . It is 23.7 A wide andextends 34 A per 10 bp of sequence. The double helix makes one complete turn about its axis every 10.4-10.5 basepairs in solution. This frequency of twist (known as the helical pitch) depends largely on stacking forces that eachbase exerts on its neighbours in the chain.

Other conformations are possible; A-DNA, B-DNA, C-DNA, D-DNA[16] , E-DNA[17] , L-DNA(enantiomeric formof D-DNA)[16], P-DNA[18], S-DNA, Z-DNA, etc. have been described so far.[19] In fact, only the letters F, Q, U, V,and Y are now available to describe any new DNA structure that may appear in the future. However, most of

these forms have been created synthetically and have not been observed in naturally occurring biological systems.Also note the triple-stranded DNA possibility.

A- and Z-DNA

A-DNA and Z-DNA differ significantly in their geometry and dimensions to B-DNA, although still form helicalstructures. The A form appears likely to occur only in dehydrated samples of DNA, such as those used incrystallographic experiments, and possibly in hybrid pairings of DNA and RNA strands. Segments of DNA that cellshave methylated for regulatory purposes may adopt the Z geometry, in which the strands turn about the helical axisthe opposite way to A-DNA and B-DNA. There is also evidence of protein-DNA complexes forming Z-DNAstructures.

226

The structures of A-, B-, and Z-DNA.

Guanine

o

..-H—N

Cytosine

^ ob r*>anti

C5'

axis of helixof Z-DNA

The helix axis of A-, B-, and Z-DNA.

Structural features of the three major forms of DNA

 Geometry attribute A-DNA B-DNA Z-DNA Helix sense right-handed right-handed left-handed Repeating unit lbp lbp 2bp Rotation/bp 33.6° 35.9° 6072bp Mean bp/turn 10.7 10.0 12 Inclination of bp toaxis +19° -1.2° -9° Rise/bp along axis 2.3 A 3.32 A 3.8 A Pitch/turn of helix 24.6 A 33.2 A 45.6 A Mean propeller twist +18° +16° 0° Glycosyl angle anti anti C: anti,G: syn Sugar pucker C3'-endo C2'-endo C:C2'-endo,G: C2'-exo Diameter 25.5 A 23.7 A 18.4 A

Supercoiled DNA

The B form of the DNA helix twists 360° per 10.4-10.5 bp in the absence of torsional strain. But many molecularbiological processes can induce torsional strain. A DNA segment with excess or insufficient helical twisting isreferred to, respectively, as positively or negatively "supercoiled". DNA in vivo is typically negatively supercoiled,which facilitates the unwinding (melting) of the double-helix required for RNA transcription.

Non-helical forms

Other non-double helical forms of DNA have been described, for example side-by-side (SBS) and triple helicalconfigurations. Single stranded DNA may exist in statu nascendi or as thermally induced despiralized DNA.

227

DNA bending

DNA is a relatively rigid polymer, typically modelled as a worm-like chain. It has three significant degrees offreedom; bending, twisting and compression, each of which cause particular limitations on what is possible withDNA within a cell. Twisting/torsional stiffness is important for the circularisation of DNA and the orientation ofDNA bound proteins relative to each other and bending/axial stiffness is important for DNA wrapping andcircularisation and protein interactions. Compression/extension is relatively unimportant in the absence of hightension.

Persistence length/Axial stiffness

Example sequences and their persistence lengths (B DNA)

 Sequence PersistenceLength/base pairs Random 154+10 (CA)repeat 133±10 (CAG)repeat 124±10 (TATA)repeat 137±10

DNA in solution does not take a rigid structure but is continually changing conformation due to thermal vibrationand collisions with water molecules, which makes classical measures of rigidity impossible. Hence, the bendingstiffness of DNA is measured by the persistence length, defined as:

"The length of DNA over which the time-averaged orientation of the polymer becomes uncorrelated by afactor of e."

This value may be directly measured using an atomic force microscope to directly image DNA molecules of variouslengths. In aqueous solution the average persistence length is 46-50 nm or 140-150 base pairs (the diameter of DNAis 2 nm), although can vary significantly. This makes DNA a moderately stiff molecule.

The persistence length of a section of DNA is somewhat dependent on its sequence, and this can cause significantvariation. The variation is largely due to base stacking energies and the residues which extend into the minor andmajor grooves.

Models for DNA bending

Stacking stability of base steps (B DNA)

 Step StackingAG/kcal mol" TA -0.19 T G or C A -0.55 CG -0.91 A G or C T -1.06 A A or T T -1.11 AT -1.34
 G A or T C -1.43 CCorGG -1.44 A C or G T -1.81 GC -2.17

The entropic flexibility of DNA is remarkably consistent with standard polymer physics models such as theKratky-Porod worm-like chain model. Consistent with the worm-like chain model is the observation that bendingDNA is also described by Hooke's law at very small (sub-piconewton) forces. However for DNA segments less thanthe persistence length, the bending force is approximately constant and behaviour deviates from the worm-like chainpredictions.

This effect results in unusual ease in circularising small DNA molecules and a higher probability of finding highlybent sections of DNA.

Bending preference

DNA molecules often have a preferred direction to bend, ie. anisotropic bending. This is, again, due to the propertiesof the bases which make up the DNA sequence - a random sequence will have no preferred bend direction, i.e.isotropic bending.

Preferred DNA bend direction is determined by the stability of stacking each base on top of the next. If unstable basestacking steps are always found on one side of the DNA helix then the DNA will preferentially bend away from thatdirection. As bend angle increases then steric hindrances and ability to roll the residues relative to each other alsoplay a role, especially in the minor groove. A and T residues will be preferentially be found in the minor grooves onthe inside of bends. This effect is particularly seen in DNA-protein binding where tight DNA bending is induced,such as in nucleosome particles. See base step distortions above.

DNA molecules with exceptional bending preference can become intrinsically bent. This was first observed intrypanosomatid kinetoplast DNA. Typical sequences which cause this contain stretches of 4-6 T and A residuesseparated by G and C rich sections which keep the A and T residues in phase with the minor groove on one side ofthe molecule. For example:

I I I I

I I

GATTCCCAAAAATGTCAAAAAATAGGCAAAAAATGCCAAAAAATCCCAAAC

The intrinsically bent structure is induced by the 'propeller twist' of base pairs relative to each other allowing unusualbifurcated Hydrogen-bonds between base steps. At higher temperatures this structure, and so the intrinsic bend, islost.

All DNA which bends anisotropically has, on average, a longer persistence length and greater axial stiffness. Thisincreased rigidity is required to prevent random bending which would make the molecule act isotropically.

DNA circularization

DNA circularization depends on both the axial (bending) stiffness and torsional (rotational) stiffness of the molecule.For a DNA molecule to successfully circularize it must be long enough to easily bend into the full circle and musthave the correct number of bases so the ends are in the correct rotation to allow bonding to occur. The optimumlength for circularization of DNA is around 400 base pairs (136 nm), with an integral number of turns of the DNAhelix, i.e. multiples of 10.4 base pairs. Having a non integral number of turns presents a significant energy barrier forcircularization, for example a 10.4 x 30 = 312 base pair molecule will circularize hundreds of times faster than 10.4 x

229

30.5 ~ 317 base pair molecule.

DNA stretching

Longer stretches of DNA are entropically elastic under tension. When DNA is in solution, it undergoes continuousstructural variations due to the energy available in the solvent. This is due to the thermal vibration of the moleculecombined with continual collisions with water molecules. For entropic reasons, more compact relaxed states arethermally accessible than stretched out states, and so DNA molecules are almost universally found in a tangledrelaxed layouts. For this reason, a single molecule of DNA will stretch under a force, straightening it out. Usingoptical tweezers, the entropic stretching behavior of DNA has been studied and analyzed from a polymer physicsperspective, and it has been found that DNA behaves largely like the Kratky-Porod worm-like chain model underphysiologically accessible energy scales.

Under sufficient tension and positive torque, DNA is thought to undergo a phase transition with the bases splaying

outwards and the phosphates moving to the middle. This proposed structure for overstretched DNA has been called

n si"P-form DNA," in honor of Linus Pauling who originally presented it as a possible structure of DNA

The mechanical properties DNA under compression have not been characterized due to experimental difficulties inpreventing the polymer from bending under the compressive force.

DNA melting

Melting stability of base steps (B DNA)

 Step MeltingAG/Kcal mol"1 TA -0.12 T G or C A -0.78 CG -1.44 A G or C T -1.29 A A or T T -1.04 AT -1.27 G A or T C -1.66 CCorGG -1.97 A C or G T -2.04 GC -2.70

DNA melting is the process by which the interactions between the strands of the double helix are broken, separating

the two strands of DNA. These bonds are weak, easily separated by gentle heating, enzymes, or physical force. DNA

T221melting preferentially occurs at certain points in the DNA. T and A rich sequences are more easily melted than C

and G rich regions. Particular base steps are also susceptible to DNA melting, particularly T A and T G base

steps. These mechanical features are reflected by the use of sequences such as TATAA at the start of many genes

to assist RNA polymerase in melting the DNA for transcription.

Strand separation by gentle heating, as used in PCR, is simple providing the molecules have fewer than about 10,000base pairs (10 kilobase pairs, or 10 kbp). The intertwining of the DNA strands makes long segments difficult toseparate. The cell avoids this problem by allowing its DNA-melting enzymes (helicases) to work concurrently with

230

topoisomerases, which can chemically cleave the phosphate backbone of one of the strands so that it can swivelaround the other. Helicases unwind the strands to facilitate the advance of sequence-reading enzymes such as DNApolymerase.

DNA topology

Within the cell most DNA is topologically restricted. DNA is typicallyfound in closed loops (such as plasmids in prokaryotes) which aretopologically closed, or as very long molecules whose diffusioncoefficients produce effectively topologically closed domains. Linearsections of DNA are also commonly bound to proteins or physicalstructures (such as membranes) to form closed topological loops.

Francis Crick was one of the first to propose the importance of linkingnumbers when considering DNA supercoils. In a paper published in1976, Crick outlined the problem as follows:

In considering supercoils formed by closeddouble-stranded molecules of DNA certain mathematicalconcepts, such as the linking number and the twist, areneeded. The meaning of these for a closed ribbon isexplained and also that of the writhing number of a closed

curve. Some simple examples are given, some of which

T241may be relevant to the structure of chromatin.

Analysis of DNA topology uses three values:

L = linking number - the number of times one DNA strand wraps

1 Twist = -1, Writhe = 0.

Twist = 0, Writhe = -1.

J Twist ^ +1 Writhe = 0.

Twist = 0, Writhe = +1.

\ Twist = -2. Writhe = 0.

Twist - 0, Writhe =

i A

1

o

\\ Twist = +2, Writhe = 0.

Twist = 0, Writhe = +2.

Twist = 0, Writhe = -4.

Plectonemic

Supercoiled structure of circular DNA molecules

with low writhe. Note that the helical nature of

the DNA duplex is omitted for clarity.

around the other. It is an integer for a closed loop and constantfor a closed topological domain.

T = twist - total number of turns in the double stranded DNA helix. This will normally try to be equal to thenumber turns a DNA molecule will make while free in solution, ie. number of bases/10.4.

W = writhe - number of turns of the double stranded DNA helix around the superhelical axis

L = T + W and AL = AT + AW

Any change of T in a closed topological domain must be balanced by a change in W, and vice versa. This results inhigher order structure of DNA. A circular DNA molecule with a writhe of 0 will be circular. If the twist of thismolecule is subsequently increased or decreased by supercoiling then the writhe will be appropriately altered,making the molecule undergo plectonemic or toroidal superhelical coiling.

When the ends of a piece of double stranded helical DNA are joined so that it forms a circle the strands aretopologically knotted. This means the single strands cannot be separated any process that does not involve breaking astrand (such as heating). The task of un-knotting topologically linked strands of DNA falls to enzymes known astopoisomerases. These enzymes are dedicated to un-knotting circular DNA by cleaving one or both strands so thatanother double or single stranded segment can pass through. This un-knotting is required for the replication ofcircular DNA and various types of recombination in linear DNA which have similar topological constraints.

For many years, the origin of residual supercoiling in eukaryotic genomes remained unclear. This topological puzzle

T251was referred to by some as the "linking number paradox". However, when experimentally determined structures

of the nucleosome displayed an overtwisted left-handed wrap of DNA around the histone octamer , this

• DNA nanotechnology

• Molecular models of DNA

• MDDNA: Structm

r?8i

• Abalone — Commercial software for DNA modeling

• DNAlive: a web interface to compute DNA physthe UCSC Genome browser and DNA dynamics

• DiProDB: Dinucleotide Property Databasestructural and other dinucleotide properties.

MDDNA: Structural Bioinformatics of DNA [47]

A modeling

DNAlive: a web interface to compute DNA physical properties . Also allows cross-linking of the results with

imic[491DiProDB: Dinucleotide Property Database . The database is designed to collect and analyse thermodynamic,

References

[I] Franklin, R.E. and Gosling, R.G. received 6 March 1953. Acta Cryst. (1953). 6, 673: The Structure of Sodium Thymonucleate Fibres I. TheInfluence of Water Content.; also Acta Cryst. 6, 678: The Structure of Sodium Thymonucleate Fibres II. The Cylindrically SymmetricalPatterson Function.

[2] Franklin, Rosalind (1953). "Molecular Configuration in Sodium Thymonucleate. Franklin R. and Gosling R.G" (http://www.nature.com/

nature/dna50/franklingosling.pdf) (PDF). Nature 111. 740-741. doi:10.1038/171740a0. PMID 13054694. .[3] Wilkins M.H.F., A.R. Stokes A.R. & Wilson, H.R. (1953). "Molecular Structure of Deoxypentose Nucleic Acids" (http://www.nature.com/

nature/dna50/wilkins.pdf) (PDF). Nature 171: 738-740. doi:10.1038/171738a0. PMID 13054693..[4] Leslie AG, Arnott S, Chandrasekaran R, Ratliff RL (1980). "Polymorphism of DNA double helices". ]. Mol. Biol. 143 (1): 49-72.

doi: 10.1016/0022-2836(80)90124-2. PMID 7441761.[5] Baianu, I.C. (1980). "Structural Order and Partial Disorder in Biological systems". Bull. Math. Biol. 42 (4): 464^468.

doi: 10.1016/0022-2836(80)90124-2.[6] Hosemann R., Bagchi R.N., Direct analysis of diffraction by matter, North-Holland Pubis., Amsterdam — New York, 1962[7] Baianu I.C, X-ray scattering by partially disordered membrane systems, Acta Cryst. A, 34 (1978), 751—753.[8] Bessel functions and diffraction by helical structures (http://planetphysics.org/encyclopedia/

BesselFunctionsAndTheirApplicationsToDiffractionByHelicalStructures.html)[9] X-Ray Diffraction Patterns of Double-Helical Deoxyribonucleic Acid (DNA) Crystals (http://planetphysics.org/encyclopedia/

BesselFunctionsApplicationsToDiffractionByHelicalStructures.html)[10] Dickerson RE (1989). "Definitions and nomenclature of nucleic acid structure components". Nucleic Acids Res 17 (5): 1797—1803.

doi:10.1093/nar/17.5.1797. PMID 2928107.

[II] Lu XJ, Olson WK (1999). "Resolving the discrepancies among nucleic acid conformational analyses". J Mol Biol 285 (4): 1563—1575.doi:10.1006/jmbi.l998.2390. PMID 9917397.

[12] Olson WK, Bansal M, Burley SK, Dickerson RE, Gerstein M, Harvey SC, Heinemann U, Lu XJ, Neidle S, Shakked Z, Sklenar H, Suzuki

M, Tung CS, Westhof E, Wolberger C, Berman HM (2001). "A standard reference frame for the description of nucleic acid base-pair

geometry". JMolBiolili (1): 229-237. doi:10.1006/jmbi.2001.4987. PMID 11601858.[13] http://rutchem.rutgers.edu/~xiangjun...ep_hel.gif[14] http://rutchem.rutgers.edu/~xiangjun.../examples.html

[15] Richmond, et al. (2003). "The structure of DNA in the nucleosome core". Nature 423: 145-150. doi: 10.1038/nature01595. PMID 12736678.[16] Hayashi G, HagiharaM, Nakatani K (2005). "Application of L-DNA as a molecular tag". Nucleic Acids Symp Ser (Oxf) 49: 261-262.

PMID 17150733.[17] Vargason JM, Eichman BF, Ho PS (2000). "The extended and eccentric E-DNA structure induced by cytosine methylation or bromination".

Nature Structural Biology 7: 758-761. doi:10.1038/78985.[18] Allemand, et al. (1998). "Stretched and overwound DNA forms a Pauling-like structure with exposed bases". PNAS 24: 14152—14157.

doi:10.1073/pnas.95.24.14152. PMID 9826669.

DNA structure

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[19] List of 55 fiber structures (http://rutchem.rutgers.edu/~xiangjun...iber_model.txt)

[20] BansalM (2003). "DNA structure: Revisiting the Watson-Crick double helix". Current Science 85 (11): 1556-1563.

[21] Ghosh A, Bansal M (2003). "A glossary of DNA structures from A to Z". Acta Cn'st D59: 620-626. doi:10.1107/S0907444903003251.

[22] Breslauer KJ, Frank R, Blocker H, Marky LA (1986). "Predicting DNA duplex stability from the base sequence". PNAS 83 (11):

3746-3750. PMID 3459152.[23] Richard Owczarzy (2008-08-28). "DNA melting temperature - How to calculate it?" (http://www.owczarzy.net/tm.htm).

High-throughput DNA biophysics, owczarzy.net.. Retrieved 2008-10-02.[24] Crick FH (1976). "Linking numbers and nucleosomes". Proc Natl Acad Sci USA 73 (8): 2639-43. doi: 10.1073/pnas.73.8.2639.

PMID 1066673.[25] Prunell A (1998). "A topological approach to nucleosome structure and dynamics: the linking number paradox and other issues". Biophys J

74 (5): 2531-2544. PMID 9591679.[26] Luger K, Mader AW, Richmond RK, Sargent DF, Richmond TJ (1997). "Crystal structure of the nucleosome core particle at 2.8 A

resolution". Nature 389 (6648): 251-260. doi:10.1038/38444. PMID 9305837.[27] Davey CA, Sargent DF, Luger K, Maeder AW, Richmond TJ (2002). "Solvent mediated interactions in the structure of the nucleosome core

particle at 1.9 A resolution". Journal of Molecular Biology 319 (5): 1097-1113. doi:10.1016/S0022-2836(02)00386-8. PMID 12079350.[28] http://www.biomolecular-modeling.com...one/index.html

DNA Dynamics

Molecular models of DNA structures are representations of the molecular geometry andtopology of Deoxyribonucleic acid (DNA) molecules using one of several means, with theaim of simplifying and presenting the essential, physical and chemical, properties of DNAmolecular structures either in vivo or in vitro. These representations include closely packedspheres (CPK models) made of plastic, metal wires for 'skeletal models', graphiccomputations and animations by computers, artistic rendering. Computer molecular modelsalso allow animations and molecular dynamics simulations that are very important forunderstanding how DNA functions in vivo.

The more advanced, computer-based molecular models of DNA involve molecular dynamics

simulations as well as quantum mechanical computations of vibro-rotations, delocalized

molecular orbitals (MOs), electric dipole moments, hydrogen-bonding, and so on. DNA

molecular dynamics modeling involves simulations of DNA molecular geometry and

topology changes with time as a result of both intra- and inter- molecular interactions of

DNA. Whereas molecular models of Deoxyribonucleic acid (DNA) molecules such as

closely packed spheres (CPK models) made of plastic or metal wires for 'skeletal models' are

useful representations of static DNA structures, their usefulness is very limited for

representing complex DNA dynamics. Computer molecular modeling allows both animations and molecular

dynamics simulations that are very important for understanding how DNA functions in vivo.

Spinning DNAgeneric model.

History

Double HelixDiscovery

William AstburyOswald AveryFrancis CrickErwin ChargaffMax DelbriickJerry DonohueRosalind FranklinRaymond GoslingPhoebus LeveneLinus PaulingSir John RandallErwin SchrodingerAlex StokesJames WatsonMaurice WilkinsHerbert Wilson

From the very early stages of structural studies of DNA by X-ray diffraction and biochemical means, molecularmodels such as the Watson-Crick double-helix model were successfully employed to solve the 'puzzle' of DNAstructure, and also find how the latter relates to its key functions in living cells. The first high quality X-raydiffraction patterns of A-DNA were reported by Rosalind Franklin and Raymond Gosling in 1953 . The first

calculations of the Fourier transform of an atomic helix were reported one year earlier by Cochran, Crick and Vand

121 T31

, and were followed in 1953 by the computation of the Fourier transform of a coiled-coil by Crick .

Structural information is generated from X-ray diffraction studies of oriented DNA fibers with the help of molecularmodels of DNA that are combined with crystallographic and mathematical analysis of the X-ray patterns.

141The first reports of a double-helix molecular model of B-DNA structure were made by Watson and Crick in 1953

. Last-but-not-least, Maurice F. Wilkins, A. Stokes and H.R. Wilson, reported the first X-ray patterns of in vivo

B-DNA in partially oriented salmon sperm heads . The development of the first correct double-helix molecular

model of DNA by Crick and Watson may not have been possible without the biochemical evidence for the

nucleotide base-pairing ([A—T]; [C—G]), or Chargaffs rules .Although such initial studies of

DNA structures with the help of molecular models were essentially static, their consequences for explaining the in

vivo functions of DNA were significant in the areas of protein biosynthesis and the quasi-universality of the genetic

code. Epigenetic transformation studies of DNA in vivo were however much slower to develop in spite of their

importance for embryology, morphogenesis and cancer research. Such chemical dynamics and biochemical reactions

of DNA are much more complex than the molecular dynamics of DNA physical interactions with water, ions and

proteins/enzymes in living cells.

234

Importance

An old standing dynamic problem is how DNA "self-replication" takes place in living cells that should involvetransient uncoiling of supercoiled DNA fibers. Although DNA consists of relatively rigid, very large elongatedbiopolymer molecules called "fibers" or chains (that are made of repeating nucleotide units of four basic types,attached to deoxyribose and phosphate groups), its molecular structure in vivo undergoes dynamic configurationchanges that involve dynamically attached water molecules and ions. Supercoiling, packing with histones inchromosome structures, and other such supramolecular aspects also involve in vivo DNA topology which is evenmore complex than DNA molecular geometry, thus turning molecular modeling of DNA into an especiallychallenging problem for both molecular biologists and biotechnologists. Like other large molecules and biopolymers,DNA often exists in multiple stable geometries (that is, it exhibits conformational isomerism) and configurational,quantum states which are close to each other in energy on the potential energy surface of the DNA molecule.

Such varying molecular geometries can also be computed, at least inprinciple, by employing ab initio quantum chemistry methods that canattain high accuracy for small molecules, although claims thatacceptable accuracy can be also achieved for polynucleotides, as wellas DNA conformations, were recently made on the basis of VCDspectral data. Such quantum geometries define an important class of abinitio molecular models of DNA whose exploration has barely startedespecially in connection with results obtained by VCD in solutions.More detailed comparisons with such ab initio quantum computationsare in principle obtainable through 2D-FT NMR spectroscopy andrelaxation studies of polynucleotide solutions or specifically labeled DNA, as for example with deuterium labels.

In an interesting twist of roles, the DNA molecule itself was proposed to be utilized for quantum computing. BothDNA nanostructures as well as DNA 'computing' biochips have been built (see biochip image at left).

Examples of DNA molecular models

Animated molecular models allow one to visually explore the three-dimensional (3D) structure of DNA. Onevisualization of DNA model is a space-filling, or CPK, model. Another is a wire, or skeletal type.

The hydrogen bonding dynamics and proton exchange is very different by many orders of magnitude between thetwo systems of fully hydrated DNA and water molecules in ice. Thus, the DNA dynamics is complex, involvingnanosecond and several tens of picosecond time scales, whereas that of liquid ice is on the picosecond time scale,and that of proton exchange in ice is on the millisecond time scale; the proton exchange rates in DNA and attachedproteins may vary from picosecond to nanosecond, minutes or years, depending on the exact locations of theexchanged protons in the large biopolymers.

A simple harmonic oscillator 'vibration' is only an oversimplified dynamic representation of the longitudinalvibrations of the DNA intertwined helices which were found to be anharmonic rather than harmonic as oftenassumed in quantum dynamic simulations of DNA.

DNA Spacefilling molecular model

Paracrystalline lattice models of B-DNA structures

A paracrystalline lattice, or paracrystal, is a molecular or atomic lattice with significant amounts (e.g., larger than afew percent) of partial disordering of molecular arranegements. Limiting cases of the paracrystal model arenanostructures, such as glasses, liquids, etc., that may possess only local ordering and no global order. Liquidcrystals also have paracrystalline rather than crystalline structures.

Highly hydrated B-DNA occurs naturally in living cells in such a paracrystalline state, which is a dynamic one in

spite of the relatively rigid DNA double-helix stabilized by parallel hydrogen bonds between the nucleotide

base-pairs in the two complementary, helical DNA chains (see figures). For simplicity most DNA molecular models

ommit both water and ions dynamically bound to B-DNA, and are thus less useful for understanding the dynamic

behaviors of B-DNA in vivo. The physical and mathematical analysis of X-ray and spectroscopic data for

paracrystalline B-DNA is therefore much more complicated than that of crystalline, A-DNA X-ray diffraction

patterns. The paracrystal model is also important for DNA technological applications such as DNA nanotechnology.

Novel techniques that combine X-ray diffraction of DNA with X-ray microscopy in hydrated living cells are now

also being developed (see, for example, 'Application of X-ray microscopy in the analysis of living hydrated cells"[15K

Genomic and biotechnology applications of DNA molecular modeling

There are various uses of DNA molecular modeling in Genomics and Biotechnology research applications, fromDNA repair to PCR and DNA nanostructures. Two-dimensional DNA junction arrays have been visualized byAtomic force microscopy.

Quadruplex DNA may be involved in certain cancers

DNA structure

X-ray scattering

Neutron scattering

Crystallography

Crystal lattices

2D-FT NMRI and Spectroscopy

List of nucleic acid simulation software

Sirius visualization software

X-ray microscopy

QMC@Home

Sir Lawrence Bragg, FRS

Spectroscopy

FT-NMR[18] [19]

Vibrational circular dichroism (VCD)

• NMR Atlas-database [22]

T231

• mmcif downloadable coordinate files of nucleic acids in solution from 2D-FT NMR data

[24]

• NMR constraints files for NAs in PDB format

• NMR microscopy

• Microwave spectroscopy

• FT-IR

• FT-NIR[21] [22] [23]

c ♦ i tt * i a m, • i ■ • J24! P5] [26] [21] [22] [27] [28]

• Spectral, Hyperspectral, and Chemical imaging)

[291 noi

• Raman spectroscopy/microscopy and CARS

• Fluorescence correlation spectroscopy , Fluorescence cross-correlation

a cdctP7] [38] [39]

spectroscopy and FRET

• Confocal microscopy

• Applications of Novel Techniques to Health Foods, Medical and Agricultural Biotechnology .(June 2004) I. C.Baianu, P. R. Lozano, V. I. Prisecaru and H. C. Lin., q-bio/0406047.

• F. Bessel, Untersuchung des Theils der planetarischen Storungen, Berlin Abhandlungen (1824), article 14.

• Sir Lawrence Bragg, FRS. The Crystalline State, A General survey. London: G. Bells and Sons, Ltd., vols. 1 and2., 1966., 2024 pages.

• Cantor, C. R. and Schimmel, P.R. Biophysical Chemistry, Parts I and II., San Franscisco: W.H. Freeman and Co.1980. 1,800 pages.

• Voet, D. and J.G. Voet. Biochemistry, 2nd Edn., New York, Toronto, Singapore: John Wiley & Sons, Inc., 1995,ISBN0-471-58651-X., 1361 pages.

• Watson, G. N. A Treatise on the Theory of Bessel Functions., (1995) Cambridge University Press. ISBN0-521-48391-3.

• Watson, James D. Molecular Biology of the Gene. New York and Amsterdam: W.A. Benjamin, Inc. 1965., 494pages.

• Wentworth, W.E. Physical Chemistry. A short course., Maiden (Mass.): Blackwell Science, Inc. 2000.

• Herbert R. Wilson, FRS. Diffraction of X-rays by proteins, Nucleic Acids and Viruses., London: Edward Arnold(Publishers) Ltd. 1966.

• Kurt Wuthrich. NMR of Proteins and Nucleic Acids., New York, Brisbane,Chicester, Toronto, Singapore: J.Wiley & Sons. 1986., 292 pages.

• Robinson, Bruche H.; Seeman, Nadrian C. (August 1987). "The Design of a Biochip: A Self-AssemblingMolecular-Scale Memory Device". Protein Engineering 1 (4): 295-300. ISSN 0269-2139. Link [45]

• Rothemund, Paul W. K.; Ekani-Nkodo, Axel; Papadakis, Nick; Kumar, Ashish; Fygenson, Deborah Kuchnir &Winfree, Erik (22 December 2004). "Design and Characterization of Programmable DNA Nanotubes". Journal ofthe American Chemical Society 126 (50): 16344-16352. doi:10.1021/ja0443191. ISSN 0002-7863.

• Keren, K; Kinneret Keren, Rotem S. Berman, Evgeny Buchstab, Uri Sivan, Erez Braun (November 2003)."DNA-Templated Carbon Nanotube Field-Effect Transistor" [46]. Science 302 (6549): 1380-1382.

doi: 10.1126/science. 1091022. ISSN 1095-9203.

• Zheng, Jiwen; Constantinou, Pamela E.; Micheel, Christine; Alivisatos, A. Paul; Kiehl, Richard A. & SeemanNadrian C. (2006). "2D Nanoparticle Arrays Show the Organizational Power of Robust DNA Motifs". NanoLetters 6: 1502-1504. doi:10.1021/nl060994c. ISSN 1530-6984.

• Cohen, Justin D.; Sadowski, John P.; Dervan, Peter B. (2007). "Addressing Single Molecules on DNANanostructures". Angewandte Chemie 46 (42): 7956-7959. doi:10.1002/anie.200702767. ISSN 0570-0833.

• Constantinou, Pamela E.; Wang, Tong; Kopatsch, Jens; Israel, Lisa B.; Zhang, Xiaoping; Ding, Baoquan;Sherman, William B.; Wang, Xing; Zheng, Jianping; Sha, Ruojie & Seeman, Nadrian C. (2006). "Doublecohesion in structural DNA nanotechnology". Organic and Biomolecular Chemistry 4: 3414—3419.doi:10.1039/b605212f.

• Hallin PF, David Ussery D (2004). "CBS Genome Atlas Database: A dynamic storage for bioinformatic resultsand DNA sequence data". Bioinformatics 20: 3682—3686.

• Zhang CT, Zhang R, Ou HY (2003). "The Z curve database: a graphic representation of genome sequences".Bioinformatics 19 (5): 593-599. doi:10.1093/bioinformatics/btg041

• DNA the Double Helix Game From the official Nobel Prize web site

• MDDNA: Structural Bioinformatics of DNA [47]

• Double Helix 1953—2003 National Centre for Biotechnology Education

• DNAlive: a web interface to compute DNA physical properties . Also allows cross-linking of the results with

the UCSC Genome browser and DNA dynamics.

[491

• DiProDB: Dinucleotide Property Database . The database is designed to collect and analyse thermodynamic,

structural and other dinucleotide properties.

• Further details of mathematical and molecular analysis of DNA structure based on X-ray data

• Bessel functions corresponding to Fourier transforms of atomic or molecular helices.

• Application of X-ray microscopy in analysis of living hydrated cells

T521

• overview of STM/AFM/SNOM principles with educative videos

Databases for DNA molecular models and sequencesX-ray diffraction

• NDB ID: UD0017 Database [17]

• X-ray Atlas -database

T541

• PDB files of coordinates for nucleic acid structures from X-ray diffraction by NA (incl. DNA) crystals

• Structure factors dowloadable files in CIF formatNeutron scattering

• ISIS neutron source: ISIS pulsed neutron source:A world centre for science with neutrons & muons at Harwell,near Oxford, UK.

X-ray microscopy

• Application of XElectron microscopy

• DNA under electron microscope

Application of X-ray microscopy in the analysis of living hydrated cells

Genomic and structural databases

— contains examples of base skews.

[58]

T571• CBS Genome Atlas Database —contains examples of base skews.

• The Z curve database of genomes — a 3-dimensional visualization and analysis tool of genomes

• DNA and other nucleic acids' molecular models: Coordinate files of nucleic acids molecular structure models inPDB and CIF formats [59]

Atomic force microscopy

• How SPM Works [60]

• SPM Image Gallery - AFM STM SEM MFM NSOM and more. [61]

References

[I] Franklin, R.E. and Gosling, R.G. recd.6 March 1953. Acta Cryst. (1953). 6, 673 The Structure of Sodium Thymonucleate Fibres I. TheInfluence of Water Content Acta Cryst. (1953). and 6, 678 The Structure of Sodium Thymonucleate Fibres II. The Cylindrically SymmetricalPatterson Function.

[2] Cochran, W., Crick, F.H.C. and Vand V. 1952. The Structure of Synthetic Polypeptides. 1. The Transform of Atoms on a Helix. Acta Cryst.

5(5):581-586.[3] Crick, F.H.C. 1953a. The Fourier Transform of a Coiled-Coil., Acta Crystallographica 6(8-9):685-689.[4] Watson, James D. and Francis H.C. Crick. A structure for Deoxyribose Nucleic Acid (http://www.nature.com/nature/dna50/watsoncrick.

pdf) (PDF). Nature 171, 737-738, 25 April 1953.[5] Watson, J.D; Crick F.H.C. 1953b. The Structure of DNA., Cold Spring Harbor Symposia on Qunatitative Biology 18:123-131.[6] Wilkins M.H.F., A.R. Stokes A.R. & Wilson, H.R. (1953). "Molecular Structure of Deoxypentose Nucleic Acids" (http://www.nature.com/

nature/dna50/wilkins.pdf) (PDF). Nature 171 (4356): 738-740. doi:10.1038/171738a0. PMID 13054693..[7] Elson D, Chargaff E (1952). "On the deoxyribonucleic acid content of sea urchin gametes". Experientia 8 (4): 143—145.[8] Chargaff E, Lipshitz R, Green C (1952). "Composition of the deoxypentose nucleic acids of four genera of sea-urchin". J Biol Chem 195 (1):

155-160. PMID 14938364.[9] Chargaff E, Lipshitz R, Green C, Hodes ME (1951). "The composition of the deoxyribonucleic acid of salmon sperm". J Biol Chem 192 (1):

223-230. PMID 14917668.[10] Chargaff E (1951). "Some recent studies on the composition and structure of nucleic acids". J Cell Physiol Suppl 38 (Suppl).

[II] Magasanik B, Vischer E, Doniger R, Elson D, Chargaff E (1950). "The separation and estimation of ribonucleotides in minute quantities". JBiol Chem 186 (1): 37-50. PMID 14778802.

[12] Chargaff E (1950). "Chemical specificity of nucleic acids and mechanism of their enzymatic degradation". Experientia 6 (6): 201—209.[13] Hosemann R., Bagchi R.N., Direct analysis of diffraction by matter, North-Holland Pubis., Amsterdam — New York, 1962.[14] Baianu, I.C. (1978). "X-ray scattering by partially disordered membrane systems.". Acta Cryst., A34 (5): 751—753.

doi: 10.1107/S0567739478001540.[15] Mao, Chengde; Sun, Weiqiong & Seeman, Nadrian C. (16 June 1999). "Designed Two-Dimensional DNA Holliday Junction Arrays

Visualized by Atomic Force Microscopy". Journal of the American Chemical Society 121 (23): 5437—5443. doi:10.1021/ja9900398.

[18] (http://www.jonathanpmiller.com/Karplus.html)- obtaining dihedral angles from J coupling constants[19] (http://www.spectroscopynow.com/FCKed...e/specNOW/HTML files/General_Karplus_Calculator.htm) Another

Javascript-like NMR coupling constant to dihedral[20] Lee, S. C. et al., (2001). One Micrometer Resolution NMR Microscopy. J. Magn. Res., 150: 207-213.[21] Near Infrared Microspectroscopy, Fluorescence Microspectroscopy,Infrared Chemical Imaging and High Resolution Nuclear Magnetic

Resonance Analysis of Soybean Seeds, Somatic Embryos and Single Cells., Baianu, I.C. et al. 2004., In Oil Extraction and Analysis.,!).

Luthria, Editor pp.241-273, AOCS Press., Champaign, IL.[22] Single Cancer Cell Detection by Near Infrared Microspectroscopy, Infrared Chemical Imaging and Fluorescence Microspectroscopy.2004.1.

C. Baianu, D. Costescu, N. E. Hofmann, S. S. Korban and et al., q-bio/0407006 (July 2004) (http://arxiv.org/abs/q-bio/0407006)[23] Raghavachari, R., Editor. 2001. Near-Infrared Applications in Biotechnology, Marcel-Dekker, New York, NY.[24] http://www.imaging.net/chemical-imaging/Chemical imaging[25] http://www.malvern.com/LabEng/produc...bliography.htm E. N. Lewis, E. Lee and L. H. Kidder, Combining

Imaging and Spectroscopy: Solving Problems with Near-Infrared Chemical Imaging. Microscopy Today, Volume 12, No. 6, 11/2004.[26] D.S. Mantus and G. H. Morrison. 1991. Chemical imaging in biology and medicine using ion microscopy., Microchimica Acta, 104, (1-6)

January 1991, doi: 10.1007/BF01245536[27] J. Dubois, G. Sando, E. N. Lewis, Near-Infrared Chemical Imaging, A Valuable Tool for the Pharmaceutical Industry, G.I.T. Laboratory

Journal Europe, No.1-2, 2007.[28] Applications of Novel Techniques to Health Foods, Medical and Agricultural Biotechnology.(June 2004).,I. C. Baianu, P. R. Lozano, V. I.

Prisecaru and H. C. Lin q-bio/0406047 (http://arxiv.org/abs/q-bio/0406047)[29] Chemical Imaging Without Dyeing (http://witec.de/en/download/Raman/Im...croscopy04.pdf)[30] C.L. Evans and X.S. Xie.2008. Coherent Anti-Stokes Raman Scattering Microscopy: Chemical Imaging for Biology and Medicine.,

doi: 10.1146/annurev.anchem.l.031207.112754 Annual Review of Analytical Chemistry, 1: 883-909.[31] Eigen, M., Rigler, R. Sorting single molecules: application to diagnostics and evolutionary biotechnology,(1994) Proc. Natl. Acad. Sci. USA,

91,5740-5747.[32] Rigler, M. Fluorescence correlations, single molecule detection and large number screening. Applications in biotechnology,(1995) J.

Biotechnol., 41,177-186.[33] Rigler R. and Widengren J. (1990). Ultrasensitive detection of single molecules by fluorescence correlation spectroscopy, BioScience (Ed.

Klinge & Owman) p. 180.

DNA Dynamics 239

[34] Oehlenschlager F., Schwille P. and Eigen M. (1996). Detection of HIV-1 RNA by nucleic acid sequence-based amplification combined with

fluorescence correlation spectroscopy, Proc. Natl. Acad. Sci. USA 93:1281.[35] Bagatolli, L.A., and Gratton, E. (2000). Two-photon fluorescence microscopy of coexisting lipid domains in giant unilamellar vesicles of

binary phospholipid mixtures. Biophys J., 78:290-305.[36] Schwille, P., Haupts, U., Maiti, S., and Webb. W.(1999). Molecular dynamics in living cells observed by fluorescence correlation

spectroscopy with one- and two-photon excitation. Biophysical Journal, 77(10):2251-2265.[37] FRET description (http://dwb.unl.edu/Teacher/NSF/C08/C...gmocz/fret.htm)[38] doi:10.1016/S0959-440X(00)00190-l (http://dx.doi.org/10.1016/S0959-440X(00)00190-l)Recent advances in FRET: distance

determination in protein—DNA complexes. Current Opinion in Structural Biology 2001, 11(2), 201-207[39] http://www.fretimaging.org/mcnamaraintro.html FRET imaging introduction

Interactomics

Interactomics is a discipline at the intersection of bioinformatics and biology that deals with studying both theinteractions and the consequences of those interactions between and among proteins, and other molecules within acell . The network of all such interactions is called the Interactome. Interactomics thus aims to compare suchnetworks of interactions (i.e., interactomes) between and within species in order to find how the traits of suchnetworks are either preserved or varied. From a mathematical, or mathematical biology viewpoint an interactomenetwork is a graph or a category representing the most important interactions pertinent to the normal physiologicalfunctions of a cell or organism.

Interactomics is an example of "top-down" systems biology, which takes an overhead, as well as overall, view of abiosystem or organism. Large sets of genome-wide and proteomic data are collected, and correlations betweendifferent molecules are inferred. From the data new hypotheses are formulated about feedbacks between these

[2]

molecules. These hypotheses can then be tested by new experiments .

Through the study of the interaction of all of the molecules in a cell the field looks to gain a deeper understanding ofgenome function and evolution than just examining an individual genome in isolation . Interactomics goes beyondcellular proteomics in that it not only attempts to characterize the interaction between proteins, but between allmolecules in the cell.

Methods of interactomics

The study of the interactome requires the collection of large amounts of data by way of high throughput experiments.Through these experiments a large number of data points are collected from a single organism under a small number

[2]

of perturbations These experiments include:

• Two-hybrid screening

• Tandem Affinity Purification

• X-ray tomography

• Optical fluorescence microscopy

240

Recent developments

The field of interactomics is currently rapidly expanding and developing. While no biological interactomes havebeen fully characterized. Over 90% of proteins in Saccharomyces cerevisiae have been screened and theirinteractions characterized, making it the first interactome to be nearly fully specified

Also there have been recent systematic attempts to explore the human interactome and

Other species whose interactomes have been studied in some detail include Caenorhabditis elegans and Drosophilamelanogaster.

Criticisms and concerns

Kiemer and Cesareni raise the following concerns with the current state of the field:

• The experimental procedures associated with the field are error prone leading to "noisy results". This leads to30% of all reported interactions being artifacts. In fact, two groups using the same techniques on the sameorganism found less than 30% interactions in common.

• Techniques may be biased, i.e. the technique determines which interactions are found.

• Ineractomes are not nearly complete with perhaps the exception of S. cerivisiae.

• While genomes are stable, interactomes may vary between tissues and developmental stages.

• Genomics compares amino acids, and nucleotides which are in a sense unchangeable, but interactomics comparesproteins and other molecules which are subject to mutation and evolution.

• It is difficult to match evolutionary related proteins in distantly related species.

Interactomics 241

Interaction networkProteomicsMetabolic networkMetabolic network modellingMetabolic pathwayGenomics

Mathematical biologySystems biology

• Interactomics.org . A dedicated interactomics web site operated under BioLicense.

• Interactome.org . An interactome wiki site.

[71

• PSIbase Structural Interactome Map of all Proteins.

ro]

• Omics.org . An omics portal site that is openfree (under BioLicense)

• Genomics.org .A Genomics wiki site.

• Comparative Interactomics analysis of protein family interaction networks using PSIMAP (protein structuralinteractome map)

• Interaction interfaces in proteins via the Voronoi diagram of atoms

• Using convex hulls to extract interaction interfaces from known structures. Panos Dafas, Dan Bolser, JacekGomoluch, Jong Park, and Michael Schroeder. Bioinformatics 2004 20: 1486-1490.

• PSIbase: a database of Protein Structural Interactome map (PSIMAP). Sungsam Gong, Giseok Yoon, Insoo JangBioinformatics 2005.

• Mapping Protein Family Interactions : Intramolecular and Intermolecular Protein Family Interaction Repertoiresin the PDB and Yeast, Jong Park, Michael Lappe & Sarah A. TeichmannJ.M.B (2001).

ri2i

• Semantic Systems Biology

References

[I] Kiemer, L; G Cesareni (2007). "Comparative interactomics: comparing apples and pears?". TRENDS in Biochemistry 25: 448—454.doi:10.1016/j.tibtech.2007.08.002.

[2] Bruggeman, F J; H V Westerhoff (2006). "The nature of systems biology". TRENDS in Microbiology 15: 45—50.

doi:10.1016/j.tim.2006.11.003.[3] Krogan, NJ; et al. (2006). "Global landscape of protein complexes in the yeast Saccharomyeses Cerivisiae ". Nature 440: 637—643.

doi: 10.1038/nature04670.[4] further citation needed[5] http://interactomics.org[6] http://interactome.org[7] http://psibase.kobic.re.kr[8] http://omics.org[9] http://genomics.org[10] http://bioinformatics.oxfordjournals...ull/21/15/3234

Article Sources and Contributors

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Algebraic logic Source: http://en.wikipedia.org/w/index.php'?oldid=340372691 Contributors: CBM, CBM2, Chalst, Charles Matthews, Elwikipedista, EmilJ, Giftlite, Gregbard, Hmains, JitseNiesen, Koavf, Mhss, Michael Hardy, PWilkinson, Palnot, Strangename, The Tetrast, Trovatore, 11 anonymous edits

Quantum logic Source: http://en.wikipedia.Org/w/index.php?oldid=353702379 Contributors: Alvin Seville, Andris, Angela, Archelon, Argumzio, Aster Rainbow, BD2412, Bci2, CSTAR,Charles Matthews, Cybercobra, DJIndica, David edwards, Dcoetzee, Dmr2, Dysprosia, Edward, EpsilonO, GTBacchus, Gaius Cornelius, Gene Ward Smith, Giftlite, GordonRoss, Gregbard, HairyDude, Headbomb, Icairns, Ilan770, Jengod, John Baez, Kimberlyg, KnightRider, Kuratowski's Ghost, Kzollman, Lethe, Linas, Lucidish, Met mht, Meznaric, Mhss, Michael Hardy, Modify,Oerjan, Parkyere, Pohta ce-am pohtit, PowerUserPCDude, RsimmondsOl, Sheliak, Shlomi Hillel, Steven Johns ton, Stevertigo, T=0, Trovatore, Uncia, V79, Zumbo, ^^s, 40 anonymous edits

Quantum computer Source: http://en.wikipedia.org/w/index.php?oldid=354261630 Contributors: -Ozone-, 194.117.133.xxx, lmujin22, 41ex, A5b, AAAAA, AWeishaupt, Aarchiba,Abdullahazzam, Ajb, Albedo, Ale2006, Alex R S, Alksentrs, Alsandro, Amcfreely, Amwebb, AndrewStuckey, Andrewpmk, Andris, Antandrus, Antlegs, Anville, Anwar saadat, Arcfrk,Archelon, Arnero, ArnoldReinhold, Asmeurer, Asparagus, Atropos235, Auric, AxelBoldt, B9 hummingbird hovering, Bci2, Beagel, Beeban, Ben Standeven, Bencoder, Bender235, Bevo,Bibliosapien, Bigmantonyd, Bihco, BjohnsonOO, Bletchley, Bobby D. Bryant, Bobol92, Bond4154, Booyabazooka, Brandon, Brighterorange, Brilliand, Bryan Derksen, Bubba hotep,BumbleFootClown, Burgaz, CBM, CSTAR, CYD, Captanplutol23, Card, Cenarium, Charles Matthews, CharlesGillingham, Chris 73, CloudNine, Cometstyles, Connelly, Couchpotato99, CountCaspian, Craig Pemberton, Creidieki, Crunkcar, Cryptonaut, Curtdbz, Cyan, Cyp, DV8 2XL, Dan East, Dan Granahan, Danko Georgiev MD, Danny, Dar-Ape, DarkFalls, DarkShroom, Daveagp,David Battle, David Gerard, David n m bond, DavidB, DavidLevinson, David go thberg, Davidmenz, Dead3y3, DethmeOw, Dgrant, Dr.K., DuckFeather, Durval, Dysprosia, Eaglizard, Edd Porter,Edonovan, Edward, Eigenlambda, Ekangas, El C, Elb2000, Eluchil, Epo, ErinM, Eurobas, EyulOO, FKmailliW, Fattony77, Favonian, Fgrosshans, Foxxygirltamara, Frankenpuppy, Fullstop,Furrykef, Fyyer, G Colyer, GBL, GaaraMsg, GaeusOctavius, Gail, Gaius Cornelius, Galwhaa, Gary King, Gauge, Gentgeen, GeorgelOO, Giftlite, Gioto, Glenn, Gnixon, Goldsmitharmy,Graham87, Green caterpillar, GregorB, Gtg207u, HRV, Hadal, Hanjabba, Hannover.post, Hans Adler, Harold f, Harry Potter, Harryboyles, Hatethedj, Havanafreestone, Headbomb, Hfastedge,Hmrox, Hulagutten, HumphreyW, Husond, Hyandat, Hyperdivision, Iain David Stewart, Ihopel27, Ikh, Ilia Kr., Dispirit, Indosauros, Insurrectionist, Intgr, Inwind, Isaacsurh, Iseeaboar, Isnow,Ispy 1981, J.delanoy, JMK, JRGregory, Jao, Jarekadam, JavOs, Jbw2, Jeargle, Jeff G., Jengod, Jitse Niesen, Jj 137, Jkasd, Jni, JohnCD, Jon5I3, JonHarder, Jorfer, Jotomicron, Jrockley, JustinStafford, Jwoehr, KD5TVI, Kannan karthik, Kate, Keegan, Keenan Pepper, Kevin B12, Kevyn, Kine, Kizeral, Korepin, Ksn, Kuru, LC, Liftarn, Ligulem, Linas, Linus M., Looxix, Lostart, Lotu,LunatikOwl, Lunkwill, Lupin, MBisanz, MER-C, MagnaMopus, Manoliisfat, Marco de Mol, Marksuppes, Martaen, MartinSieg, Mat8989, Matt Crypto, Mattblack82, Matthewsim, MauriceCarbonaro, Mav, Maximus Rex, MementoVivere, Michael Hardy, MichaelMcGuffin, Michal Jurosz, Mikel024, Millerc, Mindmatrix, Miym, Mjager, Moment, Moonriddengirl, Mpassman,MrOllie, Mro, MujO, MuncherOfSpleens, Ndickson, N0I888, Noldoaran, Norm mit, Not enough names left, NotThatJamesBrown, Nurg, Nzv8fan, Octopus-Hands, Officiallyover, Ojigiri, OlegAlexandrov, Oliver Pereira, Onaillim, Oneyd, Onorem, Pagrashtak, Pak21, Pakaran, Palfrey, PatrickHoo, PaulCook, Peter bertok, Peterdjones, Phil Boswell, Phoneused, Physis, Piano non troppo,Pietzsche, Pohta ce-am pohtit, Poor Yorick, Populus, Powo, Pwjb, Pyrospirit, Qwertyus, REQC, RG2, RHaworth, RJRocket53, RTC, Racklever, Rajrajmarley, Ravedave, ReallyMale, RedThunder, RedWolf, Remy B, Revived, Rich Farmbrough, Ripper234, Roadrunner, Robert Merkel, RobertG, RobinK, Robma, RonanSandford, Ronz, RoyBoy, Ruud Koot, Rwwww, Sajendra,Sam Hocevar, Sambarrows, Sanders muc, SandyGeorgia, Sathimantha, Scott McNay, Scottcraig, Selain03, Seraph 31, Shepelyansky, Shoyer, Simetrical, SimonMayer, Skippydo, Sligocki,Smite-Meister, Snakeyes (usurped), Snowolf, Speedplane, Spikeukl4, Spin-Half, Sploo22, Squiggle, Steamturn, Stevertigo, Stsang, Supaman89, Superm401, Susvolans, Svick, Symmetry singer,TALlama, Taed, Taejo, Talon Artaine, Tarotcards, Tboonsun, Techman224, Tellyaddict, That Guy, From That Show!, The Belgain, The Rogue Penguin, Tim Starling, Timwi, Tobyc75, Togo,Tom harrison, Tomatoman, Tomstdenis, Trel234, Tree Biting Conspiracy, Tricky Wiki44, Troelssj, Turdus, Turnstep, Ultra megatron, Uncle G, UncleDouggie, Undecided, Vaspian, Verbal,Vincenzo.romano, VodkaJazz, Wafulz, Weekwhom, Wereon, Whispering, Who, Wikiborg, Wikiklrsc, Wikiscient, WilliamKF, Wim van Dam, WindOwl, Wish Wellingtons, Wolfkeeper,Woohookitty, Wrdavenport, Wtanaka, X1011, Xiong Chiamiov, Yongxiangu, Zflood, 629 anonymous edits

Quantum chemistry Source: http://en.wikipedia.org/w/index.php'?oldid=354070567 Contributors: 144.189.40.xxx, 208.40.185.xxx, 41ex, Acroterion, Alansohn, Alex '05, Auntof6, Ayla,BTDenyer, Bci2, Bduke, Bob, BrianY, Bubbha, CDN99, Capecodeph, ChemGardener, Chuunen Baka, CloudNine, Cmdrjameson, CommonsDelinker, Conversion script, Cool3, Cypa, Danhe,EdJohnston, Edsanville, EmilyT, Euryalus, Fygoat, Gentgeen, Gershom, Giftlite, Glenn, GregorB, Haljolad, HappyCamper, Headbomb, Holdran, Hugo-cs, Ian Pitchford, Ithacagorges, Itub,Jantop, JerrySteal, Jheald, Kaliumfredrik, Karol Langner, Keenan Pepper, Keilana, Koinut, Krash, La goutte de pluie, Lampuchi, Ligulem, Lijuni, Looxix, M stone, Martin Hedegaard, Meisfunny,Milo, Nickptar, Noisy, Nzzl, Okedem, P99am, Perelaar, RA0808, Ratol, Rifleman 82, SHL-at-Sv, SQL, Sadi Carnot, Salsb, Shalom Yechiel, Shanel, Sidhekin, Smoe, Sunev, Tasudrty, Terhorstj,Timwi, UninvitedCompany, Vb, Vgy7ujm, Vig vimarsh, Voigfdsa, Vsmith, W.F.Galway, Wiki alf, Xebvor, Yurik, Zarniwoot, Zeimusu, AjieKcaH/rbp, f^vsv £.Uf' 144 anonymous edits

Density functional theory Source: http://en.wikipedia.org/w/index.php?oldid=353188446 Contributors: Ae-a, Agilemolecule, AlbertoCastro, Apple2, AskHL, Azo bob, Bachrach44, Baxxterr,Bduke, BluePlatypus, Bob K31416, Brews ohare, Buriti, Bwschnei, Charles Matthews, Chemuser, Chymicus, Dirac66, Ebuchol, Edsanville, Emersoni, Enpi, Evgeny, FelixP, Fuzheado, Gafnero,Geboy, Geling, Giftlite, Headbomb, Hourahine, Iamthealchemist, Ianbolland, Isilanes, Isnow, Itamblyn, JaGa, Jitse Niesen, Joy, Karol Langner, Lfh, Lucaskw, MaxBoldin, Michael Hardy,MuDavid, NNemec, Nick Mks, Ouji-fin, P99am, Petulda, Poszwa, Pt, Raghunathan, Rangek, Rhobite, RoibI, Royalbooksnap, Rundquist, Ruud Koot, Salsb, Samprox, Sbandrews, Sbo,SebastianHelm, Shaddack, Spellchecker, Stone, Svenbor, TDogg310, THEN WHO WAS PHONE?, Tdoune, Terhorstj, Tim Starling, Tobias Bergemann, Toulouse, Trigger hippie77, V8rik,Vexedd, Vmilman, Vsmith, Wavefunk, WijzeWillem, Wik, WikipAcct, WilliamDParker, Wiz9999, Wolf2046, Xavier andrade, Youandme, Zanimum, Zarniwoot, 192 anonymous edits

Birefringence Source: http://en.wikipedia.org/w/index.php?oldid=353773007 Contributors: A. B., Ackbeet, Avihu, Bluemoose, Brews ohare, Bryan Derksen, Catskul, Chocofever, Ciphers,Cmdrjameson, Conscious, Corvus cornix, Cutler, DKToptics, Dougher, DrBob, Drewmk2, Elert, Ellieandaedanforever, Ellywa, Foofighter20x, GeoGreg, Hankwang, Headbomb, Heron, Hul2,Icep, JTN, Jeroen94704, JerrySteal, Johnpseudo, Kar.ma, Karol Langner, Keenan Pepper, Kodang, Krlhc8, Laundrypowder, Leeworth, LiDaobing, Lzur, Michael Hardy, Mikael Haggstrom,MrBell, Ms2ger, Mwtoews, NaBUru38, Nvpatentlawyer, ObsessiveMathsFreak, Ojigiri, Paolo.dL, Peterlewis, Professorgt, Pwjb, Qfl247, Quantumobserver, Rikvoerman, Salthebad, Saperaud,Sdornan, Shrampes, Siim, Spiegelberg88, Srleffler, Stefan.bucur, Steve Quinn, Stevenj, Tantalate, Twthmoses, Ufim, Vsmith, YoavShapira, Ytterbium, 98 anonymous edits

Polarization spectroscopy Source: http://en.wikipedia.org/w/index.php?oldid=336954I87 Contributors: Evgeny, Jovianeye, Rich257, ZooFari

Polarized IR Spectroscopy Source: http://en.wikipedia.org/w/index.php?oldid=l6987408 Contributors: 194.200.130.xxx, Aboalbiss, Ahoerstemeier, Anna Lincoln, Annabel, Antandrus,Arcadian, Arnero, Ary29, Bensaccount, BigFatBuddha, Biophysik, Bobthebuilder37, Bomemir, Borgx, BountyTJ, Bubba hotep, CLW, Calaschysm, Charles Matthews, Christopherlin, ChuckSirloin, Cobi, Coffee, CommonsDelinker, Conversion script, Cwkmail, DMacks, DavidRKelly, Deglr6328, DerHexer, Dieter Baurecht, Dr.Soft, Drbreznjev, Drmies, El C, Eno-ja,Fieldday-sunday, Finalnight, Francs2000, Freestyle-69, Fresheneesz, Fuhghettaboutit, Fyver528, Gentgeen, GeorgHH, GermanX, Giftlite, Gilliam, Greggklein, Grimlock, Guillom, HYPN2457,Hankwang, HappyCamper, Haukurth, Heron, Hesacon, Hollgor, II MusLiM HyBRiD II, Ian Pitchford, Imedio, Informationtheory, J.delanoy, Jackol, Jaraalbe, Jcwf, Johnbrownsbody, Junglecat,Jusdafax, Kcordina, Kkmurray, Kwiskool, Lifer21, Lightmouse, Littleghoti, Logger9, Lorenzarius, LouisBB, LukeSurl, Martyjmch, Materialscientist, Michael Hardy, Mjwlancs, Mythealias,Nakon, NewEnglandYankee, Nivix, Nmathew, Old Moonraker, Peterlewis, Pharmacomancer, Pit, Punctilius, Quadell, Quantockgoblin, Rifleman 82, Rob Hooft, Ronningt, SABenyunes, SamHocevar, SantoshS, Shalom Yechiel, Skier Dude, Smokefoot, SomeguyI221, Srnec, Stephenb, Stokerm, SuperTycoon, TechPurism, The wub, Tiago Becerra Paolini, Urbansky, V8rik, Vcelloho,Vector Potential, Vegaswikian, Veinor, Visor, Vsmith, Werson, Wikieditor06, Wmahan. Yashkochar. 253 anonymous edits

Circular dkhroism Source: http://en.wikipedia.org/w/index.php?oldid=355135441 Contributors: AJim, Andrew Rodland, Atlant, Bci2, Bensaccount, Biophysik, Bjsamelsonjones, BryanDerksen, ChemGardener, Christopherlin, Crystal whacker, Dave3457, DeadEyeArrow, Dirac66, DrEricYH, Dwmyers, Elementl6, Evercat, Frultbat, Herr blaschke, ILike2BeAnonymous,Icairns, Jammedshut, Jeodesic, Jfitzger, Johann Wolfgang, Karol Langner, Kinlee, Kjaergaard, Kkmurray, Loohcsnuf, LostLucidity, Maartend8, Mark Oakley, Materialscientist, Mboverload,Michael Hardy, Miguel Andrade, Mikaduki, Mikegretes, Mklewpatinond, Nakane, Nikai, Noosentaal, Obradovic Goran, PaddyM, Paolo.dL, PierreAbbat, RASnyder, Steve Quinn, Synchronism,The wub, Thorwald, Tldcollins, V8rik, WillowW, Zen Mind, 82 anonymous edits

Vibrational circular dichroism Source: http://en.wikipedia.org/w/index.php?oldid=354811869 Contributors: Aktsu, Auntof6, Bci2, Buurma, Dave3457, Jndurand, LilHelpa, Petulda, R'n'B,

Slaweks, Wnt, 3 anonymous edits

Optical rotatory dispersion Source: http://en.wikipedia.org/w/index.php?oldid=331863840 Contributors: BobbyBoulders, Chutznik, Dirac66, GTBacchus, Karol Langner, SemperBlotto,Srleffler, V8rik, YellowMonkey, 6 anonymous edits

Raman spectroscopy Source: http://en.wikipedia.org/w/index.php?oldid=352085509 Contributors: AJim, ARBradley4015, Afrine, Akv, Andrewavalon, Annabel, ArepoEn, Asfarer,Birdbrainscan, Blind cyclist, Brat32, Bullraker, Cdegallo, Charles Matthews, Christopherlin, Cyblor, D.Wardle, D3 TECHNOLOGIES, David Eppstein, Dazzaling69, Dch312, Dfbaum,Editore99, Fang Aili, Ferini, GT, Gabi bart, Gaius Cornelius, Galoubet, Gene Nygaard, Gene s, Gentgeen, Gerkleplex, GermanX, Gioto, Gunnar Larsson, Hankwang, Jaeger5432, Jaganath,

Jameslh, Janke, Jll, Jmameren, Jofox, Jonnyapple, Judenicholson, Keramamide, Kkmurray, Kraftlos, Kwamikagami, Latch.r, LordDamorcro, Loreshadow, LostLucidity, Lotje, MARKELLOS,MICKYGAL007, Magicalsaumy, Mahendra Kulkarni, Manulinho72, MarcoTolo, Martin Hedegaard, Measly Swan, Merope, Michbich, Mill ham, Minored, Mippi283, Moxfyre, Mythealias,Nihonjoe, Nikai, Nmnogueira, Paul August, Paul venter, Pavlina2.0, Pcarbonn, Pericles899, Petergans, Piano non troppo, Pixeltoo, Quantumobserver, RTC, Ravi khanna, Redleaf, RichFarmbrough, Rob Hooft, Ronningt, Rossheth, Ruliel23, Shashang, Shreevatsa, Smalljim, Srosie68, TDogg310, Tantalate, Tha Stunna, The number c, The wub, Thue, Tillwe, Tmb4bd,Tomatoman, Tomgally, Tzontonel, Uther Dhoul, Will4235, Wilson003, Yasuakinaito, Zylorian, 159 anonymous edits

Coherent anti-Stokes Raman spectroscopy Source: http://en.wikipedia.org/w/index.php?oldid=340339638 Contributors: Alash, Delldot, Epotma, Feezo, Gwernol, HLOfferhaus, Interiot,Kkmurray, Lightmouse, MWS, Maartend8, Nerdseeksblonde, Nick Y., Ohnoitsjamie, PigFlu Oink, Rich Farmbrough, ShakingSpirit, Signalhead, The wub, Thehelpfulone, V8rik, Vladsinger, 29anonymous edits

Raman Microscopy Source: http://en.wikipedia.org/w/index.php?oldid=308343741 Contributors: Gabi bart, Xezbeth

Imaging spectroscopy Source: http://en.wikipedia.org/w/index.php'?oldid=346629165 Contributors: Andyphil, Bci2, Curaci, Donarreiskoffer, HYPN2457, IdglOl, Ivan Shmakov, JFBolton,Jaeger5432, Jim.henderson, Kkmurray, Larryloz, Ligulem, NathanHagen, Nbarth, Omegatron, Pearle, Pjvpjv, SchaeOOl, Steve Quinn, ThaddeusB, Wadje, Zowie, 22 anonymous edits

Chemical imaging Source: http://en.wikipedia.org/w/index.php?oldid=352448633 Contributors: Alansohn, Andyphil, AngelOfSadness, Annabel, Banus, Batykefer, Bci2, BierHerr, Chris thespeller, Closedmouth, D6, Davewild, Editore99, Fgnievinski, Gabi bart, GeeJo, HYPN2457, Iridescent, JIP, Jim.henderson, Kkmurray, Larryloz, Mdd, Mkansiz, Natalie Erin, Skysmith, Stone,Tassedethe, Ultraexactzz, Wilson003, 40 anonymous edits

Spin polarization Source: http://en.wikipedia.org/w/index.php?oldid=337393318 Contributors: Arnero, Ctchiang, Kusma, Michael Hardy, Mindmatrix, RDR, SCEhardt, Shaddack, Tayga,V8rik, Zawersh, 4 anonymous edits

Polarized Neutron Spectroscopy Source: http://en.wikipedia.org/w/index.php'?oldid=315969727 Contributors: Cardamon, Chrisainthere, EBlackburn, Eubene, Joachim Wuttke, Neelix,Tpikonen, 3 anonymous edits

Polarized Muon Spectroscopy Source: http://en.wikipedia.org/w/index.php'?oldid=353396210 Contributors: BWDuncan, Dalibor Bosits, DanMS, Galaxiaad, Gene Nygaard, Grj23, JHBrewer,Jcwf, Kite0419, Kusma, Materialscientist, Pionade, RDR, Richtea2007, Sergio.ballestrero, Slavomirkapusta, Snafu450, Strait, Thinking of England, WikHead, 20 anonymous edits

Time-resolved spectroscopy Source: http://en.wikipedia.org/w/index.php?oldid=353725604 Contributors: Azo bob, Cenarium, Christopherlin, GregorB, Hankwang, Man It's So Loud In Here,SJP, THEN WHO WAS PHONE?, 12 anonymous edits

Terahertz spectroscopy Source: http://en.wikipedia.org/w/index.php?oldid=323341545 Contributors: Frankhindle, Johnlp, Kkmurray, Rich Farmbrough, Zroutik, 1 anonymous edits

Applied spectroscopy Source: http://en.wikipedia.org/w/index.php?oldid=352902543 Contributors: Bambika, Draganakusiclazic, Egpetersen, Graeme Bartlett, Headbomb, Itub, Jaeger5432,Kkmurray, Millosh, Peterlewis, Pro crast in a tor, Sbialkow, Woohookitty, 6 anonymous edits