# 7.1: Introduction to Reversible Binding

$$\newcommand{\vecs}{\overset { \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}{\| #1 \|}$$ $$\newcommand{\inner}{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}{\| #1 \|}$$ $$\newcommand{\inner}{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$

Learning Objectives

• write equations for the dissociation constant (KD), mass balance of total macromolecule (M0), total ligand (L0), and [ML] as a function of L or Lo ([ML] = [M0][L]/(KD+ [L]) (when Lo >> Mo or when free [L] is known) and Y = fractional saturation = Y = ([ML]/[M0] = [L]/(KD+ [L])
• decide which of two given equations for [ML] should be used under conditions when the above conditions for L0 and L are given
• based on the equation ([ML] = [M0][L]/(KD+ [L]) draw qualitative graphs for different given L0, L, and Kd values
• determine fraction saturation given relatives values of Kd and L, assuming L0 >> M0
• compare relative % bound for covalent binding of protons to an acid and noncovalent binding of a ligand to a macromolecule given pka/pH and Kd/L values
• describe differences in binding curves for binding of a ligand to a macromolecule and the dimerization of a macromolecule
• derive an equation which shows the relationships between the rate constant for binding (kon), dissociation (koff) and the thermodynamic dissociation (Kd) or equilibrium constant (Keq).
• describe the structural and mathematic differences between specific and nonspecific binding
• given a Kd, estimate t1/2 values for the lifetime of the ML complex.
• describe techniques used to determine ML for given L or L0 values, including those that do and do not require separation of ML from M , so that Kd values for a M and L interaction can be determined
• List advantages of isothermal titration calorimetry and surface plasmon resonance in determination of binding interaction parameters