8.4: Treatment of Data

Important

Do the data analysis in the lab before you leave for the day so that your TA can help you. If you use Logger Pro to do your analysis, use the lab computers which have a specific version of LoggerPro that can read the .txt files created from your data collection.

The data from this experiment can be displayed using either Logger Pro or MatLab software. In either case, you will need to have the .txt files exported for each of the experimental runs.

• There is a MatLab live script file available here (click and login with Duke credentials).
• The instructions below are for using Logger Pro® software.

Logger Pro is available from www.oit.duke.edu for free download. There are both PC and Macintosh versions available. There are complete download and installation instructions in the Documents section of the Sakai site for the course. See your TA or the Lab Manager if you have any problems or questions. After installing we suggest you update to the latest version at www.vernier.com.

Data visualization using Logger Pro

1. Click on the icon on the Windows or Macintosh Desktop to start Logger Pro. The program will load and you will see the main screen.

   

   Figure \(\PageIndex{1}\): Import function on Logger Pro.

2. Select Import From and Text File from the File menu. Locate and Highlight your first runa1X.txt file in the Open dialog box. Click Open to import the data file into Logger Pro.

   

   Figure \(\PageIndex{2}\): Copy and Paste Caption here. (Copyright; author via source)

   
   The data file will be entered into the table on the left of the screen and a graph of transmittance vs time (in seconds) will be displayed in the graph window. Double-click the word Latest appearing at the very top of the Data Table. A Data Set Options box appears. Change the name of the data set to Run A.

3. Repeat Step 2 three more times opening the second, third and fourth data files from your experimental work. With each new file opened data columns will be added to the table and graph window. Change the Data Set names to Run B, Run C and Run D respectively.

   

   Figure \(\PageIndex{3}\): Transmittance vs time plot.

4. Select Graph Options from the Options menu. Make sure Connect Points is NOT checked in the Graph Options tab of the Graph Options dialog box. Check Point Symbols. Click on the Axis Options tab. Un-check Transmittance and put a check in Absorbance in each one of the four data sets. (Run A though Run D). You will have to click the little + to the left of the column titles to see the Absorbance check boxes. Check to be sure the Scaling is set to Autoscale for both X- and Y-axes. Click Done. Your graph window will update to show the absorbance vs. time data for your first assay.

   

   Figure \(\PageIndex{3}\): Absorbance vs time plot.

5. Move now to the table window. Slide the horizontal scroll bar at the bottom of the data table window all the way to the left. Notice that for the first approximately 20 seconds of each run the absorbance is zero – because you were adding the enzyme, mixing the reaction and putting the cell into the spectrometer during this time. Click and drag the mouse, down and to the right, to highlight all of the data cells that represent zero absorbance, and maybe a few cells with non-zero absorbance. These data are suspect because you were setting-up the reaction and spectrometer.
   
   Hit the Delete key on the keyboard to remove these data from the runs. This will leave only the stable and reliable data from the four runs. You should now see a nice view of how the absorbance varies with time for each of the four runs (i.e., for the four different substrate concentrations).

   

   Figure \(\PageIndex{4}\): Absorbance vs time with initial points removed

6. Select Save from the File menu to save your work.

Data Analysis using Logger Pro

The kinetic data are analyzed using Logger Pro® software. The first step is to calculate reaction velocity from the absorbance vs. time data for each of your runs.

A. Steps 1-9 must be completed before leaving the laboratory

1. Select New Calculated Column from the Data menu. A New Calculated Column dialog box opens. Enter a name and a short name for this new column. Enter the units (Abs/sec). Also select the Data Set from the drop-down menu. Leave check Add to All Similar Data Sets.
2. Click on the button in the New Calculated Column dialog box. Select Derivative from the Calculus option. Go to the pull-down menu under Variables (Columns) and Select Absorbance. Then click Done in the New Calculated Column box.
3. Select Graph Options from the Options menu. Select the Axis Options tab. Remove the checks from Absorbance in each of the four runs and put checks in the appropriate Velocity columns so as to show velocity vs. time for runs A through D.

4. Click Done to close the Graph Options box. Your velocity data should look something like this image shown here.

5. To do a Linear Least-Squares analysis of these velocity lines, click the button found in the button bar at the top of the Logger Pro screen. A Select Columns dialog box will appear. The four velocity columns should already be highlighted within this box; if not, highlight all four. Click OK to close the Select Columns box. You will see Linear Least-Squares lines appear in the graph window. There will also be an information box associated with each Linear Least-squares line where you will see values for the slope, intercept and correlation.
6. Double-click inside one of these information boxes. A Linear Fit Options box appears. Check Show Uncertainty, and click OK. The standard deviation of the slope and intercept will be added to the information box. You can use these as a good estimate of the uncertainty in slope and intercept of your linear fit. Repeat this procedure for the other three linear fit lines.
7. Repeat the procedure with your second set of runs. Review the data with your TA to be sure you have sufficient results to continue with the analysis. The intercepts are estimates of the initial velocities of the reactions. You should see good agreement in these values for the replicate runs for each substrate concentration. If not, you should do another run of that substrate concentration.
8. Save all of your data files (.txt files) and this Logger Pro file in a single folder and upload it to Sakai so that you have access to it outside of lab.

b. Outside Lab: Complete the Following Calculations and Questions

1. Create a table or an Excel spreadsheet that summarizes the results. For each concentration of L-DOPA, calculate the mean initial velocity from your replicate runs, and use this value of V for further analysis.
2. Using the Beer-Lambert law (equation 19), and the molar absorptivity of dopachrome at the peak maximum of the band in the visible spectrum (3500 M–1 cm–1), convert each value of V into units of moles liter–1 sec–1.
3. Analyze the dependence of velocity (V) on L-DOPA concentration (in units of moles per liter) using (1) a non-linear, curve fit to the Michaelis Menton Equation (see below); and, a Lineweaver-Burk plot and (2) either the Eadie-Hofstee plot (for students with family names beginning A-M) or the Hanes-Wolf plot (for students with family names beginning N-Z) plot. Evaluate KM and Vmax. Discuss the relative merits of each treatment.
4. Approximate k2 using Eq. (10). Show a sample calculation.

Note on conducting a non-linear fit using Logger Pro:

1. Open Logger Pro and enter your initial velocity vs. substrate concentration data. You might want to add a point representing zero velocity at zero substrate concentration. A graph of your data will appear in the Graph Window (be sure you are not connecting your data points with a line).

2. Select Curve Fit from the Analyze menu. Click on the Define Function button in the Curve Fit window. Enter the form of the Michaelis-Menton Equation as Ax/(B+x) where, A = Vmax; x = substrate concentration; and, B = Km. Click OK.

3. Click on the Try Fit button. A curve fit will be created and results for the variables A and B (i.e., Vmax and Km) will be displayed in the right hand side of the window.

4. Click OK, and you will be returned to the main Logger Pro Window. You will see the curve fit through the data and you will also see a data box giving the equation for the curve and the values for the variables. Double click on this box and set it to show 4 significant figures. Also turn on Show Uncertainties and Display on Graph.

Discussion Questions:

This section should include (but not be limited to) the following:

1. A qualitative description of uncertainties, noting the most significant uncertainties and the extent to which they affect the results. (In other words, consider all the measurements that have gone into this work (including measurements involved in creating stock solutions, reaction solutions, and absorbance readings. How do these measurements contribute to the accuracy of your results, and which are most significant?)

2. A discussion of the importance of controlling reaction conditions (consider concentration, pH, temperature, timing).

3. An interpretation of the kinetic results with the assumption that \(k_2\) refers to the decomposition of the enzyme-substrate complex (equation (2)) and that \(K_M\) is related to the affinity of the enzyme for the substrate (equation (11)). Literature values are available and you should find at least two or more sources.

4. Discuss the dependence of V on the concentration of substrate.

5. Discuss the relative merits of the non-linear (the Lineweaver-Burk treatment) and the linear (Eadie-Hofstee or alternative Hanes-Wolf) treatments of your data.