9.4: Part II, Does the type of apple matter?

Pre-lab assignment for Part II: Does the type of apple affect rate of browning?

📅 Due before Wet Lab Meeting for Part II 

Complete any unfinished business from Part I, and review the reading and assignments from Part I.
Read section 9.4 for this part of the module.  Then complete the following written assignment and submit your work before the deadline. Do not use AI/LLMs to complete any part of this assignment.

1. Identify the independent and dependent variables in Equation \ref{mm}.  What must be varied to determine \(v_{\text{max}}\) and \(K_M\)?
2. Examine Equation \ref{mm}. Predict the appearance of a graph of initial rate, \(v_0\) versus substrate concentration, \(\left[S_0\right]\). Consider the dependence of the initial rate on low substrate concentration (as \(\left[S_0\right]\) approaches 0) and high concentration (as \(\left[S_0\right]\) approaches \(\infty\)).
3. Create a table similar to the one below in which you will add rows 2 through 7 (this was part of the pre-lab assignment). Keep in mind that the data analysis procedure amplifies the uncertainty in measurements made with low substrate concentrations.  If you decide to run the reactions unbuffered, the last column gives the volume of water, and the substrate solution should be made in water. If you decide to run the reactions buffered, the last column gives the volume of buffer, and the substrate solution should be made in buffer.

   Run #	Volume of Enzyme	Volume of Substrate	Volume of Buffer or Water
   Run 4	0.50 mL	2.00 mL	0 mL
   Run 5 ...	0.50 mL	…	…
   Run 11	0.50 mL	0.125 mL	1.875 mL
   Run 12	0.50 mL	0 mL	2.00 mL
   Run 13	0 mL	2.00 mL	0.50 mL

4. How do Runs 12 and 13 differ from Runs 4 - 11? Why is it important to collect the data in Runs 12 and 13?

Thinking About the Data from Part II

*Note that there is a CoLab tutorial to help you through this, but you may use any software you prefer to accomplish this work.

1. Determine the initial rate of the reaction for each mixture and tabulate the results in your notebook. 

2. If needed, calculate a “corrected” rate for trials 1-8 by subtracting the rates determined for the two controls (Runs 12 and 13).  This is usually not necessary.

3. Create a graph showing the dependence of rate on substrate concentration.  Ideally, all the rates should be plotted on the same axes.  Describe in words how the substrate concentration affects rate, comparing your result to your predicted graph.  Team members should reach consensus on a common description.  

4. The kinetic parameters for this reaction may also be extracted directly from your graph of rate versus substrate concentration by fitting the data with a nonlinear equation of the form: \[y=\frac{C x}{D+x} \label{lb}\]

5. Explain the shape of this graph in terms of the Michaelis-Menton Equation. 

6. We can simplify the determination of the kinetic parameters if we linearize the rate expression. Many scientists have found it useful to graph \(\frac{1}{rate}\)  or \(\frac{1}{v_0}\)  versus \(\frac{1}{[S_0]}\) for mixtures with different substrate concentrations but constant enzyme concentration. Such a plot is often referred to as a Lineweaver-Burk plot. Show how the Michaelis-Menton equation can be linearized.

7. What are the slope and intercept of this linear graph?

8. Prepare a Lineweaver-Burk plot to extract the kinetic parameters of the catecholase/catechol reaction using the linearized equation.  

9. Compare the Michaelis-Menton nonlinear fit to the Lineweaver-Burke linearization fit.

   1. Make a graph of [S] vs Initial Velocity with three data series: \(v_0(expt)\) (symbols), \(v_0(MMfit)\) (solid line), and \(v_0(LBfit)\) (dashed line). 
   2. To create the latter, you will need to transform the Lineweaver-Burke fit "back" to a Michaelis-Menton plot. Discuss with your classmates how you can do this.
   3. Create a residual plot for the experimental data compared to the two fits
   4. Discuss the conclusions you make from this graph in your notebook.

10. One person from your team should post the 'best' \(V_max\) and \(K_M\) values (derived from LB or MM) obtained and the type of apple analyzed in the shared data spreadsheet. Please be sure to enter the data carefully on the correct line of the spreadsheet. The other tema members should check the data entries to ensure they are accurate.

11. What are the units for your \({v_{max}}\)  and \(K_M\) values?  Use the extinction coefficient of \(1.03 \times 10^4\) L mol\(^{-1}\) for 1,2-benzoquinone at 540 nm to convert these to concentration units.

12. Compare the values of \({v_{max}}\)  and \(K_M\) determined using the Lineweaver-Burk plot and using non-linear curve fitting.  Are there substrate concentrations for which one method provides a better fit?

13. Tabulate the  \({v_{max}}\)  and \(K_M\) values for each type of apple (or other fruit) studied.  Do these values predict that different types of apples (or other fruit) brown at different rates?  Explain your answer. If possible, compare your tabulated results to those of others from your class, and use the class’ values to support your answer.

14. What does the value of \({v_{max}}\)  tell you about the reaction?  What does the value of \(K_M\) tell you about the reaction?

15. Suppose you want to make a fruit salad with apples. What factors would you consider when preparing the apples and the salad? Discuss based on your kinetics results.