# Introduction to Enzyme Kinetics

In this exercise we will use a spreadsheet model to generate some plots of enzyme kinetic behavior. The same kinds of techniques we used before for the titration curves will be used. You may want to review Introduction to pH, Titration Curves, and Buffers for using Excel.

For this exercise we need to set up columns for the various parameters in the Michaelis-Menten equation. Analogously to our titration exercise, we will use the M-M equation as our model for the enzyme reaction system.Set up your spread sheet as in the figure:

The top row is just labels. Note the form of the M-M equation in cell D2: =(A2*C2)/(B2+C2)

Now enter the values Vmax = 3 and Km = 0.5 and fill both columns A & B down to row 52 ("capture" the cells and then use the Fill command under the Edit menu, or the keystroke combination, command D):

Next fill the substrate column with concentrations from 0 - 5 (Go to Edit - Fill - Series, when the dialog box comes up click on the radio button for columns under Series in, then set the step value to 0.1 and the Stop value to 5 and click OK. ), and finally fill the M-M equation column down to row 52:

Next plot your results. Go to Insert - Chart... and choose X,Y Scatter and smooth curve from the dialog box:

Then proceed to make your plot with properly labeled axis, grid etc.:

Duplicate and copy your spread sheet columns (capture the columns with the mouse, then click on a cell, say F, and hit enter):

Then change the value of Km to 0.1, then go back to the Chart page and go under Chart to Add Data... In the dialog box enter the location of the new M-M data, for the example above the entry is =Sheet1!\$I\$2:\$I\$52.

Repeat this operation using Km = 2:

## Questions: M-M Plot

1. Ignoring the known values for Km and Vmax, find them graphically from your plots. (Remember, Km = [S] at Vmax/2.) How do these values compare to each other and to the "real" values.

2. How accurate and effective do you think this plot is for finding values from real data? What are its problems?

## Lineweaver-Burke Double-reciprocal Plot

Now go back to your sheet and create two new columns for the reciprocals of [S] and v:

Make a new chart of this data, labeling appropriately etc. but plot only points on the scatter plot:

Now go back and add a line to the plot by going under Chart, Add Trendline. In the dialog boxes choose linear, then double-click on the line and under options choose display equation and r-squared... and finally forecast backward 1:

## Questions: L-B Plot

1. Find values for Km and Vmax by finding the intercepts (determine the values graphically) and taking the reciprocals (- reciprocal for Km).
2. Note the equation for the line (y = 0.6667x + 0.3333). Find values for Km and Vmax using this equation. (Remember that this equation is in the form y = ax + b. Thus if we set y = 0, the equation becomes ax = -b and we can find the value of the x-intercept, and if we set x = 0, it becomes y = b.)
• Note the value of R2. This is a statistical function, the regression" which indicates how closely the data points fit a linear function. A value of 1 indicates a perfect fit, a rare occurrence in the real world!

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