Spreadsheet Activity #12a: Enzyme Kinetics - Hyperbolic (non-linear) Data Fit
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The rates of enzyme-catalyzed reactions are dependent on the amount of catalyst, the concentration of substrate (reactant), and the affinity of the substrate for the enzyme, and the maximum velocity at which the enzyme can function. The "velocity" of an enzyme can be accurately portrayed by the Michaelis-Menten equation:
V = Vmax * [S] / ([S] + Km)
where V = velocity, Vmax = maximum velocity, [S] = substrate concentration, and Km is the Michaelis-Menton constant. To determine the values of Vmax and Km for a given enzyme, a series of reactions are run at increasing substrate concentrations. The velocity of the reaction at each substrate concentrations is plotted and the data fitted with the Michaelis-Menten equation above.
Plot the following data with [S] on the x-axis and V on the y-axis.
Create a series of data that can be plotted as a best-fit line using the Michaelis-Menten equation. Enter your own values for Vmax
and Km in separate cells that can be edited to create a good fit. Also calculate the residuals and the
residuals squared for your best fit line.
Determine the best values for Vmax and Km by
minimizing the sum of the residuals squared. Plot your best fit line on
the chart with the data given.
(Click to download data: 12EnzKin)
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Spreadsheet 12: Enzyme
Kinetics - Fitting Non-linear Data |
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V = Vmax
* ( [S] / ([S} + Km ) |
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Equation Variables: |
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Vmax= |
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nmole/L/min |
. |
. |
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Km= |
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umole/L |
. |
. |
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Actual Data: |
Calculated Fit from Equation: |
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[S] |
V |
V |
Residuals |
Res.^2 |
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(umol/L) |
(nmol/L/min) |
. |
. |
. |
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0.00 |
0.0 |
. |
. |
. |
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8.33 |
13.8 |
. |
. |
. |
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10.00 |
16.0 |
. |
. |
. |
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12.50 |
19.0 |
. |
. |
. |
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16.70 |
23.6 |
. |
. |
. |
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20.00 |
26.7 |
. |
. |
. |
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25.00 |
30.8 |
. |
. |
. |
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33.30 |
36.3 |
. |
. |
. |
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40.00 |
40.0 |
. |
. |
. |
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50.00 |
44.4 |
. |
. |
. |
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60.00 |
48.0 |
. |
. |
. |
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80.00 |
53.4 |
. |
. |
. |
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100.00 |
57.1 |
. |
. |
. |
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200.00 |
66.7 |
. |
. |
. |
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Sum of Residuals^2 = |
. |
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Excel Programming Tips: |
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A special [add-on] tool in Excel is the “Solver” option, located under the Tools button on the menu bar. Solver directs Excel to find the best values in selected cells so that a separate cell is minimized (e.g., sum of residuals squared). If Solver is installed on your machine, you can use this option to rapidly find the best values for Vmax and Km. |
Note: Data
taken from Biochemical Calculations, 2nd Ed. I.H. Segel