11. Calculate K and Vmax from the following data: [S] (µM) 0.1 0.2 0.4 0.8 1.6 vo (mm. s¯¹) S 0.34 0.53 0.74 0.91 1.04
11. Calculate K and Vmax from the following data: [S] (µM) 0.1 0.2 0.4 0.8 1.6 vo (mm. s¯¹) S 0.34 0.53 0.74 0.91 1.04
Biochemistry
9th Edition
ISBN:9781319114671
Author:Lubert Stryer, Jeremy M. Berg, John L. Tymoczko, Gregory J. Gatto Jr.
Publisher:Lubert Stryer, Jeremy M. Berg, John L. Tymoczko, Gregory J. Gatto Jr.
Chapter1: Biochemistry: An Evolving Science
Section: Chapter Questions
Problem 1P
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![### Enzyme Kinetics: Michaelis-Menten Parameters
#### Problem 11: Calculation of \( K_M \) and \( V_{\max} \)
Given the following substrate concentration \([S]\) in micromolar (\(\mu M\)) and initial velocity \(v_0\) in millimolar per second (\(mM \cdot s^{-1}\)), calculate the Michaelis-Menten constant \(K_M\) and the maximum reaction velocity \(V_{\max}\).
| \([S]\) (\(\mu M\)) | \(v_0\) (\(mM \cdot s^{-1}\)) |
|:------------------:|:------------------:|
| 0.1 | 0.34 |
| 0.2 | 0.53 |
| 0.4 | 0.74 |
| 0.8 | 0.91 |
| 1.6 | 1.04 |
### Explanation
- **Substrate Concentration \([S]\)**: The table displays five different substrate concentrations measured in micromolar (\(\mu M\)).
- **Initial Velocity \(v_0\)**: The initial reaction rate (velocity) corresponding to each substrate concentration is presented in millimolar per second (\(mM \cdot s^{-1}\)).
#### Steps to Calculate \(K_M\) and \(V_{\max}\):
1. **Plot the Data**: Create a graph plotting \([S]\) on the x-axis against \(v_0\) on the y-axis to visualize the Michaelis-Menten kinetic curve.
2. **Linear Transformation**: Convert the data using the Lineweaver-Burk plot (double reciprocal plot) where \(1/v_0\) is plotted against \(1/[S]\). This linear transformation allows for the determination of \(K_M\) and \(V_{\max}\) through the slope and y-intercept:
\[
\frac{1}{v_0} = \frac{K_M}{V_{\max}} \cdot \frac{1}{[S]} + \frac{1}{V_{\max}}
\]
3. **Determine Parameters**:
- The y-intercept of the Lineweaver-Burk plot equals \(\frac{1}{](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc62819af-1f81-4d59-bfb3-1ca1702855ed%2F484f0be2-7392-4202-9b73-7dceac162d74%2F48o4rb5_processed.png&w=3840&q=75)
Transcribed Image Text:### Enzyme Kinetics: Michaelis-Menten Parameters
#### Problem 11: Calculation of \( K_M \) and \( V_{\max} \)
Given the following substrate concentration \([S]\) in micromolar (\(\mu M\)) and initial velocity \(v_0\) in millimolar per second (\(mM \cdot s^{-1}\)), calculate the Michaelis-Menten constant \(K_M\) and the maximum reaction velocity \(V_{\max}\).
| \([S]\) (\(\mu M\)) | \(v_0\) (\(mM \cdot s^{-1}\)) |
|:------------------:|:------------------:|
| 0.1 | 0.34 |
| 0.2 | 0.53 |
| 0.4 | 0.74 |
| 0.8 | 0.91 |
| 1.6 | 1.04 |
### Explanation
- **Substrate Concentration \([S]\)**: The table displays five different substrate concentrations measured in micromolar (\(\mu M\)).
- **Initial Velocity \(v_0\)**: The initial reaction rate (velocity) corresponding to each substrate concentration is presented in millimolar per second (\(mM \cdot s^{-1}\)).
#### Steps to Calculate \(K_M\) and \(V_{\max}\):
1. **Plot the Data**: Create a graph plotting \([S]\) on the x-axis against \(v_0\) on the y-axis to visualize the Michaelis-Menten kinetic curve.
2. **Linear Transformation**: Convert the data using the Lineweaver-Burk plot (double reciprocal plot) where \(1/v_0\) is plotted against \(1/[S]\). This linear transformation allows for the determination of \(K_M\) and \(V_{\max}\) through the slope and y-intercept:
\[
\frac{1}{v_0} = \frac{K_M}{V_{\max}} \cdot \frac{1}{[S]} + \frac{1}{V_{\max}}
\]
3. **Determine Parameters**:
- The y-intercept of the Lineweaver-Burk plot equals \(\frac{1}{
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