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M04.02.08 Enzyme kinetics
Enzyme Kinetics: An Overview with Examples and Calculations
Enzyme kinetics is the study of the rates at which enzymatic reactions occur and the factors that influence these rates. This field of biochemistry is essential for understanding how enzymes work, how they are regulated, and how their activity can be modulated for therapeutic purposes.
Basic Concepts of Enzyme Kinetics
- Enzyme-Substrate Interaction
- Active Site: The specific region on the enzyme where the substrate binds.
- Enzyme-Substrate Complex (ES): The intermediate formed when an enzyme binds to its substrate.
- Michaelis-Menten Kinetics The Michaelis-Menten equation describes the rate of enzymatic reactions by relating the reaction rate (v) to the substrate concentration ([S]):𝑣=𝑉max[𝑆]𝐾𝑚+[𝑆]v=Km+[S]Vmax[S]
- 𝑉maxVmax: The maximum reaction rate achieved by the enzyme at saturating substrate concentration.
- 𝐾𝑚Km: The Michaelis constant, which is the substrate concentration at which the reaction rate is half of 𝑉maxVmax.
- Lineweaver-Burk Plot The Lineweaver-Burk plot is a double reciprocal plot of the Michaelis-Menten equation:1𝑣=𝐾𝑚𝑉max[𝑆]+1𝑉maxv1=Vmax[S]Km+Vmax1This plot helps determine 𝑉maxVmax and 𝐾𝑚Km values more accurately by plotting 1/𝑣1/v versus 1/[𝑆]1/[S].
Examples and Calculations
Example 1: Determining 𝑉maxVmax and 𝐾𝑚Km
Consider an enzyme-catalyzed reaction with the following data:
| [S] (mM) | v (μmol/min) |
|---|---|
| 0.1 | 0.91 |
| 0.2 | 1.67 |
| 0.5 | 3.33 |
| 1.0 | 5.00 |
| 2.0 | 6.25 |
| 5.0 | 7.14 |
| 10.0 | 8.00 |
To determine 𝑉maxVmax and 𝐾𝑚Km, plot 1/𝑣1/v versus 1/[𝑆]1/[S]:
- Calculate the reciprocal values for the plot.
| [S] (mM) | v (μmol/min) | 1/[S] (1/mM) | 1/v (min/μmol) |
|---|---|---|---|
| 0.1 | 0.91 | 10.0 | 1.10 |
| 0.2 | 1.67 | 5.0 | 0.60 |
| 0.5 | 3.33 | 2.0 | 0.30 |
| 1.0 | 5.00 | 1.0 | 0.20 |
| 2.0 | 6.25 | 0.5 | 0.16 |
| 5.0 | 7.14 | 0.2 | 0.14 |
| 10.0 | 8.00 | 0.1 | 0.13 |
- Plot these values and find the y-intercept (1𝑉maxVmax1) and slope (𝐾𝑚𝑉maxVmaxKm).
- From the plot, determine 𝑉maxVmax and 𝐾𝑚Km.
Example 2: Effect of Inhibitors
Enzyme inhibitors can be classified as competitive, non-competitive, or uncompetitive, each affecting enzyme kinetics differently.
- Competitive Inhibition: Inhibitor competes with substrate for the active site.
- 𝑉maxVmax remains the same.
- 𝐾𝑚Km increases.
- Lineweaver-Burk Plot: Lines intersect on the y-axis.
- Non-Competitive Inhibition: Inhibitor binds to an allosteric site, not the active site.
- 𝑉maxVmax decreases.
- 𝐾𝑚Km remains the same.
- Lineweaver-Burk Plot: Lines intersect on the x-axis.
- Uncompetitive Inhibition: Inhibitor binds only to the enzyme-substrate complex.
- Both 𝑉maxVmax and 𝐾𝑚Km decrease.
- Lineweaver-Burk Plot: Lines are parallel.
Calculation Example
Consider an enzyme with and without a competitive inhibitor. The data without the inhibitor:
| [S] (mM) | v (μmol/min) |
|---|---|
| 0.1 | 1.00 |
| 0.2 | 1.82 |
| 0.5 | 4.00 |
| 1.0 | 6.67 |
| 2.0 | 8.33 |
| 5.0 | 9.09 |
| 10.0 | 9.52 |
With the inhibitor:
| [S] (mM) | v (μmol/min) |
|---|---|
| 0.1 | 0.50 |
| 0.2 | 0.91 |
| 0.5 | 2.00 |
| 1.0 | 3.33 |
| 2.0 | 4.17 |
| 5.0 | 4.55 |
| 10.0 | 4.76 |
- Plot Lineweaver-Burk plots for both sets of data.
- Determine 𝑉maxVmax and 𝐾𝑚Km values from the y-intercepts and slopes.
- Compare the results to see the effect of the competitive inhibitor.
By understanding enzyme kinetics, including how different factors and inhibitors affect enzyme activity, we can better grasp the mechanisms underlying enzymatic reactions and their implications in health and disease.