Michaelis-Menten Equation
Model enzyme reaction rates based on substrate concentration.
The core equation of enzyme kinetics in biochemistry.
The Formula
v = (V_max × [S]) / (K_m + [S])
The Michaelis-Menten equation describes how fast an enzyme converts substrate into product. Reaction speed increases with substrate concentration, but plateaus at the maximum rate.
Variables
| Symbol | Meaning |
|---|---|
| v | Reaction velocity (rate of product formation) |
| V_max | Maximum reaction rate (when enzyme is fully saturated) |
| [S] | Substrate concentration (mol/L) |
| K_m | Michaelis constant — substrate concentration at half V_max (mol/L) |
Example 1
An enzyme has V_max = 100 μmol/min and K_m = 5 mM. Find the rate at [S] = 10 mM.
v = (100 × 10) / (5 + 10)
v = 1000 / 15
v ≈ 66.7 μmol/min
Example 2
Same enzyme. Find the rate when [S] = K_m = 5 mM.
v = (100 × 5) / (5 + 5)
v = 500 / 10
v = 50 μmol/min (exactly half of V_max, as expected)
When to Use It
Use the Michaelis-Menten equation when:
- Studying how enzyme activity changes with substrate concentration
- Determining K_m and V_max from experimental data
- Comparing enzyme efficiency between different enzymes
- Modeling drug metabolism and pharmacokinetics