Michaelis-Menten Equation
The Michaelis-Menten equation V = Vmax[S]/(Km+[S]) describes enzyme kinetics and how reaction rate depends on substrate concentration.
The Formula
The Michaelis-Menten equation describes the rate of an enzyme-catalyzed reaction as a function of substrate concentration. It was first proposed by Leonor Michaelis and Maud Menten in 1913 in Germany.
At low substrate concentrations, the reaction rate increases nearly linearly with substrate. At high substrate concentrations, the enzyme becomes saturated and the rate approaches V_max.
Variables
| Symbol | Meaning |
|---|---|
| V | Reaction rate (velocity) at a given substrate concentration (mol/L·s or similar units) |
| V_max | Maximum reaction rate when all enzyme active sites are saturated |
| [S] | Substrate concentration (in mol/L) |
| K_m | Michaelis constant — the substrate concentration at which V = V_max/2 (in mol/L) |
Key Properties
| Condition | Result |
|---|---|
| [S] much less than K_m | V ≈ (V_max/K_m)[S] — rate is proportional to [S] |
| [S] = K_m | V = V_max / 2 — rate is half of maximum |
| [S] much greater than K_m | V ≈ V_max — enzyme is saturated |
Example 1
An enzyme has V_max = 100 μmol/min and K_m = 5 mM. What is the reaction rate when [S] = 10 mM?
V = V_max [S] / (K_m + [S])
V = 100 × 10 / (5 + 10)
V = 1000 / 15
V ≈ 66.7 μmol/min (two-thirds of V_max)
Example 2
An experiment shows that when [S] = 2 mM, the rate is 40 μmol/min, and V_max = 120 μmol/min. What is K_m?
Rearrange: K_m = [S](V_max − V) / V
K_m = 2 × (120 − 40) / 40
K_m = 2 × 80 / 40
K_m = 4 mM
When to Use It
The Michaelis-Menten equation is fundamental to biochemistry and pharmacology.
- Characterizing enzyme activity and efficiency
- Determining K_m to compare enzyme-substrate affinity (lower K_m = higher affinity)
- Drug design — understanding how inhibitors affect enzyme kinetics
- Metabolic pathway modeling in systems biology
- Industrial enzyme applications (food processing, biofuels)
A low K_m means the enzyme reaches half-maximum rate at a low substrate concentration — it has high affinity for the substrate. A high V_max means the enzyme can process substrate very quickly when saturated.