Michaelis-Menten Equation
Reference for the Michaelis-Menten equation v = Vmax[S] / (Km + [S]).
Covers Km, Vmax, Lineweaver-Burk plot, and enzyme inhibition types.
Need to calculate, not just reference? Use the interactive version.
Open Michaelis-Menten Enzyme Kinetics Calculator →
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
Key Notes
- K_m measures enzyme-substrate affinity: a low K_m means the enzyme reaches half-maximal speed at low substrate concentration (high affinity); a high K_m means low affinity — useful for comparing enzymes
- The Lineweaver-Burk plot (1/v vs 1/[S]) linearizes the curve so K_m and V_max can be read from axis intercepts — y-intercept = 1/V_max, x-intercept = −1/K_m
- Competitive inhibitors raise apparent K_m without changing V_max; non-competitive inhibitors lower apparent V_max without changing K_m — this distinction guides drug mechanism analysis
- The equation assumes a single-substrate steady-state reaction — most metabolic enzymes handle two or more substrates and require more complex kinetic models (Ping-Pong, sequential)
Key Notes
- Michaelis-Menten equation: v = Vmax × [S] / (Km + [S]): v is reaction velocity, [S] is substrate concentration, Vmax is the maximum velocity (all enzyme saturated), and Km is the Michaelis constant — the substrate concentration at which v = Vmax/2.
- Km reflects enzyme-substrate affinity: Low Km: the enzyme binds substrate tightly (reaches half-max velocity at low [S]). High Km: weak binding, needs more substrate. Km is not the same as the dissociation constant Kd (which measures binding, not catalysis rate), but it is a useful proxy.
- Lineweaver-Burk (double reciprocal) plot: 1/v = (Km/Vmax)(1/[S]) + 1/Vmax: Plotting 1/v vs 1/[S] gives a straight line. y-intercept = 1/Vmax; x-intercept = −1/Km; slope = Km/Vmax. Used to determine Km and Vmax graphically and to identify inhibition type.
- Types of inhibition: Competitive: inhibitor resembles substrate, blocks active site — raises apparent Km, Vmax unchanged. Noncompetitive: binds elsewhere — lowers apparent Vmax, Km unchanged. Uncompetitive: binds only enzyme-substrate complex — lowers both Vmax and Km.
- Applications: Michaelis-Menten kinetics is used in drug design (targeting enzymes with competitive inhibitors — statins inhibit HMG-CoA reductase; ACE inhibitors block angiotensin-converting enzyme), metabolic flux modeling, industrial enzyme optimization (in food processing, biofuel production), and pharmacokinetics.