Enzyme Kinetics (Michaelis-Menten) Calculator
Calculate enzyme reaction velocity (V), Michaelis constant (Km), maximum velocity (Vmax), turnover number (kcat), and catalytic efficiency using the Michaelis-Menten model.
Formulas Used
Michaelis-Menten Equation:
V = (Vmax · [S]) / (Km + [S])
Rearrangements:
- Km = [S] · (Vmax − V) / V
- Vmax = V · (Km + [S]) / [S]
- [S] = Km · V / (Vmax − V)
- kcat = Vmax / [E]t
- Catalytic Efficiency = kcat / Km (M⁻¹s⁻¹)
Where:
- V = reaction velocity (µmol/min)
- Vmax = maximum reaction velocity (µmol/min)
- [S] = substrate concentration (µM)
- Km = Michaelis constant — [S] at V = Vmax/2 (µM)
- kcat = turnover number (s⁻¹)
- [E]t = total enzyme concentration (µM)
Assumptions & References
- Steady-state assumption: the enzyme-substrate complex [ES] reaches a constant concentration rapidly (Briggs & Haldane, 1925).
- [S] ≫ [E]t: substrate concentration greatly exceeds enzyme concentration so [S] is not depleted.
- Single-substrate, single-product reaction with no product inhibition.
- No cooperativity (Hill coefficient = 1); use the Hill equation for cooperative enzymes.
- Diffusion-limited enzymes (catalytically perfect) have kcat/Km ≈ 10⁸–10⁹ M⁻¹s⁻¹.
- Units assume Vmax in µmol/min, [S] and Km in µM, [E]t in µM.
- References: Michaelis L & Menten ML (1913). Biochem Z 49:333–369. | Berg JM et al. Biochemistry, 9th ed. W.H. Freeman.