Turnover Number Calculators

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The turnover number (kcat) is the maximum number of substrate molecules converted to product per enzyme molecule per second when the enzyme is fully saturated with substrate. It is also called the catalytic constant or molecular activity. kcat = Vmax / [E]total, where [E]total is the total enzyme concentration. kcat units are s⁻¹ (also called 'per second'). Typical enzyme kcat values range from 1 to 10⁶ s⁻¹. The catalytic efficiency (kcat/Km) measures how efficiently an enzyme works at low substrate concentrations and has a theoretical maximum of ~10⁸–10⁹ M⁻¹s⁻¹ (the diffusion limit).

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Turnover Number Formula

kcat = Vmax / [E]total

[E]total = total enzyme concentration (M). kcat units: s⁻¹ (substrate molecules per enzyme molecule per second at saturation). Example: Vmax = 5 × 10⁻⁸ M/s; [E] = 1 × 10⁻⁸ M: kcat = 5 × 10⁻⁸ / 1 × 10⁻⁸ = 5 s⁻¹.

Catalytic Efficiency (kcat/Km)

kcat/Km (M⁻¹s⁻¹) = catalytic efficiency; also called specificity constant or apparent second-order rate constant. Measures enzyme performance at low [S] (where most enzyme is unbound). Theoretical maximum: ~10⁸–10⁹ M⁻¹s⁻¹ (rate limited by diffusion). Enzymes with kcat/Km near diffusion limit are called 'perfect enzymes': acetylcholinesterase (~1.5 × 10⁸); carbonic anhydrase (~8 × 10⁷); catalase (~4 × 10⁷).

Notable kcat Values

  • Carbonic anhydrase: ~600,000 s⁻¹ (fastest enzyme)
  • Catalase: ~10,000,000 s⁻¹ (fastest overall)
  • Lysozyme: ~0.5 s⁻¹ (very slow)
  • DNA polymerase III: ~1,000 s⁻¹
  • Ribonuclease A: ~1,000 s⁻¹

Glossary

kcat (Turnover Number)
Maximum substrate molecules converted per enzyme per second at substrate saturation; kcat = Vmax/[E]_total; units s⁻¹; carbonic anhydrase ~600,000 s⁻¹; lysozyme ~0.5 s⁻¹.
Catalytic Efficiency (kcat/Km)
kcat/Km in M⁻¹s⁻¹; enzyme performance at low [S]; diffusion limit ~10⁸–10⁹; 'perfect enzymes' (acetylcholinesterase, TPI) approach this limit; best single measure of enzyme quality.
Diffusion Limit
The maximum rate at which enzyme and substrate can encounter each other in solution (~10⁸–10⁹ M⁻¹s⁻¹); the theoretical ceiling for kcat/Km; enzymes approaching this limit are called catalytically perfect.

Frequently Asked Questions

kcat (turnover number) = the maximum number of substrate molecules an enzyme molecule converts to product per second when fully saturated with substrate. Units: s⁻¹. Derivation: kcat = Vmax / [E]_total. At saturating [S]: all enzyme molecules are in ES complexes → maximum reaction rate. kcat reflects the rate-limiting step in the catalytic cycle — the chemical step or product release. High kcat: enzyme quickly processes each bound substrate molecule. Low kcat: enzyme is slow at the chemical conversion step (e.g., lysozyme 0.5 s⁻¹; RNA processing enzymes < 1 s⁻¹). Comparison: Vmax depends on both kcat and enzyme concentration; kcat is intrinsic to the enzyme.

kcat/Km (M⁻¹s⁻¹) = the apparent second-order rate constant for enzyme-substrate encounter; the best measure of enzyme efficiency under physiological conditions (where [S] << Km). High kcat/Km: enzyme converts substrate efficiently even at low [S] — the enzyme is productive on most encounters with substrate. Interpretation: kcat/Km = kcat / Km. A high kcat alone doesn't mean efficient if Km is also very high (substrate must be at very high concentration for saturation). Diffusion limit: ~10⁸–10⁹ M⁻¹s⁻¹ — the fastest physically possible rate; enzyme would need to process every substrate molecule it encounters. 'Catalytically perfect' enzymes (acetylcholinesterase, triose phosphate isomerase): kcat/Km approaches diffusion limit → evolution has maximized catalytic efficiency.

From Michaelis-Menten data: (1) Run an enzyme kinetics experiment: measure initial velocity (v₀) at multiple substrate concentrations [S]. (2) Fit data to v₀ = Vmax × [S] / (Km + [S]) using non-linear regression or Lineweaver-Burk plot. (3) Extract Vmax and Km. (4) Measure or know [E]_total (enzyme concentration in the assay). (5) Calculate kcat = Vmax / [E]_total. Example: Vmax = 2.4 × 10⁻⁷ M/s; [E] = 5 × 10⁻⁹ M: kcat = 2.4 × 10⁻⁷ / 5 × 10⁻⁹ = 48 s⁻¹. Note: [E]_total must be active enzyme concentration — determined by active site titration (not just protein concentration, which may include inactive forms).

In the simple Michaelis-Menten mechanism: E + S ⇌ ES → E + P. Rate constants: k₁ (association), k₋₁ (dissociation), k₂ (catalytic step). kcat = k₂ (the rate constant for the chemical step). Km = (k₋₁ + k₂)/k₁. In a more complex mechanism with multiple steps after ES: kcat = 1 / (Σ 1/kᵢ) for each sequential step → kcat is limited by the slowest step. Product release is often rate-limiting: for DNA polymerase and others, kcat is limited by the rate at which the product dissociates from the enzyme. Significance: a mutation that accelerates the chemical step may still not increase kcat if product release is still rate-limiting. Directed evolution and rational enzyme design often aim to improve the rate-limiting step.