kcat Calculators

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kcat (the catalytic rate constant or turnover number) is the maximum number of substrate molecules that one enzyme molecule can convert to product per second when the enzyme is fully saturated with substrate. It has units of s⁻¹ (reciprocal seconds) and is calculated as kcat = Vmax / [E]total. kcat is an intrinsic property of the enzyme–substrate pair under defined conditions, independent of enzyme concentration. Together with Km, kcat defines enzyme performance: catalytic efficiency = kcat/Km (M⁻¹s⁻¹), the second-order rate constant for productive encounters between enzyme and substrate at low substrate concentrations.

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kcat Definition and Formula

kcat = Vmax / [E]total

Vmax = maximum velocity (mol/L/s or M/s); [E]total = total enzyme concentration (M). Units of kcat: s⁻¹. Example: Vmax = 5 × 10⁻⁴ M/s, [E] = 10⁻⁸ M: kcat = 5 × 10⁻⁴ / 10⁻⁸ = 5 × 10⁴ s⁻¹.

Physical Meaning

kcat = 1/s means one product formed per enzyme per second at saturation. kcat = 1000 s⁻¹ means the enzyme turns over 1000 substrate molecules per second per active site. For multi-step reactions, kcat is the rate constant of the slowest (rate-limiting) step — the step that limits the maximum catalytic throughput.

kcat/Km — Catalytic Efficiency

kcat/Km = rate of productive substrate encounters at low [S]

Units: M⁻¹s⁻¹. The diffusion-limited maximum is ~10⁸–10⁹ M⁻¹s⁻¹ — enzymes reaching this are called 'kinetically perfect'. Examples of kinetically perfect enzymes: acetylcholinesterase (kcat/Km ≈ 1.5 × 10⁸ M⁻¹s⁻¹), catalase (4 × 10⁸), fumarase (1.6 × 10⁸).

Representative kcat Values

  • Carbonic anhydrase: ~10⁶ s⁻¹ (fastest known enzyme)
  • Acetylcholinesterase: ~1.4 × 10⁴ s⁻¹
  • Lysozyme: ~0.5 s⁻¹ (slow, structural enzyme)
  • Restriction enzymes (EcoRI): ~0.02 s⁻¹

Glossary

kcat (Turnover Number)
The maximum substrate molecules converted per enzyme active site per second at saturation: kcat = Vmax / [E]total; units s⁻¹; an intrinsic enzyme property independent of concentration.
Catalytic Efficiency (kcat/Km)
The second-order rate constant for productive enzyme-substrate encounters at low [S]; units M⁻¹s⁻¹; maximum (diffusion-limited) value ≈ 10⁸–10⁹ M⁻¹s⁻¹.
Kinetically Perfect Enzyme
An enzyme with kcat/Km near the diffusion limit (~10⁸–10⁹ M⁻¹s⁻¹), meaning every substrate encounter leads to product; examples: acetylcholinesterase, catalase, fumarase.

Frequently Asked Questions

kcat (turnover number) is the maximum number of substrate molecules converted to product per enzyme active site per second when the enzyme is fully saturated. kcat = Vmax / [E]total; units s⁻¹. It is an intrinsic property of the enzyme independent of how much enzyme is present. High kcat means a fast enzyme; low kcat means a slow one. Carbonic anhydrase has kcat ≈ 10⁶ s⁻¹; restriction enzymes have kcat ≈ 0.02 s⁻¹ — a difference of 5 × 10⁷-fold.

kcat = Vmax / [E]total. First, determine Vmax from a Michaelis-Menten fit to v vs. [S] data (or from the y-intercept of a Lineweaver-Burk plot: y-intercept = 1/Vmax). Then determine [E]total by measuring protein concentration (A280, Bradford, or BCA assay). Divide: kcat = Vmax / [E]total. Ensure [E]total is the active enzyme concentration, not total protein — if the preparation has inactive enzyme, kcat will be underestimated. Active site titration (burst kinetics) gives true active [E].

Vmax is the maximum observed reaction velocity for a specific amount of enzyme — it changes when you add more or less enzyme (Vmax = kcat × [E]total). kcat is the intrinsic turnover rate per active site — it does not change with enzyme concentration and is comparable across experiments and laboratories. Vmax is useful for a specific experimental setup; kcat is the fundamental kinetic constant for the enzyme. To compare enzyme speed meaningfully, always report kcat, not Vmax.

kcat/Km is the catalytic efficiency — the second-order rate constant for the reaction at [S] << Km (physiologically relevant for most enzymes in vivo). Units: M⁻¹s⁻¹. It measures how quickly the enzyme converts substrate to product when substrate is dilute. The physical upper limit is the diffusion rate of substrate to the enzyme: ~10⁸–10⁹ M⁻¹s⁻¹. Enzymes approaching this limit (acetylcholinesterase, catalase, fumarase) are called 'catalytically perfect' — every encounter with substrate leads to product formation. kcat/Km is also useful for comparing wild-type and mutant enzymes.