Catalytic Constant Calculators

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The catalytic constant (kcat), also called the turnover number, is the maximum number of substrate molecules converted to product per enzyme active site per second when fully saturated with substrate. Units: s⁻¹. Calculated as kcat = Vmax / [E]total. kcat is an intrinsic property of the enzyme-substrate pair, independent of enzyme concentration. With Km, it defines catalytic efficiency = kcat/Km (M⁻¹s⁻¹). The diffusion-limited maximum kcat/Km ≈ 10⁸–10⁹ M⁻¹s⁻¹; enzymes reaching this are called kinetically perfect.

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kcat Formula

kcat = Vmax / [E]total

Vmax = maximum velocity (mol/L/s); [E]total = active enzyme concentration (mol/L). Physical meaning: kcat = 1000 s⁻¹ means one active site converts 1000 substrate molecules per second at saturation.

Representative kcat Values

  • Carbonic anhydrase: ~10⁶ s⁻¹ (fastest known)
  • Catalase: ~4 × 10⁷ s⁻¹ (H₂O₂ decomposition)
  • Acetylcholinesterase: ~1.4 × 10⁴ s⁻¹
  • Triose phosphate isomerase: ~4.3 × 10³ s⁻¹
  • Lysozyme: ~0.5 s⁻¹ (slow structural enzyme)
  • EcoRI restriction enzyme: ~0.02 s⁻¹

Catalytic Efficiency kcat/Km

kcat/Km (M⁻¹s⁻¹) is the second-order rate constant at low [S] << Km. At low substrate: v ≈ (kcat/Km) × [E] × [S]. Diffusion limit: ~10⁸–10⁹ M⁻¹s⁻¹. Kinetically perfect enzymes (acetylcholinesterase, catalase, fumarase) achieve this limit.

Measuring kcat

Measure Vmax from Michaelis-Menten fit; measure [E]total by protein quantification (A280, BCA) or active site titration (burst kinetics). kcat = Vmax/[E]total. Active site titration gives true functional enzyme concentration; total protein gives underestimate of kcat if inactive enzyme is present.

Glossary

kcat (Catalytic Constant)
Maximum substrate molecules converted per active site per second at saturation: kcat = Vmax/[E]total; units s⁻¹; intrinsic enzyme property independent of concentration.
Catalytic Efficiency (kcat/Km)
Second-order rate constant at low [S]: units M⁻¹s⁻¹; maximum ~10⁸–10⁹ M⁻¹s⁻¹ (diffusion limit); best single measure of enzyme performance.
Active Site Titration
A method determining true functional enzyme concentration by measuring burst product release; gives more accurate kcat than using total protein concentration.

Frequently Asked Questions

kcat (turnover number) = maximum substrate molecules converted per enzyme active site per second at saturation: kcat = Vmax/[E]total; units s⁻¹. Vmax = kcat × [E]total — it changes with enzyme concentration; kcat does not. kcat is the intrinsic catalytic rate constant comparable across labs and studies. Vmax is useful for a specific experimental setup. To compare enzyme speeds, always use kcat, not Vmax — a higher Vmax could simply mean more enzyme was used.

kcat/Km (M⁻¹s⁻¹) measures how rapidly an enzyme converts substrate to product when [S] << Km — the condition for most enzymes in vivo. It integrates both speed (kcat) and affinity (1/Km) into one measure. Higher kcat/Km = better enzyme at physiological substrate levels. The diffusion-limited maximum is ~10⁸–10⁹ M⁻¹s⁻¹. Enzymes at this limit are 'kinetically perfect' — every substrate encounter leads to product. kcat/Km is also the key parameter for comparing wild-type vs. mutant enzymes in directed evolution.

Step 1: Measure Vmax by fitting the Michaelis-Menten equation (v = Vmax×[S]/(Km+[S])) to initial velocity data at multiple substrate concentrations. Step 2: Measure [E]total — either total active protein (A280, BCA, Bradford assay) or true active sites by burst kinetics titration (preferred for mechanistic accuracy). Step 3: kcat = Vmax / [E]total. If total protein is used and some enzyme is inactive, the calculated kcat will be an underestimate of the true value.

Low kcat reflects: (1) Difficult chemical steps with high activation energy — lysozyme cleaves strong glycosidic bonds (kcat ~0.5 s⁻¹); (2) Rate-limiting conformational changes; (3) Multi-step mechanisms where the slowest step limits kcat regardless of chemistry. There is no universal selective pressure for high kcat — if an enzyme is not rate-limiting in a metabolic pathway, moderate kcat is sufficient. Evolution optimizes entire pathways, not individual enzymes in isolation. Enzymes in fast-responding signaling pathways (acetylcholinesterase) face stronger selection for high kcat.