Km (Michaelis Constant) Calculators

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Km (the Michaelis constant) is the substrate concentration at which an enzyme operates at half its maximum velocity (v = Vmax/2). It is a key parameter in the Michaelis-Menten equation: v = Vmax × [S] / (Km + [S]). Low Km indicates high affinity between the enzyme and its substrate (the enzyme is half-saturated at very low substrate concentrations). High Km indicates low affinity (large amounts of substrate needed to half-saturate the enzyme). Km values for most enzymes range from micromolar (10⁻⁶ M) to millimolar (10⁻³ M). Km is determined by measuring initial velocities at multiple substrate concentrations and fitting the Michaelis-Menten equation using nonlinear regression.

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Km in the Michaelis-Menten Equation

v = Vmax × [S] / (Km + [S])

At [S] = Km: v = Vmax/2 (by definition). At [S] << Km: v ≈ (Vmax/Km) × [S] — first-order in [S]. At [S] >> Km: v ≈ Vmax — zero-order in [S]. Km units = same as [S] (M, mM, μM, μg/mL, etc.).

Km and Enzyme Affinity

Km ≈ Kd (dissociation constant) when product release is fast (kcat << k₋₁). In this case: low Km → high affinity (binds substrate tightly). However, Km is a kinetic constant, not a pure thermodynamic binding constant. Km = (k₋₁ + kcat) / k₁. For slow product release (kcat ≈ k₋₁): Km > Kd. Km and Kd are equal only in the limiting case of rapid equilibrium.

Typical Km Values

  • Hexokinase (glucose substrate): Km ≈ 0.1 mM — high affinity, saturated at physiological glucose (~5 mM)
  • Glucokinase (glucose): Km ≈ 10 mM — low affinity, acts as glucose sensor above 5 mM
  • Carbonic anhydrase (CO₂): Km ≈ 8 mM
  • Alcohol dehydrogenase (ethanol): Km ≈ 1 mM
  • Chymotrypsin (Phe-Ala-Ala substrate): Km ≈ 2.5 mM

Competitive Inhibition Changes Km

Apparent Km with competitive inhibitor [I]: Km_app = Km × (1 + [I]/Ki). Vmax is unchanged. This is why competitive inhibition can be overcome by increasing [S].

Glossary

Km (Michaelis Constant)
The substrate concentration at which enzyme velocity = Vmax/2; low Km = high affinity; high Km = low affinity; units same as [S]; determined by nonlinear regression of velocity vs. [S] data.
Hexokinase vs. Glucokinase
Hexokinase Km(glucose) ≈ 0.1 mM (high affinity, saturated at physiological glucose); glucokinase Km ≈ 10 mM (low affinity, acts as glucose sensor in pancreatic β-cells and liver).
Apparent Km
Km in the presence of a competitive inhibitor: Km_app = Km(1+[I]/Ki); increases with inhibitor concentration; returns to true Km when [I] = 0; Vmax is unchanged.

Frequently Asked Questions

Km is the substrate concentration at which an enzyme's reaction velocity equals half its maximum (v = Vmax/2). It is defined by the Michaelis-Menten equation: v = Vmax × [S]/(Km + [S]). Low Km: the enzyme is half-saturated at low [S] → high affinity for the substrate → the enzyme operates near Vmax even at low substrate levels. Example: hexokinase Km(glucose) ≈ 0.1 mM — fully active at physiological glucose (~5 mM). High Km: the enzyme needs high [S] to be half-saturated → low affinity. Example: glucokinase Km(glucose) ≈ 10 mM — only active when glucose is above ~5 mM, making it a glucose sensor in pancreatic β-cells.

Measure initial velocities (v₀) at 6–10 substrate concentrations spanning 0.2 × Km to 10 × Km (if Km is approximately known). Conditions: constant enzyme concentration; measure initial rate (< 10% substrate consumed); constant pH and temperature; no product present initially. Analysis: best method = nonlinear least squares regression of v vs. [S] data directly to the Michaelis-Menten equation (GraphPad Prism, R: nls()). Historical methods: Lineweaver-Burk (1/v vs. 1/[S]): gives Km as negative x-intercept (−1/Km); statistically biased — not preferred for parameter estimation. Eadie-Hofstee (v vs. v/[S]): more balanced error distribution. Report Km ± SE from the nonlinear fit.

Kd (dissociation constant): a thermodynamic equilibrium constant measuring the affinity of enzyme for substrate: Kd = k₋₁/k₁. Lower Kd = tighter binding. Km (Michaelis constant): a kinetic constant: Km = (k₋₁ + kcat)/k₁. Km approximates Kd only when kcat << k₋₁ (the rapid equilibrium assumption). In most real enzymes: kcat is not negligible compared to k₋₁, so Km > Kd. This means Km overestimates Kd (makes binding appear weaker than it really is). For a very fast enzyme (high kcat), Km >> Kd. When Km is reported, it should be understood as a kinetic parameter, not a binding constant.

Physiologically, Km sets the operating range of an enzyme: if [S] in the cell << Km: the enzyme operates in the first-order regime (v ∝ [S]); rate is sensitive to substrate concentration changes. If [S] in the cell >> Km: enzyme is near Vmax; rate is insensitive to substrate changes (zero-order). If [S] in the cell ≈ Km: enzyme operates at half-Vmax; rate is maximally sensitive to substrate changes. Most cellular enzymes operate near or below their Km — this maximizes sensitivity for metabolic regulation. Notable exception: hexokinase (Km = 0.1 mM vs. ~5 mM glucose) operates well above Km → near Vmax → rate independent of glucose fluctuations. Glucokinase (Km = 10 mM) → operates below Km at typical glucose → acts as a glucose sensor.