v = Vmax × [S] / (Km + [S])
The Michaelis-Menten equation v = Vmax[S]/(Km+[S]) describes how enzyme reaction velocity depends on substrate concentration. Vmax is the maximum velocity at saturating substrate. Km (Michaelis constant) equals the substrate concentration at which v = Vmax/2 — it reflects the enzyme's affinity for substrate (lower Km = higher affinity). At [S] << Km: v ≈ (Vmax/Km)[S] (first-order). At [S] >> Km: v ≈ Vmax (zero-order). The catalytic efficiency kcat/Km measures overall enzyme performance; the theoretical maximum is the diffusion limit (~10⁸–10⁹ M⁻¹s⁻¹). Lineweaver-Burk plot (1/v vs 1/[S]) linearizes the equation for determining Vmax and Km. Competitive inhibitors increase apparent Km; non-competitive inhibitors decrease apparent Vmax.