Simulate enzyme reaction velocity in real time · v = Vmax·[S] / (Km + [S])
Substrate concentration
Maximum reaction velocity
Substrate concentration at which v = Vmax/2
Total enzyme concentration (optional)
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µmol/(L·min)—
%The Michaelis-Menten equation describes the initial velocity of a single-substrate enzymatic reaction as a function of substrate concentration. Its modern form rests on the quasi-steady-state assumption (QSSA) introduced by Briggs & Haldane (1925): after a brief initial transient, the concentration of the enzyme–substrate complex [ES] remains approximately constant, so that d[ES]/dt ≈ 0.
Vmax is the limiting rate approached when all enzyme active sites are saturated with substrate — it is never truly reached at finite [S]. Km (Michaelis constant) equals the substrate concentration at which v = Vmax/2. In the Briggs–Haldane treatment, Km = (k−1 + kcat) / k1, so it reflects both binding affinity and the catalytic step — it equals the true dissociation constant Kd only when kcat ≪ k−1.
The turnover number kcat (s−1) is the maximum number of substrate molecules converted to product per active site per second at saturating [S]. The specificity constant kcat/Km (M−1s−1) is the apparent second-order rate constant at sub-saturating [S] and measures catalytic efficiency. Its upper bound is set by the rate of enzyme–substrate diffusion in aqueous solution: 108–109 M−1s−1 (Garrett & Grisham, 2010; Berg et al., 2015). Enzymes approaching this limit — such as triose phosphate isomerase or carbonic anhydrase — are said to have achieved catalytic perfection.
The Lineweaver-Burk plot (double reciprocal 1/v vs. 1/[S]) linearizes the equation: slope = Km/Vmax, Y-intercept = 1/Vmax, X-intercept = −1/Km. Although historically useful for visualizing inhibition patterns, it amplifies errors at low [S] and has been largely replaced by nonlinear regression for parameter estimation.
Validity of the QSSA: the simulator warns when [Et] ≥ 10% of ([S] + Km), which is the standard criterion for QSSA breakdown (Srinivasan, 2022; Briggs & Haldane, 1925). Under these conditions the measured Vmax and Km are no longer reliable. The model also assumes initial-rate conditions ([P] ≈ 0) and a single-substrate mechanism.