Michaelis-Menten v

Michaelis-Menten equation

The Michaelis-Menten equation ties the rate of an enzymatic reaction to substrate concentration: v = Vmax·[S] / (Km + [S]). Here Vmax is the maximum rate, reached when the enzyme is saturated, and Km is the substrate concentration where v equals Vmax/2. That Km value tells you how well the enzyme grabs its substrate, so a lower Km means tighter affinity. Plotted out, you get a saturation hyperbola. Run a quick example with Vmax = 100, Km = 10 and [S] = 5, and v = 100·5/(10+5) = 33.3. The Lineweaver-Burk plot (1/v vs 1/[S]) straightens the curve into a line, letting you pull Km and Vmax off the slope and intercepts. Michaelis and Menten proposed it back in 1913.

Applications

It underpins enzyme kinetic work in biochemistry, shows up in pharmacology through analogous models for receptor-binding, EC50 and IC50, drives enzyme activity assays in the clinical laboratory (AST, ALT, amylase), and helps spot competitive and non-competitive inhibitors during drug design.

FAQ

What does Km represent? It's the [S] where v hits half of Vmax. In practice it gauges how strongly the enzyme binds its substrate, so low Km goes with high affinity.

When is the equation not valid? It breaks down for multi-substrate enzymes, for allosteric ones that give a sigmoidal curve (where you'd use the Hill equation), and whenever [E] is on the same order as [S]. It also leans on a stationary state for [ES].

How are Km and Vmax obtained experimentally? You measure v across several [S] values, then either fit the hyperbola directly by non-linear regression or use linearisations like Lineweaver-Burk (1/v vs 1/[S]) and Eadie-Hofstee.