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A single molecule of the enzyme catalase can decompose millions of toxic hydrogen peroxide molecules every second, but no matter how much substrate you pour in, it eventually hits a hard speed limit.

The Enzyme Speed Limit

Enzymes catalyze reactions by reversibly binding a substrate (SS) at their active site to form an enzyme-substrate complex (ESES), which then converts into product (PP) and releases the free enzyme (EE): E+S⇌k1k−1ES→k2E+PE + S \underset{k_{-1}}{\overset{k_1}{\rightleftharpoons}} ES \xrightarrow{k_2} E + P
At very low substrate concentrations, active sites sit empty, so adding more substrate speeds up the reaction linearly; but once every active site is constantly filled, the enzyme becomes saturated.
How can we turn this saturation curve into exact mathematical parameters to compare different enzymes?

The Michaelis-Menten Equation

In 1913, German biochemist Leonor Michaelis and Canadian physician Maud Menten formulated a quantitative model for this hyperbolic relationship by measuring how sucrose breaks down with invertase.
The Michaelis-Menten equation predicts the initial velocity (v0v_0, the reaction rate before substrate depletes) as a function of substrate concentration [S][S]: v0=Vmax⁡[S]Km+[S]v_0 = \frac{V_{\max}[S]}{K_m + [S]}
Here, Vmax⁡V_{\max} is the theoretical maximum rate when all enzyme active sites are occupied, and KmK_m (the Michaelis constant) is the substrate concentration at which the reaction operates at exactly half its maximum speed (12Vmax⁡\frac{1}{2}V_{\max}).
What do these numerical constants actually reveal about how tightly an enzyme binds and how rapidly it works?

Affinity, Turnover, and Efficiency