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How does the Michaelis-Menten equation describe enzyme reaction rates?

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A multi-panel diagram illustrates how a substrate binds to an enzyme's active site through induced fit, leading to product formation, and shows how non-substrates and allosteric regulators can alter enzyme activity by binding to different sites on the enzyme. — Enzyme In the induced-fit theory of enzyme-substrate binding, a substrate approaches the surface of an enzyme (step 1 in box A, B, C) and causes a change in the enzyme shape that results in the correct alignment of the catalytic groups (triangles A and B; circles C and D represent substrate-binding groups on the enzyme that are essential for catalytic activity). The catalytic groups react with the substrate to form products (step 2). The products then separate from the enzyme, freeing it to repeat the sequence (step 3). Boxes D and E represent examples of molecules that are too large or too small for proper catalytic alignment. Boxes F and G demonstrate binding of an inhibitor molecule (I and I′) to an allosteric site, thereby preventing interaction of the enzyme with the substrate. Box H illustrates binding of an allosteric activator (X), a nonsubstrate molecule capable of reacting with the enzyme.

Michaelis-Menten kinetics describes the velocity and mechanism of enzyme-catalyzed reactions by assuming the rapid, reversible formation of a complex between an enzyme and its substrate.12

The relationship is expressed by the equation:
$V = \frac{V_{M} [S]}{K_{M} + [S]}$

In this equation:
* $V$ : The reaction velocity.2
* $V_{M}$ : The maximal reaction velocity, achieved when all active sites on the enzyme are filled with substrate.12
* $[S]$ : The concentration of the substrate.2
* $K_{M}$ : The Michaelis constant.2

When plotted with reaction velocity ( $V$ ) on the y-axis and substrate concentration ( $[S]$ ) on the x-axis, the resulting curve is typically hyperbolic. This model serves as the foundation for kinetic studies of enzymes and helps explain how the rate of product formation is proportional to the concentration of the enzyme-substrate complex.21