Michaelis-Menten kinetics mixed order kinetics

Michaelis-Menten kinetics is often referred to as mixed-order kinetics because it displays characteristics of both zero-order and first-order kinetics, depending on the concentration of the substrate.

Michaelis-Menten Kinetics Overview

The Michaelis-Menten model describes the rate of enzyme-catalyzed reactions. The fundamental equation is:

$v = \frac{V_{m a x} [S]}{K_{m} + [S]}$

Where:

$v$ is the reaction velocity.
$V_{m a x}$ is the maximum velocity of the reaction when the enzyme is fully saturated with substrate.
$[S]$ is the substrate concentration.
$K_{m}$ is the Michaelis constant, representing the substrate concentration at which the reaction rate is half of $V_{m a x}$ .

Mixed-Order Kinetics

In the context of Michaelis-Menten kinetics:

First-Order Kinetics: When the substrate concentration $[S]$ is much less than $K_{m}$ (i.e., $[S] ≪ K_{m}$ ), the term $K_{m} + [S]$ in the denominator is approximately equal to $K_{m}$ . Therefore, the Michaelis-Menten equation simplifies to:
$v \approx \frac{V_{m a x} [S]}{K_{m}}$
This means the reaction rate is directly proportional to the substrate concentration $[S]$ , which is the hallmark of first-order kinetics.
Zero-Order Kinetics: When the substrate concentration $[S]$ is much greater than $K_{m}$ (i.e., $[S] ≫ K_{m}$ ), the term $K_{m} + [S]$ is approximately equal to $[S]$ . Therefore, the Michaelis-Menten equation simplifies to:
$v \approx V_{m a x}$
Here, the reaction rate approaches $V_{m a x}$ and becomes independent of the substrate concentration. This is characteristic of zero-order kinetics, where the rate is constant and does not depend on the concentration of the reactant.

Summary of Mixed Order

First-Order Kinetics: At low substrate concentrations, the reaction rate is dependent on the substrate concentration, and the kinetics appear first-order.
Zero-Order Kinetics: At high substrate concentrations, the reaction rate approaches a maximum value ( $V_{m a x}$ ) and becomes independent of substrate concentration, showing zero-order kinetics.

Thus, Michaelis-Menten kinetics is termed "mixed-order" because the reaction order varies with substrate concentration. At low concentrations, it behaves like a first-order reaction, while at high concentrations, it behaves like a zero-order reaction. This dual behavior is what characterizes the mixed-order kinetics of Michaelis-Menten enzyme-catalyzed reactions.