In the Michaelis-Menten kinetics, how is Km defined?

In Michaelis-Menten kinetics, ( K_m ) is defined as the Michaelis constant, which represents the substrate concentration at which the reaction rate is half of its maximum velocity, ( V_{max} ). It provides insight into the affinity of the enzyme for its substrate; a lower ( K_m ) value indicates a higher affinity.

The correct expression for ( K_m ) is derived from the rate constants of the enzyme-catalyzed reaction. Specifically, it is calculated using the rate constants for the formation and breakdown of the enzyme-substrate complex. The formula ( K_m = \frac{k_{-1} + k_2}{k_1} ) captures this relationship, where ( k_1 ) is the rate constant for the formation of the enzyme-substrate complex, ( k_{-1} ) is the rate constant for its breakdown to free enzyme and substrate, and ( k_2 ) is the rate constant for the conversion of the enzyme-substrate complex to product and free enzyme.

This understanding is crucial because it relates the kinetics of enzyme action (how fast an enzyme converts substrate into product) directly to the relative concentrations and rates. Each of the other options does not define (