Nonlinear Pharmacokinetics: Michaelis-Menten Equation

Vmax is the maximum process rate at which drug metabolism occurs, representing the saturation point of metabolic enzymes. KM, the Michaelis constant, indicates the drug concentration at which the process rate reaches half its maximum value. Together, these parameters define the capacity-limited kinetics of drug elimination.

When drug concentration (Cp) is much lower than KM, elimination follows first-order kinetics, with rate proportional to concentration. As Cp approaches and exceeds KM, kinetics transition to mixed-order, then zero-order elimination at high concentrations. At zero-order, the elimination rate becomes constant and independent of drug concentration.

At therapeutic doses, phenytoin and salicylates follow first-order elimination. However, at elevated doses, these drugs saturate hepatic mixed-function oxidases, the enzymes responsible for their metabolism. This saturation shifts their kinetics to zero-order elimination, where the metabolic rate plateaus regardless of further dose increases.

The Michaelis-Menten plot illustrates how elimination rate changes with drug concentration. It shows an initial linear increase at low concentrations, transitions to mixed-order kinetics at intermediate concentrations, and reaches a plateau at Vmax. This graphical representation demonstrates the shift from first-order to zero-order elimination patterns.

When KM equals Cp, the process rate operates at exactly half its maximum capacity. If KM exceeds Cp, the process mimics first-order elimination typical of most drugs at therapeutic levels. Conversely, when KM is less than Cp, the process maintains a constant rate similar to zero-order elimination.

Capacity-limited kinetics, described by the Michaelis-Menten equation, accounts for enzyme saturation during drug metabolism. Unlike linear first-order kinetics where elimination rate is always proportional to concentration, capacity-limited kinetics show variable elimination rates depending on whether metabolic enzymes are saturated or unsaturated.

The Michaelis-Menten equation applies when drug metabolism is limited by enzyme capacity rather than drug availability. This occurs particularly with drugs that saturate hepatic enzymes at therapeutic or elevated doses. Understanding when this equation applies helps predict how elimination rate changes across different dose ranges and plasma concentrations.