The Michaelis–Menten equation is a fundamental model for describing capacity-limited kinetics in drug metabolism. It offers insights into the rate of decline of plasma drug concentration C_p over time, with V_max and K_M as pivotal parameters.

V_max represents the maximum achievable process rate, while K_M, known as the Michaelis constant, signifies the drug concentration at which the process rate reaches half its maximum. This relationship between V_max, K_M, and C_p gives rise to three distinct scenarios that shed light on the dynamics of drug metabolism.

First, when K_M = C_p, the process rate operates at half its maximum capacity. Conversely, if K_M > C_p, the process rate mirrors first-order elimination, a pattern typically observed in most drugs at therapeutic levels. On the other hand, when K_M < C_p, the process maintains a constant rate akin to zero-order elimination. Certain drugs, such as salicylates and phenytoin, follow first-order kinetics at lower therapeutic doses. In this state, the rate of drug elimination is proportional to the drug concentration. However, when these drugs are administered at elevated therapeutic doses, their metabolism saturates the hepatic mixed-function oxidases. This saturation shifts the kinetics to a zero-order pattern, where the elimination rate becomes constant and independent of drug concentration. The graphical representation of the Michaelis–Menten equation, known as the Michaelis–Menten plot, illustrates an initial linear rate increase with concentration, transitioning to mixed-order kinetics at higher concentrations and ultimately culminating in a plateau at V_max.

In summary, the Michaelis–Menten equation serves as a foundational tool for understanding the intricacies of capacity-limited drug metabolism. It delineates the interplay between V_max, K_M, and C_p in shaping the rate of drug elimination within the body.