Properties of the Michaelis-Menten equation and its integrated form which are useful in pharmacokinetics

Abstract

Some old equations are reviewed and some new equations have been derived which indicate certain properties of the Michaelis-Menten equation and its integrated forms. Simulated data which obey Michaelis-Menten kinetics have been plotted in various ways to illustrate special relationships. An equation is derived which accurately estimates the slope of the apparently linear decline (k o ) of concentrations from the values of C o , K m , and V m . This indicates the hybrid nature of k o . It is pointed out that if a metabolite is formed by Michaelis-Menten kinetics, then (a) one would not expect linear plots of cumulative amount of metabolite excreted in the urine vs. time, and (b) the plasma clearance of the drug will change with dose, and the plasma clearance of the drug would be expected to be different following administration of the same dose in a rapidly available and a slowly available dosage form. The distortion in parameter values when data arising from Michaelis-Menten kinetics are evaluated by classical linear pharmacokinetics is indicated .