The kinetics of slow-binding and slow, tight-binding inhibition: the effects of substrate depletion

Inhibitors with dissociation constants in the micromolar to nanomolar range are important, but hard to characterize kinetically, especially when the substrate concentration in the assay is less than Km. When inhibition increases during the course of the assay (slow-binding inhibition) the concentration of substrate may decrease appreciably. Methods that take substrate depletion into account are described for analysing experiments in which the initial substrate concentration is below Km. Fitting progress curves gives the rate constants for the second (slow) step in a two-step mechanism. An approximate value for the overall dissociation constant may be determined from measurements of rates when the reaction is treated as a first-order process. When the concentrations of inhibitor and enzyme are comparable numerical methods are required. Procedures, suitable for implementation on a microcomputer, for the solution of the differential equations and the fitting of progress curves are described.