Abstract

The relationship between the inhibition constant (K_i) and fractional inhibition (in particular I₅₀) in classical steady-state enzyme kinetics has been analyzed. The analysis covers enzyme reactions with different numbers of reactants, different reaction mechanisms, and different types and mechanisms of inhibition. The assumptions are made that the product concentrations are very low and that the products have much lower affinities for the enzyme than those of the substrates. The following generalized conclusions are drawn. (a) Fractional velocity (f_v) and fractional inhibition (f_i) in the presence of an inhibitor (I) can be expressed by f_v = 1/[1 + (I/K_i)(E_x/E_t)] and f_i = 1/[1 + (K_i/I)(E_t/E_x)], respectively, where E_t is the total amount of enzyme and E_x is the amount of the enzyme species with which the inhibitor may combine. (b) In a multisubstrate reaction, if all the substrates with which the inhibitor does not compete are at saturating concentrations, the relationship between K_i and I₅₀ is the same as for a one-substrate reaction. (c) Inhibition of either the competitive, noncompetitive, or uncompetitive type produces a generalized relationship, K_i/I₅₀ = E_x/E_t. This relationship indicates that K_i will never be greater than I₅₀, and that the ratio of K_i and I₅₀ provides a simple experimental method for determination of the availability of the enzyme species for inhibitor binding on the distribution of enzyme forms in an enzyme reaction. (d) In partial noncompetitive inhibition, K_ii I₅₀ > K_i, or K_i > I₅₀ > K_ii, depending upon whether the crossover point in the Lineweaver-Burk plot is above or below the horizontal axis (where K_ii and K_i[unknown] are the K_i values obtained from the intercept and slope, respectively); noncompetitive inhibition, K_i is always equal to I_5O. Examples are cited of one-substrate reactions indicating that competitive, noncompetitive, or uncompetitive inhibition can be illustrated or detected by novel graphical methods different from those currently available.