The relationship between the inhibition constant (Ki) 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 (fv) and fractional inhibition (fi) in the presence of an inhibitor (I) can be expressed by fv = 1/[1 + (I/Ki)(Ex/Et)] and fi = 1/[1 + (Ki/I)(Et/Ex)], respectively, where Et is the total amount of enzyme and Ex 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 Ki 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, Ki/I50 = Ex/Et. This relationship indicates that Ki will never be greater than I50, and that the ratio of Ki 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, Kii I50 > Ki, or Ki > I50 > Kii, depending upon whether the crossover point in the Lineweaver-Burk plot is above or below the horizontal axis (where Kii and Ki[unknown] are the Ki values obtained from the intercept and slope, respectively); noncompetitive inhibition, Ki is always equal to I5O. 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.
ACKNOWLEDGMENTS I am grateful to Professor Paul Talalay for valuable suggestions and advice during the course of these studies. I would like to thank Miss Julia T. Hawkins for reading and checking the manuscript, and Dr. Daniel M. Byrd, III, for valuable comments on the manuscript.
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