Kinetics of the reversible inhibition of enzyme-catalysed reactions by tight-binding inhibitors

A theoretical kinetic study has been undertaken to determine the kinetic characteristics of enzymic reactions that are reversibly inhibited by a substrate analogue at concentrations comparable to that of the enzyme. A general rate equation, that allows for the combination of such a tight-binding inhibitor with one or more enzyme forms of any reaction mechanism, has been derived and shown to be quadratic with square and linear terms in v which represents that true initial steady-state velocity. It has been concluded that, from plots of v against total enzyme concentration at fixed total inhibitor concentration, the concentration of enzyme catalytic sites can be determined irrespective of the nature of the inhibition and the reaction mechanism. However, plots of v(or i/v) against total inhibitor concentration can be used for this purpose only if the dissociation constant associated with the inhibitor is virtually zero. Particular initial rate equations have been obtained for the cases in which the tight-binding inhibitor gives rise to competitive, non-competitive and uncompetitive inhibition with respect to one of the substrates of a bireactant mechanism. From these equations it has been deduced that, in the presence of inhibitor, plots of i/v against the reciprocals of the substrate concentrations yield families of concave-down, non-rectangular hyperbolas. The difficulties associated with the determination of inhibition constants for tight-binding inhibitors are discussed.