Application of the principle of microscopic reversibility to the steady-state rate equation for a general mechanism for an enzyme reaction with substrate and modifier

Quasi-equilibrium assumption for arbitrary mechanism of enzymatic reaction. Criteria for existence of equilibrium segments

The possible application of the quasi-equilibrium assumption for an arbitrary mechanism of enzymatic reaction is considered. It is shown at what ratios of kinetic constants a segment consisting of two, three, and four intermediates may be considered as an equilibrium one. Expressions for evaluation of accuracy of distribution of intermediate concentrations inside the equilibrium segment and accuracy of determination of intermediate concentrations inside and outside the equilibrium segment as a function of the ratio of kinetic constants are derived. A method for determination of the limitations on the ratio of rate constants for an equilibrium segment of arbitrary structure is suggested.

The quasi-equilibrium assumption for Bi-Bi ordered bisubstrate enzymatic reaction. How to discriminate the mechanism correctly

Application of the quasi-equilibrium assumption for the steady-state kinetics of bisubstrate irreversible enzymatic reactions in the case of ordered binding of substrates (Bi-Bi ordered mechanism) is considered. The necessary and sufficient conditions for application of the quasi-equilibrium assumption have been found and accuracy of this assumption has been numerically evaluated. The limitations on application of the quasi-equilibrium assumption have been shown and errors of its application have been analyzed. It is shown that possible discrimination of substrate binding order using asymmetrical expressions grounded on the quasi-equilibrium assumption is inconsistent because such asymmetrical expressions arise from incorrect application of the quasi-equilibrium assumption. Moreover, it has been proved in the general case that mechanisms generating such substrate-asymmetrical expressions for the steady-state rate of enzymatic reaction do not exist. The error source when using graphical interpretation for discrimination of mechanisms of bisubstrate enzymatic reactions has been determined. The strategy to avoid such errors is pointed out.

Quasi-equilibrium assumption in enzyme kinetics. Necessary and sufficient conditions and accuracy of its application for single-substrate reactions

Steady-state kinetics of compulsory-ordered single-substrate irreversible and reversible enzyme reactions with two, three, and arbitrary number of intermediates were observed. Necessary and sufficient conditions for application of the quasi-equilibrium assumption and restrictions of this assumption were found in cases of two and three intermediates in the equilibrium segment. For all cases, accuracy of the quasi-equilibrium assumption was evaluated.