Kinetics of the enzyme titration process by reversible modifiers

The effect of reversible modifiers on the initial rate of enzyme catalysed reactions has been investigated in a quasi-equilibrium approximation using the general modifier mechanism of Botts and Morales. It has been shown that, when investigating the dependence of the initial rate on the modifier concentration at a fixed substrate concentration, the kinetics of enzyme titration by reversible modifiers can generally be described using two kinetic constants. Just as the dependence of the initial rate on the substrate concentration (at a fixed modifier concentration) is described using two kinetic constants: the Michaelis constant K_m and the limiting rate V_m. Only one constant M₅₀ is needed to describe the kinetics of linear inhibition, and in the case of nonlinear inhibition and activation, along with M₅₀ the constant Q_M is also needed.

Knowing the values of the constants M₅₀ and Q_M, it is possible to unambiguously determine the modification efficiency, that is, to calculate how many times the initial rate of the enzyme catalysed reaction will change when a certain modifier concentration is added to the incubation medium.

The properties of these fundamental constants have been analysed in detail and the dependence of these constants on other parameters of the Botts-Morales model have been shown. Equations describing the dependence of relative reaction rates on the modifier concentration using these kinetic constants are presented. Various ways of linearising these equations for calculating the kinetic constants M₅₀ and Q_M from experimental data are also presented.