Golicnik_2003_J.Chem.Inf.Comput.Sci_43_1486

We revisit a previous analysis of the classical Michaelis-Menten enzyme reaction for the case in which the free enzyme incurs the loss of its activity by an irreversible inhibitor concentration dependent but time unaltered rate constant (see Golicnik, M. J. Chem. Inf. Comput. Sci. 2002, 42, 157-161). We study the kinetic model of an enzyme-catalyzed reaction in the presence of an equimolar irreversible inhibitor showing a time dependent inactivation rate constant because of considerable inhibitor amount depletion during the course of the reaction. We show that an analytical solution containing the nonelementary Gauss hypergeometric function can be found for the reactants in equation Phi of an implicit type that precludes direct calculation of the extent of reaction at any time. The transformation theory of the hypergeometric function is used to obtain rapidly convergent power series, and for the root calculation of equation Phi the divergence-proof root bracketing algorithm according to Van Wijngaarden-Dekker-Brent is performed. Numerically generated data are analyzed according to this mathematical procedures, and the results are compared with ones obtained by the numerical integration treatment.