Kinetics of suicide substrates steady-state treatments and computer-aided exact solutions

A steady-state differential equation that describes the kinetics of suicide substrate was derived for a scheme presented by Walsh et al. (Walsh, C., Cromartie, T., Marcotte, P. and Spencer, R. (1978) Methods Enzymol. 53, 437–448). Using its analytical solutions, the progress curves of substrate disappearance, product formation and enzyme inactivation were calculated for a hypothetical model system, and were compared with the exact solutions which were obtained by the numerical computation on a set of rate equations. The results obtained with the present analytical solutions were much more consistent with the exact solutions than those obtained using Waley's solutions (Waley, S.G. (1980) Biochem. J. 185, 771–773). The most important factor for a system of suicide substrates was found to be the term (1 + r)μ instead of rμ as proposed by Waley, where r is the ratio of the rate constant of product formation to that of enzyme inactivation and μ is the ratio of initial concentration of enzyme to that of suicide substrate. In cases where this term has a value greater than unity, all the molecules of suicide substrate are used up leaving some enzyme molecules still active. To the contrary, in cases where the term has a value smaller than unity, all the enzyme molecules are inactivated with some molecules of suicide substrate being left unreacted. When the term is equal to unity, then all the enzyme molecules are inactivated and all the molecules of the suicide substrate are converted. Practical methods for estimating kinetic parameters are described.