A method,based on statistical moments,to evaluate the kinetic parameters involved in unstable enzyme systems

The evaluation of individual rate constants involved in any reaction mechanism of an enzymatic systems first requires experimental monitoring of the time course of the concentration or product rate creation or of any enzyme species. The experimental progress curves obtained must then be fitted to the corresponding theoretical symbolic equation. Nevertheless, in some cases, e.g. when the equation involves two or more exponential terms, this fit is not easy and sometimes impossible. Simplification of the equation is usually required by assuming, for example, that the system has reached the steady-state, assuming an initial steady-state of a segment in the scheme of the reaction mechanism or assuming rapid equilibrium in one or more of the reversible steps, if there are any. But, obviously, simplified equations produce either fewer individual rate constants or global constants consisting of algebraic associations of individual rate constants or individual rate constants or global constants that might considerably differ from the real ones due to the approaches made. In this contribution, we suggest an alternative procedure for evaluating the rate constants of enzyme reactions corresponding to enzyme systems where one or more of the species involved is unstable or where one or more of the enzyme species is irreversibly inhibited, or both. The procedure is based on the numerical determination of statistical moments from experimental time progress curves. The fitting of these experimentally obtained moments to the corresponding theoretical expressions allows us, in most cases, to evaluate of all of the rate constants involved, with only a small error. To verify the goodness of the suggested procedure, it was applied to an unstable enzyme system which had previously been analysed with other methods. Finally, it is indicated how this procedure could also be extrapolated for application to any stable or unstable enzyme system.