Quantitative determination of the steady-state kinetics of multienzyme reactions using the algebraic rate equations for the component single-enzyme reactions

Abstract

Methods are given whereby the steady-state kinetic characteristics of multienzyme reactions consisting of individual single-enzyme reactions linked by freely diffusible intermediates can be determined quantitatively from the experimentally determined complete algebraic rate equations for the individual reactions. The approach is based on the fact that a valid steady-state rate equation for such a multienzyme reaction, in terms of the rate equations for the individual reactions, can be obtained simply from knowledge of the relative rates of the individual reactions when the multienzyme reaction is in the steady state. A number of model multienzyme reactions, which differ as to structural arrangement of the individual reactions, are examined by this approach. Simple mathematical methods which are applicable to most of these models are given for direct calculation of dependent variables. It is either pointed out or demonstrated with Mathematica that the rate equations for all of these models can be handled very easily with the aid of a personal computer equipped with appropriate equation-solving software. Since the approach permits evaluation of all dependent variables for any specific combination of values for the kinetic parameters and independent variables, numerical values for the flux control coefficients of the individual enzymes can be obtained by direct calculation for a wide variety of conditions and can be compared with those obtained according to the methods of Metabolic Control Analysis. Several such comparisons have been made and in all cases identical results were obtained. The intuitive notion that the individual enzymes of a multienzyme reaction would be equally rate limiting if the total amount of enzyme were being used with maximum efficiency is tested and shown to be incorrect. In the course of this test the flux control coefficient for the individual enzymes were found to be appropriate indicators of relative rate limitation or control by the enzymes and to account properly for differences in specific activity among the enzymes.