Prediction of the form of steady-state rate equations from kinetic data

Abstract

The procedures of fitting kinetic data to initial steady-state rate equations are generally complex when double reciprocal plots of initial velocity vs. initial concentration of reactant (substrate, product or modifier) are not linear. For a general enzyme mechanism, if the initial enzyme concentration and all initial reactant concentrations but one are held constant, then the initial steady-state velocity can be written as a ratio of polynomials in the variable reactant concentration. An examination of some of the properties of the steady-state rate equation for a general enzyme mechanism leads to the proposal of a simple graphical procedure for carrying out preliminary analyses of experimental data. This qualitative procedure, which depends on obtaining initial steady-state velocities at very low and very high reactant concentrations provides a means for determining (1) the difference between the minimum power to which the variable reactant concentration is raised in the numerator polynomial and the minimum power to which it is raised in the denominator polynomial, and (2) the difference between the maximum power to which the variable reactant concentration is raised in the denominator polynomial and the maximum power to which it is raised in the numerator polynomial of the steady-state rate equation. For steady-state rate equations involving quadratic and higher power terms in the variable reactant concentration, this procedure should provide valuable preliminary information on the structure of the rate equation. In addition, the possibility of obtaining quantitative estimates of expressions involving some of the constants appearing in steady-state rate equations is examined.