Derivation of a Theory to Estimate the Kinetic Parameters for Systems with Multiple Substrates Competing for the Same Active Site on an Enzyme

摘要

In studies to characterize the kinetic parameters for catalytic hydrolysis of the organophosphorus nerve agent 1,2,2-trimethylpropyl methylphosphonofluoridate (GD) by human paraoxonase (HuPON1), it was found that standard analysis techniques could not be employed because the kinetic parameters for the GD isomers were not significantly different from each other. Separation of the racemic mixture into component stereoisomers for individual study is feasible but extremely expensive. It was recognized that a theory was required that would allow estimates of kinetic parameters of each isomer to be obtained under conditions of simultaneous hydrolysis of all four stereoisomers. This report presents a synopsis of the derivation of theoretical solutions for the time-course of the four substrates (the stereoisomers) undergoing simultaneous hydrolysis by a single active site of an enzyme. The enzyme 'steady state' assumption made in the derivation is tested by comparing the theoretical solution against solutions obtained by high accuracy numerical integration of the state equations. The theoretical solutions are used to estimate the kinetic parameters for racemic GD hydrolysis by human PON1. The graphs of the theoretical solutions onto Lineweaver-Burke, Eadie-Hofstee, and Hanes-Woolf plots provide visual demonstrations of the inadequacy of those techniques for the determination of kinetic parameters for multiple substrate systems.