Using computer algebra to determine rate constants in biochemistry

In earlier work we have described how computer algebra may be used to derive composite rate laws for complete systems of equations, using the mathematical technique of Gröbner Bases (Bennett, Davenport and Sauro, 1988). Such composite rate laws may then be fitted to experimental data to yield estimates of kinetic parameters. Recently we have been investigating the practical application of this methodology to the estimation of kinetic parameters for the closed two enzyme system of aspartate aminotransferase (AAT) and malate dehydrogenase (MDH) (Fisher 1990a; Fisher 1990b; Bennett and Fisher, 1990): aspartate + alpha-ketoglutamate <--> glutamate + oxaloacetate; oxaloacetate + NADH <--> malate + NAD. In this paper we present a fuller (although not yet complete) analysis of the system. We show how symbolic estimates of the error behaviour of the parameters can be made, and used to identify those which are of kinetic significance. Finally we consider how metabolic control analysis can be applied directly to such a system.