Transient enzyme kinetics: Graph-theoretic approach

A graph-theoretic approach is shown to simplify the analysis of transient enzyme kinetics. The coefficients of the characteristic polynomial for kinetic equations are obtained by graphical construction of directed trees and sub-trees in the kinetic scheme. An example of kinetic schemes, providing a simple time-dependent analytical solution, is demonstrated. This example describes a substrate-inhibited enzymatic reaction and interprets the pH-dependent inhibition of the lactate dehydrogenase. It is shown that rapid equilibrium in some parts of the kinetic scheme can simplify the analysis. The enzyme pre-incubation with a product is shown to be characterized by the non-monotonous transient kinetics. This phenomenon is useful to estimate correctly the kinetic parameters. It is supposed that the lactate dehydrogenase substrate inhibition can be important for switching the glycolytic fluxes.