A kinetic description of sequential, reversible, Michaelis-Menten reactions: practical application of theory to metabolic pathways

Abstract

Equations are presented which describe a linear coupled system of reactions that utilize a single substrate and convert it to product by way of several intermediate enzyme catalysed steps. The present analysis extends previous results by assuming that the enzymes obey reversible Michaelis-Menten kinetics. In order for the system to reach steady state one must assume that the initial substrate concentration and the final product concentration are buffered to a constant value. Using the present analysis it can be shown that the system will not enter a steady state if the maximal velocity of any forward reaction is less than the steady state flux through the system. This condition represents a practical test for determining if a system will enter steady state but is valid only when the rate of the primary enzyme is not affected allosterically be intermediates in the pathway. The equations are used to analyse a portion of the rat liver glycogenic pathway that catalyses the conversion of glucose to fructose 1,6-bisphosphate.