Michaelis-Menten Relations for Complex Enzymatic Networks

TL;DR

This paper investigates the conditions under which complex enzymatic networks exhibit Michaelis-Menten kinetics, revealing that such relations hold under specific rate conditions and no flux between parallel pathways, with implications for experimental studies.

Contribution

It provides theoretical criteria for when complex enzymatic networks follow Michaelis-Menten relations, extending understanding beyond single-pathway models.

Findings

Michaelis-Menten relation holds under specific rate conditions.

No flux between parallel pathways is necessary for the relation.

Criteria established for experimental verification in complex networks.

Abstract

All biological processes are controlled by complex systems of enzymatic chemical reactions. Although the majority of enzymatic networks have very elaborate structures, there are many experimental observations indicating that some turnover rates still follow a simple Michaelis-Menten relation with a hyperbolic dependence on a substrate concentration. The original Michaelis-Menten mechanism has been derived as a steady-state approximation for a single-pathway enzymatic chain. The validity of this mechanism for many complex enzymatic systems is surprising. To determine general conditions when this relation might be observed in experiments, enzymatic networks consisting of coupled parallel pathways are investigated theoretically. It is found that the Michaelis-Menten equation is satisfied for specific relations between chemical rates, and it also corresponds to the situation with no fluxes between parallel pathways. Our results are illustrated for simple models. The importance of the Michaelis-Menten relationship and derived criteria for single-molecule experimental studies of enzymatic processes are discussed.