Quasi-steady state reduction for the Michaelis-Menten reaction-diffusion system

TL;DR

This paper develops quasi-steady state reductions for the spatially diffusing Michaelis-Menten reaction system, extending classical homogeneous models to include diffusion effects with numerical validation.

Contribution

It introduces a heuristic method for deriving reduced ODE models for diffusion-including Michaelis-Menten systems, supported by numerical evidence.

Findings

Reduced models accurately approximate full reaction-diffusion dynamics

Validates the heuristic reduction method through numerical simulations

Extends QSS reduction applicability to spatially heterogeneous systems

Abstract

The Michaelis-Menten mechanism is probably the best known model for an enzyme-catalyzed reaction. For spatially homogeneous concentrations, QSS reductions are well known, but this is not the case when chemical species are allowed to diffuse. We will discuss QSS reductions for both the irreversible and reversible Michaelis-Menten reaction in the latter case, given small initial enzyme concentration and slow diffusion. Our work is based on a heuristic method to obtain an ordinary differential equation which admits reduction by Tikhonov-Fenichel theory. We will not give convergence proofs but we provide numerical results that support the accuracy of the reductions.