On the quasi-steady-state approximation in an open Michaelis--Menten reaction mechanism

TL;DR

This paper investigates the validity of the quasi-steady-state approximation in open Michaelis--Menten reactions with substrate inflow, analyzing invariant slow manifolds and time scales to extend classical results.

Contribution

It extends the understanding of quasi-steady-state conditions to open systems with substrate inflow, providing new invariant manifold and time scale estimates.

Findings

Identifies invariant slow manifolds in open Michaelis--Menten systems.

Provides conditions under which the quasi-steady-state approximation holds in open systems.

Highlights the role of singular perturbation parameters in higher order approximations.

Abstract

The conditions for the validity of the standard quasi-steady-state approximation in the Michaelis--Menten mechanism in a closed reaction vessel have been well studied, but much less so the conditions for the validity of this approximation for the system with substrate inflow. We analyze quasi-steady-state scenarios for the open system attributable to singular perturbations, as well as less restrictive conditions. For both settings we obtain distinguished invariant slow manifolds and time scale estimates, and we highlight the special role of singular perturbation parameters in higher order approximations of slow manifolds. We close the paper with a discussion of distinguished invariant manifolds in the global phase portrait.