Quasi-steady-state approximations derived from the stochastic model of enzyme kinetics

TL;DR

This paper derives and compares various quasi-steady-state approximations (QSSAs) for stochastic enzyme kinetics models, linking their validity conditions to those established in deterministic frameworks using multiscaling techniques.

Contribution

It introduces a stochastic derivation of QSSAs for enzyme kinetics and connects their validity to deterministic conditions through multiscaling analysis.

Findings

QSSAs derived from stochastic models align with deterministic conditions in large volume limits.

Different assumptions about species abundance lead to standard, total, and reverse QSSAs.

Multiscaling techniques validate the applicability of QSSAs in stochastic enzyme kinetics.

Abstract

In this paper we derive several quasi steady-state approximations (QSSAs) to the stochastic reaction network describing the Michaelis-Menten enzyme kinetics. We show how the different assumptions about chemical species abundance and reaction rates lead to the standard QSSA (sQSSA), the total QSSA (tQSSA), and the reverse QSSA (rQSSA) approximations. These three QSSAs have been widely studied in the literature in deterministic ordinary differential equation (ODE) settings and several sets of conditions for their validity have been proposed. By using multiscaling techniques introduced in Kang (and Kurtz 2013) and Ball et al. (2006) we show that these conditions for deterministic QSSAs largely agree with the ones for QSSAs in the large volume limits of the underlying stochastic enzyme kinetic network.