Stochastic Total Quasi-Steady-State Approximation for the Michaelis-Menten Scheme

TL;DR

This paper develops a stochastic total quasi-steady-state approximation (tQSSA) for the Michaelis-Menten scheme, extending its validity across the entire parameter domain to better model molecular fluctuations in biochemical systems.

Contribution

It provides a comprehensive derivation of the stochastic tQSSA applicable to all parameter regimes, improving upon previous limited cases.

Findings

Derivation of a stochastic tQSSA valid for the full parameter domain

Enhanced modeling of enzyme kinetics with molecular fluctuations

Improved accuracy over previous approximations in stochastic regimes

Abstract

In biochemical systems the Michaelis-Menten (MM) scheme is one of the best-known models of the enzyme- catalyzed kinetics. In the academic literature the MM approximation has been thoroughly studied in the context of differential equation models. At the level of the cell, however, molecular fluctuations have many important consequences, and thus, a stochastic investigation of the MM scheme is often necessary. In their work Barik et al. [Biophysical Journal, 95, 3563-3574, (2008)] presented a stochastic approximation of the MM scheme. They suggested a substitution of the propensity function in the reduced master equation with the total quasi-steady- state approximation (tQSSA) rate. The justification of the substitution, however, was provided for a special case only and did not cover the whole parameter domain of the tQSSA. In this manuscript we present a derivation of the stochastic tQSSA that is valid for the entire tQSSA parameter domain.