Efficacy of quasi-steady-state approximation in Michaelis–Menten kinetics: a stochastic signature

Abstract

Michaelis–Menten (MM) scheme serves as the benchmark model to characterize enzyme kinetics. Standard theoretical analyses of product formation rate for such a scheme are based on the quasi-steady-state approximation (QSSA). There exist well-established criteria, applicable to both deterministic and stochastic scenarios, to judge the validity of QSSA. These criteria are given in terms of initial concentrations and rate parameters. In this work, we present a complementary stochastic signature to investigate the legitimacy of QSSA in MM kinetics with a finite copy number of species. Our condition is formulated in terms of the time-evolution of the product of coefficients of variation of suitable pair of species population. It can be measured, in principle, from time-series data of molecular population, avoiding estimation of model kinetic parameters.