Limitations of the stochastic quasi-steady-state approximation in open biochemical reaction networks

TL;DR

This paper demonstrates that the stochastic quasi-steady-state approximation often overestimates noise in open biochemical networks, especially for efficient enzymes, with errors up to 30%, challenging its usual validity assumptions.

Contribution

It reveals limitations of the stochastic quasi-steady-state approximation in open enzyme reactions and provides a formula for its error in predicting noise levels.

Findings

Overestimation of noise by the reduced master equation at low molecule counts.

Maximum error of about 30% for highly efficient enzymes.

Validation of theoretical predictions with experimental enzyme data.

Abstract

The application of the quasi-steady-state approximation to the Michaelis-Menten reaction embedded in large open chemical reaction networks is a popular model reduction technique in deterministic and stochastic simulations of biochemical reactions inside cells. It is frequently assumed that the predictions of the reduced master equations obtained using the stochastic quasi-steady-state approach are in very good agreement with the predictions of the full master equations, provided the conditions for the validity of the deterministic quasi-steady-state approximation are fulfilled. We here use the linear-noise approximation to show that this assumption is not generally justified for the Michaelis-Menten reaction with substrate input, the simplest example of an open embedded enzyme reaction. The reduced master equation approach is found to considerably overestimate the size of intrinsic noise at low copy numbers of molecules. A simple formula is obtained for the relative error between the predictions of the reduced and full master equations for the variance of the substrate concentration fluctuations. The maximum error is reached when modeling moderately or highly efficient enzymes, in which case the error is approximately 30%. The theoretical predictions are validated by stochastic simulations using experimental parameter values for enzymes involved in proteolysis, gluconeogenesis and fermentation.