Investigating the two-moment characterisation of subcellular biochemical networks

TL;DR

This paper extends the two-moment approximation (2MA) for stochastic biochemical networks to include non-elementary reactions and relative concentrations, demonstrating its effectiveness on a yeast cell cycle model and capturing experimental cycle time clustering.

Contribution

It introduces an extended 2MA framework that accounts for non-elementary reactions and relative concentrations, enhancing analytical modeling of cellular noise.

Findings

The extended 2MA accurately reproduces cell cycle time clustering.

Coupling between mean and (co)variance explains multiple MPF resettings.

Model aligns well with experimental observations.

Abstract

While ordinary differential equations (ODEs) form the conceptual framework for modelling many cellular processes, specific situations demand stochastic models to capture the influence of noise. The most common formulation of stochastic models for biochemical networks is the chemical master equation (CME). While stochastic simulations are a practical way to realise the CME, analytical approximations offer more insight into the influence of noise. Towards that end, the two-moment approximation (2MA) is a promising addition to the established analytical approaches including the chemical Langevin equation (CLE) and the related linear noise approximation (LNA). The 2MA approach directly tracks the mean and (co)variance which are coupled in general. This coupling is not obvious in CME and CLE and ignored by LNA and conventional ODE models. We extend previous derivations of 2MA by allowing a) non-elementary reactions and b) relative concentrations. Often, several elementary reactions are approximated by a single step. Furthermore, practical situations often require the use relative concentrations. We investigate the applicability of the 2MA approach to the well established fission yeast cell cycle model. Our analytical model reproduces the clustering of cycle times observed in experiments. This is explained through multiple resettings of MPF, caused by the coupling between mean and (co)variance, near the G2/M transition.