Molecular finite-size effects in stochastic models of equilibrium chemical systems

TL;DR

This paper introduces the crowded reaction-diffusion master equation (cRDME) to account for molecular size effects in stochastic chemical systems, revealing significant deviations from classical models and aligning well with Brownian dynamics simulations.

Contribution

The paper derives an exact solution for cRDME, extending the classical RDME to include volume exclusion effects, and demonstrates the impact of crowding on stochastic chemical kinetics.

Findings

Crowding alters noise characteristics and skewness in chemical systems.

Increased molecular size shifts reaction equilibria towards more product formation.

Statistics from cRDME agree with Brownian dynamics simulations.

Abstract

The reaction-diffusion master equation (RDME) is a standard modelling approach for understanding stochastic and spatial chemical kinetics. An inherent assumption is that molecules are point-like. Here we introduce the crowded reaction-diffusion master equation (cRDME) which takes into account volume exclusion effects on stochastic kinetics due to a finite molecular radius. We obtain an exact closed form solution of the RDME and of the cRDME for a general chemical system in equilibrium conditions. The difference between the two solutions increases with the ratio of molecular diameter to the compartment length scale. We show that an increase in molecular crowding can (i) lead to deviations from the classical inverse square root law for the noise-strength; (ii) flip the skewness of the probability distribution from right to left-skewed; (iii) shift the equilibrium of bimolecular reactions so that more product molecules are formed; (iv) strongly modulate the Fano factors and coefficients of variation. These crowding-induced effects are found to be particularly pronounced for chemical species not involved in chemical conservation laws.Finally we show that statistics obtained using the vRDME are in good agreement with those obtained from Brownian dynamics with excluded volume interactions.