Reaction Brownian Dynamics and the effect of spatial fluctuations on the gain of a push-pull network

TL;DR

This paper introduces a Brownian Dynamics algorithm that accurately simulates reaction-diffusion systems while obeying detailed balance, and demonstrates how spatial fluctuations influence the gain in a cellular push-pull network.

Contribution

The authors develop a detailed-balance-preserving Brownian Dynamics algorithm for reaction-diffusion systems and analyze the impact of spatial fluctuations on network gain.

Findings

The algorithm accurately reproduces equilibrium and dynamical quantities.

Spatial fluctuations can reduce the gain of a push-pull network.

Diffusive behavior influences the response sensitivity of biochemical networks.

Abstract

Brownian Dynamics algorithms are widely used for simulating soft-matter and biochemical systems. In recent times, their application has been extended to the simulation of coarse-grained models of cellular networks in simple organisms. In these models, components move by diffusion, and can react with one another upon contact. However, when reactions are incorporated into a Brownian Dynamics algorithm, attention must be paid to avoid violations of the detailed-balance rule, and therefore introducing systematic errors in the simulation. We present a Brownian Dynamics algorithm for reaction-diffusion systems that rigorously obeys detailed balance for equilibrium reactions. By comparing the simulation results to exact analytical results for a bimolecular reaction, we show that the algorithm correctly reproduces both equilibrium and dynamical quantities. We apply our scheme to a ``push-pull'' network in which two antagonistic enzymes covalently modify a substrate. Our results highlight that the diffusive behaviour of the reacting species can reduce the gain of the response curve of this network.