Brownian Dynamics algorithms have been widely used for simulating systems in soft-condensed matter physics. In recent times, their application has been extended to the simulation of coarse-grained models of biochemical networks. In these models, components move by diffusion and interact with one another upon contact. However, when reactions are incorporated into a Brownian dynamics algorithm, care must be taken to avoid violations of the detailed-balance rule, which would introduce systematic errors in the simulation. We present a Brownian dynamics algorithm for simulating 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 spatial fluctuations of the network components can strongly reduce the gain of the response of a biochemical network.

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Journal J. Chem. Phys.
Morelli, M.J, & ten Wolde, P.R. (2008). Reaction Brownian dynamics and the effect of spatial fluctuations on the gain of a push-pull network. J. Chem. Phys., 129(Article number: 54112), 1–11. doi:10.1063/1.2958287