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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. [ABSTRACT FROM AUTHOR]

In many stochastic simulations of biochemical reaction networks, it is desirable to “coarse grain” the reaction set, removing fast reactions while retaining the correct system dynamics. Various coarse-graining methods have been proposed, but it remains unclear which methods are reliable and which reactions can safely be eliminated. We address these issues for a model gene regulatory network that is particularly sensitive to dynamical fluctuations: a bistable genetic switch. We remove protein-DNA and/or protein-protein association-dissociation reactions from the reaction set using various coarse-graining strategies. We determine the effects on the steady-state probability distribution function and on the rate of fluctuation-driven switch flipping transitions. We find that protein-protein interactions may be safely eliminated from the reaction set, but protein-DNA interactions may not. We also find that it is important to use the chemical master equation rather than macroscopic rate equations to compute effective propensity functions for the coarse-grained reactions. [ABSTRACT FROM AUTHOR]

We present a method for computing stationary distributions for activated processes in equilibrium and nonequilibrium systems using forward flux sampling. In this method, the stationary distributions are obtained directly from the rate constant calculations for the forward and backward reactions; there is no need to perform separate calculations for the stationary distribution and the rate constant. We apply the method to the nonequilibrium rare event problem proposed by Maier and Stein, to nucleation in a 2-dimensional Ising system, and to the flipping of a genetic switch. [ABSTRACT FROM AUTHOR]

A correction to the article "Eliminating fast reactions in stochastic simulations of biochemical networks: A bistable genetic switch" that was published in 2008 is presented.