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In recent years, several particle-based stochastic simulation algorithms(PSSA) have been developed to study the spatially resolved dynamics ofbiochemical networks at a molecular scale. A challenge all these approacheshave to address is to allow for simulations at cell-biologically relevanttimescales without neither neglecting important spatial and biochemicalproperties of the simulated system nor introducing ad-hoc assumptions not basedon physical principles. Here we describe a PSSA that permits large time stepswhile still retaining a high degree of accuracy. The approach addresses thetypical disadvantage of Brownian dynamics, namely the need to use small timesteps to resolve bimolecular encounters accurately, by estimating the number ofotherwise unnoticed encounters with the help of the Green's functions of thediffusion equation incorporating molecular interactions. This method haspreviously been proposed for purely absorbing boundary conditions andirreversible bimolecular reactions. Building on those ideas, we developed ageneral-purpose PSSA that is applicable to a broad class of reaction-diffusionproblems by incorporating reflective and radiation boundary conditions andreversible reactions. We furthermore discuss how reaction-diffusion systems on2D membranes can be described and derive small time expansions of the Green'sfunctions that substantially speed up key calculations, particularly in theproblematic case of molecules in close proximity. Finally, we point out theformal relationship between our and exact algorithms. The proposed algorithmmay serve as an easily implementable and flexible, computationally efficient,coarse-grained description of reaction-diffusion systems in 2D and 3D thatnevertheless provides a stochastic, detailed representation at the level ofindividual particle trajectories in space and time.

Coarse-Grained Stochastic Particle-based Reaction-Diffusion Simulation Algorithm