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Coarse-graining the calcium dynamics on a stochastic reaction-diffusion lattice model

We develop a coarse grained (CG) approach for efficiently simulating calcium dynamics in the endoplasmic reticulum membrane based on a fine stochastic lattice gas model. By grouping neighboring microscopic sites together into CG cells and deriving CG reaction rates using local mean field approximation, we perform CG kinetic Monte Carlo (kMC) simulations and find the results of CG-kMC simulations are in excellent agreement with that of the microscopic ones. Strikingly, there is an appropriate range of coarse proportion $m$, corresponding to the minimal deviation of the phase transition point compared to the microscopic one. For fixed $m$, the critical point increases monotonously as the system size increases, especially, there exists scaling law between the deviations of the phase transition point and the system size. Moreover, the CG approach provides significantly faster Monte Carlo simulations which are easy to implement and are directly related to the microscopics, so that one can study the system size effects at the cost of reasonable computational time.