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We develop a coarse grained (CG) approach for efficiently simulating calciumdynamics in the endoplasmic reticulum membrane based on a fine stochasticlattice gas model. By grouping neighboring microscopic sites together into CGcells and deriving CG reaction rates using local mean field approximation, weperform CG kinetic Monte Carlo (kMC) simulations and find the results of CG-kMCsimulations 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 comparedto the microscopic one. For fixed $m$, the critical point increasesmonotonously as the system size increases, especially, there exists scaling lawbetween the deviations of the phase transition point and the system size.Moreover, the CG approach provides significantly faster Monte Carlo simulationswhich are easy to implement and are directly related to the microscopics, sothat one can study the system size effects at the cost of reasonablecomputational time.

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