  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.
