Spatial stochastic modeling of intracellular Ca$^{2+}$ dynamics using two-regime methods

The signaling pathways in many cell types depend on the controlled release of calcium ions from the endoplasmatic reticulum (ER) into the cytoplasm, via clusters of inisitol triphosphate (IP$_3$) receptor channels. At low concentrations, Ca$^{2+}$ ions facilitate channel activation, while acting as inhibitory agents at high concentrations. An activation event causes the opening of other channels in a cluster, resulting in a calcium puff. We simulate calcium ion dynamics using a recently-developed hybrid two-regime technique, wherein the positions of calcium ions in the vicinity of a channel cluster are tracked by employing an off-lattice Brownian dynamics algorithm. An efficient compartment-based algorithm is used in the remainder of the computational domain to correctly capture the diffusive spread of ions. We characterize calcium puffs via the distributions of inter-puff times and amplitudes and investigate the influence of diffusive noise on the puff characteristics by comparing our results with data obtained from an effective non-spatial model.