Particle-based multiscale modeling of intracellular calcium dynamics

Intracellular calcium is regulated by the release of Ca$^{2+}$ ions from the endoplasmic reticulum via inisitol-4,5-triphosphate receptor channels. The resulting dynamics are highly diverse, lead to local calcium "puffs" as well as global waves propagating through cells. Local fluctuations in the number of calcium ions play a crucial role in the onset of these features. Previous modeling studies have focused on stochastic channel models coupled to deterministic diffusion of ions, thereby neglecting local fluctuations of the ion number. Tracking of individual ions is computationally difficult due to the scale separation in the Ca$^{2+}$ concentration when channels are in the open or closed states. In this paper, a spatial multiscale model for investigating of the dynamics of puffs is presented. It couples Brownian motion (diffusion) of ions with a stochastic channel gating model. The model is used to analyze calcium puff statistics. Concentration time traces as well as channel state information are studied. We identify the regime in which puffs can be found and develop a mean-field theory to extract the boundary of this regime. Puffs are only possible when the time scale of channel inhibition is sufficiently large. Implications for the understanding of puff generation and termination are discussed.