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Intracellular calcium is regulated in part by the release of Ca$^{2+}$ ionsfrom the endoplasmic reticulum via inositol-4,5-triphosphate receptor (IP$_3$R)channels (among other possibilities such as RyR and L-type calcium channels).The resulting dynamics are highly diverse, lead to local calcium "puffs" aswell as global waves propagating through cells, as observed in {\it Xenopus}oocytes, neurons, and other cell types. Local fluctuations in the number ofcalcium ions play a crucial role in the onset of these features. Previousmodeling studies of calcium puff dynamics stemming from IP$_3$R channels havepredominantly focused on stochastic channel models coupled to deterministicdiffusion of ions, thereby neglecting local fluctuations of the ion number.Tracking of individual ions is computationally difficult due to the scaleseparation in the Ca$^{2+}$ concentration when channels are in the open orclosed states. In this paper, a spatial multiscale model for investigating ofthe dynamics of puffs is presented. It couples Brownian motion (diffusion) ofions with a stochastic channel gating model. The model is used to analyzecalcium puff statistics. Concentration time traces as well as channel stateinformation are studied. We identify the regime in which puffs can be found anddevelop a mean-field theory to extract the boundary of this regime. Puffs areonly possible when the time scale of channel inhibition is sufficiently large.Implications for the understanding of puff generation and termination arediscussed.

Particle-based Multiscale Modeling of Calcium Puff Dynamics