  Intracellular calcium is regulated in part by the release of Ca$^{2+}$ ions
from 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" as
well as global waves propagating through cells, as observed in {\it Xenopus}
oocytes, neurons, and other cell types. Local fluctuations in the number of
calcium ions play a crucial role in the onset of these features. Previous
modeling studies of calcium puff dynamics stemming from IP$_3$R channels have
predominantly 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.
