Modeling stochastic Ca$^{2+}$ release from a cluster of IP$_3$-sensitive receptors

We focused our attention on Ca$^{2+}$ release from the endoplasmic reticulum through a cluster of inositol 1,4,5-trisphosphate (IP$_3$) receptor channels. The random opening and closing of these receptors introduce stochastic effects that have been observed experimentally. Here, we present a stochastic version of Othmer-Tang model for IP$_3$ receptor clusters. We address the average behavior of the channels in response to IP$_3$ stimuli. We found, by stochastic simulation, that the shape of the receptor response to IP$_3$ (fraction of open channels versus [IP$_3$]), is affected by the cytosolic Ca$^{2+}$ level. We also study several aspects of the stochastic properties of Ca${2+}$ release and we compare with experimental observations.