Simplified model of cytosolic Ca2+ dynamics in the presence of one or several clusters of Ca2+ -release channels.

Calcium release from intracellular stores plays a key role in the regulation of a variety of cellular activities. In various cell types this release occurs through inositol-triphosphate (IP3) receptors which are Ca2+ channels whose open probability is modulated by the cytosolic Ca2+ concentration itself. Thus, the combination of Ca2+ release and Ca2+ diffusion evokes a variety of Ca2+ signals depending on the number and relative location of the channels that participate of them. In fact, a hierarchy of Ca2+ signals has been observed in Xenopus laevis oocytes, ranging from very localized events (puffs and blips) to waves that propagate throughout the cell. In this cell type channels are organized in clusters. The behavior of individual channels within a cluster cannot be resolved with current optical techniques. Therefore, a combination of experiments and mathematical modeling is unavoidable to understand these signals. However, the numerical simulation of a detailed mathematical model of the problem is very hard given the large range of spatial and temporal scales that must be covered. In this paper we present an alternative model in which the cluster region is modeled using a relatively fine grid but where several approximations are made to compute the cytosolic Ca2+ concentration ([Ca;{2+}]) distribution. The inner-cluster [Ca;{2+}] distribution is used to determine the openings and closings of the channels of the cluster. The spatiotemporal [Ca;{2+}] distribution outside the cluster is determined using a coarser grid in which each (active) cluster is represented by a point source whose current is proportional to the number of open channels determined before. A full reaction-diffusion system is solved on this coarser grid.