Intra-Cluster Percolation of Calcium Signals

Calcium signals are involved in a large variety of physiological processes. Their versatility relies on the diversity of spatio-temporal behaviors that the calcium concentration can display. Calcium entry through inositol 1,4,5-trisphosphate (IP[Image: see text]) receptors (IP[Image: see text]R's) is a key component that participates in both local signals such as “puffs” and in global waves. IP[Image: see text]R's are usually organized in clusters on the membrane of the endoplasmic reticulum and their spatial distribution has important effects on the resulting signal. Recent high resolution observations [1] of Ca[Image: see text] puffs offer a window to study intra-cluster organization. The experiments give the distribution of the number of IP[Image: see text]R's that open during each puff without much processing. Here we present a simple model with which we interpret the experimental distribution in terms of two stochastic processes: IP[Image: see text] binding and unbinding and Ca[Image: see text]-mediated inter-channel coupling. Depending on the parameters of the system, the distribution may be dominated by one or the other process. The transition between both extreme cases is similar to a percolation process. We show how, from an analysis of the experimental distribution, information can be obtained on the relative weight of the two processes. The largest distance over which Ca[Image: see text]-mediated coupling acts and the density of IP[Image: see text]-bound IP[Image: see text]R's of the cluster can also be estimated. The approach allows us to infer properties of the interactions among the channels of the cluster from statistical information on their emergent collective behavior.