Intra-cluster percolation of calcium signals.

Calcium signals are involved in a large variety of physiological processes. Their versatility relies on the diversity of spatiotemporal behaviors that the calcium concentration can display. Calcium entry through inositol 1,4,5-trisphosphate (IP3) receptors (IP3R's) is a key component that participates in both local signals such as "puffs" and in global waves. IP3R's areusually 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 of Ca2+ puffs offer a window to study intra-cluster organization. The experiments give the distribution of the number of IP3R'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: IP3 binding and unbinding and Ca2+-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 case sis 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 Ca2+-mediated coupling acts and the density of IP3-bound IP3R'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.