Derivation of Ca2+ signals from puff properties reveals that pathway function is robust against cell variability but sensitive for control

Ca2+ is a universal second messenger in eukaryotic cells transmitting information through sequences of concentration spikes. A prominent mechanism to generate these spikes involves Ca2+ release from the endoplasmic reticulum Ca2+ store via inositol 1,4,5-trisphosphate (IP3)-sensitive channels. Puffs are elemental events of IP3-induced Ca2+ release through single clusters of channels. Intracellular Ca2+ dynamics are a stochastic system, but a complete stochastic theory has not been developed yet. We formulate the theory in terms of interpuff interval and puff duration distributions because, unlike the properties of individual channels, they can be measured in vivo. Our theory reproduces the typical spectrum of Ca2+ signals like puffs, spiking, and bursting in analytically treatable test cases as well as in more realistic simulations. We find conditions for spiking and calculate interspike interval (ISI) distributions. Signal form, average ISI and ISI distributions depend sensitively on the details of cluster properties and their spatial arrangement. In contrast to that, the relation between the average and the standard deviation of ISIs does not depend on cluster properties and cluster arrangement and is robust with respect to cell variability. It is controlled by the global feedback processes in the Ca2+ signaling pathway (e.g., via IP3-3-kinase or endoplasmic reticulum depletion). That relation is essential for pathway function because it ensures frequency encoding despite the randomness of ISIs and determines the maximal spike train information content. Hence, we find a division of tasks between global feedbacks and local cluster properties that guarantees robustness of function while maintaining sensitivity of control of the average ISI.