Modeling IP(3)-induced Ca(2+) signaling based on its interspike interval statistics

Inositol 1,4,5-trisphosphate (IP(3)) induced Ca(2+) signaling is a second messenger system used by almost all eukaryotic cells. Recent research demonstrated randomness of Ca(2+) signaling on all structural levels. We compile 8 general properties of Ca(2+) spiking common to all cell types investigated and suggest a theory of Ca(2+) spiking starting from the random behavior of IP(3) receptor channel clusters mediating the release of Ca(2+) from the endoplasmic reticulum capturing all general properties and pathway specific behavior. Spike generation begins after the absolute refractory period of the previous spike. According to its hierarchical spreading from initiating channel openings to cell level, we describe it as a first passage process from none to all clusters open while the cell recovers from the inhibition which terminated the previous spike. Our theory reproduces the exponential stimulation response relation of the average interspike interval (ISI) T(av) and its robustness properties, random spike timing with a linear moment relation between T(av) and the ISI standard deviation and its robustness properties, sensitive dependency of T(av) on diffusion properties, and non-oscillatory local dynamics. We explain large cell variability of T(av) observed in experiments by variability of channel cluster coupling by Ca(2+) induced Ca(2+) release, the number of clusters and IP(3) pathway components expression levels. We predict the relation between puff probability and agonist concentration, and [IP(3)] and agonist concentration. Differences of spike behavior between cell types and stimulating agonists are explained by the different types of negative feedback terminating spikes. In summary, the hierarchical random character of spike generation explains all of the identified general properties.