Modeling IP3 induced Ca2+ signaling based on its interspike interval statistics

Inositol 1,4,5-trisphosphate (IP3) induced Ca2+ signaling is a second messenger system used by almost all eukaryotic cells. Recent research identified 8 general properties of Ca2+ spiking common to all cell types investigated and demonstrated randomness of Ca2+ signaling on all structural levels. We suggest a theory of Ca2+ spiking starting from the random behaviour of IP3 receptor channel clusters mediating the release of Ca2+ from the endoplasmic reticulum. 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 quantitatively all general properties for different IP3 pathways including the exponential stimulation response relation of the average interspike interval (ISI) Tav and its robustness properties, random spike timing with a linear moment relation between Tav and the ISI standard deviation and its robustness properties, sensitive dependency of Tav on diffusion properties, and non-oscillatory local dynamics. We explain large cell variability of Tav observed in experiments by variability of channel cluster coupling by Ca2+ induced Ca2+ release, the number of clusters and IP3 pathway components expression levels. We predict the relation between puff probability and agonist concentration, and [IP3] and agonist concentration. Differences of spike behaviour 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.