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 demonstrated randomness of Ca²⁺ signaling on all structural levels. We compile eight general properties of Ca²⁺ spiking common to all cell types investigated and suggest a theory of Ca²⁺ spiking starting from the random behavior of IP₃ receptor channel clusters mediating the release of Ca²⁺ 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 T_av and its robustness properties, random spike timing with a linear moment relation between T_av and the interspike interval SD and its robustness properties, sensitive dependency of T_av on diffusion properties, and nonoscillatory local dynamics. We explain large cell variability of T_av observed in experiments by variability of channel cluster coupling by Ca²⁺-induced Ca²⁺ release, the number of clusters, and IP₃ pathway component expression levels. We predict the relation between puff probability and agonist concentration and [IP₃] 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.