Calcium waves in a grid of clustered channels with synchronous IP₃ binding and unbinding

Calcium signals in cells occur at multiple spatial scales and variable temporal duration. However, a physical explanation for transitions between long-lasting global oscillations and localized short-term elevations (puffs) of cytoplasmic Ca²⁺ is still lacking. Here we introduce a phenomenological, coarse-grained model for the calcium variable, which is represented by ordinary differential equations. Due to its small number of parameters, and its simplicity, this model allows us to numerically study the interplay of multi-scale calcium concentrations with stochastic ion channel gating dynamics even in larger systems. We apply this model to a single cluster of inositol trisphosphate (IP ₃) receptor channels and find further evidence for the results presented in earlier work: a single cluster may be capable of producing different calcium release types, where long-lasting events are accompanied by unbinding of IP ₃ from the receptor (Rückl et al., PLoS Comput. Biol. 11, e1003965 (2015)). Finally, we show the practicability of the model in a grid of 64 clusters which is computationally intractable with previous high-resolution models. Here long-lasting events can lead to synchronized oscillations and waves, while short events stay localized. The frequency of calcium releases as well as their coherence can thereby be regulated by the amplitude of IP ₃ stimulation. Finally the model allows for a new explanation of oscillating [IP ₃], which is not based on metabolic production and degradation of IP ₃.