A phenomenological cluster-based model of Ca2+ waves and oscillations for Inositol 1,4,5-trisphosphate receptor (IP3R) channels

Clusters of IP3 receptor channels in the membranes of the endoplasmic reticulum (ER) of many non-excitable cells release calcium ions in a cooperative manner giving rise to dynamical patterns such as Ca2+ puffs, waves, and oscillations that occur on multiple spatial and temporal scales. We introduce a minimal yet descriptive reaction-diffusion model of IP3 receptors for a saturating concentration of IP3 using a principled reduction of a detailed Markov chain description of individual channels. A dynamical systems analysis reveals the possibility of excitable, bistable and oscillatory dynamics of this model that correspond to three types of observed patterns of calcium release -- puffs, waves, and oscillations respectively. We explain the emergence of these patterns via a bifurcation analysis of a coupled two-cluster model, compute the phase diagram and quantify the speed of the waves and period of oscillations in terms of system parameters. We connect the termination of large-scale Ca2+ release events to IP3 unbinding or stochasticity.