Phenomenological cluster-based model of Ca2+ waves and oscillations for inositol 1,4,5-trisphosphate receptor (IP3 R) channels

Clusters of IP3 receptor channels in the membranes of the endoplasmic reticulum of many nonexcitable 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.