  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.
