Selection of intracellular calcium patterns in a model with clusteredCa2+release channels

A two-dimensional model is proposed for intracellular ${\mathrm{Ca}}^{2+}$ waves, which incorporates both the discrete nature of ${\mathrm{Ca}}^{2+}$ release sites in the endoplasmic reticulum membrane and the stochastic dynamics of the clustered inositol 1,4,5-triphosphate $\left({\mathrm{IP}}_3\right)$ receptors. Depending on the ${\mathrm{Ca}}^{2+}$ diffusion coefficient and concentration of ${\mathrm{IP}}_3,$ various spontaneous ${\mathrm{Ca}}^{2+}$ patterns, such as calcium puffs, local waves, abortive waves, global oscillation, and tide waves, can be observed. We further investigate the speed of the global waves as a function of the ${\mathrm{IP}}_3$ concentration and the ${\mathrm{Ca}}^{2+}$ diffusion coefficient and under what conditions the spatially averaged ${\mathrm{Ca}}^{2+}$ response can be described by a simple set of ordinary differential equations.