Role of connectivity and fluctuations in the nucleation of calcium waves in cardiac cells.

Spontaneous calcium release (SCR) occurs when ion channel fluctuations lead to the nucleation of calcium waves in cardiac cells. This phenomenon is important since it has been implicated as a cause of various cardiac arrhythmias. However, to date, it is not understood what determines the timing and location of spontaneous calcium waves within cells. Here, we analyze a simplified model of SCR in which calcium release is modeled as a stochastic processes on a two-dimensional network of randomly distributed sites. Using this model we identify the essential parameters describing the system and compute the phase diagram. In particular, we identify a critical line which separates pinned and propagating fronts, and show that above this line wave nucleation is governed by fluctuations and the spatial connectivity of calcium release units. Using a mean-field analysis we show that the sites of wave nucleation are predicted by localized eigenvectors of a matrix representing the network connectivity of release sites. This result provides insight on the interplay between connectivity and fluctuations in the genesis of SCR in cardiac myocytes.