Nonlinear onset of calcium wave propagation in cardiac cells.

Spontaneous calcium (Ca) waves in cardiac myocytes are known to underlie a wide range of cardiac arrhythmias. However, it is not understood which physiological parameters determine the onset of waves. In this study, we explore the relationship between Ca signaling between ion channels and the nucleation of Ca waves. In particular, we apply a master equation approach to analyze the stochastic interaction between neighboring clusters of ryanodine receptor (RyR) channels. Using this analysis, we show that signaling between clusters can be described as a barrier hopping process with exponential sensitivity to system parameters. A consequence of this feature is that the probability that Ca release at a cluster induces release at a neighboring cluster exhibits a sigmoid dependence on the Ca content in the cell. This nonlinearity originates from the regulation of RyR opening due to more than one Ca ion binding site, in conjunction with Ca mediated cooperativity between RyR channels in clusters. We apply a spatially distributed stochastic model of Ca cycling to analyze the physiological consequences of this nonlinearity, and show that it explains the sharp onset of Ca wave nucleation in cardiac cells. Furthermore, we show that this sharp onset can serve as a mechanism for Ca alternans under physiologically relevant conditions. Thus our findings identify the nonlinear features of Ca signaling which potentially underlie the onset of Ca waves and Ca alternans in cardiac cells.