Discrete Stochastic Modeling of Calcium Channel Dynamics

We propose a discrete stochastic model for calcium dynamics in living cells. A set of probabilities for the opening/closing of calcium channels is assumed to depend on the calcium concentration. We study this model in one dimension, analytically in the limit of a large number of channels per site $N$, and numerically for small $N$. As the number of channels per site is increased, the transition from a nonpropagating region of activity to a propagating one changes from one described by directed percolation to that of deterministic depinning in a spatially discrete system. Also, for a small number of channels a propagating calcium wave can leave behind a novel fluctuation-driven state.