  We propose a simple discrete stochastic model for calcium dynamics in living
cells. Specifically, the calcium concentration distribution is assumed to give
rise to a set of probabilities for the opening/closing of channels which
release calcium thereby changing those probabilities. We study this model in
one dimension, analytically in the mean-field limit of 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 non-propagating region of activity to a
propagating one changes in nature 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, in a parameter range where the limiting deterministic
model exhibits only single pulse propagation.
