Fire-diffuse-fire calcium waves in confined intracellular spaces.

The propagation of fire-diffuse-fire Ca(2+) waves through a three-dimensional rectangular domain is considered. The domain is infinite in extent in the direction of propagation but with lateral barriers to diffusion which contain Ca(2+) pumps. The Ca(2+) concentration profile due to the firing of a release site (spark) is derived analytically based on the Green's function for the diffusion equation on the domain. The existence, stability and speed of these waves is shown to be critically dependent on the dimensions of the domain and the Ca(2+) pump rate. It is shown that the smaller the dimensions of the region, the lower the Ca(2+) release flux required for wave propagation, and the higher the wave speed. Also it is shown that the region may support multiple Ca(2+) wavefronts of varying wave speed. This model is relevant to subsarcolemmal waves in atrial myocytes (Kockskämper et al., 2001, Biophys. J. 81, 2590-2605), and the results may be of importance in understanding the roles of the endoplasmic/sarcoplasmic reticulum, surface membranes and Ca(2+) pumps in the intracellular Ca(2+) dynamics of cells.