Mathematical model for agonist-induced oscillatory calcium waves in non-excitable mammalian cells

Many non-excitable cells display cytosolic Ca²⁺ oscillations resulting from the periodic release of Ca²⁺ from intracellular stores. Recent observations in hepatocytes and some other cell types have shown that agonist-induced Ca²⁺ oscillations often display an intracellular spatial organization and do not occur synchronously within the cell. Ca²⁺ waves evoked by different agonists originate from the same subcellular locus and propagate through the cell with a constant rate of progress and amplitude. This indicates that Ca²⁺ waves are driven by a self-propagating mechanism and not by diffusion alone. We propose a simplified one-dimensional mathematical model to describe this phenomenon based on the mechanism of calcium-induced calcium release. The numerical solution of the system of two coupled non-linear partial differential equations reproduces many of the main features observed experimentally.