2009 Math Biology Seminar - 04

Calcium is a ubiquitous signaling molecule involved in the regulation of a wide range of processes. In cardiac cells, calcium plays a key role in mediating the electrical-excitation and contraction processes. Three mathematical models of calcium regulation are derived and analyzed. Using a simplified model, we first show that release localization, diffusion, and single-channel activity modulate the onset of calcium oscillations. These factors are of particular importance in cardiac cells where calcium release is spatially inhomogeneous and inherently stochastic. However, models that take these effects into account are computationally expensive to simulate. Using a variety of asymptotic approximations, we derive a simplified yet reliable model of stochastic calcium flux through a release unit. Finally, we use a whole-cell model to explore the role of calcium oscillations in the generation of periodic action potentials based on recent experimental studies on the sinoatrial node and embryonic cardiac cells.