| Calcium is an important signaling molecule involved in the regulation of a wide range of processes. In cardiac cells, calcium mediates the excitation and contraction processes. Disturbance of calcium handling has been implicated as a possible initiator of fatal arrhythmias. In this thesis, three mathematical models of calcium regulation are derived and analyzed in order to gain understandings on different aspects of intracellular calcium release and control.;Although spatial inhomogeneity and stochastic release are important, detailed physiological models that also incorporate these effects are computationally expensive to simulate. Using a variety of asymptotic approximations, we derive a simplied yet reliable model of stochastic calcium flux through a release unit that incorporates the interactions of ryanodine receptors with cytoplasmic and sarcoplasmic reticulum calcium, and also calsequestrin. We then use the model to study stochastic spark initiation and termination.;Intracellular calcium release can induce an action potential through the activity of the Na+-Ca2+ exchanger. Recently, periodic calcium release has been proposed as the pacemaking mechanism in the sinoatrial node. Using phase-resetting experiments, we study the nature of the oscillator which results from the interaction of the calcium and the membrane-potential clocks. Compared to results obtained from a single membrane-potential clock models, a different phase-response curve is obtained from the two-clocks model.;Ordinary differential equations models are widely used to study calcium regulation in different cell types. There, a cell is taken as a well-mixed compartment with homogeneous calcium concentration. Using a generic model for calcium oscillation, we investigate the effect of spatial diffusion, release localization, and stochastic channel activities on calcium release and oscillation. A linear stability analysis reveals that lowering the value of the diffusion coefficient can significantly affect the critical IP3 level for oscillation onset as well as the frequency of oscillation. Moreover, by incorporating additive white noise into the model, we observe that regular periodic release can occur in the parameter regime in which oscillation is not observed deterministically. |
