In this thesis, we examine hybrid numerical models of calcium-induced calcium release using deterministic PDEs for the diffusion of cytosolic calcium and a stochastic process for channel receptor reactions. We study several simplifying approximations with the goal of improving the computational efficiency of these models without reducing their accuracy.
Specifically, we consider ignoring the time needed for the spatial profile due to a recently opened channel to equilibrate to a steady-state distribution, we consider taking the concentrations of cytosolic buffers to be uniform throughout the cytosol and independent of time, we examine the approximation of the open channel influx by a point source, and we study a coarse-graining approach to modeling larger-scale effects created by the concerted action of multiple channels.
Finally, we construct from experimental data a novel set of binding and dissociation rates for the receptor reactions of a tetrameric IP3-sensitive calcium channel.
Nixon, Andrew T L.,
"On Numerical Models of Calcium-Induced Calcium Release"
Applied Mathematics Theses and Dissertations.
Brown Digital Repository. Brown University Library.