| Summary: | Intracellular calcium ions (Ca²⁺) play important roles in neurobiology by either triggering or modulating a large number of processes which are associated with nerve cell behaviour. In spite of this importance, it is very difficult experimentally to obtain quantitative information on the dynamics of intracellular calcium. For this reason, Connor and Nikolakopoulou [13] formulated a diffusion model based upon experimentally estimated parameters. They used this model to study the spatial distribution of calcium within the cytoplasm and the increases in the concentration of intracellular calcium ions that a given influx of calcium through the cell membrane can bring about. The mathematical model consists of a system of five reaction-diffusion equations which is treated as a two-point initial-boundary-value problem with constant initial states and nonlinear boundary conditions. Analytical results reveal that the system admits a unique spatially homogeneous stationary state which is asymptotically stable. A regular perturbation technique is used for constructing an approximate transient solution which possesses transition layers. A simplified comparison theorem for parabolic equations is used to provide analytical bounds on the approximate solution. Finally, a B-spline collocation code, called PDECOL, is used to supplement the analytical results to provide a detailed description of the calcium dynamics. === Science, Faculty of === Mathematics, Department of === Graduate
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