Abstract: Mathematical and computational modeling of calcium
signalling in nerve cells has produced considerable insights into how
the cells contracts with other cells under the variation of biophysical
and physiological parameters. The modeling of calcium signaling in
astrocytes has become more sophisticated. The modeling effort has
provided insight to understand the cell contraction. Main objective
of this work is to study the effect of voltage gated (Operated)
calcium channel (VOC) on calcium profile in the form of advection
diffusion equation. A mathematical model is developed in the form
of advection diffusion equation for the calcium profile. The model
incorporates the important physiological parameter like diffusion
coefficient etc. Appropriate boundary conditions have been framed.
Finite volume method is employed to solve the problem. A program
has been developed using in MATLAB 7.5 for the entire problem
and simulated on an AMD-Turion 32-bite machine to compute the
numerical results.
Abstract: Chemical reaction and diffusion are important phenomena in quantitative neurobiology and biophysics. The knowledge of the dynamics of calcium Ca2+ is very important in cellular physiology because Ca2+ binds to many proteins and regulates their activity and interactions Calcium waves propagate inside cells due to a regenerative mechanism known as calcium-induced calcium release. Buffer-mediated calcium diffusion in the cytosol plays a crucial role in the process. A mathematical model has been developed for calcium waves by assuming the buffers are in equilibrium with calcium i.e., the rapid buffering approximation for a one dimensional unsteady state case. This model incorporates important physical and physiological parameters like dissociation rate, diffusion rate, total buffer concentration and influx. The finite difference method has been employed to predict [Ca2+] and buffer concentration time course regardless of the calcium influx. The comparative studies of the effect of the rapid buffered diffusion and kinetic parameters of the model on the concentration time course have been performed.