Adaptive Numerical Simulation of Reaction-Diffusion Systems
Dr. Nagaiah ChamakuriApril 17, 2007, 3:30 p.m. HF 136
In my talk I will present the adaptive numerical simulation of intracellular calcium dynamics. Calcium is an important second messenger in cell communication. The dynamics of intracellular calcium is determined by the liberation and uptake by cellular stores as well as reactions with buffers. We develop models and numerical tools to study the liberation of calcium from the endoplasmic reticulum (ER). This process is characterized by the existence of multiple length scales. The modeling of diffusion, binding and membrane transport of calcium ions in cells leads to a system of reaction-diffusion equations. We used piecewise linear finite elements for the spatial discretization and time discretization by a linearly implicit Runge-Kutta scheme. In our description the dynamics of IP3-controlled channels remains discrete and stochastic. The strongly localized temporal behavior due to the on-off behavior of channels as well as their spatial localization is treated by an adaptive numerical method. We present sequential and parallelized numerical results.