Parallel numerical solution of intracellular calcium dynamics

Abstract

We present a parallel numerical approach for 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 the problem leads to a nonlinear reaction-diffusion system with natural boundary conditions in 2D. We used piecewise linear finite elements for the spatial discretization and time discretization by a linearly implicit Runge-Kutta scheme. We used the CHACO package for the domain decomposition. In our description the dynamics of IP 3-controlled channels remains discrete and stochastic. It is implemented in the numerical simulation by a stochastic source term in the reaction diffusion equation. 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.