Calcium waves are an important means of intrcellular signaling. Intracellular calcium release at the endoplasmatic reticulum is a prime example of the role of stochastic effects in cellular systems. Realistic models consist of deterministic systems of reaction-diffusion equations in three dimensional space coupled to stochastic transitions of calcium channels at the domain boundary. The resulting dynamics has multiple time and space scales, which complicates computer simulations. In this talk we focus on the PDE aspect of the numerical computations. We use adaptive linear finite elements to efficiently resolve the extreme spatial gradients of concentration variables close to a channel. Further, parallel computing is needed for realistic simulations. We describe the algorithmic approach and we demonstrate its efficiency by computational examples. Our single channel model matches experimental data by Mak et al. (PNAS 95, 1998) and results in intriguing dynamics if calcium is used as a carrier. Random openings of the channel accumulate in bursts of calcium blips that may prove central for the understanding of cellular calcium dynamics. We plan to extend our computations to more realistic domain geometries and to use local time stepping methods.

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Last updated: 19 Jul 2024