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Adaptive space and time numerical simulation of reaction-diffusion models for intracellular calcium dynamics

by Nagaiah, Ch.; Rüdiger, S.; Warnecke, G.; Falcke, M..

Series: 2010-31, Preprints

92C15 Developmental biology, pattern formation
92C40 Biochemistry, molecular biology
65N99 None of the above, but in this section

Adaptive in space and time for the numerical simulation of stochastic and deterministic equations for intracellular calcium dynamics is presented. The modeling of diffusion, reaction and membrane transport of calcium ions in cells leads to a system of reaction-diffusion equations. We describe the modulation of cytosolic and ER calcium concentrations close to the membrane of the cell organelle. A conforming piecewise linear finite element method is used for the spatial discretization while lineary implicit methods, Rosenbrock type methods, are used for the time integration. We adopt a hybrid algorithm to solve the stochastic part. The space grid is adjusted to the strong localization of the calcium release following stochastic channel transitions. By automatically adapting the spatial meshes and time steps to the proper scales during the transitions of channel states, the method accurately resolves the evolution of intracellular calcium concentrations as well as buffer concentrations. This article emphasizes the adaptive and efficient hybrid numerical simulations in two space dimensions. The presented worke establishes the basis for future simulations in a realistic 3D geometry.

reaction-diffusion, intracellular calcium dynamics