Homogenization results for the calcium dynamics in living cells

Via the periodic unfolding method, the effective behavior of a nonlinear system of coupled reaction-diffusion equations arising in the modeling of the dynamics of calcium ions in living cells is analyzed. We deal, at the microscale, with two reaction-diffusion equations governing the concentration of calcium ions in the endoplasmic reticulum and, respectively, in the cytosol, coupled through an interfacial exchange term. Depending on the magnitude of this term, various models arise at the macroscale. In particular, we obtain, at the limit, a bidomain model. Such a model is widely used for studying the dynamics of the calcium ions, which are recognized to be important intracellular messengers between the endoplasmic reticulum and the cytosol inside the biological cells.