Nonlinear Model of Calcium Excitations in Biomembranes

A model is proposed to describe the calcium redistribution in biological substances. The model takes into consideration that calcium can be located inside or outside a cell. Calcium is redistributed due to its transport from the cell volume into the outer space and backward. The model makes allowance for the calcium diffusion into the outer space. It is shown that there are two modes of functioning of the system. In one of them, the initial perturbation of the calcium concentration in the extracellular space monotonically vanishes in time. In the other mode, this perturbation first grows, but afterward decreases to the zero value. The calcium concentration in the intracellular space is shown to be a critical parameter that governs the system operation mode.