Modeling the spatiotemporal intracellular calcium dynamics in nerve cell with strong memory effects

Abstract

Abstract Calcium signaling in nerve cells is a crucial activity for the human brain to execute a diversity of its functions. An alteration in the signaling process leads to cell death. To date, several attempts registered to study the calcium distribution in nerve cells like neurons, astrocytes, etc. in the form of the integer-order model. In this paper, a fractional-order mathematical model to study the spatiotemporal profile of calcium in nerve cells is assembled and analyzed. The proposed model is solved by the finite element method for space derivative and finite difference method for time derivative. The classical case of the calcium dynamics model is recovered by setting the fractional parameter and that validates the model for classical sense. The numerical computations have systematically presented the impact of a fractional parameter on nerve cells. It is observed that calbindin-D28k provides a significant effect on the spatiotemporal variation of calcium profile due to the amalgamation of the memory of nerve cells. The presence of excess amounts of calbindin-D28k controls the intracellular calcium level and prevents the nerve cell from toxicity.