2D memory-based mathematical analysis for the combined impact of calcium influx and efflux on nerve cells.

In this paper, we present a calcium dynamics model that firmly orchestrates exchanges of calcium flux through intracellular/extracellular sources of calcium to investigate cellular activities and calcium homeostasis. The generalized two-dimensional space-time reaction-diffusion model is formulated and analyzed for a wide range of calcium flux. The analytical technique is applied to solve the model by use of the fractional integral transform and some special functions. The existence and uniqueness of the proposed model are discussed. Finally, the obtained results are presented graphically to show the significance of calcium flux by amalgamating the memory of cells and prove the efficiency of the method. • We developed a calcium dynamics model to investigate the interplay of calcium flux based on a reaction-diffusion equation. • We present the computational technique to derive the model's solution using integral transform and special functions. • The existence and uniqueness of the calcium dynamics model are discussed. • We estimated the concentration profile in the presence/absence of VGCC, ER leak, SERCA pump, NCX, and mitochondrial flux. • The modulation of calcium flux provides a noteworthy effect due to the intermediate memory of cells. [ABSTRACT FROM AUTHOR]