To study the effect of ER flux with buffer on the neuronal calcium

Calcium signaling is decisive for cellular functions. This calcium random walk stipulates neuronal functions. Calcium concentration could provoke gene transcription, apoptosis, neuronal plasticity, etc. A malformation in calcium could change the neuron's intracellular behavior. Calcium concentration balancing is a complex cellular mechanism. This occurrence can be handled with the Caputo fractional reaction-diffusion equation. In this mathematical modeling, we have included the STIM-Orai mechanism and Endoplasmic Reticulum (ER) flux, Inositol Triphosphate Receptor (IPR), SERCA, plasma membrane flux, voltage-gated calcium entry, and different buffer interactions. A hybrid integral transform and Green's function approach were taken to solve the initial boundary problem. A closed-form solution of a Mittag-Leffler family function plotted using MATLAB software. Different parameters impact changes in the spatiotemporal behavior of the calcium concentration. Specific roles of organelles involved in Alzheimer's disease-affected neurons are computed. Ethylene glycol tetraacetic acid (EGTA), 1,2-bis(o-aminophenoxy)ethane N,N,N,N-tetraacetic acid (BAPTA), and S100B protein effects are also observed. In all simulations, we can say S100B and the STIM-Orai effect cannot be neglected. This model lights up the different approaches for calcium signaling pathway simulation. As a consequence, we determine that a generalized reaction-diffusion approach is a better fit realistic model.