The effect of amyloid beta, membrane, and ER pathways on the fractional behavior of neuronal calcium

Calcium signal transduction is essential for cellular activities such as gene transcription, death, and neuronal plasticity. Dynamical changes in the concentration of calcium have a profound effect on the intracellular activity of neurons. The Caputo fractional reaction-diffusion equation is a useful tool for modeling the intricate biological process involved in calcium concentration regulation. We include the Amyloid Beta, STIM-Orai mechanism, voltage-dependent calcium entry, inositol triphosphate receptor (IPR), endoplasmic reticulum (ER) flux, SERCA pump, and plasma membrane flux in our mathematical model. We use Green's function and Hankel and Laplace integral transforms to solve the membrane flux problem. Our simulations investigate the effects of various factors on the spatiotemporal behavior of calcium levels, with a simulation on the buffers in Alzheimer's disease-affected neurons. We also look at the effects of calcium-binding substances like the S100B protein and BAPTA and EGTA. Our results demonstrate how important the S100B protein Amyloid beta and the STIM-Orai mechanism are, and how important they are to consider when simulating the calcium signaling system. As such, our research indicates that a more realistic and complete model for modeling calcium dynamics may be obtained by using a generalized reaction-diffusion technique.