A fractional order model for amyloid beta driven astrocyte calcium signaling

Astrocytes are specialized glial cells that help neurons to maintain the calcium signaling process in the nervous system. The endoplasmic reticulum (ER) and mitochondria are two primary intracellular compartments that regulate calcium ions ([Formula: see text]) in astrocytes. Amyloid beta are the peptides in brain which enters into cytosol through voltage gated calcium channel and influx. It disturbs the intracellular calcium signaling process, which produces calcium oscillations. A comprehensive model is presented to study the calcium concentration in different intracellular compartments. ER contains Sarcoplasmic/Endoplasmic reticulum ATPase flux, [Formula: see text] induced [Formula: see text] release flux and leak flux. Mitochondria contain a uniporter and sodium calcium exchanger. All these fluxes are considered to analyze the calcium concentration level in different compartments. Caputo fractional derivative is used to model calcium concentration. Stability and Bifurcation analysis are performed to study the role of amyloid beta which influences the calcium concentration. Adams Bashforth Moulton method is used to solve the fractional system. All numerical simulations are performed in Python.

The online version contains supplementary material available at https://doi.org/10.1007/s11571-026-10572-7.