A Multi-Parametric Study of The Impact of Aβ on Astrocytes Ca2+ Oscillations Under Fuzzy Environment

Calcium signaling plays a key role in the functioning of astrocyte, and the disruption in its natural oscillatory behaviour is strongly associated with neurological disorders like Alzheimer disease. The study shows that amyloid beta is the main cause of the calcium dysregulation in Astrocytes cell. Recent research confirms that amyloid-beta neurotoxicity primarily affects Astrocytes. In this work, a mathematical model is developed to study the effect of amyloid-beta and the extracellular potassium levels on the cytosolic calcium profile in Astrocyte. The model incorporates multiple pathways of calcium exchange that includes voltage gated calcium channel, sarcoplasmic/endoplasmic reticulum calcium ATPase, mitochondrial fluxes like uniporter and sodium-calcium exchanger etc. Calcium stores like ER and mitochondria are also included. To model more realistic, a linguistic uncertainty in biological conditions is taken into account by representing initial conditions as a triangular fuzzy number. The qualitative behaviour of the system is analysed in various aspects through equilibrium analysis, stability and bifurcation analysis. In addition, sensitivity analysis is also done to check the effect of parameters that are more sensitive to the cytosolic calcium concentration. Our results confirms that amyloid-beta directly impacts the calcium signaling pathways of Astrocytes, leading to measurable shifts in their physiological behaviour. All results are simulated in python program.