The role of calcium dynamics with amyloid beta on neuron-astrocyte coupling

Amyloid beta ($A\beta$) plaques are associated with neurodegenerative diseases such as Alzheimer's disease. Due to the involvement of $A\beta$ plaques in the functioning of the brain; cognitive decline disrupts calcium homeostasis in nerve cells and causes abnormal calcium ions ($Ca^{2+}$) signaling patterns. In consequence, there is enhanced neuronal excitability, compromised synaptic transmission, and decreased astrocytic function. Neuron-astrocyte coupling through calcium dynamics with different neuronal functions has been studied. Key signaling molecules in this process include $Ca^{2+}$, which control several cellular functions, including neurotransmission and astrocytic regulation. The mathematical model for neuron-astrocyte communication has been developed to study the importance of calcium dynamics in signal transduction between the cells. To understand the wide role of mitochondria, NCX, and amyloid beta with various necessary parameters included in the model, $Ca^{2+}$ signaling patterns have been analyzed through amplitude modulation and frequency modulation. The results of the current model are simulated and analyzed using XPPAUT. The findings of the current study are contrasted with experimental data from an existing mathematical model that illustrates the impact of calcium oscillation frequency and amplitude modulations in nerve cells.