Unravelling the spatiotemporal dynamics of amyloid- β -induced astrocyte-neuron network model in Alzheimer's disease

Recent research highlights that calcium dysfunction, emerging from impaired neuron-astrocyte interactions plays a crucial role in the pathogenesis of Alzheimer's disease (AD). In our current study, we investigate this through a computational model of bidirectional coupling between a neuron and an astrocyte within a tripartite synapse framework. Individually, neuron is designed to exhibit neuronal firing dynamics, while the astrocyte captures amyloid- $\beta$ -mediated calcium signaling. In particular, we consider the spatiotemporal version of the model across three scenarios: (i) no diffusion; (ii) diffusion in either neurons or astrocytes; and (iii) diffusion in both. Without diffusion, bifurcation analysis reveals that astrocytic feedback can trigger neuronal firing via a supercritical Andronov-Hopf bifurcation, emphasizing astrocytic regulation of excitability. With diffusion only in neurons, complex Ginzburg-Landau analysis (CGLE) reveals spiral and antispiral wave patterns. When only astrocytic diffusion is present, regular and distorted hexagonal patterns emerge. The third scenario yields Turing-like structures. We further extend the model to a spatial network to explore collective dynamics and synchronization behaviors, where stronger coupling leads to partially synchronized neuronal activity. These findings demonstrate how astrocyte-neuron crosstalk and diffusion-driven instabilities contribute to emergent wave-like activity, shedding light on spatial mechanisms in AD progression.