Aβ-mediated multiscale study of spontaneous calcium dynamics in astrocytes

Some physiological experiments in Alzheimer's disease (AD) conditions have evidenced that amyloid β-peptide (Aβ) can induce spontaneous calcium oscillations in astrocytes and spontaneous calcium hyperactivity in astrocyte networks, which disrupt neuronal transmission and brain activity. However, the dynamical mechanism and potential process behind Aβ-induced spontaneous calcium dynamics have not been elucidated. Inspired by this, we develop a mathematical model of the Aβ-mediated astrocyte network to explore the multi-scale spontaneous calcium dynamics, where the network has a 3D multi-topology structure, including link radius, Erdős-Rényi, and scale-free networks. The Aβ roles are modeled by forming new Aβ membrane pores and impairing astrocyte gap junction channels. At the single-cell scale, numerical simulations demonstrate that Aβ can induce astrocyte spontaneous calcium oscillations, the dynamical mechanism behind which is due to the occurrence of a subcritical Hopf bifurcation in astrocytes by means of nonlinear dynamics techniques. At the network scale, we find that Aβ can induce spontaneous calcium hyperactivity in astrocyte networks by establishing quantitative metrics, which is consistent with physiological experiments of Aβ-induced spontaneous calcium hyperactivity in mouse cortical models. Furthermore, the double-edged effects of Aβ on spontaneous calcium hyperactivity are found by analyzing the impact of Aβ-related parameters. Additionally, we explore the complex potential process of Aβ-induced spontaneous calcium hyperactivity by quantifying the key variables related to the targeted and activated astrocytes in the network. Moreover, a monotonically increasing relationship between inositol trisphosphate concentration and spontaneous calcium hyperactivity is identified. Our results offer mathematical support for experimental observations and provide insights for potential therapeutic strategies to treat abnormal spontaneous calcium dynamics in astrocytes in AD.