Li YuPeng, Yang XiaoLi, Yan SiLu, Yang Hao
School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710062, People's Republic of China.
Chaos. 2025 Jul 1;35(7). doi: 10.1063/5.0263923.
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.
一些在阿尔茨海默病（AD）条件下进行的生理学实验证明，淀粉样β肽（Aβ）可诱导星形胶质细胞出现自发钙振荡以及星形胶质细胞网络中的自发钙活性亢进，这会扰乱神经元传递和大脑活动。然而，Aβ诱导的自发钙动力学背后的动力学机制和潜在过程尚未阐明。受此启发，我们构建了一个Aβ介导的星形胶质细胞网络数学模型，以探索多尺度自发钙动力学，该网络具有三维多拓扑结构，包括链接半径、厄多斯 - 雷尼网络和无标度网络。通过形成新的Aβ膜孔和损害星形胶质细胞间隙连接通道来模拟Aβ的作用。在单细胞尺度上，数值模拟表明Aβ可诱导星形胶质细胞自发钙振荡，其动力学机制是通过非线性动力学技术，星形胶质细胞中发生了亚临界霍普夫分岔。在网络尺度上，我们通过建立定量指标发现Aβ可诱导星形胶质细胞网络中的自发钙活性亢进，这与Aβ诱导小鼠皮质模型中自发钙活性亢进的生理学实验结果一致。此外，通过分析与Aβ相关的参数的影响，发现了Aβ对自发钙活性亢进的双刃剑效应。另外，我们通过量化与网络中靶向和激活的星形胶质细胞相关的关键变量，探索了Aβ诱导的自发钙活性亢进的复杂潜在过程。此外，还确定了肌醇三磷酸浓度与自发钙活性亢进之间的单调递增关系。我们的结果为实验观察提供了数学支持，并为治疗AD中星形胶质细胞异常自发钙动力学的潜在治疗策略提供了见解。
