Department of Mathematics and Statistics, Mississippi State University, Mississippi State, MS, 39762, USA.
Department of Chemistry, Mississippi State University, Mississippi State, MS, 39762, USA.
Bull Math Biol. 2019 Jun;81(6):1943-1964. doi: 10.1007/s11538-019-00583-3. Epub 2019 Feb 26.
The aggregation of amyloid-𝛽 (A𝛽) proteins through their self-assembly into oligomers, fibrils, or senile plaques is advocated as a key process of Alzheimer's disease. Recent studies have revealed that metal ions play an essential role in modulating the aggregation rate of amyloid-𝛽 (A𝛽) into senile plaques because of high binding affinity between A𝛽 proteins and metal ions. In this paper, we proposed a mathematical model as a set of coupled kinetic equations that models the self-assembly of amyloid-𝛽 (A𝛽) proteins in the presence of metal ions. The numerical simulations capture four timescales in the A𝛽 dynamics associated with three important events which include the formation of the amyloid-metal complex, the homogeneous aggregation of the amyloid-metal complexes, and the non-homogeneous aggregation of the amyloid-metal complexes. The method of singular perturbation is used to identify these timescales in the framework of slow-fast systems.
淀粉样蛋白-β (Aβ) 蛋白通过自身聚合形成寡聚体、纤维或老年斑的聚集被认为是阿尔茨海默病的关键过程。最近的研究表明，金属离子在调节淀粉样蛋白-β（Aβ）聚集成老年斑的聚合速率方面起着至关重要的作用，因为 Aβ 蛋白与金属离子之间具有很高的结合亲和力。在本文中，我们提出了一个数学模型，作为一组耦合的动力学方程，用于模拟金属离子存在下淀粉样蛋白-β (Aβ) 蛋白的自组装。数值模拟捕捉到与三个重要事件相关的 Aβ 动力学中的四个时间尺度，包括淀粉样蛋白-金属复合物的形成、淀粉样蛋白-金属复合物的均相聚合以及淀粉样蛋白-金属复合物的非均相聚合。奇异摄动法用于在慢快系统框架中识别这些时间尺度。
