Hong Liu, Huang Ya-Jing, Yong Wen-An
Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Peking, P.R. China.
Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Peking, P.R. China.
Biophys J. 2015 Oct 6;109(7):1338-46. doi: 10.1016/j.bpj.2015.08.007.
It is well known that the formation of amyloid fiber may cause invertible damage to cells, although the underlying mechanism has not been fully understood. In this article, a microscopic model considering the detailed processes of amyloid formation and cell damage is constructed based on four simple assumptions, one of which is that cell damage is raised by oligomers rather than mature fibrils. By taking the maximum entropy principle, this microscopic model in the form of infinite mass-action equations together with two reaction-convection partial differential equations (PDEs) has been greatly coarse-grained into a macroscopic system consisting of only five ordinary differential equations (ODEs). With this simple model, the effects of primary nucleation, elongation, fragmentation, and protein and seeds concentration on amyloid formation and cell damage have been extensively explored and compared with experiments. We hope that our results will provide new insights into the quantitative linkage between amyloid formation and cell damage.
众所周知，淀粉样纤维的形成可能会对细胞造成可逆性损伤，尽管其潜在机制尚未完全明确。在本文中，基于四个简单假设构建了一个考虑淀粉样蛋白形成和细胞损伤详细过程的微观模型，其中一个假设是细胞损伤是由寡聚体而非成熟纤维引起的。通过采用最大熵原理，这个以无限质量作用方程形式呈现的微观模型连同两个反应对流偏微分方程（PDEs）已被大幅粗粒化为一个仅由五个常微分方程（ODEs）组成的宏观系统。利用这个简单模型，已广泛探究了初级成核、伸长、碎片化以及蛋白质和种子浓度对淀粉样蛋白形成和细胞损伤的影响，并与实验进行了比较。我们希望我们的结果将为淀粉样蛋白形成与细胞损伤之间的定量联系提供新的见解。
