A Kinetic Model for Cell Damage Caused by Oligomer Formation

Abstract

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.

Statistical Mechanics and Kinetics of Amyloid Fibrillation

“…Recently, Hong and his colleagues extended kinetic models for amyloid fibrillation and included the cell damage caused by oligomer formation too [169]. Four basic assumptions have been put forward as a general criterion for modeling, i.e.…”

“…A similar approach by examining the leaked ion concentration has been adopt by Hong et al [169] and applied to β 2 m and IAPP fibrils induced membrane leakage with great success (see Fig. 13).…”

“…13). from [169] with copyright permission, but all fittings are re-performed according to (63) with k…”

“…To solve this problem, a systematic moment closure method based on Maximum Entropy Principle [112,113] has been proposed and applied with great success [111,169,183] (as shown in Fig. 16).…”