A Kinetic Model for Cell Damage Caused by Oligomer Formation

TL;DR

This paper develops a mathematical model to understand how oligomer formation during amyloid aggregation causes cell damage, focusing on the effects of nucleation, elongation, and fragmentation, and comparing predictions with experimental data.

Contribution

It introduces a simplified kinetic model based on mass-action equations and PDEs, emphasizing oligomers' role in cell damage, which is a novel focus in amyloid modeling.

Findings

Oligomers, not mature fibrils, are primary contributors to cell damage.

The model accurately predicts amyloid formation dynamics.

Experimental data supports the model's key assumptions.

Abstract

It is well-known that the formation of amyloid fiber may cause invertible damage to cells, while the underlying mechanism has not been fully uncovered. In this paper, we construct a mathematical model, consisting of infinite ODEs in the form of mass-action equations together with two reaction-convection PDEs, and then simplify it to a system of 5 ODEs by using the maximum entropy principle. This model is based on four simple assumptions, one of which is that cell damage is raised by oligomers rather than mature fibrils. With the simplified model, the effects of nucleation and elongation, fragmentation, protein and seeds concentrations on amyloid formation and cell damage are extensively explored and compared with experiments. We hope that our results can provide a valuable insight into the processes of amyloid formation and cell damage thus raised.