  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.
