RESUMO
The aggregation of amyloid-ð½ (Að½) 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-ð½ (Að½) into senile plaques because of high binding affinity between Að½ 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-ð½ (Að½) proteins in the presence of metal ions. The numerical simulations capture four timescales in the Að½ 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.