A lattice Monte Carlo model for amyloid fibril formation

Proteins can aggregate to form amyloid fibrils, which are associated with a group of diseases collectively known as amyloidoses. Molecular dynamics simulations are widely used to study protein aggregation; however, it remains computationally challenging to investigate the entire aggregation process, from initial nucleation to the formation of mature amyloid fibrils, within a single simulation. In this study, we propose a Monte Carlo simulation based on a mathematical lattice model in which proteins are represented as spheres on a lattice. Motivated by the role of intramolecular β-sheet structures in accelerating aggregation, we classify protein states into three categories: monomer, intermediate possessing an intramolecular β-sheet structure, and fibril. By tuning the monomer-to-intermediate transition probability PMI and the intermediate-to-fibril transition probability PIF, both kinetics and morphology of amyloid fibril formation can be systematically controlled. When PMI is low, a lag time appears in the early stage of aggregation, whereas increasing PMI shortens the lag time. High values of both PMI and PIF lead to rapid aggregation and the formation of many short fibrils, while low values result in slower aggregation and fewer but longer fibrils. These results are consistent with experimental observations and indicate that amyloid fibril formation can be understood as a crystal growth process. This approach is expected to provide further insight into the universal mechanisms of amyloid fibril formation in homogeneous aqueous environments, as well as in heterogeneous and nonequilibrium systems.