Abstract: The aggregation of proteins into amyloid fibrils via erroneous folding, also known as misfolding, occurs in several diseases. As a consequence, the study of the kinetics and thermodynamics of this process is currently intensely pursued. Here, we study a minimalistic lattice-based model for amyloid formation using Monte Carlo techniques to sample the grand canonical ensemble, where the chemical potential, volume and temperature describe the system. The coarse-grained model uses orientation-dependent nearest-neighbour interactions. A previous study of this model in the canonical ensemble, where the number of peptides rather than the chemical potential is given, identified two distinct phases, one consisting of smaller aggregates and the other with elongated multilayered fibril-like aggregates.

At a certain value of the chemical potential, the model exhibits an abrupt jump in concentration, indicating a bimodal distribution of the number of peptides, N. To be able to determine the shape of this distribution in the intermediate region of suppressed N values, an artificial ω-ensemble is introduced, where the distribution of N is approximately uniform. Using this ensemble, a cusp in the Helmholtz free energy is identified, viewed as a function of N. It is concluded that this cusp is a manifestation of the phase transition previously observed in canonical simulations.