We present and study a minimal structure-based model for the self-assembly of peptides into ordered $\beta$-sheet-rich fibrils. The peptides are represented by unit-length sticks on a cubic lattice and interact by hydrogen bonding and hydrophobicity forces. Using Monte Carlo simulations with $>{10}^5$ peptides, we show that fibril formation occurs with sigmoidal kinetics in the model. To determine the mechanism of fibril nucleation, we compute the joint distribution in length and width of the aggregates at equilibrium, using an efficient cluster move and flat-histogram techniques. This analysis, based on simulations with 256 peptides in which aggregates form and dissolve reversibly, shows that the main free-energy barriers that a nascent fibril has to overcome are associated with changes in width.

• Received 1 September 2012

DOI:https://doi.org/10.1103/PhysRevLett.110.058101