  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. By Monte Carlo simulations with >100,000 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.
