Protein folding and amyloid protofibril formation of short peptides are studied through advanced Monte Carlo simulations of coarse-grained models on the face-centered cubic (fcc) and simple cubic (sc) lattices. Interacting self-avoiding walks (ISAW), hydrophobic-polar (HP), and hydrophobic-neutral-polar (H0P) models are used, where amino acids are classified into one, two, or three hydrophobicity groups, respectively. We extend the sc and fcc lattice simulations to handle multiple interacting H0P sequences, and apply them to model amyloid protofibril formation. The Wang-Landau, replica-exchange Wang-Landau, and multicanonical sampling algorithms are utilized to determine the density of states for each system with high precision. These methods are used to predict ground state energies and structures, along with average thermodynamic and structural properties for a set of biologically motivated HP model protein sequences on the fcc lattice. A comparison with analogous results for the sc lattice shows similar folding thermodynamics on both lattice geometries, with one longer HP sequence on the fcc lattice showing additional, subtle structural rearrangements after the initial hydrophobic collapse. Using the ISAW model as a testing ground, we characterize the thermodynamics of a four-body potential that successfully promotes the formation of helical bundles in fcc backbone models, which is then briefly tested for a H0P model of the Crambin protein to show a better agreement with experimental results. Finally, the formation of multi-layered protofibril structures is examined with the sc lattice model through calculation of the specific heat, cluster size distribution, and nucleation free energy barriers. We observe a two-step protofibril formation that involves both condensation and ordering processes, with a conformational rearrangement of peptide structures occurring after condensation in the case of weak intermolecular attraction. The aggregation model is used on the fcc lattice to make a comparison with the sc results for a small test system, and the predicted protofibril structures are presented for the fcc geometry.
