HP Protein Folding — Hydrophobic Collapse
HP lattice model: H (hydrophobic) and P (polar) residues on a 2D square lattice. Energy = −1 per H-H non-bonded contact. Monte Carlo annealing searches for the minimum energy fold, demonstrating hydrophobic core formation.
HP model (Lau & Dill 1989): The driving force for protein folding is burial of hydrophobic residues. On a 2D lattice, H-H contacts score −1. The native state maximizes H-H contacts. Though NP-hard in general (Crescenzi 1998), short chains are tractable. Annealing reveals funneled energy landscape — the "folding funnel" hypothesis. The contact map shows native contacts (H-H pairs). Real proteins: ~30% H residues form hydrophobic core in ∼microseconds via diffusion-collision or nucleation-condensation.