Lau-Dill hydrophobic-polar (HP) model on a 2D square lattice. Hydrophobic (H) residues maximize contacts. Watch Monte Carlo simulated annealing find low-energy configurations.
HP model (Lau-Dill 1989): residues are H (hydrophobic) or P (polar). Energy = -number of H-H contacts not along chain backbone. NP-hard in general (Crescenzi 1998). Native state = global minimum energy configuration. Levinthal paradox: random search of conformational space takes longer than age of universe — real proteins fold in microseconds. Key insight: funnel-shaped energy landscape (Wolynes-Onuchic-Bryngelson). Simulated annealing mimics chaperone-assisted folding.