Protein Folding
The HP lattice model reduces protein folding to its hydrophobic essence. A chain of H (hydrophobic) and P (polar) residues folds on a 2D grid, minimizing energy by placing H residues adjacent to each other. This NP-hard optimization problem captures the key physics: hydrophobic collapse drives the fold.
E = −∑ H–H contacts (non-sequential neighbors on lattice)
The HP model
Ken Dill's HP model (1985) captures the dominant force in protein folding: the hydrophobic effect. In water, nonpolar (H) residues are driven together to minimize their contact with the solvent. The model places residues on a 2D square lattice. Each non-sequential pair of H residues on adjacent lattice sites contributes −1 to the energy. The goal is to find the conformation with the lowest energy.
Finding the optimal fold is NP-hard, so we use a Monte Carlo method: randomly perturb the chain (corner moves, crankshaft moves, end moves) and accept or reject changes according to the Metropolis criterion with probability min(1, e−ΔE/T).