Simulated annealing minimizes energy of hydrophobic-polar sequences on a 2D lattice
2.0
0.995
Energy (HH contacts): 0
Temperature: —
Best Energy: 0
HP Model (Lau & Dill 1989): proteins are simplified to sequences of Hydrophobic and Polar residues on a 2D lattice. Energy = −1 per HH contact between non-bonded neighbors.
Simulated annealing mimics cooling: at high temperature T, bad moves are accepted with probability e^(ΔE/T), allowing escape from local minima. As T → 0, only improvements are accepted.
Finding the minimum energy conformation is NP-complete even in this simplified model. Real protein folding involves thousands of residues in 3D — the Levinthal paradox notes that random search would take longer than the age of the universe, yet proteins fold in milliseconds. Chaperone proteins, co-translational folding, and energy funnel landscapes explain this.