Protein Conformational Search: 2D HP-Lattice Monte Carlo

Search Conditions

Temperature (kT) 1.00

Hydrophobic effect 1.00×

Chaperone bias 42%

Search speed 12 moves/frame

Live Readout

Attempted moves

Current energy

0 ε

Best energy found

0 ε

Acceptance rate

How it works

This is a 2D lattice reduction of protein folding — Dill's HP model. The 20-residue chain is a self-avoiding walk on a square grid; each residue is either H (hydrophobic) or P (polar). The only energy term is a bonus for every pair of non-bonded H residues that end up on adjacent lattice cells — the 2D stand-in for the hydrophobic core that drives real proteins to collapse:

E = −ε · Σ [ Hi & Hj adjacent, |i−j| ≥ 2 ]

The chain explores conformation space with the classic pivot algorithm: pick a random hinge residue, rotate everything past it by ±90°/180°, and keep the move only if the walk stays self-avoiding. A trial move is then accepted with the Metropolis rule:

accept if ΔE ≤ 0
accept with prob. exp(−ΔE·β) if ΔE > 0,  β = (1/kT)·(1 + 3·chaperone)

Temperature — higher kT accepts more energy-raising moves, so the chain explores more of the landscape but folds less tightly.
Hydrophobic effect — scales ε, the reward per buried H–H contact; stronger values steepen the funnel toward compact cores.
Chaperone bias — raises the effective β on top of temperature, favoring moves that don't raise energy — a simplified stand-in for how real chaperones suppress kinetic traps, not a literal chaperone mechanism.

Hydrophobic (H) Polar (P) Energy history