MODEL PROTEIN FOLDING · COMPUTING · MONTE CARLO · under KEEPER ERIS
Metropolis & Simulated Annealing
Metropolis (1953) keeps a move that raises the energy by ΔE with probability e^(−ΔE/T). Annealing (Kirkpatrick 1983) lowers T slowly so the chain can escape traps. Here a 48-mer is annealed against a quench, with every acceptance table built by the I-13 VM.
Dave (t249u): "can you build some pages on protein folding, the math and the difficulty, edutaiton please, use this wasm engine"
Dave’s I-13 engine on this page
booting I-13 v0.3…
LIT What the VM computes here: At every temperature stage, the VM computes the acceptance table e^(−k/T) for k = 1…4 lost contacts, and JS’s random draws are tested against those VM numbers. After every stage the VM recounts the chain’s energy from raw coordinates, and any disagreement throws.
LIT Metropolis, Rosenbluth, Rosenbluth, Teller & Teller (J Chem Phys 21:1087, 1953): sample states with Boltzmann weight by accepting a trial move with probability min(1, e^(−ΔE/kT)).
LIT Kirkpatrick, Gelatt & Vecchi (Science 220:671, 1983): simulated annealing. Start hot (accept almost anything), cool slowly, and the walk settles into deep minima. Cool too fast (quench) and it freezes in a trap.
LIT Lattice move sets used here: pivots (rotate or reflect the tail about a residue), corner flips (swap two neighbouring steps) and kinks. Moves that cross the chain are rejected.
AMBER The 48-mer is Unger & Moult’s benchmark; the literature reports E = −23 in 2D. Our annealing on these pages has reached −21, so the CRITIC scores against −23.
MODEL Default schedule: T₀ = 2.0 → T = 0.15 over 30 stages of 400 moves.
Lab MODEL interactive, computed on the I-13 VM
T₀ · T_end · stages
Sources (browsed Oct 2026)
MODEL Two agents, as Dave set for every world. The ARTIST folds the 48-residue HP chain S5 PPHPPHHPPHHPPPPPHHHHHHHHHHPPPPPPHHPPHHPPHPPHHHHH on the square (2D) lattice with pivot, corner and kink moves. The CRITIC judges each move (Metropolis at temperature T) and scores the best fold as −E/23 (E_ref = -23, literature optimum −23 (AMBER, not re-proved here; our annealing reached −21)). It also has Dave’s I-13 VM recount every kept fold from raw coordinates. Rendered with Three.js r160 from a pinned CDN, devicePixelRatio capped at 2. Drag to orbit, scroll to zoom.
LIT on load: the seal is recomputed, the page’s facts are re-checked as arithmetic (throws on mismatch), 200 seeded ARTIST rounds must improve, the workspace loop logs 5 entries, and the OBJ and SVG exports must agree. Then the engine boots, its SHA-256 is checked, and the page’s VM results are compared with independent JS.
Gallery of kept folds (WebGL snapshots):
Workspace improvement loop: instructions for agents MODEL
- Measure: every 40 rounds, record the acceptance rate, the best score, the best E and the rounds since the last improvement.
- Try next: after a 40-round plateau, reheat T ×1.5. If acceptance is under 15%, warm T ×1.25; if over 45%, cool T ×0.7; otherwise anneal T ×0.9.
- Log back: append {entry, round, measured, tried, T} to the workspace log (in the JSON export and the list below), and have the I-13 VM recount the best fold.
- Repeat, forever: never stop improving. Re-check every claim against the engine and the sources before you make it.
Live workspace log:
Shared board MODEL ARTIST ↔ CRITIC
Background art: AMBER MODEL a generative field seeded from this page’s seal.
proving…
Seal sha256(name|slug|blurb): 14e2619bc24c36f9f8300131c62586b0e30cce1c420df086d717c9126bf8740a