MODEL PROTEIN FOLDING · BIOLOGY · BACKBONE ANGLES · under KEEPER ERIS
Ramachandran Plot · φ and ψ
Each residue’s backbone has two free torsions, φ (C–N–Cα–C) and ψ (N–Cα–C–N). The peptide bond ω is fixed near 180°. Atoms clash in most of the φ/ψ square, so helices and sheets sit in a few allowed islands. Click the plot to set φ and ψ, and the I-13 VM measures them back from the built atoms.
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: JS builds atoms by NeRF from the chosen angles. The VM then takes the raw coordinates and does the vector algebra itself (difference vectors, normalisation with its own Newton square root, projections, cross products), returning the dihedral’s cosine and sine parts. Only the final atan2 is JS, because the VM has no trigonometry.
LIT G. N. Ramachandran, C. Ramakrishnan and V. Sasisekharan (J Mol Biol 7:95, 1963) mapped which (φ, ψ) pairs avoid steric clashes. That is why only a small fraction of the 3²⁰⁰ count is physically allowed.
LIT Typical values: right-handed α-helix (−57°, −47°); 3₁₀ helix (−49°, −26°); antiparallel β (−139°, +135°); parallel β (−119°, +113°); polyproline II (−75°, +145°); left-handed α (+57°, +47°), mostly glycine.
LIT The peptide bond has partial double-bond character, so ω ≈ 180° (trans). Proline is restricted to φ ≈ −63° by its ring.
AMBER Bond lengths and angles used to build the chain are standard ideal values (N–Cα 1.458 Å, Cα–C 1.525 Å, C–N 1.329 Å), from memory of Engh & Huber, not re-browsed.
MODEL The green ellipses are hand-placed sketches of the favoured regions, not a statistical density from the PDB.
Lab MODEL interactive, computed on the I-13 VM
or click anywhere on the plot.
Sources (browsed Oct 2026)
MODEL Two agents, as Dave set for every world. The ARTIST folds the 20-residue HP chain S1 HPHPPHHPHPPHPHHPPHPH on the cubic (3D) lattice with pivot, corner and kink moves. The CRITIC judges each move (Metropolis at temperature T) and scores the best fold as −E/11 (E_ref = -11, best found by our annealing; literature optimum −11). 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): 9b67a15d0eca425c4b8adbf2c9d1f59b55ad4085dac661888baccf907571e9dd