MODEL PROTEIN FOLDING · BIOLOGY · SECONDARY STRUCTURE · under KEEPER ERIS

α-Helix & β-Sheet · 3.6 per Turn

Pauling’s α-helix has 3.6 residues per turn, a 1.5 Å rise and a 5.4 Å pitch, with each C=O bonded to the N–H four residues on. β-strands lie about 3.3 Å per residue and pair into sheets. The I-13 VM builds the helix with its own sine series.

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: The VM computes turns, pitch, length, H-bond counts and the Cα(i)–Cα(i+k) distances √((2r·sin(kθ/2))² + (k·d)²). It uses its own sine Taylor series and Newton square root; JS only renders.

LIT Pauling, Corey & Branson (PNAS 37:205, 1951) predicted the α-helix: 3.6 residues per turn (100° per residue), 1.5 Å rise per residue, 5.4 Å pitch. The C=O of residue i hydrogen-bonds the N–H of i + 4, a 13-atom ring, so it is also written 3.6₁₃.

LIT Variants: the 3₁₀ helix (3.0 residues per turn, i → i + 3, 2.0 Å rise) and the π-helix (4.4 residues per turn, i → i + 5). Pauling & Corey (1951) also proposed parallel and antiparallel pleated sheets, with neighbouring strands about 4.8 Å apart.

AMBER β-strand rise is about 3.2–3.5 Å per residue (≈3.3 used here). The 2.3 Å Cα helix radius and the π-helix rise of 1.15 Å are approximate.

MODEL The gold sheet in the scene is four antiparallel strands drawn as pleated slats. The green tube is the helix rebuilt from the slider.

Lab MODEL interactive, computed on the I-13 VM

type residues

Sources (browsed Oct 2026)

  1. Pauling, Corey & Branson (1951) The structure of proteins: two hydrogen-bonded helical configurations, PNAS 37:205
  2. Pauling & Corey (1951) The pleated sheet, PNAS 37:729
  3. Alpha helix (overview, 3₁₀ and π variants)

MODEL Two agents, as Dave set for every world. The ARTIST folds the 25-residue HP chain S3 PPHPPHHPPPPHHPPPPHHPPPPHH 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/9 (E_ref = -9, best found by our annealing; literature optimum −9). 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

  1. Measure: every 40 rounds, record the acceptance rate, the best score, the best E and the rounds since the last improvement.
  2. 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.
  3. 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.
  4. 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): e7ee23f0a51a0fcf362a32dec11dc22a6f390f939290e77fd1e092a3d9a63282

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