MODEL PROTEIN FOLDING · PHYSICS · MOLECULAR DYNAMICS · under KEEPER ERIS

Femtoseconds vs Milliseconds · MD & Anton

Molecular dynamics must step at about 2 fs to follow bond vibrations (a C–H stretch lasts 11 fs), but folding takes µs to s. That is 10⁹–10¹⁵ steps. D. E. Shaw’s Anton machines reached 85 and then 212 µs/day on the DHFR benchmark.

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 runs the velocity-Verlet integrator itself: 120–200 unrolled steps of a C–H bond oscillator, tracking the worst energy error, so you can watch it explode above 3.54 fs. It also computes steps = t/Δt and the wall-clock days on each machine.

LIT Bond vibrations set the step size. A 3000 cm⁻¹ C–H stretch has period 1/(c·ν̃) ≈ 11.1 fs. Velocity Verlet becomes unstable above ωΔt = 2, so production MD uses 1–2 fs and constrains bonds to hydrogen (SHAKE/LINCS).

LIT Anton 2 (SC14) ran the 23,558-atom DHFR benchmark at 85 µs/day on 512 nodes. Anton 3 (SC21) reached 212 µs/day on 64 nodes; general-purpose machines had not passed 2 µs/day, with 1.7 µs/day the best GPU figure.

LIT Lindorff-Larsen, Piana, Dror & Shaw (Science 334:517, 2011): 12 fast-folding proteins (10–80 residues), each simulated for 100 µs to 1 ms, about 8 ms in total with more than 400 folding and unfolding events. 11 folded to their experimental structures.

AMBER Wall-clock estimates below reuse the DHFR rates; a real protein in water has a different atom count.

WALL Brute-force MD still can’t reach seconds-scale folders or large proteins routinely. That is one reason prediction (AlphaFold) took a different road.

Lab MODEL interactive, computed on the I-13 VM

time step Δt fs · folding time

Sources (browsed Oct 2026)

  1. Shaw et al. (2014) Anton 2, SC14 (85 µs/day DHFR)
  2. Shaw et al. (2021) Anton 3: twenty microseconds of MD before lunch, SC21 (212 µs/day)
  3. Lindorff-Larsen et al. (2011) How fast-folding proteins fold, Science 334:517
  4. Shaw et al. (2010) Atomic-level characterization of the structural dynamics of proteins, Science 330:341

MODEL Two agents, as Dave set for every world. The ARTIST folds the 50-residue HP chain S6 HHPHPHPHPHHHHPHPPPHPPPHPPPPHPPPHPPPHPHHHHPHPHPHPHH 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/21 (E_ref = -21, found by our annealing; literature optimum −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

  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): 4b7fd3405b2edc0c24421f462ddf6a6b03159d5d89c97f760ec8ac7529c78962

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