MODEL PROTEIN FOLDING · PHYSICS · THERMODYNAMICS & KINETICS · under KEEPER ERIS
ΔG = ΔH − TΔS · Two-State Folding
Proteins are only marginally stable, often 5–15 kcal/mol, the small difference of two huge terms ΔH and TΔS. With a heat-capacity change ΔC_p the stability curve bends down at both ends: heat and cold denaturation. Two-state kinetics give the chevron plot.
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 evaluates ΔG(T) at 27 temperatures, using its own ln series (atanh form) and exp. It finds the cold-denaturation temperature by 50 chained bisection steps and builds the 17-point chevron. JS only plots.
LIT Gibbs free energy: ΔG = ΔH − TΔS. At the melting temperature ΔG(T_m) = 0, so ΔS_m = ΔH_m/T_m. With a constant ΔC_p: ΔG(T) = ΔH_m(1 − T/T_m) − ΔC_p[(T_m − T) + T ln(T/T_m)], the Gibbs–Helmholtz stability curve (Becktel & Schellman 1987).
LIT Two-state folding (U ⇌ N, no intermediates): K = e^(−ΔG/RT), and the folded fraction is f = 1/(1 + e^(−ΔG_unfold/RT)). Chymotrypsin inhibitor 2 was the first protein shown to fold this way (Jackson & Fersht 1991).
LIT Kinetics: k_obs = k_f + k_u. Each rate depends exponentially on denaturant (ln k_f = ln k_f⁰ − m_f[D]/RT, ln k_u = ln k_u⁰ + m_u[D]/RT), which gives the V-shaped chevron. ΔG(H₂O) = RT ln(k_f⁰/k_u⁰).
AMBER The typical range of 5–15 kcal/mol is a textbook generalisation.
MODEL The default parameters (T_m 333 K, ΔH_m 100 kcal/mol, ΔC_p 1.5 kcal/mol/K, k_f⁰ 50 s⁻¹, k_u⁰ 0.01 s⁻¹, m values 1.2/0.6) are illustrative, not a specific protein.
Lab MODEL interactive, computed on the I-13 VM
T_m K · ΔH_m · ΔC_p
Sources (browsed Oct 2026)
MODEL Two agents, as Dave set for every world. The ARTIST folds the 36-residue HP chain S4 PPPHHPPHHPPPPPHHHHHHHPPHHPPPPHHPPHPP 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/14 (E_ref = -14, proved optimal by exhaustive search here). 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): 57faf03ca89dcf10fdb0075ef101d2a811ef8df0bec40f6eefc791cb2a145e0e