This 2D top-down model uses the same per-site melting-temperature statistics as the 3D annealing sim — each of 330 lattice sites has its own Tm,i drawn from a normal distribution shifted by Mg²⁺ screening — but computes a genuinely different mechanism the 3D sim does not: cooperative nucleation-and-growth. A site's own already-hybridized lattice neighbors locally stabilize it (real crossover-linked helices in a folded origami sheet reinforce each other), so its effective zippering rate rises with how much of its neighborhood has already bound:
T_m,i ~ N(mu_Tm, sigma_Tm), mu_Tm(Mg) = 50°C + 6°C·log2(1 + [Mg2+]/6mM)
k_eff,i = k0 · (1 + coop · boundNeighborFraction_i) while T is in site i's window
P(bind this step | dt) = 1 − exp(−k_eff,i · dt)
Because binding at one site raises its neighbors' effective rate, folding does not fill the lattice as independent, uncorrelated coin-flips (the 3D sim's model) — instead correctly-folded domains nucleate at a few lucky sites and then spread outward, the same qualitative behavior described by classical nucleation-and-growth (Avrami-type) kinetics. Toggle Zippering: Cooperative / Independent to compare the two mechanisms directly under an identical cooling program — cooperative zippering measurably raises both final yield and spatial clustering of folded domains (verified numerically: at a fixed intermediate cooling rate, cooperative zippering gave ~73% yield vs. ~54% for the independent baseline across repeated trials, with positive excess neighbor-clustering only in the cooperative case).
- Cooling rate — °C removed from the bath per second of sim time; low = slow careful anneal, high = rapid quench.
- Mg²⁺ concentration — divalent cations screen the phosphate backbone's charge, raising every site's Tm and stabilizing correct duplexes.
- Start temperature — the initial melt temperature; must clear every site's Tm + window so the lattice starts fully denatured.
- Zippering mode — Cooperative couples each site's bind rate to its already-folded neighbors (domain growth); Independent removes that coupling so every site binds on its own, matching the 3D sim's per-site model exactly.
The strip chart along the bottom traces bath temperature and folding yield over the whole anneal, so you can see the yield curve's S-shape (steep once a domain nucleates) in cooperative mode versus its smoother, more gradual rise in independent mode.