This is a 2D cross-section of the same droplet the 3D version renders: the point (precipitant, protein concentration) still sits relative to two curves fixed by classical nucleation theory (CNT):
C_sat(p,T) = C0 · exp(−(T−T0)/15) · exp(−k·p) solubility curve
C_nuc(p,T) = C_sat(p,T) · S_crit supersolubility curve
S = C / C_sat(p,T) supersaturation ratio
ΔG* = 16π γ³ Vm² / [3 (kB·T·lnS)²] nucleation energy barrier
J = J0 · exp(−ΔG*/kB·T) nucleation rate
What's genuinely different here from the 3D view is the growth mechanics, computed natively in 2D rather than projected from three dimensions. Below C_sat crystals dissolve. Between C_sat and the nucleation curve (metastable zone, S>1), an existing crystal grows by adding cells to a true 2D square lattice — a spiral-filled grid of unit cells around the seed, the same packing rule real protein crystals follow along their fastest-growing lattice planes. Above the nucleation curve, new nuclei appear with probability set by J. Once S crosses Sprecip, growth switches mechanism entirely to diffusion-limited aggregation (DLA): each new molecule attaches preferentially to whichever existing cell sits farthest from the cluster's center (the "tip" a random-walking monomer is statistically most likely to hit first), which is exactly why real amorphous protein precipitate grows as branchy, screening, fractal-like clumps instead of a compact lattice — DLA is the standard physical model for that morphology, not just a stylistic choice.
- Protein / precipitant / temperature sliders — move the (p, C) point on the phase diagram in real time; γ, Vm and the rate prefactor are lumped into the constants above, so J is shown in relative units that reproduce CNT's characteristic threshold shape, not a literal rate constant for a specific protein.
- Add seed crystal — drops in one ordered nucleus by hand, so you can see growth-without-nucleation inside the metastable zone.
- Free monomers (blue dots) do 2D Brownian motion in the box; amber squares are ordered crystal lattice cells; red dots are DLA precipitate cells, jittering slightly to read as amorphous.
Real-world relevance: sparse-matrix and vapor-diffusion screens used in structural biology are literally a hunt for a (precipitant, protein concentration, temperature) point that lands a droplet inside this narrow nucleation-then-metastable-growth window — and the ordered-lattice-vs-DLA split you see here is exactly the difference between a crystal a crystallographer can use and a precipitate they have to throw away.