Whether a protein solution stays clear, grows ordered crystals, or dumps out as useless amorphous precipitate is set entirely by where the point (precipitant, protein concentration) sits on the phase diagram, relative to two curves:
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
Below C_sat the drop is undersaturated — any crystal dissolves. Between C_sat and C_nuc is the metastable zone: the drop is supersaturated (S>1) so an existing crystal keeps growing, but the energy barrier is too high for a new nucleus to appear on its own — this is exactly where crystallographers want to sit, growing a few large crystals from a seed instead of many small ones. Above C_nuc is the nucleation (labile) zone, where classical nucleation theory (CNT) predicts a nucleation rate that turns on sharply once S crosses the threshold:
ΔG* = 16π γ³ Vm² / [3 (kB·T·lnS)²] nucleation energy barrier
J = J0 · exp(−ΔG*/kB·T) nucleation rate
because ΔG* shrinks as (ln S)⁻², J rises almost step-like once S passes the critical value — a small change in concentration flips the drop from "nothing happens" to "nucleates everywhere." Push S far enough (well past the nucleation curve) and growth outruns the molecules' ability to organize into a lattice at all — they lock into a disordered, gel-like amorphous precipitate instead of a crystal.
- 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 crystal nucleus by hand, so you can see growth-without-nucleation inside the metastable zone.
- The 3D view renders free protein monomers as small spheres doing Brownian motion, and crystals as a growing cubic lattice (or a jittering disordered cluster once S is deep in the precipitation regime).
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.