Coactivators such as BRD4 and Mediator subunits carry intrinsically disordered regions (IDRs) studded with weak, multivalent binding "stickers" — bromodomains reading H3K27ac marks, low-complexity domains contacting one another. Below a critical valency × affinity product these molecules stay dissolved; above it, the network of weak contacts percolates and the mixture demixes into a dense, liquid-like condensate coexisting with a dilute phase — this is the sticker-and-spacer model of biomolecular phase separation (Banani, Rosen & Brangwynne).
Each particle obeys overdamped Langevin dynamics — the same equation used to model any molecule diffusing in a viscous, thermally noisy medium:
γ dr/dt = -∇U(r) + η(t), ⟨η(t)η(t')⟩ = 2γk_BT δ(t-t')
U(r) = k_rep(d0-r)² for r < d0 (excluded-volume repulsion)
U(r) = -ε_eff(r_c-r) for d0 ≤ r < r_c (multivalent sticker attraction)
ε_eff = ε_max · valency · (1 − 0.95 · JQ1_dose)
- Coactivator count — raises local concentration, the same lever real transcriptional condensates use: super-enhancers recruit far more BRD4/Mediator than ordinary enhancers.
- IDR valency / sticker strength — the pairwise attraction ε_eff; below the percolation threshold (ε_eff/k_BT ≲ 1) the system stays a dilute gas, above it a single dominant droplet nucleates.
- BET-inhibitor dose (JQ1) — models a bromodomain inhibitor competitively occupying the acetyl-lysine reader pocket, directly cutting ε_eff and dissolving the condensate even at fixed valency — exactly how BET inhibitors preferentially collapse super-enhancer transcription in MYC-driven cancers.
- Thermal agitation — scales the Langevin noise term; higher agitation resists condensation, lower agitation favours it, mirroring how phase boundaries shift with temperature in real LLPS systems.
The droplet count and largest-condensate fraction are recomputed each cycle from a distance-based cluster graph (union-find over pairs closer than the sticker-contact radius) — a live order parameter for the phase transition, exactly as fluorescence-recovery droplet-counting assays quantify real condensates under the microscope.