Fig. 3: Theoretical and simulated half-FRAP curves relate the dip depth to the underlying molecular properties.

a Model describing the LLPS scenario. The condensate interface was modeled as a boundary that attenuates the diffusive flux. b Theoretically predicted half-FRAP curves in the non-bleached half for the LLPS model. The curves are plotted versus time divided by the characteristic diffusion time τ_D = R²/4D, showing that the dip depth is independent of the diffusion coefficient D and condensate radius R. c Relationship between dip depth and boundary strength h⁻¹ in the LLPS model. d Model describing the ICBS scenario. The binding reaction was modeled as a pseudo first-order reaction with rates \({k}_{{{{{{\rm{on}}}}}}}^{*}\) and k_off, where each particle could interact with only one binding site at a time. e Theoretically predicted half-FRAP curves in the non-bleached half for the ICBS model. For fast binding (\({k}_{{{{{{\rm{on}}}}}}}^{*}\)R²/D » 1), the model converges to a pure diffusion model with an effective diffusion coefficient D_eff = D/(1+\({k}_{{{{{{\rm{on}}}}}}}^{*}\)/k_off). For strong and slow binding (\({k}_{{{{{{\rm{on}}}}}}}^{*}\)R²/D « 1), it converges to a reaction-dominant model in which the recovery is governed by the dissociation rate. The respective curves are plotted versus time divided by τ_D,eff = R²/4D_eff (black curve) and τ_R = 1/k_off (blue curve), showing that the dip depth is independent of the effective diffusion coefficient and the dissociation rate, respectively. f Relationship between dip depth and binding strength \({k}_{{{{{{\rm{on}}}}}}}^{*}\)/k_off in the ICBS model. g Schematic representation of the simulation setup including two clusters of immobile binding sites (red), mobile protein particles (blue) and solvent particles (not depicted). A representative snapshot showing the protein distribution after the number of proteins at each binding site cluster had reached a plateau is shown to the right. h Simulated half-FRAP curves in the non-bleached half for proteins with different intermolecular interaction strength ∆A. For ∆A < 1, the simulation corresponds to ICBS; for ∆A ≥ 1, the simulation corresponds to LLPS, with the system moving deeper into the 2-phase regime with increasing ∆A. The number of interaction partners was not restricted. i, Relationship between dip depth and intermolecular interaction strength ∆A.