Fig. 4. Thermodynamics of a prewetting transition explain observed elongation dynamics.

a, ZO-1 condensates nucleate at the cell–cell interface (arrows), elongate and fuse into a continuous belt (double-sided arrow) in WT cells. In ∆L27-PATJ cells, condensates nucleate but fail to elongate along the interface (stars). b, Traces showing extensions of single condensate in WT and ∆L27-PATJ (Extended Data Fig. 5a–c). Bold lines indicate the mean of n = 32 WT and n = 24 ∆L27-PATJ traces. c, Total condensate intensity normalized to initial intensity of each condensate in WT and ∆L27-PATJ. Bold lines indicate the mean of n = 31 WT and n = 19 ∆L27-PATJ traces. d, Sketch of the polarized membrane domains: apical, lateral and interface. Bottom diagram depicts the binding affinity of ZO-1 to the membrane, which is highest at the interface. e, Thermodynamic free energy as a function of ZO-1 surface density. For the apical and lateral membrane (top), the dilute phase has the lowest free energy, whereas at the apical–lateral interface (bottom), owing to a higher binding affinity, the condensed phase has the lowest free energy. f, Sketch of elongation of a nucleated ZO-1 condensate along the apical–lateral membrane interface via a prewetting transition. The derived growth velocity $v$ of surface condensates as a function of binding affinity ${\mathit{ϵ}}_{\mathrm{int}}$ to the apical interface is shown (Extended Data Fig. 5e,l and Supplementary Note 1). g, Numerical solutions to the surface condensation theory for two different values of the relative binding affinity $\mathrm{\Delta }\overline{\mathit{ϵ}}$ of ZO-1 to the interface. Dynamics for $\mathrm{\Delta }\overline{\mathit{ϵ}}=0.43$ (top) and $\mathrm{\Delta }\overline{\mathit{ϵ}}=0.19$ (bottom). h, Theoretical condensate extension (top) and mass increase (bottom) as functions of binding affinity. Solid green and magenta lines correspond to relative binding affinities $\mathrm{\Delta }\overline{\mathit{ϵ}}=0.43$ and $\mathrm{\Delta }\overline{\mathit{ϵ}}=0.22$, respectively. The dim lines correspond to relative binding affinities $\mathrm{\Delta }\overline{\mathit{ϵ}}=\mathrm{0.46,\; 0.45,\; 0.44,\; 0.42,\; 0.41,\; 0.4}$ and $\mathrm{\Delta }\overline{\mathit{ϵ}}=\mathrm{0.25,\; 0.24,\; 0.23,\; 0.21,\; 0.20,\; 0.19}$, respectively. a, b and c show n = 4 biological replicates. Scale bar, 1 µm.

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