Extended Data Fig. 6: Growth of the condensed film.
From: A hydrodynamic instability drives protein droplet formation on microtubules to nucleate branches

a, Schematic of the model for growth of the condensed protein film. Microtubules of radius ri are spaced periodically by a distance \(2\bar{R}\), where \(\bar{R}=1/\sqrt{\pi nl}\) where l is the typical microtubule length and n is the number density of microtubules. Soluble protein phase separates from solution and nucleates a spatially uniform condensed film on the microtubule surface, whose interfacial position we denote by \(r=\xi \left(t\right)\). b, Final film thickness h versus initial concentration c0 as measured by atomic force microscopy (blue) and as predicted by equation (19) (black) and using \(1/{c}_{{\rm{R}}}\left({\bar{R}}^{2}/{r}_{{\rm{i}}}^{2}-1\right)\) as a least-squares fit parameter. c, Evolution of the interfacial position of the film ξ/ri over time T for \(S={r}_{{\rm{i}}}/{r}_{{\rm{o}}}\in \left[0.5,0.7\right]\), which is our experimentally observed range of S. Solid lines are the exact solution and dashed lines are the asymptotic formula (34b).