LAUSR

Liquid–liquid phase separation1,2 occurs not only in bulk liquid, but also on surfaces. In physiology, the nature and function of condensates on cellular structures remain unexplored. Here we study how the condensed protein TPX2 behaves on microtubules to initiate branching microtubule nucleation3–5, which is critical for spindle assembly in eukaryotic cells6–10. Using fluorescence, electron and atomic force microscopies and hydrodynamic theory, we show that TPX2 on a microtubule reorganizes according to the Rayleigh–Plateau instability, like dew droplets patterning a spider web11,12. After uniformly coating microtubules, TPX2 forms regularly spaced droplets, from which branches nucleate. Droplet spacing increases with greater TPX2 concentration. A stochastic model shows that droplets make branching nucleation more efficient by confining the space along the microtubule where multiple necessary factors colocalize to nucleate a branch. Branching microtubule nucleation plays a major part in cellular processes driving eukaryotic cell division. A combination of microscopy approaches and hydrodynamic theory is used to show how the condensed protein TPX2 on a microtubule reorganizes according to the Rayleigh–Plateau instability.