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A hydrodynamic instability drives protein droplet formation on microtubules to nucleate branches


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 nucleation3,4,5, which is critical for spindle assembly in eukaryotic cells6,7,8,9,10. 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.

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Fig. 1: TPX2 uniformly coats microtubules and then forms periodically spaced droplets that can nucleate branches.
Fig. 2: AFM measurements reveal condensed TPX2 dynamics on microtubules.
Fig. 3: Hydrodynamic theory predicts TPX2 droplet formation on a microtubule surface.
Fig. 4: A stochastic model predicts that TPX2 droplets enhance the efficiency of branching microtubule nucleation.

Data availability

Source data are provided with this paper. All other data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

Code availability

Algorithms and simulation codes are described in Methods and Supplementary Information.


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We thank S. Lee, T.-M. Chou and M. Libera at Stevens Institute of Technology for access to their atomic force microscope; I. Armstrong and S. Dutta at Bruker for access to and support for their atomic force microscope; M. King, B. Bratton, M. Safari, M. Koch, P. Ronceray and N. Wingreen for discussions; A. Thawani for purification of TPX2; H. Ando, C. Holmes, physiology students V. Baena, D. Laundon and L. Ma, and the Physiology Course at the Marine Biological Lab for assisting with the first AFM trials; and Princeton’s Imaging and Analysis Center, which is partially supported by the Princeton Center for Complex Materials, an NSF-MRSEC programme (DMR-1420541). B.G. was supported by PD Soros and NSF GRFP. S.U.S. was supported by NIH NCI NRSA 1F31CA236160 and NHGRI training grant 5T32HG003284. This work was funded by NIH NIA 1DP2GM123493, Pew Scholars Program 00027340, Packard Foundation 2014-40376 and CPBF NSF PHY-1734030.

Author information




S.U.S., B.G., J.W.S., H.A.S. and S.P. conceptualized the project. B.G. and S.U.S. performed fluorescence microscopy, and B.G. performed analysis of fluorescence microscopy data. B.G. performed TPX2-only electron microscopy with assistance from R.A.-A. and S.U.S., theory and simulations. S.U.S. and B.G. performed AFM, and S.U.S. performed analysis of AFM data. S.U.S. performed meiotic cytosol experiments. R.A.-A. performed branching reconstitution and multiple-protein electron microscopy, and S.U.S. performed analysis of branching reconstitution data. S.U.S. and B.G. wrote the paper with assistance from J.W.S., H.A.S. and S.P. J.W.S., H.A.S. and S.P. supervised the research. All authors discussed and interpreted results and revised the paper.

Corresponding authors

Correspondence to Joshua W. Shaevitz, Howard A. Stone or Sabine Petry.

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Competing interests

The authors declare no competing interests.

Additional information

Peer review informationNature Physics thanks Amy Gladfelter and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Statistics of droplet patterned microtubules imaged with TIRF microscopy.

a, Histogram of droplet sizes and spacings for TIRF experiments at 1 μM GFP–TPX2. N = 35 microtubules were analyzed with a mean size of 0.5 ± 0.1μm and spacing 0.6 ± 0.2μm (mean ± standard deviation). b, Average power spectrum of GFP–TPX2 fluorescence intensities of droplet patterns for TIRF experiments at 1 μM GFP–TPX2 (N = 35 microtubules). The peak indicates the emergence of a periodic pattern with wavelength \({\lambda }_{\max }=0.6\pm 0.1\,\mu {\rm{m}}\) (mean ± standard deviation), in agreement with the histogram analysis. Shaded regions are 95% bootstrap confidence intervals. For calculation details, see Methods.

Source data

Extended Data Fig. 2 TPX2 on the microtubule can appear uniform when imaged via optical microscopy.

a, TIRF microscopy time lapses showing that a 0.1 μM TPX2 coating does not break up into visible droplets like the 1 μM TPX2 coating does. b, Branching microtuble nucleation visualized by TIRF microscopy in X. laevis meiotic cytosol at 0.1 μM TPX2, indicating that branching can occur from diffraction limited droplets.

Extended Data Fig. 3 Raw and smoothed AFM height profiles, and power spectra of raw height profiles.

a, Raw height profiles of the topographies in Fig. 2a. The smoothed profile from Fig. 2b is shown again for reference. b, Power spectra of the raw height profiles in (a). The red curve shows the mean ± standard error of the mean over nine topographies of the microtubule after the droplet pattern had formed. The frequency f at which the peak in the red curve occurs gives the droplet spacing measured for this microtubule, according to λ = 1/f.

Source data

Extended Data Fig. 4 Schematic of the Rayleigh-Plateau instability.

The viscosity of the condensed film is μ, γ is the surface tension of the interface, and p is the far field pressure provided by the solvent. The microtubule has radius ri. Initially, the interface is flat at \(\xi \left(z,t=0\right)={r}_{{\rm{o}}}\), but this scenario is unstable against the capillary pressure γ/ro, so \(\xi \left(z,t\right)\) will evolve to a lower energy state. The unit normal n and unit tangent t track the geometry of the interface during its evolution.

Extended Data Fig. 5 AFM height profiles and power spectra at additional TPX2 concentrations.

For 0.1 μM, the power spectrum is averaged over N = 5 topographies after the droplet pattern had formed. For 0.6 μM, N = 3. For 0.8 μM, N = 4; the uncoated height profile for this specific microtubule is unavailable because the sample moved after TPX2 addition. Height profiles were smoothed using a moving-average window of 40nm. All power spectra after droplet formation show mean ± standard error of the mean.

Source data

Extended Data Fig. 6 Growth of the condensed film.

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).

Source data

Extended Data Fig. 7 Average power spectra from AFM data for all concentrations of TPX2 and for uncoated, initially TPX2-coated, C-terminal-TPX2-bound, and kinesin-1-bound microtubules.

Peaks indicate characteristic wavelengths that correspond to a typical droplet spacing (Supplementary Table 3) (N = 25, 17, 23, and 21 microtubules, respectively, for increasing TPX2 concentration). Also included are average power spectra for uncoated microtubules (N = 29 microtubules), microtubules initially coated uniformly with TPX2 (N = 25 microtubules), kinesin-bound microtubules (N = 19 microtubules), and C-terminal-TPX2-bound microtubules (N = 4 microtubules)—none of which show any characteristic spatial features. For kinesin-bound microtubules, h = 2.9 ± 2.0nm, consistent with what one would expect for the kinesin construct used27,28. For C-terminal-TPX2-bound microtubules, h = 3.7 ± 1.8nm. Heights are mean ± standard deviation. Shaded regions represents 95% bootstrap confidence intervals.

Source data

Extended Data Fig. 8 The growth of the instability for early times is exponential.

The average spectral amplitude at the most unstable frequency grows exponentially for early times (black line, N = 21 microtubules). Spectral amplitude = \(\sqrt{{\rm{spectral}}\ {\rm{power}}}\). Individual measurements are black dots. Shaded region represents 95% bootstrap confidence intervals. At later times, the spectral amplitude levels off due to nonlinear forces as the pattern sets in. For the exponential fit (red), \({\sigma }_{\max }=0.03\,{\min }^{-1}\), with R2 = 0.95.

Source data

Extended Data Fig. 9 γ-TuRC localization on bare microtubules.

Typical electron microscopy experiment with just γ-TuRC and microtubules. Clearly, the localization of γ-TuRC to the microtubule without TPX2 and augmin is negligible (Supplementary Table 4). Scale bar is 100 nm.

Extended Data Fig. 10 Parametric study of Monte Carlo simulations.

a, Time τ to colocalize two distinct factors, and hence form a branch, as a function of N and s for a uniform and periodic protein coating. For a given s, the periodic coating is uniformly more efficient at colocalizing well-mixed factors. Each data point is the average of 107 independent simulations. b, Typical histogram of 107 independent simulations for F = 2, N = 50, and s = 10.

Supplementary information

Supplementary Information

Theoretical derivations, experimental materials and methods, Supplementary Tables 1–5 and references.

Reporting Summary

Supplementary Video 1

Rayleigh–Plateau instability of TPX2 on microtubules visualized using TIRF microscopy. GFP–TPX2 at 1 μM was spiked onto a passivated glass surface covered with Alexa568-labelled microtubules at t = 0 s. TPX2 coats the microtubules and then proceeds to break up into droplets. Scale bar, 1 μm.

Supplementary Video 2

Microtubule branches nucleating from TPX2 droplets on a preexisting microtubule. During acquisition, only the soluble tubulin channel was imaged to enable capturing nucleation and polymerization of branched microtubules at high temporal resolution. Scale bar, 5 μm.

Supplementary Video 3

Branching microtubule nucleation visualized using TIRF microscopy. TPX2 at 0.1 μM is added to X. laevis meiotic cytosol purified from eggs. TPX2 coats the mother microtubule, from which daughter microtubules then nucleate, leading to an autocatalytic branched network. The frame dimensions are 16 μm × 22 μm.

Supplementary Video 4

Rayleigh–Plateau instability of TPX2 on microtubules probed using AFM. GFP–TPX2 at 0.2 ± 0.1 μM was spiked onto a mica surface covered with microtubules during acquisition. The uniform film of TPX2 is established at t = 0 s, after which the film breaks up into droplets. The frame dimensions are 2 μm × 2 μm.

Source data

Source Data Fig. 2

AFM line scans and average power spectra.

Source Data Fig. 3

AFM wavelength versus film thickness data points and theory curve.

Source Data Fig. 4

Monte Carlo colocalization time data.

Source Data Extended Data Fig. 1

TIRF histogram data and average power spectrum.

Source Data Extended Data Fig. 3

Raw and smoothed AFM line scans; individual power spectra.

Source Data Extended Data Fig. 5

AFM line scans and power spectra.

Source Data Extended Data Fig. 6

Film thickness versus concentration data and fit curve.

Source Data Extended Data Fig. 7

All averaged AFM power spectra.

Source Data Extended Data Fig. 8

All averaged spectral amplitude versus time plots.

Source Data Extended Data Fig. 10

Monte Carlo colocalization time and histogram data.

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Setru, S.U., Gouveia, B., Alfaro-Aco, R. et al. A hydrodynamic instability drives protein droplet formation on microtubules to nucleate branches. Nat. Phys. 17, 493–498 (2021).

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