A hydrodynamic instability drives protein droplet formation on microtubules to nucleate branches - PubMed (original) (raw)
A hydrodynamic instability drives protein droplet formation on microtubules to nucleate branches
Sagar U Setru et al. Nat Phys. 2021 Apr.
No abstract available
Conflict of interest statement
Competing interests The authors declare no competing interests.
Figures
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 uM GFP-TPX2. N=35 microtubules were analyzed with a mean size of 0.5 +/− 0.1 um and spacing 0.6 +/− 0.2 um (mean +/− standard deviation). (b) Average power spectrum of GFP-TPX2 fluorescence intensities of droplet patterns for TIRF experiments at 1 uM GFP-TPX2 (N=35 microtubules). The peak indicates the emergence of a periodic pattern with wavelength lambda_max = 0.6 +/− 0.1 um (mean +/− standard deviation), in agreement with the histogram analysis. Shaded regions are 95% bootstrap confidence intervals. For calculation details, see Methods.
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 uM TPX2 coating does not break up into visible droplets like the 1 uM TPX2 coating does. (b) Branching microtuble nucleation visualized by TIRF microscopy in X. laevis meiotic cytosol at 0.1 uM 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 lambda = 1/f.
Extended Data Fig. 4. Schematic of the Rayleigh-Plateau instability.
The viscosity of the condensed film is mu, gamma is the surface tension of the interface, and p_infinity is the far field pressure provided by the solvent. The microtubule has radius r_i Initially, the interface is flat at xi(z, t=0) = r_o, but this scenario is unstable against the capillary pressure gamma/r_o, so xi(z, t) 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 +/− 0.05 uM, the power spectrum is averaged over N=5 topographies after the droplet pattern had formed. For 0.6 +/− 0.3 uM, N = 3. For 0.8 +/− 0.4 uM, 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 40 nm. All power spectra after droplet formation show mean +/− standard error of the mean.
Extended Data Fig. 6. Growth of the condensed film.
(a) Schematic of the model for growth of the condensed protein film. Microtubules of radius r_i are spaced periodically by a distance 2R, where R = 1/sqrt(pi * n * l) 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(t). (b) Final film thickness h versus initial concentration c_0 as measured by atomic force microscopy (blue) and as predicted by equation (19) (black) using a least-squares fit. (c) Evolution of the interfacial position of the film xi/r_i over time T for S = r_i/r_o between [0.5, 0.7], which is our experimentally observed range of S. Solid lines are the exact solution and dashed lines are the asymptotic formula (34b).
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; the growth of the instability for early times is exponential.
Peaks indicate characteristic wavelengths that correspond to a typical droplet spacing (Table S3) (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 +/− 2.0 nm, consistent with what one would expect for the kinesin construct used. For C-terminal-TPX2-bound microtubules, h = 3.7 +/− 1.8 nm. Heights are mean +/− standard deviation. Shaded regions represents 95% bootstrap confidence intervals.
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(spectral 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 1/min, with R2 = 0.75.
Extended Data Fig. 9. g-TuRC localization on bare microtubules.
Typical electron microscopy experiment with just g-TuRC and microtubules. Clearly, the localization of g-TuRC to the microtubule without TPX2 and augmin is negligible (Table S4). Scale bar is 100 nm.
Extended Data Fig. 10. Parametric study of Monte Carlo simulations.
(a) Time tau 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.
Figure 1:. TPX2 uniformly coats microtubules and then forms periodically spaced droplets that can nucleate branches.
(a) Initial films and subsequent droplets of TPX2 on microtubules visualized using TIRF microscopy (Movie 1). 1 _μ_M GFP-TPX2 was spiked onto a passivated glass surface coated with Alexa568-labeled microtubules. Scale bars are 1 _μ_m. (b) Large field of view of a TIRF experiment after droplets have formed along microtubules. GFP-TPX2 concentration is 1 _μ_M. Microtubules with a droplet pattern are marked with a number. Scale bars are 5 _μ_m. (c) TPX2 droplets on microtubules imaged using electron microscopy. 0.1 _μ_M GFP-TPX2 was incubated with microtubules bound to a carbon grid. Scale bars are 100 nm. (d) Branched microtubules nucleating from TPX2 droplets formed along the initial mother microtubule, assembled in vitro as in [18] (Movie 2). Recombinant GFP-augmin and _γ_-TuRC purified from X. laevis meiotic cytosol were included. Arrows indicate branched microtubules. Scale bars are 5 _μ_m (top) and 1 _μ_m (bottom). Only the soluble Cy5-tubulin channel (magenta) was imaged over time to enable a higher frame rate. The GFP-TPX2 and GFP-augmin channel (cyan) and the A568 template microtubule channel (red) were only imaged at the start at 60 s.
Figure 2:. AFM measurements reveal condensed TPX2 dynamics on microtubules.
(a) Time-lapse AFM height topographies of TPX2 uniformly coating and then forming regularly spaced droplets on a microtubule. GFP-TPX2 at 0.1 _μ_M was spiked onto microtubules adhered to a mica surface during data acquisition. This is the entire measured span of the microtubule in the top left of Movie 4. The topography was smoothed using a 40 nm × 40 nm median filter. White carets mark droplets. Scale bar is 100 nm. (b) Height profiles centered on the microtubule long axis before coating (black), just after coating (blue), and when droplets have formed on the microtubule surface (red). Height profiles were smoothed using a moving-average window of 40 nm. The raw height profiles and their power spectra are shown in Fig. S3. (c) Averaged power spectra calculated from the raw height profiles across many microtubules for uncoated (black, N = 22 microtubules), uniformly coated (blue, N = 23 microtubules), and droplet-patterned microtubules (red, N = 17 microtubules). A peak is seen only in the data for droplet-patterned microtubules, corresponding to a droplet spacing of 260 ± 20 nm (mean ± standard deviation). Shaded regions are 95% bootstrap confidence intervals.
Figure 3:. Hydrodynamic theory predicts TPX2 droplet formation on a microtubule surface.
(a) Schematic of the Rayleigh-Plateau instability. TPX2 initially coats the microtubule uniformly with thickness h = _r_o – _r_i. This film breaks up into droplets with spacing _λ_max due to capillary forces on a time scale r_o_μ/γ, where μ is the condensate viscosity and γ is the surface tension. (b) Dispersion relation showing the growth rate versus wave number for different aspect ratios _r_i/_r_o. The most unstable mode (black circles and line) grows most quickly and corresponds to the observed droplet spacing _λ_max. (c) Theoretical prediction for _λ_max (solid orange line). Overlaid are AFM measurements of the average film thickness and droplet spacing for each TPX2 concentration. The average droplet spacing corresponds to the peak of the averaged power spectra at a given concentration (Fig. S7, Table S3). There are no fit parameters. The shaded area encompasses the wavelengths that grow within 10% of the maximum growth rate for each h. In order of increasing concentration, N = 25; 17; 23; and 21 microtubules. Error bars are standard deviations for h and bootstrapped standard deviations for _λ_max.
Figure 4:. A stochastic model predicts that TPX2 droplets enhance the efficiency of branching microtubule nucleation.
(a) Electron microscopy images show ring-shaped _γ_-TuRCs (black arrows) localizing to regularly spaced TPX2 droplets along the microtubule in the presence of augmin. Scale bars are 100 nm. (b) Schematic of branching factors binding to a microtubule coated with a uniform TPX2 layer versus periodic TPX2 droplets. (c) Monte Carlo simulations show that droplets colocalize two necessary factors faster than a uniform coating. Here, k_on_l/_k_off = 10. These results are not sensitive to this parameter choice (Fig. S10). Each datapoint is the average of 107 independent simulations.
References
- Shin Y. & Brangwynne CP Liquid phase condensation in cell physiology and disease. Science 357 (2017). - PubMed
- Petry S, Groen A, Ishihara K, Mitchison T. & Vale R. Branching microtubule nucleation in xenopus egg extracts mediated by augmin and tpx2. Cell 152, 768–777 (2013). URL http://www.sciencedirect.com/science/article/pii/S0092867413000159. - PMC - PubMed
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