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# Nucleation landscape of biomolecular condensates

## Abstract

All structures within living cells must form at the right time and place. This includes condensates such as the nucleolus, Cajal bodies and stress granules, which form via liquid–liquid phase separation of biomolecules, particularly proteins enriched in intrinsically disordered regions (IDRs)1,2. In non-living systems, the initial stages of nucleated phase separation arise when thermal fluctuations overcome an energy barrier due to surface tension. This phenomenon can be modelled by classical nucleation theory (CNT), which describes how the rate of droplet nucleation depends on the degree of supersaturation, whereas the location at which droplets appear is controlled by interfacial heterogeneities3,4. However, it remains unknown whether this framework applies in living cells, owing to the multicomponent and highly complex nature of the intracellular environment, including the presence of diverse IDRs, whose specificity of biomolecular interactions is unclear5,6,7,8. Here we show that despite this complexity, nucleation in living cells occurs through a physical process similar to that in inanimate materials, but the efficacy of nucleation sites can be tuned by their biomolecular features. By quantitatively characterizing the nucleation kinetics of endogenous and biomimetic condensates in living cells, we find that key features of condensate nucleation can be quantitatively understood through a CNT-like theoretical framework. Nucleation rates can be substantially enhanced by compatible biomolecular (IDR) seeds, and the kinetics of cellular processes can impact condensate nucleation rates and specificity of location. This quantitative framework sheds light on the intracellular nucleation landscape, and paves the way for engineering synthetic condensates precisely positioned in space and time.

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## Data availability

Source data for Figs. 13 are provided with the paper. All other data are available from the corresponding authors upon reasonable request.

## Code availability

Custom code used to process and analyse the images, as detailed in the Methods, is available from the corresponding authors upon reasonable request.

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## Acknowledgements

We thank members of the Brangwynne laboratory for helpful discussions and comments on this manuscript. We thank laboratory members Y. Kim, M. Walls and D. Bracha for providing plasmids. This work was supported by the Howard Hughes Medical Institute, and grants from the AFOSR MURI (FA9550-20-1-0241), and the Princeton Center for Complex Materials, an MRSEC (NSF DMR-2011750). We also thank Princeton’s School of Engineering and Applied Sciences for supporting this work through a Focused Research Team award. S.F.S. is supported by JSPS Postdoctoral Fellowships for Research Abroad. P.R. is supported by the NSF through the Center for the Physics of Biological Function (PHY-1734030), by the French Government programme ‘Investissements d’Avenir’ managed by the French National Research Agency (ANR-16-CONV-0001) and by the Excellence Initiative of Aix-Marseille University—A*MIDEX.

## Author information

Authors

### Contributions

S.F.S., P.R., D.W.S., M.P.H. and C.P.B. designed the research; S.F.S. and D.W.S. performed the experiments; S.F.S. analysed the data; P.R. and M.P.H took the lead in the theoretical formalism; S.F.S., P.R., M.P.H. and C.P.B. wrote, and all authors reviewed and edited, the paper.

### Corresponding author

Correspondence to Clifford P. Brangwynne.

## Ethics declarations

### Competing interests

C.P.B. is a founder and consultant of Nereid Therapeutics. S.F.S., P.R., D.W.S. and M.P.H. declare no competing interests.

Peer review information Nature thanks Mike Sleutel 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 figures and tables

### Extended Data Fig. 1 Nucleation process of various endogenous and biomimietic condensates.

a, Time-lapse images of U2OS cells show the nucleation of Cajal bodies (coilin-EYFP) and nuclear speckles (SRRM1-EYFP) in mitosis, DNA repair condensates (miRFP-53BP1) upon 10 µg/ml bleomycin treatment, and engineered FUS condensates. Scale bars, 10 µm. b, (i) Number density of condensates, ρ, as a function of time, t, for nucleoli and Cajal bodies in mitosis, stress granules (SGs) upon 400 µM As treatment, and 53BP1 condensates upon 10 µg/ml bleomycin treatment. The nucleation rate, J, is quantified by the slope. Here, t = 0 is $${t}_{0}-5$$ (min). (ii) Mean nucleation rate, J, and its standard deviation for nucleoli (n = 6), Cajal bodies (n = 9), SGs (n = 24) and DNA repair condensates (n = 9); n = number of cells. c, Schematic diagram of the nucleation process of intracellular condensates.

### Extended Data Fig. 2 Quasi-1D nucleation probability.

a, (i) Fluorescence images of U2OS cells expressing HNRNPA1C -Corelets before and after blue light activation. Scale bar, 10 µm. (ii) Droplet number density as a function of time upon iterative blue-light activation and deactivation. (iii) Quasi-1D nucleation probability $${p}_{{\rm{nuc}}}^{{\rm{rel}}}$$ in the indicated region which include nucleoli (A) or not (B). b, Quasi-1D nucleation probability $${p}_{{\rm{nuc}}}^{{\rm{rel}}}$$ of U2OS cells expressing FUSN-Corelets and FUSN-miRFP-TRF1 in the indicated region ((i) low and (ii) high supersaturation), calculated from five successive activation cycles. Scale bar, 10 µm.

### Extended Data Fig. 3 Photo-activated phase separation in nucleus and cytoplasm.

a, Photo-activated phase separation in nucleus. (i) Confocal images of U2OS cells with different expression levels of FUSN Corelets (FUSN IDRs (red) and Cores (green)) after light-activation. The cells display nucleation and growth (NG) regimes between the binodal boundary and spinodal region, and spinodal decomposition (SD). Scale bars, 10 µm. (ii) Connected network-like growth and coarsening akin to spinodal decomposition. Scale bar, 10 µm. b, Photo-activated phase separation in cytoplasm. (i) Time-lapse confocal images of photo-activated U2OS cells expressing FUSN-Corelets composed of Core without NLS and FUSN-mCh-sspb. Scale bars, 10 µm. (ii) Time change of light-induced droplet number density, ρ. The shaded error bars show standard deviation.

### Extended Data Fig. 4 Phase separation behaviors of HNRNPA1C-Corelets.

a, Time-lapse confocal images of photo-activated U2OS cells with different expression levels of HNRNPA1C-Corelets. Nucleation growth (NG) regime near the binodal boundary (top) and spinodal region (bottom). Scale bars, 10 µm. b, Phase diagram of HNRNPA1C-Corelets as functions of Core concentration and Core-to-IDR ratio (n = 161). Solid circles exhibit cells where nucleation growth is observed, while empty triangles and squares show cells where no phase separation and spinodal decomposition are observed, respectively. The colours of solid circles indicate the observed nucleation rate, J. n: number of cells.

### Extended Data Fig. 5 Model fit parameters and chi-square values.

ab, Model fit parameters of $${S}^{\ast }$$, $${\rm{\kappa }}$$, $${{\rm{\chi }}}_{{\rm{red}}}^{2}$$ for various biomimetic condensates. The errors show the standard errors with 68% confidence intervals of the fits by equation (1). The parameter $${{\rm{\chi }}}_{{\rm{red}}}^{2}\gg 1$$ indicates a poor model fit while $${{\rm{\chi }}}_{{\rm{red}}}^{2}\lesssim 1$$ indicates a good model fit. c, $${S}^{\ast }$$ (top) and $${\rm{\kappa }}$$ (bottom) obtained from fits to equation (1) for FUSN Corelets with (n = 23) or without (n = 76) FUSN (WT) seeds and G3BP1 corelets ± 400 µM As (n=45). Error bars represent standard fit errors.

### Extended Data Fig. 6 Delay time against supersaturation.

Delay time, $${t}_{0}$$, against supersaturation, S, for FUSN-Corelets (n = 70), HNRNPA1C-Corelets (n = 60), and FUSN Corelets plus FUSN (WT) seeds (n = 23) with 1/24 < f < 1/10. The dashed lines show the best power-law fits. Error bars for $${t}_{0}$$ and S show the standard errors of the fits and standard deviation, respectively. n: number of cells.

### Extended Data Fig. 7 J against S with various ranges of Core-to-IDR ratio.

Nucleation rate, J, plotted against the degree of supersaturation, S, for (i) FUSN-Corelets (n = 26 for 1/24 < f < 1/18, n = 33 for 1/18 ≤ f < 1/12 and n = 56 for 1/12 ≤ f < 1/6) and (ii) HNRNPA1C-Corelets (n = 12 for 1/24 < f < 1/18, n = 38 for 1/18 ≤ f < 1/12 and n = 18 for 1/12 ≤ f < 1/6). Error bars for J and S show the standard errors of the fits and standard deviation, respectively. See Extended Data Fig. 5 for model fit parameters and $${\chi }_{{\rm{red}}}^{2}$$. n: number of cells.

### Extended Data Fig. 8 Seeded nucleation near the binodal boundary and spinodal region.

Time-lapse confocal images of U2OS cells expressing FUSN-Corelets and FUSN-miRFP-TRF1 near the binodal boundary (a) and spinodal region (c). The insets show the regions indicated by the arrows. Scale bars, 10 µm. b, The seeded condensates, which are indicated in a, are enlarged. Scale bar, 1 µm.

### Extended Data Fig. 9 Nucleation of FUSN-Corelets with tyrosine-mutated FUSN-seeds.

ac, Fluorescent images of U2OS cells expressing FUSN-Corelets and FUSN (−5YS, −27YS)-miRFP-TRF1 or HNRNPA1C-miRFP-TRF1 before and after blue light activation. The insets and enlarged images show the regions indicated by the squares. Scale bars, 10 µm. Scale bar of the enlarged image, 1 µm. d, Nucleation rate, J, plotted against the degree of supersaturation, S, for FUSN-Corelets (1/24 < f < 10) and FUSN-Corelets (1/30 < f < 10) with FUSN (−15YS, −27YS)-miRFP-TRF1 ($${n}_{15\text{YS}}$$, $${n}_{27\text{YS}}=\mathrm{12,5}$$) or HNRNPA1C-miRFP-TRF1 (n = 8). n: number of cells.

### Extended Data Fig. 10 Specificity of the nucleation of endogenous condensates.

a, Confocal images of G3BP KO cells expressing G3BP1 corelets and iRFP-tagged FXR1/UBAP2L/LSM14 before and after blue light activation in the absence of As. Scale bars, 1 µm. b, Nucleation rate of endogenous condensates against nominal supersaturation. Nucleation rate, J, plotted against the nominal supersaturation, $${S}_{\text{nom}}$$, for nucleoli (n = 6) and Cajal bodies (n = 9) in mitosis and 53BP1 condensates (n = 9) upon 10 µg/ml bleomycin treatment. n: number of cells.

## Supplementary information

### Supplementary Information

This file contains supplementary text for theoretical discussion and clarification, equations and references.

### Supplementary Video 1

Live imaging of photo-activated nucleation in nucleus. Live imaging of a U2OS cell undergoing photo-activated nucleation of FUSN–Corelets upon blue light. Video corresponds to Fig. 1.

### Supplementary Video 2

Live imaging of photo-activated nucleation in cytoplasm. Live imaging of a U2OS cell undergoing photo-activated nucleation of FUSN–Corelets, where core does not have NLS, upon blue light. Video corresponds to Extended Data Fig.3.

### Supplementary Video 3

Live imaging of photo-activated network-like coarsening. Live imaging of a U2OS cell undergoing network-like coarsening akin to spinodal decomposition of FUSN–Corelets upon blue light. Video corresponds to Extended Data Fig.3.

### Supplementary Video 4

Live imaging of seeded nucleation near the binodal line. Live imaging of a U2OS cell undergoing seeded nucleation of FUSN–Corelets and FUSN(WT)–miRFP–TRF1 upon blue light. Video corresponds to Fig. 2.

### Supplementary Video 5

Live imaging of seeded nucleation near the spinodal region. Live imaging of a U2OS cell undergoing seeded nucleation of FUSN–Corelets and FUSN(WT)–miRFP–TRF1 upon blue light. Video corresponds to Fig. 2.

### Supplementary Video 6

Live imaging of unseeded nucleation. Live imaging of a U2OS cell undergoing seeded nucleation of FUSN–Corelets and HNRNPA1C–miRFP–TRF1 upon blue light. Video corresponds to Fig. 2.

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Shimobayashi, S.F., Ronceray, P., Sanders, D.W. et al. Nucleation landscape of biomolecular condensates. Nature (2021). https://doi.org/10.1038/s41586-021-03905-5

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