Elastic ripening and inhibition of liquid–liquid phase separation

Abstract

Phase separation is a central concept of materials physics1,2,3 and has recently emerged as an important route to compartmentalization within living cells4,5,6. Biological phase separation features activity7, complex compositions8 and elasticity9, which reveal important gaps in our understanding of this universal physical phenomenon. Here, we explore the impact of elasticity on phase separation in synthetic polymer networks. We show that compressive stresses in a polymer network can suppress phase separation of the solvent that swells it, stabilizing mixtures well beyond the liquid–liquid phase-separation boundary. Network stresses also drive a new form of ripening, driven by transport of solute down stiffness gradients. This elastic ripening can be much faster than conventional Ostwald ripening driven by surface tension.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Fig. 1: Network stiffness controls droplet nucleation.
Fig. 2: Stiffness gradients drive solute transport and ripening.
Fig. 3: Rate of ripening increases with stiffness difference.

Data availability

The data represented in Figs. 1b and 3 are available as Source Data. All other data that support the findings of this study are available from the corresponding author on reasonable request.

Code availability

The code that supports the findings of this study is available from the corresponding author on reasonable request.

References

  1. 1.

    Gibbs, J. W. On the equilibrium of heterogeneous substances. Trans. Conn. Acad. Arts Sci. 3, 108 (1876).

    MATH  Google Scholar 

  2. 2.

    Cahn, J. W. & Hilliard, J. E. Free energy of a nonuniform system. I. Interfacial free energy. J. Chem. Phys. 28, 258 (1958).

    ADS  Article  Google Scholar 

  3. 3.

    Tanaka, H. Viscoelastic phase separation. J. Phys.: Condens. Matter 12, R207 (2000).

    ADS  Google Scholar 

  4. 4.

    Brangwynne, C. P. et al. Germline P granules are liquid droplets that localize by controlled dissolution/condensation. Science 324, 1729 (2009).

    ADS  Article  Google Scholar 

  5. 5.

    Hyman, A. A., Weber, C. A. & Jülicher, F. Liquid-liquid phase separation in biology. Annu. Rev. Cell Dev. Biol. 30, 39 (2014).

    Article  Google Scholar 

  6. 6.

    Shin, Y. & Brangwynne, C. P. Liquid phase condensation in cell physiology and disease. Science 357, eaaf4382 (2017).

    Article  Google Scholar 

  7. 7.

    Weber, C. A., Zwicker, D., Jülicher, F. & Lee, C. F. Physics of active emulsions. Rep. Prog. Phys. 82, 064601 (2019).

    ADS  MathSciNet  Article  Google Scholar 

  8. 8.

    Jacobs, W. M. & Frenkel, D. Phase transitions in biological systems with many components. Biophys. J. 112, 683 (2017).

    ADS  Article  Google Scholar 

  9. 9.

    Style, R. W. et al. Liquid-liquid phase separation in an elastic network. Phys. Rev. X 8, 011028 (2018).

    Google Scholar 

  10. 10.

    Kim, J. Y. et al. Scale-free fracture in soft solids. Preprint at http://arXiv.org/abs/arXiv:1811.00841 (2018).

  11. 11.

    Shin, Y. et al. Liquid nuclear condensates mechanically sense and restructure the genome. Cell 175, 1481 (2018).

    Article  Google Scholar 

  12. 12.

    Veatch, S. L. & Keller, S. L. Separation of liquid phases in giant vesicles of ternary mixtures of phospholipids and cholesterol. Biophys. J. 85, 3074 (2003).

    ADS  Article  Google Scholar 

  13. 13.

    Vitale, S. A. & Katz, J. L. Liquid droplet dispersions formed by homogeneous liquid–liquid nucleation: ‘the ouzo effect’. Langmuir 19, 4105 (2003).

    Article  Google Scholar 

  14. 14.

    Rubinstein, M. & Colby, R. H. Polymer Physics (Oxford University Press, 2003).

  15. 15.

    Gent, A. N. & Wang, C. Fracture mechanics and cavitation in rubber-like solids. J. Mater. Sci. 26, 3392 (1991).

    ADS  Article  Google Scholar 

  16. 16.

    Zimberlin, J. A., Sanabria-DeLong, N., Tew, G. N. & Crosby, A. J. Cavitation rheology for soft materials. Soft Matter 3, 763 (2007).

    ADS  Article  Google Scholar 

  17. 17.

    Weber, C. A., Lee, C. F. & Jülicher, F. Droplet ripening in concentration gradients. New J. Phys. 19, 053021 (2017).

    ADS  Article  Google Scholar 

  18. 18.

    de Gennes, P.-G., Brochard-Wyart, F. & Quere, D. Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves (Springer, 2004).

  19. 19.

    Zwicker, D., Decker, M., Jaensch, S., Hyman, A. A. & Jülicher, F. Centrosomes are autocatalytic droplets of pericentriolar material organized by centrioles. Proc. Natl Acad. Sci. USA 111, E2636 (2014).

    ADS  Article  Google Scholar 

  20. 20.

    Zwicker, D., Seyboldt, R., Weber, C. A., Hyman, A. A. & Jülicher, F. Growth and division of active droplets provides a model for protocells. Nat. Phys. 13, 408 (2017).

    Article  Google Scholar 

  21. 21.

    Brangwynne, C. P., Mitchison, T. J. & Hyman, A. A. Active liquid-like behavior of nucleoli determines their size and shape in Xenopus laevis oocytes. Proc. Natl Acad. Sci. USA 108, 4334 (2011).

    ADS  Article  Google Scholar 

  22. 22.

    Feric, M. et al. Coexisting liquid phases underlie nucleolar subcompartments. Cell 165, 1686 (2016).

    Article  Google Scholar 

  23. 23.

    Taylor, N. et al. Biophysical characterization of organelle-based RNA/protein liquid phases using microfluidics. Soft Matter 12, 9142 (2016).

    ADS  Article  Google Scholar 

  24. 24.

    Rotsch, C. & Radmacher, M. Drug-induced changes of cytoskeletal structure and mechanics in fibroblasts: an atomic force microscopy study. Biophys. J. 78, 520 (2000).

    ADS  Article  Google Scholar 

  25. 25.

    Gardel, M. L. et al. Prestressed F-actin networks cross-linked by hinged filamins replicate mechanical properties of cells. Proc. Natl Acad. Sci. USA 103, 1762 (2006).

    ADS  Article  Google Scholar 

  26. 26.

    Hoffman, B. D., Massiera, G., Van Citters, K. M. & Crocker, J. C. The consensus mechanics of cultured mammalian cells. Proc. Natl Acad. Sci. USA 103, 10259 (2006).

    ADS  Article  Google Scholar 

  27. 27.

    Blanchoin, L., Boujemaa-Paterski, R., Sykes, C. & Plastino, J. Actin dynamics, architecture, and mechanics in cell motility. Physiol. Rev. 94, 235 (2014).

    Article  Google Scholar 

  28. 28.

    Needleman, D. & Dogic, Z. Active matter at the interface between materials science and cell biology. Nat. Rev. Mater. 2, 17048 (2017).

    ADS  Article  Google Scholar 

  29. 29.

    Style, R. W. et al. Stiffening solids with liquid inclusions. Nat. Phys. 11, 82 (2015).

    Article  Google Scholar 

  30. 30.

    Lifshitz, I. M. & Slyozov, V. V. The kinetics of precipitation from supersaturated solid solutions. J. Phys. Chem. Solids 19, 35 (1961).

    ADS  Article  Google Scholar 

Download references

Acknowledgements

We acknowledge the Swiss National Science Foundation, National Centre of Competence in Research ‘Bio-Inspired Materials’ for funding, as well as L. Wilen, S. Kumar and T. Cohen for helpful discussions.

Author information

Affiliations

Authors

Contributions

T.S. and K.A.R., under the supervision of R.W.S. and E.R.D., designed, performed, analysed and interpreted the experiments. E.V.-H., under the supervision of D.Z., performed the numerical simulations. E.R.D., K.A.R. and R.W.S. wrote the paper with contributions from E.V.-H. and D.Z.

Corresponding authors

Correspondence to Robert W. Style or Eric R. Dufresne.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Physics thanks Christoph Weber 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.

Supplementary information

Extended Data Fig. 1 Saturation concentration is independent of Young’s modulus.

The saturation volume fraction of fluorinated oil in silicone gels of four different stiffnesses, at \(4{0}^{\circ }\)C.

Extended Data Fig. 2 Quench rate dependence of nucleation temperature.

The nucleation temperature of samples with the same stiffness (680 kPa) and different quench rates.

Supplementary information

Supplementary Information

Supplementary Figs. 1–13, methods, legends for videos, and references.

Supplementary Video 1

Time evolution of droplets on the soft side (10 kPa) of the gradient, far from the interface.

Supplementary Video 2

Time evolution of droplets on the stiff side (700 kPa) of the gradient, far from the interface.

Supplementary Video 3

Time evolution of droplets at the interface of the gradient.

Supplementary Video 4

Time evolution of two droplets of different sizes in a homogeneous gel.

Supplementary Video 5

Average droplet radius profile over time for experiment and simulation, with E = 750 kPa and using simulation parameters γ = 4.4 nN m−1 and δ = 40 μm.

Source data

Source Data Fig. 1b

Source data for figure 1, panel b

Source Data Fig. 3

Source data for figure 3, panels a–c, d

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Rosowski, K.A., Sai, T., Vidal-Henriquez, E. et al. Elastic ripening and inhibition of liquid–liquid phase separation. Nat. Phys. 16, 422–425 (2020). https://doi.org/10.1038/s41567-019-0767-2

Download citation

Further reading