Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Spontaneous shear flow in confined cellular nematics

Nature Physics volume 14, pages 728–732 (2018)Cite this article

Subjects

An Author Correction to this article was published on 28 June 2019

This article has been updated

Abstract

In embryonic development or tumour evolution, cells often migrate collectively within confining tracks defined by their microenvironment1,2. In some of these situations, the displacements within a cell strand are antiparallel3, giving rise to shear flows. However, the mechanisms underlying these spontaneous flows remain poorly understood. Here, we show that an ensemble of spindle-shaped cells plated in a well-defined stripe spontaneously develops a shear flow whose characteristics depend on the width of the stripe. On wide stripes, the cells self-organize in a nematic phase with a director at a well-defined angle with the stripe’s direction, and develop a shear flow close to the stripe’s edges. However, on stripes narrower than a critical width, the cells perfectly align with the stripe’s direction and the net flow vanishes. A hydrodynamic active gel theory provides an understanding of these observations and identifies the transition between the non-flowing phase oriented along the stripe and the tilted phase exhibiting shear flow as a Fréedericksz transition driven by the activity of the cells. This physical theory is grounded in the active nature of the cells and based on symmetries and conservation laws, providing a generic mechanism to interpret in vivo antiparallel cell displacements.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

Buy

All prices are NET prices.

Fig. 1: Confined RPE1 cells align together with a tilt angle and develop a shear flow.
Fig. 2: Influence of the width of the confining stripe on the behaviour of the cells.
Fig. 3: Below a critical width, the cells orient along the stripe and do not flow on average.
Fig. 4: Comparison of the experimental results with the active gel theory.

Change history

  • 28 June 2019

    An amendment to this paper has been published and can be accessed via a link at the top of the paper.

References

  1. McLennan, R. et al. Multiscale mechanisms of cell migration during development: theory and experiment. Development 139, 2935–2944 (2012).

    Article  Google Scholar 

  2. Clark, A. G. & Vignjevic, D. M. Modes of cancer cell invasion and the role of the microenvironment. Curr. Opin. Cell Biol. 36, 13–22 (2015).

    Article  Google Scholar 

  3. Weigelin, B., Bakker, G.-J. & Friedl, P. Intravital third harmonic generation microscopy of collective melanoma cell invasion. IntraVital 1, 32–43 (2012).

    Article  Google Scholar 

  4. Trepat, X. et al. Physical forces during collective cell migration. Nat. Phys. 5, 426–430 (2009).

    Article  Google Scholar 

  5. Reffay, M. et al. Interplay of RhoA and mechanical forces in collective cell migration driven by leader cells. Nat. Cell Biol. 16, 1–9 (2014).

    Article  Google Scholar 

  6. Hakim, V. & Silberzan, P. Collective cell migration: a physics perspective. Rep. Prog. Phys. 80, 76601 (2017).

    Article  Google Scholar 

  7. Petitjean, L. et al. Velocity fields in a collectively migrating epithelium. Biophys. J. 98, 1790–1800 (2010).

    Article  ADS  Google Scholar 

  8. Londono, C. et al. Nonautonomous contact guidance signaling during collective cell migration. Proc. Natl Acad. Sci. USA 111, 1807–1812 (2014).

    Article  ADS  Google Scholar 

  9. Garcia, S. et al. Physics of active jamming during collective cellular motion in a monolayer. Proc. Natl Acad. Sci. USA 112, 15314–15319 (2015).

    Article  ADS  Google Scholar 

  10. Sepúlveda, N. et al. Collective cell motion in an epithelial sheet can be quantitatively described by a stochastic interacting particle model. PLoS Comput. Biol. 9, e1002944 (2013).

    Article  MathSciNet  Google Scholar 

  11. Basan, M., Elgeti, J., Hannezo, E., Rappel, W.-J. & Levine, H. Alignment of cellular motility forces with tissue flow as a mechanism for efficient wound healing. Proc. Natl Acad. Sci. USA 110, 2452–2459 (2013).

    Article  ADS  Google Scholar 

  12. Kabla, A. J. Collective cell migration: leadership, invasion and segregation. J. R. Soc. Interface 9, 3268–3278 (2012).

    Article  Google Scholar 

  13. Duclos, G., Garcia, S., Yevick, H. G. & Silberzan, P. Perfect nematic order in confined monolayers of spindle-shaped cells. Soft Matter 10, 2346–2353 (2014).

    Article  ADS  Google Scholar 

  14. Elsdale, T. Parallel orientation of fibroblasts in vitro. Exp. Cell Res. 51, 439–450 (1968).

    Article  Google Scholar 

  15. Kemkemer, R., Teichgräber, V., Schrank-Kaufmann, S., Kaufmann, D. & Gruler, H. Nematic order–disorder state transition in a liquid crystal analogue formed by oriented and migrating amoeboid cells. Eur. Phys. J. E 110, 101–110 (2000).

    Article  Google Scholar 

  16. Duclos, G., Erlenkämper, C., Joanny, J.-F. & Silberzan, P. Topological defects in confined populations of spindle-shaped cells. Nat. Phys. 13, 58–62 (2016).

    Article  Google Scholar 

  17. Lois, C., García-Verdugo, J. M. & Alvarez-Buylla, A. Chain migration of neuronal precursors. Science 271, 978–981 (1996).

    Article  ADS  Google Scholar 

  18. Nam, S. C. et al. Dynamic features of postnatal subventricular zone cell motility: A two-photon time-lapse study. J. Comp. Neurol. 505, 190–208 (2007).

    Article  Google Scholar 

  19. Wan, L. Q. et al. Micropatterned mammalian cells exhibit phenotype-specific left–right asymmetry. Proc. Natl Acad. Sci. USA 108, 12295–12300 (2011).

    Article  ADS  Google Scholar 

  20. Raymond, M. J., Ray, P., Kaur, G., Singh, A. V. & Wan, L. Q. Cellular and nuclear alignment analysis for determining epithelial cell chirality. Ann. Biomed. Eng. 44, 1475–1486 (2016).

    Article  Google Scholar 

  21. Kawaguchi, K., Kageyama, R. & Sano, M. Topological defects control collective dynamics in neural progenitor cell cultures. Nature 545, 327–331 (2017).

    Article  ADS  Google Scholar 

  22. Deforet, M., Hakim, V., Yevick, H. G., Duclos, G. & Silberzan, P. Emergence of collective modes and tri-dimensional structures from epithelial confinement. Nat. Commun. 5, 3747 (2014).

    Article  ADS  Google Scholar 

  23. Saw, T. B. et al. Topological defects in epithelia govern cell death and extrusion. Nature 544, 212–216 (2017).

    Article  ADS  Google Scholar 

  24. Chen, T.-H. et al. Left–right symmetry breaking in tissue morphogenesis via cytoskeletal mechanics. Circ. Res. 110, 551–559 (2012).

    Article  Google Scholar 

  25. Tee, Y. H. et al. Cellular chirality arising from the self-organization of the actin cytoskeleton. Nat. Cell Biol. 17, 445–457 (2015).

    Article  Google Scholar 

  26. Xu, J. et al. Polarity reveals intrinsic cell chirality. Proc. Natl Acad. Sci. USA 104, 9296–9300 (2007).

    Article  ADS  Google Scholar 

  27. Marchetti, M. C. et al. Hydrodynamics of soft active matter. Rev. Mod. Phys. 85, 1143–1189 (2013).

    Article  ADS  Google Scholar 

  28. Kruse, K., Joanny, J. F., Jülicher, F., Prost, J. & Sekimoto, K. Generic theory of active polar gels: a paradigm for cytoskeletal dynamics. Eur. Phys. J. E 16, 5–16 (2005).

    Article  Google Scholar 

  29. Voituriez, R., Joanny, J.-F. & Prost, J. Spontaneous flow transition in active polar gels. Europhys. Lett. 70, 404–410 (2005).

    Article  ADS  Google Scholar 

  30. de Gennes, P.-G. & Prost, J. The Physics of Liquid Crystals 2nd edn (Oxford Univ. Press, Oxford, 2003).

  31. Prost, J., Jülicher, F. & Joanny, J.-F. Active gel physics. Nat. Phys. 11, 111–117 (2015).

    Article  Google Scholar 

  32. Fürthauer, S., Strempel, M., Grill, S. W. & Jülicher, F. Active chiral fluids. Eur. Phys. J. E 35, 89 (2012).

    Article  Google Scholar 

  33. Fürthauer, S., Strempel, M., Grill, S. W. & Jülicher, F. Active chiral processes in thin films. Phys. Rev. Lett. 110, 048103 (2013).

    Article  ADS  Google Scholar 

  34. Rezakhaniha, R. et al. Experimental investigation of collagen waviness and orientation in the arterial adventitia using confocal laser scanning microscopy. Biomech. Model. Mechanobiol. 11, 461–473 (2012).

    Article  Google Scholar 

  35. Rasband, W. S. ImageJv1.46b (US National Institutes of Health, Bethesda, Maryland, 1997–2012).

  36. Duclos, G. et al. in Cell Migration: Methods and Protocols, Methods in Molecular Biology (ed. Gautreau, A.) 1749, 387–399 (Humana Press, New York, 2018).

Download references

Acknowledgements

We thank the members of the Biology-inspired Physics at MesoScales (BiPMS) group and, in particular, F. Ascione, T. Sarkar and H. G. Yevick. We also thank L. Valon for suggesting the use of RPE1 cells. V.Y. gratefully acknowledges the CelTisPhyBio Labex and the EU PRESTIGE programme for financial support. G.S. is supported by the Francis Crick Institute, which receives its core funding from Cancer Research UK (FC001317), the UK Medical Research Council (FC001317) and the Wellcome Trust (FC001317). The BiPMS group and the Physical Approach of Biological Problems group are members of the CelTisPhyBio Labex. The BiPMS group is a member of the Institut Pierre-Gilles de Gennes.

Author information

Author notes

  1. These authors contributed equally: G. Duclos, C. Blanch-Mercader and V. Yashunsky.

Authors and Affiliations

  1. Laboratoire PhysicoChimie Curie, Institut Curie, PSL Research University - Sorbonne Universités, UPMC – CNRS, Equipe Labellisée Ligue Contre le Cancer, Paris, France

    G. Duclos, C. Blanch-Mercader, V. Yashunsky, J.-F. Joanny, J. Prost & P. Silberzan

  2. The Francis Crick Institute, London, UK

    G. Salbreux

  3. ESPCI Paris, Paris, France

    J.-F. Joanny

  4. Mechanobiology Institute – National University of Singapore, Singapore, Singapore

    J. Prost

Authors
  1. G. Duclos
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. Blanch-Mercader
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. Yashunsky
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. G. Salbreux
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. J.-F. Joanny
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. J. Prost
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. P. Silberzan
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

G.D. and P.S. designed the research. G.D. and V.Y. performed the experiments and C.B.-M. and G.S. developed the theory. P.S., J.P. and J.-F.J. supervised the research. All authors analysed the data and participated in writing the manuscript.

Corresponding authors

Correspondence to J. Prost or P. Silberzan.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

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

Supplementary information

Supplementary Information

Supplementary Figures 1–10, Supplementary Material, Supplementary References 1–30

Life Sciences Reporting Summary

Supplementary Video 1

Shear flow of RPE1 cells in a confining stripe: RPE1 cells in a confining adhesive stripe reach a steady-state characterized by a tilt angle of the cell bodies relatively to the stripe direction and by a shear flow at the proximity of the edge. The width of the stripe is 1,000 µm and corresponds to the width of the image.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Duclos, G., Blanch-Mercader, C., Yashunsky, V. et al. Spontaneous shear flow in confined cellular nematics. Nature Phys 14, 728–732 (2018). https://doi.org/10.1038/s41567-018-0099-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41567-018-0099-7

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing