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.

  • Article
  • Published:

Defect-mediated dynamics of coherent structures in active nematics

Nature Physics volume 19, pages 1355–1361 (2023)Cite this article

Subjects

Abstract

Active fluids, such as cytoskeletal filaments, bacterial colonies and epithelial cell layers, exhibit distinctive orientational coherence, often characterized by nematic order and its breakdown, defined by the presence of topological defects. In contrast, little is known about positional coherence, that is, whether there is an organization in the underlying fluid motion—despite this being both a prominent and an experimentally accessible feature. Here we characterize the organization of fluid motion in active nematics using the notion of Lagrangian coherent structures by analyzing experimental data of two-dimensional mixtures of microtubules and kinesin, as well as numerical data obtained from the simulation of the active nematodynamic equations. Coherent structures consist of moving attractors and repellers, which orchestrate complex motion. To understand the interaction of positional and orientational coherence, we analyse experiments and simulations and find that +1/2 defects move and deform the attractors, functioning as control centres for collective motion. Additionally, we find that regions around isolated +1/2 defects undergo high bending and low stretching/shearing deformations, consistent with the local stress distribution. The stress is the minimum at the defect, whereas high differential stress along the defect orientation induces folding. Our work offers a new perspective to describe and control self-organization in active fluids, with potential applications to multicellular systems.

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

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Lagrangian view of an active nematic fluid.
Fig. 2: Dynamics of a two-dimensional microtubule-based extensile active nematic system assembled on an oil–water interface.
Fig. 3: Dynamics of an extensile active suspension of microtubule bundles and kinesin at an oil–water interface with a 2 μM ATP concentration.
Fig. 4: Lagrangian analysis of a simulated extensile active nematic fluid.
Fig. 5: Stress and deformation around an isolated +1/2 defect in simulated extensile active nematics.

Similar content being viewed by others

Data availability

The experimental and simulated data that support the findings of this study are available from the corresponding authors upon request.

Code availability

The codes used in this work are available from the corresponding authors upon request.

References

  1. Vicsek, T. & Zafeiris, A. Collective motion. Phys. Rep. 517, 71–140 (2012).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  3. Kruse, K., Joanny, J., Jülicher, F., Prost, J. & Sekimoto, K. Asters, vortices, and rotating spirals in active gels of polar filaments. Phys. Rev. Lett. 92, 078101 (2004).

    Article  ADS  Google Scholar 

  4. Ballerini, M. et al. Interaction ruling animal collective behavior depends on topological rather than metric distance: evidence from a field study. Proc. Natl Acad. Sci. USA 105, 1232–1237 (2008).

    Article  ADS  Google Scholar 

  5. Zhang, H., Ber, A., Florin, E. & Swinney, H. Collective motion and density fluctuations in bacterial colonies. Proc. Natl Acad. Sci. USA 107, 13626–13630 (2010).

    Article  ADS  Google Scholar 

  6. Bricard, A., Caussin, J., Desreumaux, N., Dauchot, O. & Bartolo, D. Emergence of macroscopic directed motion in populations of motile colloids. Nature 503, 95–98 (2013).

    Article  Google Scholar 

  7. Dombrowski, C., Cisneros, L., Chatkaew, S., Goldstein, R. & Kessler, J. Self-concentration and large-scale coherence in bacterial dynamics. Phys. Rev. Lett. 93, 098103 (2004).

    Article  ADS  Google Scholar 

  8. Copenhagen, K., Alert, R., Wingreen, N. S. & Shaevitz, J. W. Topological defects promote layer formation in Myxococcus xanthus colonies. Nat. Phys. 17, 211–215 (2021).

    Article  Google Scholar 

  9. Meacock, O. J., Doostmohammadi, A., Foster, K. R., Yeomans, J. M. & Durham, W. M. Bacteria solve the problem of crowding by moving slowly. Nat. Phys. 17, 205–210 (2021).

    Article  Google Scholar 

  10. Friedl, P. & Gilmour, D. Collective cell migration in morphogenesis, regeneration and cancer. Nat. Rev. Mol. Cell Biol. 10, 445–457 (2009).

    Article  Google Scholar 

  11. Ladoux, B. & Mège, R. Mechanobiology of collective cell behaviours. Nat. Rev. Mol. Cell Biol. 18, 743–757 (2017).

    Article  Google Scholar 

  12. Doostmohammadi, A., Ignés-Mullol, J., Yeomans, J. & Sagués, F. Active nematics. Nat. Commun. 9, 3246 (2018).

    Article  ADS  Google Scholar 

  13. Serra, M., Streichan, S., Chuai, M., Weijer, C. J. & Mahadevan, L. Dynamic morphoskeletons in development. Proc. Natl Acad. Sci. USA 117, 11444–11449 (2020).

    Article  ADS  Google Scholar 

  14. Wensink, H. et al. Meso-scale turbulence in living fluids. Proc. Natl Acad. Sci. USA 109, 14308–14313 (2012).

    Article  ADS  MATH  Google Scholar 

  15. Giomi, L. Geometry and topology of turbulence in active nematics. Phys. Rev. X 5, 031003 (2015).

    Google Scholar 

  16. Shankar, S. & Marchetti, M. C. Hydrodynamics of active defects: from order to chaos to defect ordering. Phys. Rev. X 9, 041047 (2019).

    Google Scholar 

  17. Tan, A. J. et al. Topological chaos in active nematics. Nat. Phys. 15, 1033–1039 (2019).

    Article  Google Scholar 

  18. Haller, G. Lagrangian coherent structures. Annu. Rev. Fluid Mech. 47, 137–162 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  19. Serra, M. & Haller, G. Objective Eulerian coherent structures. Chaos 26, 053110 (2016).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  20. Hadjighasem, A., Farazmand, M., Blazevski, D., Froyland, G. & Haller, G. A critical comparison of Lagrangian methods for coherent structure detection. Chaos 27, 053104 (2017).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  21. Serra, M., Sathe, P., Beron-Vera, F. & Haller, G. Uncovering the edge of the polar vortex. J. Atmos. Sci. 74, 3871–3885 (2017).

    Article  ADS  Google Scholar 

  22. Serra, M. et al. Search and rescue at sea aided by hidden flow structures. Nat. Commun. 11, 2525 (2020).

    Article  ADS  Google Scholar 

  23. Nolan, P. J., Serra, M. & Ross, S. D. Finite-time Lyapunov exponents in the instantaneous limit and material transport. Nonlinear Dyn. 100, 3825–3852 (2020).

    Article  Google Scholar 

  24. Truesdell, C. & Noll, W. The Non-Linear Field Theories of Mechanics (Springer, 2004).

  25. Giona, M. & Adrover, A. Nonuniform stationary measure of the invariant unstable foliation in Hamiltonian and fluid mixing systems. Phys. Rev. Lett. 81, 3864 (1998).

    Article  ADS  Google Scholar 

  26. Serra, M., Vétel, J. & Haller, G. Exact theory of material spike formation in flow separation. J. Fluid Mech. 845, 51–92 (2018).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  27. Sanchez, T., Chen, D., DeCamp, S., Heymann, M. & Dogic, Z. Spontaneous motion in hierarchically assembled active matter. Nature 491, 431–434 (2012).

    Article  Google Scholar 

  28. De Gennes, P. & Prost, J. The Physics of Liquid Crystals 2nd edn (Oxford Univ. Press, 1993).

  29. Shendruk, T. N., Doostmohammadi, A., Thijssen, K. & Yeomans, J. M. Dancing disclinations in confined active nematics. Soft Matter 13, 3853–3862 (2017).

    Article  ADS  Google Scholar 

  30. Doering, C. R. & Thiffeault, J.-L. Multiscale mixing efficiencies for steady sources. Phys. Rev. E 74, 025301 (2006).

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  33. Dreher, D., Pasakarnis, L. & Brunner, D. Snapshot: mechanical forces in development II. Cell 165, 1028–1028 (2016).

    Article  Google Scholar 

  34. Aragona, M. et al. A mechanical checkpoint controls multicellular growth through YAP/TAZ regulation by actin-processing factors. Cell 154, 1047–1059 (2013).

    Article  Google Scholar 

  35. Balasubramaniam, L. et al. Investigating the nature of active forces in tissues reveals how contractile cells can form extensile monolayers. Nat. Mater. 20, 1156–1166 (2021).

  36. Maroudas-Sacks, Y. et al. Topological defects in the nematic order of actin fibres as organization centres of hydra morphogenesis. Nat. Phys. 17, 251–259 (2021).

    Article  Google Scholar 

Download references

Acknowledgements

We acknowledge T. N. Shendruk, A. Doostmohammadi, K. Thijssen and J. M. Yeomans for providing the dataset29 analysed in Supplementary Fig. 3. We are grateful to S. Shankar and N. Molinari for helpful discussions. This work is partially supported by the Schmidt Science Fellowship and the Postdoc Mobility Fellowship from the Swiss National Foundation (M.S.); the Netherlands Organization for Scientific Research (NWO/OCW) as part of the Frontiers of Nanoscience program and the Vidi scheme (L.G.); the Department of Energy, Office of Basic Energy Sciences, under award no. DESC0019733 (Z.D.); and the NSF Simons Center for Mathematical and Statistical Analysis of Biology via award no. 1764269 (L.M.).

Author information

Authors and Affiliations

  1. Department of Physics, University of California San Diego, San Diego, CA, USA

    Mattia Serra

  2. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA

    Mattia Serra & L. Mahadevan

  3. Department of Physics, University of California, Santa Barbara, Santa Barbara, CA, USA

    Linnea Lemma & Zvonimir Dogic

  4. Instituut-Lorentz, Universiteit Leiden, Leiden, Netherlands

    Luca Giomi

  5. Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA, USA

    L. Mahadevan

  6. Department of Physics, Harvard University, Cambridge, MA, USA

    L. Mahadevan

Authors
  1. Mattia Serra
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Linnea Lemma
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Luca Giomi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zvonimir Dogic
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. L. Mahadevan
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

M.S. and L.M. designed research, M.S. performed the research. M.S., L.L., L.G., Z.D. and L.M. contributed to the new experimental, numerical and analytical tools. M.S., L.L., L.G., Z.D. and L.M. analysed the data, and M.S. and L.M. wrote the manuscript. All authors commented on the manuscript.

Corresponding authors

Correspondence to Mattia Serra or L. Mahadevan.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Physics thanks the anonymous reviewers for their contribution to the peer review of this work

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 Sections 1–10 and Figs. 1–10.

Supplementary Video 1

Time evolution video associated with Fig. 2a–c.

Supplementary Video 2

Time evolution video associated with Fig. 2d–f.

Supplementary Video 3

Time evolution video associated with Fig. 3.

Supplementary Video 4

Time evolution video associated with Fig. 4.

Supplementary Video 5

Time evolution of defect velocities and backward FTLE field associated with Fig. 4 for increasing T.

Supplementary Video 6

Time evolution of defect velocities and backward FTLE field associated with Fig. 3 for increasing T.

Supplementary Video 7

Time evolution video associated with Supplementary Fig. 4.

Supplementary Video 8

Time evolution video associated with Supplementary Fig. 2.

Supplementary Video 9

Time evolution of defect velocities and backward FTLE field associated with Supplementary Fig. 4 for increasing T.

Supplementary Video 10

Eulerian and Lagrangian analyses of the dancing disclinations flow in confined active nematics (Supplementary Section 6).

Supplementary Video 11

Time evolution video associated with Supplementary Fig. 6.

Supplementary Video 12

Time evolution video associated with Supplementary Fig. 7a.

Supplementary Video 13

Time evolution video associated with Supplementary Fig. 8a,b.

Supplementary Video 14

Time evolution video associated with Supplementary Fig. 8d–i.

Supplementary Video 15

Time evolution video associated with Supplementary Fig. 9a–i.

Supplementary Video 16

Time evolution video associated with Supplementary Fig. 10a–i.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Serra, M., Lemma, L., Giomi, L. et al. Defect-mediated dynamics of coherent structures in active nematics. Nat. Phys. 19, 1355–1361 (2023). https://doi.org/10.1038/s41567-023-02062-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41567-023-02062-y

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