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Odd dynamics of living chiral crystals

Nature volume 607, pages 287–293 (2022)Cite this article

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Abstract

Active crystals are highly ordered structures that emerge from the self-organization of motile objects, and have been widely studied in synthetic1,2 and bacterial3,4 active matter. Whether persistent  crystalline order can emerge  in groups of autonomously developing multicellular organisms is currently unknown. Here we show that swimming starfish embryos spontaneously assemble into chiral crystals that span thousands of spinning organisms and persist for tens of hours. Combining experiments, theory and simulations, we demonstrate that the formation, dynamics and dissolution of these living crystals are controlled by the hydrodynamic properties and the natural development of embryos. Remarkably, living chiral crystals exhibit self-sustained chiral oscillations as well as various unconventional deformation response behaviours recently predicted for odd elastic materials5,6. Our results provide direct experimental evidence for how non-reciprocal interactions between autonomous multicellular components may facilitate non-equilibrium phases of chiral active matter.

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Fig. 1: Developing starfish embryos self-organize into living chiral crystals.
Fig. 2: Single-embryo properties facilitate formation, rotations and dissolution of clusters.
Fig. 3: Crystalline order first increases and then decreases as embryos develop.
Fig. 4: Defect strains and displacement waves exhibit signatures of odd elasticity.

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Data availability

All data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

Code availability

The computational methods that support the plots within this paper are described in the Supplementary Information and the underlying code is available from the corresponding author upon reasonable request.

References

  1. Palacci, J., Sacanna, S., Preska Steinberg, A., Pine, D. J. & Chaikin, P. M. Living crystals of light-activated colloidal surfers. Science 339, 936–940 (2013).

    Article  ADS  CAS  Google Scholar 

  2. Bililign, E. S. et al. Motile dislocations knead odd crystals into whorls. Nat. Phys. 18, 212–218 (2022).

    Article  CAS  Google Scholar 

  3. Petroff, A. P., Wu, X.-L. & Libchaber, A. Fast-moving bacteria self-organize into active two-dimensional crystals of rotating cells. Phys. Rev. Lett. 114, 158102 (2015).

    Article  ADS  Google Scholar 

  4. Petroff, A. P. & Libchaber, A. Nucleation of rotating crystals by Thiovulum majus bacteria. New J. Phys. 20, 015007 (2018).

    Article  ADS  Google Scholar 

  5. Scheibner, C. et al. Odd elasticity. Nat. Phys. 16, 475–480 (2020).

    Article  CAS  Google Scholar 

  6. Braverman, L., Scheibner, C., VanSaders, B. & Vitelli, V. Topological defects in solids with odd elasticity. Phys. Rev. Lett. 127, 268001 (2021).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  7. Anderson, P. W. More is different. Science 177, 393–396 (1972).

    Article  ADS  CAS  Google Scholar 

  8. Ashcroft, N. W. & Mermin, N. D. Solid State Physics (Saunders College Publishing/Harcourt College Publishers, 1976).

  9. Li, R. & Bowerman, B. Symmetry breaking in biology. Cold Spring Harb. Perspect. Biol. 2, a003475 (2010).

    Article  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  11. Grzybowski, B. A., Stone, H. A. & Whitesides, G. M. Dynamic self-assembly of magnetized, millimetre-sized objects rotating at a liquid–air interface. Nature 405, 1033–1036 (2000).

    Article  ADS  CAS  Google Scholar 

  12. Lee, W., Amini, H., Stone, H. A. & Di Carlo, D. Dynamic self-assembly and control of microfluidic particle crystals. Proc. Natl Acad. Sci. USA 107, 22413–22418 (2010).

    Article  ADS  CAS  Google Scholar 

  13. Naganathan, S. R., Fürthauer, S., Nishikawa, M., Jülicher, F. & Grill, S. W. Active torque generation by the actomyosin cell cortex drives left–right symmetry breaking. eLife 3, e04165 (2014).

    Article  Google Scholar 

  14. Smith, D. J., Montenegro-Johnson, T. D. & Lopes, S. S. Symmetry-breaking cilia-driven flow in embryogenesis. Annu. Rev. Fluid Mech. 51, 105–128 (2019).

    Article  ADS  MathSciNet  Google Scholar 

  15. Riedel, I. H., Kruse, K. & Howard, J. A self-organized vortex array of hydrodynamically entrained sperm cells. Science 309, 300–303 (2005).

    Article  ADS  CAS  Google Scholar 

  16. Sokolov, A., Aranson, I. S., Kessler, J. O. & Goldstein, R. E. Concentration dependence of the collective dynamics of swimming bacteria. Phys. Rev. Lett. 98, 158102 (2007).

    Article  ADS  Google Scholar 

  17. Shen, Z., Würger, A. & Lintuvuori, J. S. Hydrodynamic self-assembly of active colloids: chiral spinners and dynamic crystals. Soft Matter 15, 1508–1521 (2019).

    Article  ADS  CAS  Google Scholar 

  18. Bäuerle, T., Löffler, R. C. & Bechinger, C. Formation of stable and responsive collective states in suspensions of active colloids. Nat. Commun. 11, 2547 (2020).

    Article  ADS  Google Scholar 

  19. Koch, A.-J. & Meinhardt, H. Biological pattern formation: from basic mechanisms to complex structures. Rev. Mod. Phys. 66, 1481–1507 (1994).

    Article  ADS  Google Scholar 

  20. Wang, G. et al. Emergent field-driven robot swarm states. Phys. Rev. Lett. 126, 108002 (2021).

    Article  ADS  CAS  Google Scholar 

  21. Omar, A. K., Klymko, K., GrandPre, T. & Geissler, P. L. Phase diagram of active brownian spheres: crystallization and the metastability of motility-induced phase separation. Phys. Rev. Lett. 126, 188002 (2021).

    Article  ADS  CAS  Google Scholar 

  22. Avron, J. E. Odd viscosity. J. Stat. Phys. 92, 543–557 (1998).

    Article  MathSciNet  Google Scholar 

  23. Soni, V. et al. The odd free surface flows of a colloidal chiral fluid. Nat. Phys. 15, 1188–1194 (2019).

    Article  CAS  Google Scholar 

  24. Banerjee, D., Vitelli, V., Jülicher, F. & Surówka, P. Active viscoelasticity of odd materials. Phys. Rev. Lett. 126, 138001 (2021).

    Article  ADS  MathSciNet  CAS  Google Scholar 

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

    Article  ADS  Google Scholar 

  26. Shankar, S., Souslov, A., Bowick, M. J., Cristina Marchetti, M. & Vitelli, V. Topological active matter. Nat. Rev. Phys.4, 380–398 (2022).

  27. Cates, M. E. & Tailleur, J. Motility-induced phase separation. Annu. Rev. Condens. Matter Phys. 6, 219–244 (2015).

    Article  ADS  CAS  Google Scholar 

  28. Bi, D., Lopez, J. H., Schwarz, J. M. & Manning, M. L. A density-independent rigidity transition in biological tissues. Nat. Phys. 11, 1074–1079 (2015).

    Article  CAS  Google Scholar 

  29. Hartmann, R. et al. Emergence of three-dimensional order and structure in growing biofilms. Nat. Phys. 15, 251 (2019).

    Article  CAS  Google Scholar 

  30. Qin, B. et al. Cell position fates and collective fountain flow in bacterial biofilms revealed by light-sheet microscopy. Science 369, 71–77 (2020).

    Article  ADS  CAS  Google Scholar 

  31. Collinet, C. & Lecuit, T. Programmed and self-organized flow of information during morphogenesis. Nat. Rev. Mol. Cell Biol. 22, 245–265 (2021).

    Article  CAS  Google Scholar 

  32. Rosenthal, S. B., Twomey, C. R., Hartnett, A. T., Wu, H. S. & Couzin, I. D. Revealing the hidden networks of interaction in mobile animal groups allows prediction of complex behavioral contagion. Proc. Natl Acad. Sci. USA 112, 4690–4695 (2015).

    Article  ADS  CAS  Google Scholar 

  33. Bialek, W. et al. Statistical mechanics for natural flocks of birds. Proc. Natl Acad. Sci. USA 109, 4786–4791 (2012).

    Article  ADS  CAS  Google Scholar 

  34. Drescher, K. et al. Dancing volvox: hydrodynamic bound states of swimming algae. Phys. Rev. Lett. 102, 168101 (2009).

    Article  ADS  Google Scholar 

  35. Lauga, E. The Fluid Dynamics of Cell Motility (Cambridge Texts in Applied Mathematics, Cambridge Univ. Press, 2020).

  36. Gilpin, W., Prakash, V. N. & Prakash, M. Vortex arrays and ciliary tangles underlie the feeding–swimming trade-off in starfish larvae. Nat. Phys. 13, 380–386 (2017).

    Article  CAS  Google Scholar 

  37. Wan, K. Y. et al. Reorganization of complex ciliary flows around regenerating Stentor coeruleus. Phil. Trans. R. Soc. B 375, 20190167 (2020).

    Article  Google Scholar 

  38. Ishikawa, T., Pedley, T. J., Drescher, K. & Goldstein, R. E. Stability of dancing Volvox. J. Fluid Mech. 903, A11 (2020).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  39. Nelson, D. R. & Halperin, B. I. Dislocation-mediated melting in two dimensions. Phys. Rev. B 19, 2457 (1979).

    Article  ADS  CAS  Google Scholar 

  40. Zahn, K. & Maret, G. Dynamic criteria for melting in two dimensions. Phys. Rev. Lett. 85, 3656 (2000).

    Article  ADS  CAS  Google Scholar 

  41. Battle, C. et al. Broken detailed balance at mesoscopic scales in active biological systems. Science 352, 604–607 (2016).

    Article  ADS  CAS  Google Scholar 

  42. Li, J., Horowitz, J. M., Gingrich, T. R. & Fakhri, N. Quantifying dissipation using fluctuating currents. Nat. Commun. 10, 1666 (2019).

    Article  ADS  Google Scholar 

  43. Reuther, A. et al. Interactive supercomputing on 40,000 cores for machine learning and data analysis. IEEE High Perf. Ext. Comp. Conf. 1, 1–6 (2018).

    Google Scholar 

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Acknowledgements

We thank C. Scheibner, W. Irvine, N. Wingreen, J. Liu, Y.-C. Chao and R. E. Goldstein for valuable discussions. This research was supported by a Sloan Foundation Grant (G-2021-16758) to N.F. and J.D., and a National Science Foundation CAREER Award to N.F. T.H.T. acknowledges support from the NSF-Simons Center for Mathematical and Statistical Analysis of Biology at Harvard (award number 1764269) and Harvard Quantitative Biology Initiative as an NSF-Simons Postdoctoral Fellow. T.H.T. acknowledges support from the Center for Systems Biology Dresden as ELBE Postdoctoral Fellow. A.M. acknowledges support from a Longterm Fellowship from the European Molecular Biology Organization (ALTF 528-2019) and a Postdoctoral Research Fellowship from the Deutsche Forschungsgemeinschaft (Project 431144836). Y.C. acknowledges support from MIT Department of Physics Curtis Marble Fellowship. P.J.F. and S.G. acknowledge support from the Gordon and Betty Moore Foundation as Physics of Living Systems Fellows through grant no. GBMF4513. J.D. was supported by the Robert E. Collins Distinguished Scholarship fund. N.F., J.D. and S.G. are grateful to the KITP programme ACTIVE20: Symmetry, Thermodynamics and Topology in Active Matter, supported in part by the National Science Foundation under grant no. NSF PHY-1748958. We thank the MIT SuperCloud43 for providing access to its HPC resources.

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Author notes

  1. These authors contributed equally: Tzer Han Tan, Alexander Mietke

Authors and Affiliations

  1. Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Tzer Han Tan, Junang Li, Yuchao Chen, Hugh Higinbotham, Peter J. Foster, Shreyas Gokhale & Nikta Fakhri

  2. Quantitative Biology Initiative, Harvard University, Cambridge, MA, USA

    Tzer Han Tan

  3. Center for Systems Biology Dresden, Dresden, Germany

    Tzer Han Tan

  4. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Alexander Mietke & Jörn Dunkel

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Contributions

N.F., J.D., T.H.T. and A.M. conceived the project. T.H.T. and A.M. are joint first authors. J.L. and Y.C. are joint second authors. T.H.T. designed and performed experiments and analysed data. A.M. developed the theory, performed simulations and analysed data. J.L. performed experiments and analysed data. Y.C. analysed data. H.H. performed experiments. P.J.F. performed experiments and analysed data. S.G. analysed data. N.F. and J.D. designed experiments and theory and supervised research. All authors discussed the results and co-wrote the paper.

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Correspondence to Nikta Fakhri.

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Supplementary information

Supplementary Information

This file contains Supplementary Sections 1 -6, including: Experiment; Theory; Data Analysis; Table of symbols; Uncropped morphology images sections and legends for the Supplementary Videos.

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Tan, T.H., Mietke, A., Li, J. et al. Odd dynamics of living chiral crystals. Nature 607, 287–293 (2022). https://doi.org/10.1038/s41586-022-04889-6

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