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.
Your institute does not have access to this article
Subscribe to Nature+
Get immediate online access to the entire Nature family of 50+ journals
Subscribe to Journal
Get full journal access for 1 year
only $3.90 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Get time limited or full article access on ReadCube.
All prices are NET prices.
All data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.
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.
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).
Bililign, E. S. et al. Motile dislocations knead odd crystals into whorls. Nat. Phys. 18, 212–218 (2022).
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).
Petroff, A. P. & Libchaber, A. Nucleation of rotating crystals by Thiovulum majus bacteria. New J. Phys. 20, 015007 (2018).
Scheibner, C. et al. Odd elasticity. Nat. Phys. 16, 475–480 (2020).
Braverman, L., Scheibner, C., VanSaders, B. & Vitelli, V. Topological defects in solids with odd elasticity. Phys. Rev. Lett. 127, 268001 (2021).
Anderson, P. W. More is different. Science 177, 393–396 (1972).
Ashcroft, N. W. & Mermin, N. D. Solid State Physics (Saunders College Publishing/Harcourt College Publishers, 1976).
Li, R. & Bowerman, B. Symmetry breaking in biology. Cold Spring Harb. Perspect. Biol. 2, a003475 (2010).
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).
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).
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).
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).
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).
Riedel, I. H., Kruse, K. & Howard, J. A self-organized vortex array of hydrodynamically entrained sperm cells. Science 309, 300–303 (2005).
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).
Shen, Z., Würger, A. & Lintuvuori, J. S. Hydrodynamic self-assembly of active colloids: chiral spinners and dynamic crystals. Soft Matter 15, 1508–1521 (2019).
Bäuerle, T., Löffler, R. C. & Bechinger, C. Formation of stable and responsive collective states in suspensions of active colloids. Nat. Commun. 11, 2547 (2020).
Koch, A.-J. & Meinhardt, H. Biological pattern formation: from basic mechanisms to complex structures. Rev. Mod. Phys. 66, 1481–1507 (1994).
Wang, G. et al. Emergent field-driven robot swarm states. Phys. Rev. Lett. 126, 108002 (2021).
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).
Avron, J. E. Odd viscosity. J. Stat. Phys. 92, 543–557 (1998).
Soni, V. et al. The odd free surface flows of a colloidal chiral fluid. Nat. Phys. 15, 1188–1194 (2019).
Banerjee, D., Vitelli, V., Jülicher, F. & Surówka, P. Active viscoelasticity of odd materials. Phys. Rev. Lett. 126, 138001 (2021).
Christina Marchetti, M. et al. Hydrodynamics of soft active matter. Rev. Mod. Phys. 85, 1143–1189 (2013).
Shankar, S., Souslov, A., Bowick, M. J., Cristina Marchetti, M. & Vitelli, V. Topological active matter. Nat. Rev. Phys.4, 380–398 (2022).
Cates, M. E. & Tailleur, J. Motility-induced phase separation. Annu. Rev. Condens. Matter Phys. 6, 219–244 (2015).
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).
Hartmann, R. et al. Emergence of three-dimensional order and structure in growing biofilms. Nat. Phys. 15, 251 (2019).
Qin, B. et al. Cell position fates and collective fountain flow in bacterial biofilms revealed by light-sheet microscopy. Science 369, 71–77 (2020).
Collinet, C. & Lecuit, T. Programmed and self-organized flow of information during morphogenesis. Nat. Rev. Mol. Cell Biol. 22, 245–265 (2021).
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).
Bialek, W. et al. Statistical mechanics for natural flocks of birds. Proc. Natl Acad. Sci. USA 109, 4786–4791 (2012).
Drescher, K. et al. Dancing volvox: hydrodynamic bound states of swimming algae. Phys. Rev. Lett. 102, 168101 (2009).
Lauga, E. The Fluid Dynamics of Cell Motility (Cambridge Texts in Applied Mathematics, Cambridge Univ. Press, 2020).
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).
Wan, K. Y. et al. Reorganization of complex ciliary flows around regenerating Stentor coeruleus. Phil. Trans. R. Soc. B 375, 20190167 (2020).
Ishikawa, T., Pedley, T. J., Drescher, K. & Goldstein, R. E. Stability of dancing Volvox. J. Fluid Mech. 903, A11 (2020).
Nelson, D. R. & Halperin, B. I. Dislocation-mediated melting in two dimensions. Phys. Rev. B 19, 2457 (1979).
Zahn, K. & Maret, G. Dynamic criteria for melting in two dimensions. Phys. Rev. Lett. 85, 3656 (2000).
Battle, C. et al. Broken detailed balance at mesoscopic scales in active biological systems. Science 352, 604–607 (2016).
Li, J., Horowitz, J. M., Gingrich, T. R. & Fakhri, N. Quantifying dissipation using fluctuating currents. Nat. Commun. 10, 1666 (2019).
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).
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.
The authors declare no competing interests.
Peer review information
Nature thanks Vivek Prakash, Anton Souslov 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.
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.
About this article
Cite this article
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