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Odd dynamics of living chiral crystals


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.

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.


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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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Authors and Affiliations



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.

Corresponding author

Correspondence to Nikta Fakhri.

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Nature thanks Vivek Prakash, Anton Souslov and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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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.

Supplementary Video 1

Supplementary Video 2

Supplementary Video 3

Supplementary Video 4

Supplementary Video 5

Supplementary Video 6

Supplementary Video 7

Supplementary Video 8

Supplementary Video 9

Supplementary Video 10

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Tan, T.H., Mietke, A., Li, J. et al. Odd dynamics of living chiral crystals. Nature 607, 287–293 (2022).

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