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.

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.

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.

These authors contributed equally: Tzer Han Tan, Alexander Mietke

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

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

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

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.

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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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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