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Ferromagnetic and antiferromagnetic order in bacterial vortex lattices

Nature Physics volume 12, pages 341–345 (2016)Cite this article

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Abstract

Despite their inherently non-equilibrium nature1, living systems can self-organize in highly ordered collective states2,3 that share striking similarities with the thermodynamic equilibrium phases4,5 of conventional condensed-matter and fluid systems. Examples range from the liquid-crystal-like arrangements of bacterial colonies6,7, microbial suspensions8,9 and tissues10 to the coherent macro-scale dynamics in schools of fish11 and flocks of birds12. Yet, the generic mathematical principles that govern the emergence of structure in such artificial13 and biological6,7,8,9,14 systems are elusive. It is not clear when, or even whether, well-established theoretical concepts describing universal thermostatistics of equilibrium systems can capture and classify ordered states of living matter. Here, we connect these two previously disparate regimes: through microfluidic experiments and mathematical modelling, we demonstrate that lattices of hydrodynamically coupled bacterial vortices can spontaneously organize into distinct patterns characterized by ferro- and antiferromagnetic order. The coupling between adjacent vortices can be controlled by tuning the inter-cavity gap widths. The emergence of opposing order regimes is tightly linked to the existence of geometry-induced edge currents15,16, reminiscent of those in quantum systems17,18,19. Our experimental observations can be rationalized in terms of a generic lattice field theory, suggesting that bacterial spin networks belong to the same universality class as a wide range of equilibrium systems.

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Figure 1: Edge currents determine antiferromagnetic and ferromagnetic order in a square lattice of bacterial vortices.
Figure 2: Best-fit mean-field LFT model captures the phase transition in the square lattice.
Figure 3: Frustration in triangular lattices determines the preferred order.

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Acknowledgements

We thank V. Kantsler and E. Lushi for assistance and discussions. This work was supported by European Research Council Advanced Investigator Grant 247333 (H.W. and R.E.G.), EPSRC (H.W. and R.E.G.), an MIT Solomon Buchsbaum Fund Award (J.D.) and an Alfred P. Sloan Research Fellowship (J.D.).

Author information

Author notes

  1. Hugo Wioland & Francis G. Woodhouse

    Present address: Present addresses: Institut Jacques Monod, Centre Nationale pour la Recherche Scientifique (CNRS), UMR 7592, Université Paris Diderot, Sorbonne Paris Cité, F-75205 Paris, France (H.W.); Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, UK (F.G.W.).,

Authors and Affiliations

  1. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, UK

    Hugo Wioland, Francis G. Woodhouse & Raymond E. Goldstein

  2. Institut Jacques Monod, Centre Nationale pour la Recherche Scientifique (CNRS), UMR 7592, Université Paris Diderot, Sorbonne Paris Cité, F-75205 Paris, France

    Hugo Wioland

  3. Faculty of Engineering, Computing and Mathematics, The University of Western Australia, 35 Stirling Highway, Crawley, Perth, Western Australia 6009, Australia

    Francis G. Woodhouse

  4. Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139-4307, USA

    Jörn Dunkel

Authors
  1. Hugo Wioland
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  2. Francis G. Woodhouse
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  4. Raymond E. Goldstein
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Contributions

All authors designed the research and collaborated on theory. H.W. performed experiments and PIV analysis. H.W. and F.G.W. analysed PIV data and performed parameter inference. F.G.W. and J.D. wrote simulation code. All authors wrote the paper.

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Correspondence to Raymond E. Goldstein.

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The authors declare no competing financial interests.

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Wioland, H., Woodhouse, F., Dunkel, J. et al. Ferromagnetic and antiferromagnetic order in bacterial vortex lattices. Nature Phys 12, 341–345 (2016). https://doi.org/10.1038/nphys3607

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