Living organisms form a large variety of hierarchically structured extracellular functional tissues. Remarkably, these materials exhibit regularity and structural coherence across multiple length scales, far beyond the size of a single cell. Here, synchrotron-based nanotomographic imaging in combination with machine-learning-based segmentation is used to reveal the structural synchronization process of nacre forming in the shell of the mollusc Unio pictorum. We show that the emergence of this highly regular layered structure is driven by a disorder-to-order transition achieved through the motion and interaction of screw-like structural dislocations with an opposite topological sign. Using an analogy to similar processes observed in liquid-crystalline systems, we demonstrate that these microstructural faults act as dissipative topological defects coupled by an elastic distortion field surrounding their cores. Their mutual annihilation results in structural synchronization that is simulated using the classical Kuramoto model. The developed experimental, theoretical and numerical framework provides a comprehensive physical view of the formation of biogenic materials.
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The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.
Code for the Kuramoto simulation is publicly available at https://github.com/Maxim-A-Beliaev/kuramoto-sim.
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I.Z. acknowledges financial support provided by Bundesministerium für Bildung und Forschung through grant 03Z22EN11. We acknowledge the ESRF for providing beam time on ID16A for proposals SC4155 and IHLS2846. Finally, we thank L. Bertinetti (B CUBE, Technische Universität Dresden) for critically assessing the manuscript.
The authors declare no competing interests.
Peer review information Nature Physics thanks Julyan Cartwright and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
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Motion and annihilation of a dislocation pair. Each frame represents a 2D slice through the tomography data perpendicular to the direction of growth. Time in the video represents the growth of the nacreous ultrastructure. White and black represent the organic and mineral components, respectively. The right-handed and left-handed defects are marked in blue and red, respectively.
Simulated evolution of topography at the front of the growing structure, obtained using the Kuramoto model. Time in the video represents the growth of the structure.
Simulated evolution of the phase field at the front of the growing structure, obtained using the Kuramoto model. Time in the video represents the growth of the structure.
Simulated evolution of the elastic energy field at the front of the growing structure, obtained using the Kuramoto model. Time in the video represents the growth of the structure.
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Beliaev, M., Zöllner, D., Pacureanu, A. et al. Dynamics of topological defects and structural synchronization in a forming periodic tissue. Nat. Phys. 17, 410–415 (2021). https://doi.org/10.1038/s41567-020-01069-z