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A density-independent rigidity transition in biological tissues

Nature Physics volume 11, pages 1074–1079 (2015)Cite this article

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Abstract

Cell migration is important in many biological processes, including embryonic development, cancer metastasis and wound healing. In these tissues, a cell’s motion is often strongly constrained by its neighbours, leading to glassy dynamics. Although self-propelled particle models exhibit a density-driven glass transition, this does not explain liquid-to-solid transitions in confluent tissues, where there are no gaps between cells and therefore the density is constant. Here we demonstrate the existence of a new type of rigidity transition that occurs in the well-studied vertex model for confluent tissue monolayers at constant density. We find that the onset of rigidity is governed by a model parameter that encodes single-cell properties such as cell–cell adhesion and cortical tension, providing an explanation for liquid-to-solid transitions in confluent tissues and making testable predictions about how these transitions differ from those in particulate matter.

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Figure 1: Energy barriers for local cellular rearrangements.
Figure 2: A rigidity transition in confluent tissues.
Figure 3: Analysis of the vibrational density of states.
Figure 4: Shear modulus as a function of p0α∗ − p0, which is the system-specific distance to the rigidity transition.
Figure 5: A simple four-cell model.

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Acknowledgements

We would like to thank G. Salbreux and M. C. Marchetti for substantial and useful comments on this manuscript. M.L.M. acknowledges support from the Alfred P. Sloan Foundation, and M.L.M. and D.B. acknowledge support from NSF-CMMI-1334611 and NSF-DMR-1352184. M.L.M. and D.B. also would like to thank the KITP at the University of California Santa Barbara for hospitality, supported in part by NSF PHY11-25915. The authors also acknowledge the Syracuse University HTC Campus Grid and NSF award ACI-1341006.

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Authors and Affiliations

  1. Department of Physics, Syracuse University, Syracuse, New York 13244, USA

    Dapeng Bi, J. H. Lopez, J. M. Schwarz & M. Lisa Manning

  2. Syracuse Biomaterials Institute, Syracuse, New York 13244, USA

    J. M. Schwarz & M. Lisa Manning

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  1. Dapeng Bi
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Contributions

D.B., M.L.M. and J.M.S. conceived and designed the project, which was executed and analysed by D.B. and J.H.L., with oversight from J.M.S. and M.L.M. D.B., J.M.S. and M.L.M. prepared the manuscript.

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Correspondence to M. Lisa Manning.

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Bi, D., Lopez, J., Schwarz, J. et al. A density-independent rigidity transition in biological tissues. Nature Phys 11, 1074–1079 (2015). https://doi.org/10.1038/nphys3471

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