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  • Open Access

Motility-Driven Glass and Jamming Transitions in Biological Tissues

Dapeng Bi1,3, Xingbo Yang1,4, M. Cristina Marchetti1,2, and M. Lisa Manning1,2

  • 1Department of Physics and Soft Matter Program, Syracuse University, Syracuse, New York 13244, USA
  • 2Syracuse Biomaterials Institute, Syracuse University, Syracuse, New York 13244, USA
  • 3Center for Studies in Physics and Biology, Rockefeller University, New York 10065, USA
  • 4Department of Physics, Northwestern University, Evanston, Illinois 60208, USA

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Phys. Rev. X 6, 021011 – Published 21 April, 2016

DOI: https://doi.org/10.1103/PhysRevX.6.021011

Abstract

Cell motion inside dense tissues governs many biological processes, including embryonic development and cancer metastasis, and recent experiments suggest that these tissues exhibit collective glassy behavior. To make quantitative predictions about glass transitions in tissues, we study a self-propelled Voronoi model that simultaneously captures polarized cell motility and multibody cell-cell interactions in a confluent tissue, where there are no gaps between cells. We demonstrate that the model exhibits a jamming transition from a solidlike state to a fluidlike state that is controlled by three parameters: the single-cell motile speed, the persistence time of single-cell tracks, and a target shape index that characterizes the competition between cell-cell adhesion and cortical tension. In contrast to traditional particulate glasses, we are able to identify an experimentally accessible structural order parameter that specifies the entire jamming surface as a function of model parameters. We demonstrate that a continuum soft glassy rheology model precisely captures this transition in the limit of small persistence times and explain how it fails in the limit of large persistence times. These results provide a framework for understanding the collective solid-to-liquid transitions that have been observed in embryonic development and cancer progression, which may be associated with epithelial-to-mesenchymal transition in these tissues.

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Cell motion inside dense tissues governs many biological processes, including embryonic development and cancer metastasis. Although recent experiments have suggested that these tissues exhibit a jamming transition from a fluidlike to a solidlike state, it remains unclear how cell motility and cell-cell interactions control this transition. Using a new model that captures both of these effects, we demonstrate that the jamming transition is controlled by single-cell speed, the persistence of single-cell motion, and a mechanical parameter that characterizes the competition between cell-cell adhesion and cortical tension. We also identify an experimentally accessible structural order parameter—the cell shape index—that specifies the entire transition surface.

We consider a model for a tissue without gaps between cells, where each cell is centered at a point and cell shapes are given by the Voronoi tessellation of the entire set of points. We vary model parameters and analyze the mean-squared displacements of cell trajectories. We find that in some parameter regimes the cells can move far from their starting positions and the tissue behaves as a fluid, and in other parameter regimes the cells rattle in a “cage” formed by their neighbors and the tissue behaves as a solid. This signature is associated with the so-called “jamming transition” that also occurs in polymers and foams. We discover that the transition occurs at a particular value of the cell shape index; this finding provides biologists and biophysicists with a new, simple way to determine the mechanical properties of a tissue just by imaging cell membranes. This prediction has been verified in tissues cultures from human asthma patients, and our theory makes additional predictions that could help explain aspects of the epithelial-to-mesenchymal transition (i.e., the process that allows cells to escape from a solid mass like a tumor).

We expect that our findings will motivate future studies taking into account additional cellular processes such as frictional forces between cells and cell division.

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Phys. Rev. X 6, 021011– Published 21 April, 2016
  • Received 25 October 2015
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This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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