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Correlating cell shape and cellular stress in motile confluent tissues

  1. M. Cristina Marchettic
  1. aDepartment of Molecular and Cellular Biology, Harvard University, Cambridge, MA 02138;
  2. bDepartment of Physics, Northeastern University, Boston, MA 02115;
  3. cPhysics Department, Syracuse University, Syracuse, NY 13244
  1. Edited by William Bialek, Princeton University, Princeton, NJ, and approved October 11, 2017 (received for review April 14, 2017)


Using a self-propelled Voronoi model of epithelia known to predict a liquid–solid transition, we examine the interplay between cell motility and cell shape, tuned by cortex contractility and cell–cell adhesion, in controlling the mechanical properties of tissue. Our work provides a unifying framework for existing, seemingly distinct notions of stress in tissues and relates stresses to material properties. In particular, we show that the temporal correlation function of shear stresses can be used to define an effective tissue viscosity that diverges at the liquid–solid transition. This finding suggests a unique way of analyzing traction force microscopy data that may provide information on tissue rheology.


Collective cell migration is a highly regulated process involved in wound healing, cancer metastasis, and morphogenesis. Mechanical interactions among cells provide an important regulatory mechanism to coordinate such collective motion. Using a self-propelled Voronoi (SPV) model that links cell mechanics to cell shape and cell motility, we formulate a generalized mechanical inference method to obtain the spatiotemporal distribution of cellular stresses from measured traction forces in motile tissues and show that such traction-based stresses match those calculated from instantaneous cell shapes. We additionally use stress information to characterize the rheological properties of the tissue. We identify a motility-induced swim stress that adds to the interaction stress to determine the global contractility or extensibility of epithelia. We further show that the temporal correlation of the interaction shear stress determines an effective viscosity of the tissue that diverges at the liquid–solid transition, suggesting the possibility of extracting rheological information directly from traction data.


  • ?1To whom correspondence should be addressed. Email: xingbo_yang{at}fas.harvard.edu.
  • Author contributions: X.Y., D.B., M.L.M., and M.C.M. designed research; X.Y., D.B., M.C., M.M., M.L.M., and M.C.M. performed research; X.Y., D.B., and M.C. analyzed data; and X.Y., D.B., M.L.M., and M.C.M. wrote the paper.

  • The authors declare no conflict of interest.

  • This article is a PNAS Direct Submission.

  • This article contains supporting information online at www.danielhellerman.com/lookup/suppl/doi:10.1073/pnas.1705921114/-/DCSupplemental.

Published under the PNAS license.

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