As an injury heals, an embryo develops or a carcinoma spreads, epithelial cells systematically change their shape. In each of these processes cell shape is studied extensively whereas variability of shape from cell to cell is regarded most often as biological noise. But where do cell shape and its variability come from? Here we report that cell shape and shape variability are mutually constrained through a relationship that is purely geometrical. That relationship is shown to govern processes as diverse as maturation of the pseudostratified bronchial epithelial layer cultured from non-asthmatic or asthmatic donors, and formation of the ventral furrow in the Drosophila embryo. Across these and other epithelial systems, shape variability collapses to a family of distributions that is common to all. That distribution, in turn, is accounted for by a mechanistic theory of cell–cell interaction, showing that cell shape becomes progressively less elongated and less variable as the layer becomes progressively more jammed. These findings suggest a connection between jamming and geometry that spans living organisms and inert jammed systems, and thus transcends system details. Although molecular events are needed for any complete theory of cell shape and cell packing, observations point to the hypothesis that jamming behaviour at larger scales of organization sets overriding geometric constraints.

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Change history

  • 18 May 2018

    In the first correction to this Article, the authors added James P. Butler and Jeffrey J. Fredburg as equally contributing authors. However, this was in error; the statement should have remained indicating that Lior Atia, Dapeng Bi and Yasha Sharma contributed equally. This has now been corrected.


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The authors thank M. L. Manning, H. Feldman and E. Millet for helpful discussions. This work was conducted with support from the Harvard Catalyst Clinical and Translational Science Center (National Center for Advancing Translational Sciences, National Institutes of Health Award UL1 TR001102) and financial contributions from Harvard University and its affiliated academic healthcare centres; the content is solely the responsibility of the authors and does not necessarily represent the official views of Harvard Catalyst, Harvard University and its affiliated academic healthcare centres, or the National Institutes of Health. This work was funded by the National Cancer Institute (grant number 1U01CA202123), the National Heart Lung and Blood Institute (grant numbers R01HL107561, PO1HL120839 and T32 HL007118) and the National Research Foundation of Korea (grant number NRF-2014R1A6A3A04059713).

Author information

Author notes

  1. These authors contributed equally: Lior Atia, Dapeng Bi and Yasha Sharma.


  1. Harvard T.H. Chan School of Public Health, Boston, MA, USA

    • Lior Atia
    • , Yasha Sharma
    • , Jennifer A. Mitchel
    • , Bomi Gweon
    • , Stephan A. Koehler
    • , Stephen J. DeCamp
    • , Bo Lan
    • , Jae Hun Kim
    • , Rebecca Hirsch
    • , Jin-Ah Park
    • , James P. Butler
    •  & Jeffrey J. Fredberg
  2. Department of Physics, Northeastern University, Boston, MA, USA

    • Dapeng Bi
  3. Department of Biomedical Engineering, Hanyang University, Seoul, Korea

    • Bomi Gweon
  4. Harvard University, School of Engineering and Applied Sciences, Cambridge, MA, USA

    • Adrian F. Pegoraro
    •  & David A. Weitz
  5. The Forsyth Institute, Cambridge, MA, USA

    • Kyu Ha Lee
    •  & Jacqueline R. Starr
  6. Department of Biology, Massachusetts Institute of Technology, Cambridge, MA, USA

    • Adam C. Martin
  7. Department of Medicine, Brigham and Women’s Hospital and Harvard Medical School, Boston, MA, USA

    • James P. Butler


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L.A. designed and performed the HBEC experiment, developed the cell shape algorithm, analysed the corresponding data, contributed to manuscript preparation and oversaw the project. D.B. performed theoretical and computational analysis of the SPV model, guided analysis and interpretation of data and contributed to manuscript preparation. Y.S. analysed Drosophila data, assisted with statistical analysis and contributed to manuscript preparation. J.A.M. designed and performed layer maturation and compression experiments with HBECs and contributed to manuscript preparation. B.G. designed and performed stretching experiments with MDCKs. S.K. analysed MDCK data and performed computational simulations. S.J.D. designed the jamming superfamily figure and assisted with statistical analysis. B.L. assisted with preparation of slides in the HBEC experiment. J.H.K. analysed the dynamics of cellular motions in HBECs. R.H. assisted with cell culture in the HBEC experiment. A.F.P. designed and performed the experiments on MDCKs and contributed to manuscript preparation. K.H.L. performed statistical analysis. J.R.S. designed and performed statistical analysis. D.A.W. guided interpretation of the cell shape data. A.C.M. provided imaging data from Drosophila and contributed to manuscript preparation. J.-A.P. designed and guided the experiment on HBECs and contributed to the manuscript preparation. J.P.B. guided data interpretation and analysis, and contributed to manuscript preparation. J.J.F. oversaw the project, and contributed to experimental design, data analysis and manuscript preparation.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to Jeffrey J. Fredberg.

Supplementary information

  1. Supplementary Material

    Discussion, Supplementary Data, Supplementary Figures S1–S12, Supplementary Table S1, Supplementary References 49–77

  2. Supplementary Movie 1

    Proliferating Madin Darby canine kidney (MDCK) cells follow the same relationship as HBEC cells (Fig. 1) with shape and shape variability mutually constrained.

  3. Supplementary Movie 2

    During ventral furrow formation in this WT Drosophila embryo, cell aspect ratio follows the same relationship as HBEC cells with shape and shape variability mutually constrained. Accompanies Fig. 2

  4. Supplementary Movie 3

    While cells in this cta mutant Drosophila embryo attempt to form the ventral furrow, cell aspect ratio follows the same relationship as HBEC cells with shape and shape variability mutually constrained. Accompanies Fig. 2

  5. Supplementary Movie 4

    While cells in twist RNAi embryo attempt to form the ventral furrow, cell aspect ratio follows the same relationship as HBEC cells, with shape and shape variability becoming mutually constrained. Accompanies Fig. 2

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