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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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).
The authors declare no competing interests.
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Discussion, Supplementary Data, Supplementary Figures S1–S12, Supplementary Table S1, Supplementary References 49–77
Proliferating Madin Darby canine kidney (MDCK) cells follow the same relationship as HBEC cells (Fig. 1) with shape and shape variability mutually constrained.
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
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
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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Atia, L., Bi, D., Sharma, Y. et al. Geometric constraints during epithelial jamming. Nature Phys 14, 613–620 (2018). https://doi.org/10.1038/s41567-018-0089-9
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