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.
Subscribe to Journal
Get full journal access for 1 year
only $4.92 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
Liu, A. J. & Nagel, S. R. Jamming is not just cool any more. Nature 396, 21–22 (1998).
Trappe, V., Prasad, V., Cipelletti, L., Segre, P. N. & Weitz, D. A. Jamming phase diagram for attractive particles. Nature 411, 772–775 (2001).
de Gennes, P. & Badoz, J. Fragile Objects: Soft Matter, Hard Science, and the Thrill of Discovery (Copernicus, New York, NY, 1996).
Park, J. A. et al. Unjamming and cell shape in the asthmatic airway epithelium. Nat. Mater. 14, 1040–1048 (2015).
Farhadifar, R., Roper, J. C., Aigouy, B., Eaton, S. & Julicher, F. The influence of cell mechanics, cell–cell interactions, and proliferation on epithelial packing. Curr. Biol. 17, 2095–2104 (2007).
Sadati, M., Taheri Qazvini, N., Krishnan, R., Park, C. Y. & Fredberg, J. J. Collective migration and cell jamming. Differentiation 86, 121–125 (2013).
Pawlizak, S. et al. Testing the differential adhesion hypothesis across the epithelial−mesenchymal transition. New J. Phys. 17, 083049 (2015).
Nnetu, K. D., Knorr, M., Pawlizak, S., Fuhs, T. & Kas, J. A. Slow and anomalous dynamics of an MCF-10A epithelial cell monolayer. Soft Matter 9, 9335–9341 (2013).
Kim, S. & Hilgenfeldt, S. Cell shapes and patterns as quantitative indicators of tissue stress in the plant epidermis. Soft Matter 11, 7270–7275 (2015).
Garcia, S. et al. Physics of active jamming during collective cellular motion in a monolayer. Proc. Natl Acad. Sci. USA 112, 15314–15319 (2015).
Gilmour, D., Rembold, M. & Leptin, M. From morphogen to morphogenesis and back. Nature 541, 311–320 (2017).
Gibson, M. C., Patel, A. B., Nagpal, R. & Perrimon, N. The emergence of geometric order in proliferating metazoan epithelia. Nature 442, 1038–1041 (2006).
Xiong, F. et al. Interplay of cell shape and division orientation promotes robust morphogenesis of developing epithelia. Cell 159, 415–427 (2014).
Saw, T. B. et al. Topological defects in epithelia govern cell death and extrusion. Nature 544, 212–216(2017).
Edwards, S. F. & Oakeshott, R. B. S. Theory of powders. Physica A 157, 1080–1090 (1989).
Martiniani, S., Schrenk, K. J., Ramola, K., Chakraborty, B. & Frenkel, D. Numerical test of the Edwards conjecture shows that all packings are equally probable at jamming. Nat. Phys. 13, 848–851 (2017).
Martin, A. C., Kaschube, M. & Wieschaus, E. F. Pulsed contractions of an actin-myosin network drive apical constriction. Nature 457, 495–499 (2009).
Xie, S. & Martin, A. C. Intracellular signalling and intercellular coupling coordinate heterogeneous contractile events to facilitate tissue folding. Nat. Commun. 6, 7161(2015).
Sweeton, D., Parks, S., Costa, M. & Wieschaus, E. Gastrulation in Drosophila: the formation of the ventral furrow and posterior midgut invaginations. Development 112, 775–789 (1991).
Parks, S. & Wieschaus, E. The Drosophila gastrulation gene concertina encodes a G alpha-like protein. Cell 64, 447–458 (1991).
Xie, S., Mason, F. M. & Martin, A. C. Loss of Galpha12/13 exacerbates apical area dependence of actomyosin contractility. Mol. Biol. Cell 27, 3526–3536 (2016).
Vivek, S., Kelleher, C. P., Chaikin, P. M. & Weeks, E. R. Long-wavelength fluctuations and the glass transition in two dimensions and three dimensions. Proc. Natl Acad. Sci. USA 114, 1850–1855 (2017).
Illing, B. et al. Mermin–Wagner fluctuations in 2D amorphous solids. Proc. Natl Acad. Sci. USA 114, 1856–1861 (2017).
Aste, T. & Di Matteo, T. Emergence of Gamma distributions in granular materials and packing models. Phys. Rev. E 77, 021309 (2008).
Bi, D. P., Lopez, J. H., Schwarz, J. M. & Manning, M. L. Energy barriers and cell migration in densely packed tissues. Soft Matter 10, 1885–1890 (2014).
Bi, D., Lopez, J. H., Schwarz, J. M. & Manning, M. L. A density-independent rigidity transition in biological tissues. Nat. Phys. 11, 1074–1079 (2015).
Bi, D., Yang, X., Marchetti, M. C. & Manning, M. L. Motility-driven glass and jamming transitions in biological tissues. Phys. Rev. X 6, 021011 (2016).
Sussman, D. M., Paoluzzi, M., Marchetti, M. C. & Manning, M. L. Anomalous glassy dynamics in simple models of dense biological tissue. Preprint at https://arxiv.org/abs/1712.05758 (2017).
Wilk, G., Iwasa, M., Fuller, P. E., Kandere-Grzybowska, K. & Grzybowski, B. A. Universal area distributions in the monolayers of confluent mammalian cells. Phys. Rev. Lett. 112, 138104 (2014).
Thompson, D. A. W. On Growth and Form 88–125 (Cambridge Univ. Press, Cambridge, 1917).
Hales, T. et al. A formal proof of the Kepler conjecture. Forum Math. Pi 5, 1–29 (2017).
Hales, C. T. The honeycomb conjecture. Discret. Comput. Geom. 25, 1–22 (2001).
Puliafito, A. et al. Collective and single cell behavior in epithelial contact inhibition. Proc. Natl Acad. Sci. USA 109, 739–744 (2012).
Brabletz, T., Kalluri, R., Nieto, M. A. & Weinberg, R. A. EMT in cancer. Nat. Rev. Cancer 18, 128–134 (2018).
Haeger, A., Krause, M., Wolf, K. & Friedl, P. Cell jamming: collective invasion of mesenchymal tumor cells imposed by tissue confinement. Biochim. Biophys. Acta 1840, 2386–2395 (2014).
Royou, A., Sullivan, W. & Karess, R. Cortical recruitment of nonmuscle myosin II in early syncytial Drosophila embryos: its role in nuclear axial expansion and its regulation by Cdc2 activity. J. Cell Biol. 158, 127–137 (2002).
Martin, A. C., Gelbart, M., Fernandez-Gonzalez, R., Kaschube, M. & Wieschaus, E. F. Integration of contractile forces during tissue invagination. J. Cell Biol. 188, 735–749 (2010).
Park, J. A., Fredberg, J. J. & Drazen, J. M. Putting the squeeze on airway epithelia. Physiology (Bethesda) 30, 293–303 (2015).
Tschumperlin, D. J. et al. Mechanotransduction through growth-factor shedding into the extracellular space. Nature 429, 83–86 (2004).
Trepat, X. et al. Physical forces during collective cell migration. Nat. Phys. 5, 426–430 (2009).
Henkes, S., Fily, Y. & Marchetti, M. Active jamming: Self-propelled soft particles at high density. Phys. Rev. E 84, 040301(R) (2011).
Angelini, T. E. et al. Glass-like dynamics of collective cell migration. Proc. Natl Acad. Sci. USA 108, 4714–4719 (2011).
Nnetu, K. D., Knorr, M., Kas, J. & Zink, M. The impact of jamming on boundaries of collectively moving weak-interacting cells. New J. Phys. 14, 115012 (2012).
Tambe, D. T. et al. Collective cell guidance by cooperative intercellular forces. Nat. Mater. 10, 469–475 (2011).
Banigan, E. J., Illich, M. K., Stace-Naughton, D. J. & Egolf, D. A. The chaotic dynamics of jamming. Nat. Phys. 9, 288–292 (2013).
Garrahan, J. P. Dynamic heterogeneity comes to life. Proc. Natl Acad. Sci. USA 108, 4701–4702 (2011).
Schall, P., Weitz, D. A. & Spaepen, F. Structural rearrangements that govern flow in colloidal glasses. Science 318, 1895–1899 (2007).
Mattsson, J. et al. Soft colloids make strong glasses. Nature 462, 83–86 (2009).
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.
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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
About this article
Cite this article
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
Physical Review X (2021)
Acta Mechanica Sinica (2021)
Communications Physics (2021)