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Geometric constraints during epithelial jamming

Nature Physics volume 14, pages 613–620 (2018)Cite this article

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An Author Correction to this article was published on 18 May 2018

A Publisher Correction to this article was published on 19 April 2018

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Abstract

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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Fig. 1: Across non-asthmatic and asthmatic donors of primary HBECs, and across all days of maturation, cell shape and shape variability in vitro are mutually constrained.
Fig. 2: During ventral furrow formation in Drosophila in vivo, cell shape and shape variability follow the same geometric relationship as HBECs in vitro.
Fig. 3: Within and across vastly different epithelial systems, shape variability collapses to a family of PDFs that is common to all, and perhaps universal.
Fig. 4: The jamming superfamily.

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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.

References

  1. Liu, A. J. & Nagel, S. R. Jamming is not just cool any more. Nature 396, 21–22 (1998).

    ADS  Google Scholar 

  2. Trappe, V., Prasad, V., Cipelletti, L., Segre, P. N. & Weitz, D. A. Jamming phase diagram for attractive particles. Nature 411, 772–775 (2001).

    ADS  Google Scholar 

  3. de Gennes, P. & Badoz, J. Fragile Objects: Soft Matter, Hard Science, and the Thrill of Discovery (Copernicus, New York, NY, 1996).

  4. Park, J. A. et al. Unjamming and cell shape in the asthmatic airway epithelium. Nat. Mater. 14, 1040–1048 (2015).

    ADS  Google Scholar 

  5. 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).

    Google Scholar 

  6. Sadati, M., Taheri Qazvini, N., Krishnan, R., Park, C. Y. & Fredberg, J. J. Collective migration and cell jamming. Differentiation 86, 121–125 (2013).

    Google Scholar 

  7. Pawlizak, S. et al. Testing the differential adhesion hypothesis across the epithelial−mesenchymal transition. New J. Phys. 17, 083049 (2015).

    ADS  Google Scholar 

  8. 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).

    ADS  Google Scholar 

  9. Kim, S. & Hilgenfeldt, S. Cell shapes and patterns as quantitative indicators of tissue stress in the plant epidermis. Soft Matter 11, 7270–7275 (2015).

    ADS  Google Scholar 

  10. Garcia, S. et al. Physics of active jamming during collective cellular motion in a monolayer. Proc. Natl Acad. Sci. USA 112, 15314–15319 (2015).

    ADS  Google Scholar 

  11. Gilmour, D., Rembold, M. & Leptin, M. From morphogen to morphogenesis and back. Nature 541, 311–320 (2017).

    ADS  Google Scholar 

  12. Gibson, M. C., Patel, A. B., Nagpal, R. & Perrimon, N. The emergence of geometric order in proliferating metazoan epithelia. Nature 442, 1038–1041 (2006).

    ADS  Google Scholar 

  13. Xiong, F. et al. Interplay of cell shape and division orientation promotes robust morphogenesis of developing epithelia. Cell 159, 415–427 (2014).

    Google Scholar 

  14. Saw, T. B. et al. Topological defects in epithelia govern cell death and extrusion. Nature 544, 212–216(2017).

    ADS  Google Scholar 

  15. Edwards, S. F. & Oakeshott, R. B. S. Theory of powders. Physica A 157, 1080–1090 (1989).

    ADS  MathSciNet  Google Scholar 

  16. 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).

    Google Scholar 

  17. Martin, A. C., Kaschube, M. & Wieschaus, E. F. Pulsed contractions of an actin-myosin network drive apical constriction. Nature 457, 495–499 (2009).

    ADS  Google Scholar 

  18. Xie, S. & Martin, A. C. Intracellular signalling and intercellular coupling coordinate heterogeneous contractile events to facilitate tissue folding. Nat. Commun. 6, 7161(2015).

    ADS  Google Scholar 

  19. 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).

    Google Scholar 

  20. Parks, S. & Wieschaus, E. The Drosophila gastrulation gene concertina encodes a G alpha-like protein. Cell 64, 447–458 (1991).

    Google Scholar 

  21. 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).

    Google Scholar 

  22. 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).

    ADS  Google Scholar 

  23. Illing, B. et al. Mermin–Wagner fluctuations in 2D amorphous solids. Proc. Natl Acad. Sci. USA 114, 1856–1861 (2017).

    ADS  Google Scholar 

  24. Aste, T. & Di Matteo, T. Emergence of Gamma distributions in granular materials and packing models. Phys. Rev. E 77, 021309 (2008).

    ADS  Google Scholar 

  25. 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).

    ADS  Google Scholar 

  26. 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).

    Google Scholar 

  27. 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).

    Google Scholar 

  28. 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).

  29. 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).

    ADS  Google Scholar 

  30. Thompson, D. A. W. On Growth and Form 88–125 (Cambridge Univ. Press, Cambridge, 1917).

  31. Hales, T. et al. A formal proof of the Kepler conjecture. Forum Math. Pi 5, 1–29 (2017).

    MathSciNet  Google Scholar 

  32. Hales, C. T. The honeycomb conjecture. Discret. Comput. Geom. 25, 1–22 (2001).

    MathSciNet  MATH  Google Scholar 

  33. Puliafito, A. et al. Collective and single cell behavior in epithelial contact inhibition. Proc. Natl Acad. Sci. USA 109, 739–744 (2012).

    ADS  Google Scholar 

  34. Brabletz, T., Kalluri, R., Nieto, M. A. & Weinberg, R. A. EMT in cancer. Nat. Rev. Cancer 18, 128–134 (2018).

    Google Scholar 

  35. 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).

    Google Scholar 

  36. 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).

    Google Scholar 

  37. 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).

    Google Scholar 

  38. Park, J. A., Fredberg, J. J. & Drazen, J. M. Putting the squeeze on airway epithelia. Physiology (Bethesda) 30, 293–303 (2015).

    Google Scholar 

  39. Tschumperlin, D. J. et al. Mechanotransduction through growth-factor shedding into the extracellular space. Nature 429, 83–86 (2004).

    ADS  Google Scholar 

  40. Trepat, X. et al. Physical forces during collective cell migration. Nat. Phys. 5, 426–430 (2009).

    Google Scholar 

  41. Henkes, S., Fily, Y. & Marchetti, M. Active jamming: Self-propelled soft particles at high density. Phys. Rev. E 84, 040301(R) (2011).

    ADS  Google Scholar 

  42. Angelini, T. E. et al. Glass-like dynamics of collective cell migration. Proc. Natl Acad. Sci. USA 108, 4714–4719 (2011).

    ADS  Google Scholar 

  43. 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).

    ADS  Google Scholar 

  44. Tambe, D. T. et al. Collective cell guidance by cooperative intercellular forces. Nat. Mater. 10, 469–475 (2011).

    ADS  Google Scholar 

  45. Banigan, E. J., Illich, M. K., Stace-Naughton, D. J. & Egolf, D. A. The chaotic dynamics of jamming. Nat. Phys. 9, 288–292 (2013).

    Google Scholar 

  46. Garrahan, J. P. Dynamic heterogeneity comes to life. Proc. Natl Acad. Sci. USA 108, 4701–4702 (2011).

    ADS  Google Scholar 

  47. Schall, P., Weitz, D. A. & Spaepen, F. Structural rearrangements that govern flow in colloidal glasses. Science 318, 1895–1899 (2007).

    ADS  Google Scholar 

  48. Mattsson, J. et al. Soft colloids make strong glasses. Nature 462, 83–86 (2009).

    ADS  Google Scholar 

Download references

Acknowledgements

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).

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Author notes

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

Authors and Affiliations

  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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Contributions

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.

Corresponding author

Correspondence to Jeffrey J. Fredberg.

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Supplementary information

Videos

Supplementary Material

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

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.

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

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

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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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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