Mesoscale physical principles of collective cell organization

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Abstract

We review recent evidence showing that cell and tissue dynamics are governed by mesoscale physical principles. These principles can be understood in terms of simple state diagrams in which control variables include force, density, shape, adhesion and self-propulsion. An appropriate combination of these physical quantities gives rise to emergent phenomena such as cell jamming, topological defects and underdamped waves. Mesoscale physical properties of cell assemblies are found to precede and instruct biological functions such as cell division, extrusion, invasion and gradient sensing. These properties are related to properties of biomolecules, but cannot be predicted from biochemical principles. Thus, biological function is governed by emergent mesoscale states that can be predicted by a simple set of physical properties.

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Fig. 1: Subcellular determinants of cell dynamics.
Fig. 2: Examples of emergent phenomena in cell monolayers.

adapted from ref. 2, Macmillan Publishers Ltd (a); ref. 78, Macmillan Publishers Ltd (b); and ref. 4, AAAS (c)

Fig. 3: State diagrams of cell monolayers.

adapted from ref. 86, RSC, and ref. 87, Macmillan Publishers Ltd (a); and courtesy of R. Cerbino and F. Giavazzi (b,c).

References

  1. 1.

    Alberts, B. et al. Molecular Biology of the Cell 6th edn (Garland Science, New York, NY, 2016).

  2. 2.

    Duclos, G., Erlenkämper, C., Joanny, J.-F. & Silberzan, P. Topological defects in confined populations of spindle-shaped cells. Nat. Phys. 13, 58–62 (2016).

  3. 3.

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

  4. 4.

    Sunyer, R. et al. Collective cell durotaxis emerges from long-range intercellular force transmission. Science 353, 1157–1161 (2016).

  5. 5.

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

  6. 6.

    Das, T. et al. A molecular mechanotransduction pathway regulates collective migration of epithelial cells. Nat. Cell Biol. 17, 276–287 (2015).

  7. 7.

    Hogan, B. L. & Kolodziej, P. A. Organogenesis: molecular mechanisms of tubulogenesis. Nat. Rev. Genet. 3, 513–523 (2002).

  8. 8.

    Bryant, D. M. & Mostov, K. E. From cells to organs: building polarized tissue. Nat. Rev. Mol. Cell Biol. 9, 887–901 (2008).

  9. 9.

    Kawaguchi, K., Kageyama, R. & Sano, M. Topological defects control collective dynamics in neural progenitor cell cultures. Nature 545, 327–331 (2017).

  10. 10.

    Spurlin, J. W. 3rd & Nelson, C. M. Building branched tissue structures: from single cell guidance to coordinated construction. Philos. Trans. R. Soc. B. 372, 20150527 (2017).

  11. 11.

    Laurent, J. et al. Convergence of microengineering and cellular self-organization towards functional tissue manufacturing. Nat. Biomed. Eng. 1, 939–956 (2017).

  12. 12.

    Ladoux, B. & Mege, R. M. Mechanobiology of collective cell behaviours. Nat. Rev. Mol. Cell Biol. 18, 743–757 (2017).

  13. 13.

    Kanchanawong, P. et al. Nanoscale architecture of integrin-based cell adhesions. Nature 468, 580–584 (2010).

  14. 14.

    Chen, B. C. et al. Lattice light-sheet microscopy: imaging molecules to embryos at high spatiotemporal resolution. Science 346, 1257998 (2014).

  15. 15.

    Pollard, T. D. & Borisy, G. G. Cellular motility driven by assembly and disassembly of actin filaments. Cell 112, 453–465 (2003).

  16. 16.

    Loisel, T. P., Boujemaa, R., Pantaloni, D. & Carlier, M. F. Reconstitution of actin-based motility of Listeria and Shigella using pure proteins. Nature 401, 613–616 (1999).

  17. 17.

    Finer, J. T., Simmons, R. M. & Spudich, J. A. Single myosin molecule mechanics: piconewton forces and nanometre steps. Nature 368, 113–119 (1994).

  18. 18.

    Newell-Litwa, K. A., Horwitz, R. & Lamers, M. L. Non-muscle myosin II in disease: mechanisms and therapeutic opportunities. Dis. Models Mech. 8, 1495–1515 (2015).

  19. 19.

    Mitchison, T. J., Charras, G. T. & Mahadevan, L. Implications of a poroelastic cytoplasm for the dynamics of animal cell shape. Semin. Cell Dev. Biol. 19, 215–223 (2008).

  20. 20.

    McDonald, N. A. & Gould, K. L. Linking up at the BAR: oligomerization and F-BAR protein function. Cell Cycle 15, 1977–1985 (2016).

  21. 21.

    Kruse, K., Joanny, J. F., Julicher, F., Prost, J. & Sekimoto, K. Generic theory of active polar gels: a paradigm for cytoskeletal dynamics. Eur. Phys. J. E 16, 5–16 (2005).

  22. 22.

    Jülicher, F. & Prost, J. Spontaneous oscillations of collective molecular motors. Phys. Rev. Lett. 78, 4510–4513 (1997).

  23. 23.

    Joanny, J. F. & Prost, J. Active gels as a description of the actin-myosin cytoskeleton. HFSP J. 3, 94–104 (2009).

  24. 24.

    Alvarado, J., Sheinman, M., Sharma, A., MacKintosh, F. C. & Koenderink, G. H. Force percolation of contractile active gels. Soft Matter 13, 5624–5644 (2017).

  25. 25.

    Roca-Cusachs, P., Conte, V. & Trepat, X. Quantifying forces in cell biology. Nat. Cell Biol. 19, 742–751 (2017).

  26. 26.

    Fabry, B. et al. Scaling the microrheology of living cells. Phys. Rev. Lett. 87, 148102 (2001).

  27. 27.

    Alcaraz, J. et al. Microrheology of human lung epithelial cells measured by atomic force microscopy. Biophys. J. 84, 2071–2079 (2003).

  28. 28.

    Sanghvi-Shah, R. & Weber, G. F. Intermediate filaments at the junction of mechanotransduction, migration, and development. Front. Cell Dev. Biol. 5, 81 (2017).

  29. 29.

    Goldmann, W. H. Intermediate filaments and cellular mechanics. Cell Biol. Int. 42, 132–138 (2017).

  30. 30.

    Block, J. et al. Nonlinear loading-rate-dependent force response of individual vimentin intermediate filaments to applied strain. Phys. Rev. Lett. 118, 048101 (2017).

  31. 31.

    Beil, M. et al. Sphingosylphosphorylcholine regulates keratin network architecture and visco-elastic properties of human cancer cells. Nat. Cell Biol. 5, 803–811 (2003).

  32. 32.

    Roostalu, J. & Surrey, T. Microtubule nucleation: beyond the template. Nat. Rev. Mol. Cell Biol. 18, 702–710 (2017).

  33. 33.

    Brangwynne, C. P. et al. Microtubules can bear enhanced compressive loads in living cells because of lateral reinforcement. J. Cell Biol. 173, 733–741 (2006).

  34. 34.

    Muroyama, A. & Lechler, T. Microtubule organization, dynamics and functions in differentiated cells. Development 144, 3012–3021 (2017).

  35. 35.

    Haga, R. B. & Ridley, A. J. Rho GTPases: Regulation and roles in cancer cell biology. Small GTPases 7, 207–221 (2016).

  36. 36.

    Pfeffer, S. R. Rab GTPases: master regulators that establish the secretory and endocytic pathways. Mol. Biol. Cell 28, 712–715 (2017).

  37. 37.

    Physical Sciences - Oncology Centers Network. A physical sciences network characterization of non-tumorigenic and metastatic cells. Sci. Rep. 3, 1449 (2013).

  38. 38.

    Lee, J. S. et al. Nuclear lamin A/C deficiency induces defects in cell mechanics, polarization, and migration. Biophys. J. 93, 2542–2552 (2007).

  39. 39.

    Guilak, F., Tedrow, J. R. & Burgkart, R. Viscoelastic properties of the cell nucleus. Biochem. Biophys. Res. Commun. 269, 781–786 (2000).

  40. 40.

    Takeichi, M. Dynamic contacts: rearranging adherens junctions to drive epithelial remodelling. Nat. Rev. Mol. Cell Biol. 15, 397–410 (2014).

  41. 41.

    Ladoux, B., Nelson, W. J., Yan, J. & Mege, R. M. The mechanotransduction machinery at work at adherens junctions. Integr. Biol. 7, 1109–1119 (2015).

  42. 42.

    Panorchan, P. et al. Single-molecule analysis of cadherin-mediated cell–cell adhesion. J. Cell Sci. 119, 66–74 (2006).

  43. 43.

    Shawky, J. H. & Davidson, L. A. Tissue mechanics and adhesion during embryo development. Dev. Biol. 401, 152–164 (2015).

  44. 44.

    Yonemura, S., Wada, Y., Watanabe, T., Nagafuchi, A. & Shibata, M. alpha-Catenin as a tension transducer that induces adherens junction development. Nat. Cell Biol. 12, 533–542 (2010).

  45. 45.

    Hatzfeld, M., Keil, R. & Magin, T. M. Desmosomes and intermediate filaments: their consequences for tissue mechanics. Cold Spring Harb. Perspect. Biol. 9, a029157 (2017).

  46. 46.

    Storm, C., Pastore, J. J., MacKintosh, F. C., Lubensky, T. C. & Janmey, P. A. Nonlinear elasticity in biological gels. Nature 435, 191–194 (2005).

  47. 47.

    Chang, A. C. et al. Single molecule force measurements in living cells reveal a minimally tensioned integrin state. ACS Nano 10, 10745–10752 (2016).

  48. 48.

    Balaban, N. Q. et al. Force and focal adhesion assembly: a close relationship studied using elastic micropatterned substrates. Nat. Cell Biol. 3, 466–472 (2001).

  49. 49.

    Winograd-Katz, S. E., Fassler, R., Geiger, B. & Legate, K. R. The integrin adhesome: from genes and proteins to human disease. Nat. Rev. Mol. Cell Biol. 15, 273–288 (2014).

  50. 50.

    Yao, M. et al. Mechanical activation of vinculin binding to talin locks talin in an unfolded conformation. Sci. Rep. 4, 4610 (2014).

  51. 51.

    Sun, Z., Guo, S. S. & Fassler, R. Integrin-mediated mechanotransduction. J. Cell Biol. 215, 445–456 (2016).

  52. 52.

    Dembo, M. & Wang, Y. L. Stresses at the cell-to-substrate interface during locomotion of fibroblasts. Biophys. J. 76, 2307–2316 (1999).

  53. 53.

    Bastounis, E. et al. Both contractile axial and lateral traction force dynamics drive amoeboid cell motility. J. Cell Biol. 204, 1045–1061 (2014).

  54. 54.

    Murrell, M. P. et al. Liposome adhesion generates traction stress. Nat. Phys. 10, 163–169 (2014).

  55. 55.

    Schwarz, U. S. & Soine, J. R. Traction force microscopy on soft elastic substrates: A guide to recent computational advances. Biochim. Biophys. Acta 1853, 3095–3104 (2015).

  56. 56.

    Chan, C. E. & Odde, D. J. Traction dynamics of filopodia on compliant substrates. Science 322, 1687–1691 (2008).

  57. 57.

    Elosegui-Artola, A. et al. Mechanical regulation of a molecular clutch defines force transmission and transduction in response to matrix rigidity. Nat. Cell Biol. 18, 540–548 (2016).

  58. 58.

    Maître, J.-L. et al. Adhesion functions in cell sorting by mechanically coupling the cortices of adhering cells. Science 338, 253–256 (2012).

  59. 59.

    Maruthamuthu, V., Sabass, B., Schwarz, U. S. & Gardel, M. L. Cell–ECM traction force modulates endogenous tension at cell–cell contacts. Proc. Natl Acad. Sci. USA 108, 4708–4713 (2011).

  60. 60.

    Tozluoglu, M. et al. Matrix geometry determines optimal cancer cell migration strategy and modulates response to interventions. Nat. Cell Biol. 15, 751–762 (2013).

  61. 61.

    Tozluoglu, M., Mao, Y., Bates, P. A. & Sahai, E. Cost-benefit analysis of the mechanisms that enable migrating cells to sustain motility upon changes in matrix environments. J. R. Soc. Interface 12, 1355 (2015).

  62. 62.

    Bergert, M. et al. Force transmission during adhesion-independent migration. Nat. Cell Biol. 17, 524–529 (2015).

  63. 63.

    Yeh, Y. T. et al. Three-dimensional forces exerted by leukocytes and vascular endothelial cells dynamically facilitate diapedesis. Proc. Natl Acad. Sci. USA 115, 133–138 (2018).

  64. 64.

    del Rio, A. et al. Stretching single talin rod molecules activates vinculin binding. Science 323, 638–641 (2009).

  65. 65.

    Elosegui-Artola, A. et al. Rigidity sensing and adaptation through regulation of integrin types. Nat. Mater. 13, 631–637 (2014).

  66. 66.

    Serra-Picamal, X. et al. Mechanical waves during tissue expansion. Nat. Phys. 8, 628–634 (2012).

  67. 67.

    Farooqui, R. & Fenteany, G. Multiple rows of cells behind an epithelial wound edge extend cryptic lamellipodia to collectively drive cell-sheet movement. J. Cell. Sci. 118, 51–63 (2005).

  68. 68.

    Reffay, M. et al. Interplay of RhoA and mechanical forces in collective cell migration driven by leader cells. Nat. Cell Biol. 16, 217–223 (2014).

  69. 69.

    Rossen, N. S., Tarp, J. M., Mathiesen, J., Jensen, M. H. & Oddershede, L. B. Long-range ordered vorticity patterns in living tissue induced by cell division. Nat. Commun. 5, 5720 (2014).

  70. 70.

    Marel, A. K. et al. Flow and diffusion in channel-guided cell migration. Biophys. J. 107, 1054–1064 (2014).

  71. 71.

    Zaritsky, A. et al. Seeds of locally aligned motion and stress coordinate a collective cell migration. Biophys. J. 109, 2492–2500 (2015).

  72. 72.

    Theveneau, E. et al. Collective chemotaxis requires contact-dependent cell polarity. Dev. Cell 19, 39–53 (2010).

  73. 73.

    Trepat, X. & Fredberg, J. J. Plithotaxis and emergent dynamics in collective cellular migration. Trends Cell Biol. 21, 638–646 (2011).

  74. 74.

    Malet-Engra, G. et al. Collective cell motility promotes chemotactic prowess and resistance to chemorepulsion. Curr. Biol. 25, 242–250 (2015).

  75. 75.

    Yang, T. D., Kim, H., Yoon, C., Baek, S.-K. & Lee, K. J. Collective pulsatile expansion and swirls in proliferating tumor tissue. New J. Phys. 18, 103032 (2016).

  76. 76.

    Notbohm, J. et al. Cellular contraction and polarization drive collective cellular motion. Biophys. J. 110, 2729–2738 (2016).

  77. 77.

    Deforet, M., Hakim, V., Yevick, H. G., Duclos, G. & Silberzan, P. Emergence of collective modes and tri-dimensional structures from epithelial confinement. Nat. Commun. 5, 3747 (2014).

  78. 78.

    Rodriguez-Franco, P. et al. Long-lived force patterns and deformation waves at repulsive epithelial boundaries. Nat. Mater. 16, 1029–1037 (2017).

  79. 79.

    Tlili, S. et al. Collective cell migration without proliferation: density determines cell velocity and wave velocity. R. Soc. Open Sci. 5, 172421 (2018).

  80. 80.

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

  81. 81.

    Liu, A. J. & Nagel, S. R. Nonlinear dynamics: jamming is not just cool any more. Nature 396, 21–22 (1998).

  82. 82.

    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).

  83. 83.

    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).

  84. 84.

    Merkel, M. & Manning, M. L. A geometrically controlled rigidity transition in a model for confluent 3D tissues. New J. Phys. 20, 022002 (2018).

  85. 85.

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

  86. 86.

    Malinverno, C. et al. Endocytic reawakening of motility in jammed epithelia. Nat. Mater. 16, 587–596 (2017).

  87. 87.

    Giavazzi, F. et al. Flocking transitions in confluent tissues. Soft Matter 14, 3471–3477 (2018).

  88. 88.

    Bi, D., Yang, X., Marchetti, M. C. & Manning, M. L. Motility-driven glass and jamming transitions in biological tissues. Phys. Rev. X 6 (2016).

  89. 89.

    Marchetti, M. C. et al. Hydrodynamics of soft active matter. Rev. Mod. Phys. 85, 1143–1189 (2013).

  90. 90.

    Carlsson, J. et al. The influence of oxygen on viability and proliferation in cellular spheroids. Int. J. Radiat. Oncol. Biol. Phys. 5, 2011–2020 (1979).

  91. 91.

    Conger, A. D. & Ziskin, M. C. Growth of mammalian multicellular tumor spheroids. Cancer Res. 43, 556–560 (1983).

  92. 92.

    Ewald, A. J. et al. Mammary collective cell migration involves transient loss of epithelial features and individual cell migration within the epithelium. J. Cell Sci. 125, 2638–2654 (2012).

  93. 93.

    Charras, G. & Sahai, E. Physical influences of the extracellular environment on cell migration. Nat. Rev. Mol. Cell Biol. 15, 813–824 (2014).

  94. 94.

    Vedula, S. R. et al. Emerging modes of collective cell migration induced by geometrical constraints. Proc. Natl Acad. Sci. USA 109, 12974–12979 (2012).

  95. 95.

    Kabla, A. J. Collective cell migration: leadership, invasion and segregation. J. R. Soc. Interface 9, 3268–3278 (2012).

  96. 96.

    Wang, H., Lacoche, S., Huang, L., Xue, B. & Muthuswamy, S. K. Rotational motion during three-dimensional morphogenesis of mammary epithelial acini relates to laminin matrix assembly. Proc. Natl Acad. Sci. USA 110, 163–168 (2013).

  97. 97.

    Cetera, M. et al. Epithelial rotation promotes the global alignment of contractile actin bundles during Drosophila egg chamber elongation. Nat. Commun. 5, 5511 (2014).

  98. 98.

    Chen, D. Y., Crest, J. & Bilder, D. A cell migration tracking tool supports coupling of tissue rotation to elongation. Cell Rep. 21, 559–569 (2017).

  99. 99.

    Dolega, M. E. et al. Cell-like pressure sensors reveal increase of mechanical stress towards the core of multicellular spheroids under compression. Nat. Commun. 8, 14056 (2017).

  100. 100.

    Stylianopoulos, T. et al. Causes, consequences, and remedies for growth-induced solid stress in murine and human tumors. Proc. Natl Acad. Sci. USA 109, 15101–15108 (2012).

  101. 101.

    Stylianopoulos, T. The solid mechanics of cancer and strategies for improved therapy. J. Biomech. Eng. 139 (2017).

  102. 102.

    Stenmark, H. Rab GTPases as coordinators of vesicle traffic. Nat. Rev. Mol. Cell. Biol. 10, 513–525 (2009).

  103. 103.

    Jaffe, A. B., Kaji, N., Durgan, J. & Hall, A. Cdc42 controls spindle orientation to position the apical surface during epithelial morphogenesis. J. Cell Biol. 183, 625–633 (2008).

  104. 104.

    Peaker, M. The effect of raised intramammary pressure on mammary function in the goat in relation to the cessation of lactation. J. Physiol. 301, 415–428 (1980).

  105. 105.

    Tanner, C., Frambach, D. A. & Misfeldt, D. S. Transepithelial transport in cell culture. A theoretical and experimental analysis of the biophysical properties of domes. Biophys. J. 43, 183–190 (1983).

  106. 106.

    Foty, R. A. & Steinberg, M. S. The differential adhesion hypothesis: a direct evaluation. Dev. Biol. 278, 255–263 (2005).

  107. 107.

    Hutson, M. S., Brodland, G. W., Yang, J. & Viens, D. Cell sorting in three dimensions: topology, fluctuations, and fluidlike instabilities. Phys. Rev. Lett. 101, 148105 (2008).

  108. 108.

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

  109. 109.

    Monier, B., Pelissier-Monier, A., Brand, A. H. & Sanson, B. An actomyosin-based barrier inhibits cell mixing at compartmental boundaries in Drosophila embryos. Nat. Cell Biol. 12, 60–69 (2010).

  110. 110.

    Gaggioli, C. et al. Fibroblast-led collective invasion of carcinoma cells with differing roles for RhoGTPases in leading and following cells. Nat. Cell Biol. 9, 1392–1400 (2007).

  111. 111.

    Labernadie, A. et al. A mechanically active heterotypic E-cadherin/N-cadherin adhesion enables fibroblasts to drive cancer cell invasion. Nat. Cell Biol. 19, 224–237 (2017).

  112. 112.

    Theveneau, E. & Linker, C. Leaders in collective migration: are front cells really endowed with a particular set of skills? F1000Res. 6, 1899 (2017).

  113. 113.

    Weber, G. F., Bjerke, M. A. & Desimone, D. W. A mechanoresponsive cadherin-keratin complex directs polarized protrusive behavior and collective cell migration. Dev. Cell 22, 104–115 (2011).

  114. 114.

    Nelson, C. M. On buckling morphogenesis. J. Biomech. Eng. 138, 021005 (2016).

  115. 115.

    Hannezo, E. et al. A unifying theory of branching morphogenesis. Cell 171, 242–255.e27 (2017).

  116. 116.

    Tallinen, T. et al. On the growth and form of cortical convolutions. Nat. Phys. 12, 588–593 (2016).

  117. 117.

    Hannezo, E., Prost, J. & Joanny, J. F. Instabilities of monolayered epithelia: shape and structure of villi and crypts. Phys. Rev. Lett. 107, 078104 (2011).

  118. 118.

    Shyer, A. E. et al. Villification: how the gut gets its villi. Science 342, 212–218 (2013).

  119. 119.

    Ewald, A. J., Brenot, A., Duong, M., Chan, B. S. & Werb, Z. Collective epithelial migration and cell rearrangements drive mammary branching morphogenesis. Dev. Cell 14, 570–581 (2008).

  120. 120.

    Shyer, A. E. et al. Emergent cellular self-organization and mechanosensation initiate follicle pattern in the avian skin. Science 357, 811–815 (2017).

  121. 121.

    Basan, M., Elgeti, J., Hannezo, E., Rappel, W. J. & Levine, H. Alignment of cellular motility forces with tissue flow as a mechanism for efficient wound healing. Proc. Natl Acad. Sci. USA 110, 2452–2459 (2013).

  122. 122.

    Smeets, B. et al. Emergent structures and dynamics of cell colonies by contact inhibition of locomotion. Proc. Natl Acad. Sci. USA 113, 14621–14626 (2016).

  123. 123.

    Graner, F. & Glazier, J. A. Simulation of biological cell sorting using a two-dimensional extended Potts model. Phys. Rev. Lett. 69, 2013–2016 (1992).

  124. 124.

    Wang, N., Butler, J. P. & Ingber, D. E. Mechanotransduction across the cell surface and through the cytoskeleton. Science 260, 1124–1127 (1993).

  125. 125.

    Campas, O. et al. Quantifying cell-generated mechanical forces within living embryonic tissues. Nat. Methods 11, 183–189 (2014).

  126. 126.

    Colombelli, J. et al. Mechanosensing in actin stress fibers revealed by a close correlation between force and protein localization. J. Cell Sci. 122, 1665 (2009).

  127. 127.

    Kumar, S. et al. Viscoelastic retraction of single living stress fibers and its impact on cell shape, cytoskeletal organization, and extracellular matrix mechanics. Biophys. J. 90, 3762–3773 (2006).

  128. 128.

    Thoumine, O. & Ott, A. Time scale dependent viscoelastic and contractile regimes in fibroblasts probed by microplate manipulation. J. Cell Sci. 110, 2109–2116 (1997).

  129. 129.

    Liang, C. C., Park, A. Y. & Guan, J. L. In vitro scratch assay: a convenient and inexpensive method for analysis of cell migration in vitro. Nat. Protoc. 2, 329–333 (2007).

  130. 130.

    Gardel, M. L. et al. Elastic behavior of cross-linked and bundled actin networks. Science 304, 1301–1305 (2004).

  131. 131.

    Kroy, K. & Glaser, J. The glassy wormlike chain. New J. Phys. 9, 416 (2007).

  132. 132.

    Rauzi, M., Verant, P., Lecuit, T. & Lenne, P. F. Nature and anisotropy of cortical forces orienting Drosophila tissue morphogenesis. Nat. Cell Biol. 10, 1401–1410 (2008).

  133. 133.

    Blanch-Mercader, C. et al. Effective viscosity and dynamics of spreading epithelia: a solvable model. Soft Matter 13, 1235–1243 (2017).

  134. 134.

    Sochacki, K. A. & Taraska, J. W. Correlative fluorescence super-resolution localization microscopy and platinum replica EM on unroofed cells. Methods Mol. Biol. 1663, 219–230 (2017).

  135. 135.

    O’Rourke, K. P., Dow, L. E. & Lowe, S. W. Immunofluorescent staining of mouse intestinal stem cells. Bio. Protoc. 6 (2016).

  136. 136.

    Blanch-Mercader, C. & Casademunt, J. Hydrodynamic instabilities, waves and turbulence in spreading epithelia. Soft Matter 13, 6913–6928 (2017).

  137. 137.

    Szabo, B. et al. Phase transition in the collective migration of tissue cells: experiment and model. Phys. Rev. E 74, 061908 (2006).

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Acknowledgements

We apologize to the many colleagues whose work could not be cited owing to space constraints. We thank E. Latorre, F. Giavazzi, R. Cerbino, G. Jacquemet, J. Ivaska, J. Taraska and K. Sochacki for contributing original materials, and all members of our laboratories for critical comments and encouragement. The authors acknowledge support by the Spanish Ministry of Economy, Industry and Competitiveness through the Centro de Excelencia Severo Ochoa Award to the Institute of Bioengineering of Catalonia (X.T.) and through grant BFU2015-65074-P (X.T.), the Generalitat de Catalunya (Cerca Program and 2014-SGR-927 to X.T.), the European Research Council (CoG-616480 to X.T.) and the European Commission (project 731957 to X.T.). E.S. is funded by the Francis Crick Institute, which receives its core funding from Cancer Research UK (FC001144), the UK Medical Research Council (FC001144) and the Wellcome Trust (FC001144).

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Correspondence to Xavier Trepat or Erik Sahai.

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