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Collective motility and mechanical waves in cell clusters

  • Regular Article - Living Systems
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Abstract

Epithelial cell clusters often move collectively on a substrate. Mechanical signals play a major role in organizing this behavior. There are a number of experimental observations in these systems which await a comprehensive explanation. These include: the internal strains are tensile even for clusters that expand by proliferation; the tractions on the substrate are often confined to the edges of the cluster; there can exist density waves within the cluster; and for cells in an annulus, there is a transition between expanding clusters with proliferation and the case where cells fill the annulus and rotate around it. We formulate a mechanical model to examine these effects. We use a molecular clutch picture which allows “stalling”—inhibition of cell contraction by external forces. Stalled cells are passive from a physical point of view and the un-stalled cells are active. By attaching cells to the substrate and to each other, and taking into account contact inhibition of locomotion, we get a simple picture for many of these findings as well as predictions that could be tested.

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References

  1. D.P. Thomas, G.G. Borisy, Cellular motility driven by assembly and disassembly of actin filaments. Cell 112(4), 453–465 (2003)

    Article  Google Scholar 

  2. P. Friedl, J. Locker, E. Sahai, J.E. Segall, Classifying collective cancer cell invasion. Nat. Cell Biol. 14(8), 777–783 (2012)

    Article  Google Scholar 

  3. Vincent Hakim, Pascal Silberzan, Collective cell migration: a physics perspective. Rep. Progress Phys. 80(7), 076601–47 (2017)

    Article  ADS  Google Scholar 

  4. C.G. Kleer, K.L. van Golen, T. Braun, S.D. Merajver, Persistent E-Cadherin expression in inflammatory breast cancer. Modern Pathol. 14(5), 458–464 (2001)

    Article  Google Scholar 

  5. M.K. Jolly, M. Boareto, B.G. Debeb, N. Aceto, M.C. Farach-Carson, W.A. Woodward, H. Levine, Inflammatory breast cancer: a model for investigating cluster-based dissemination. NPJ Breast Cancer 3(1), 1–8 (2017)

    Article  Google Scholar 

  6. M.C. Marchetti, J.-F. Joanny, S. Ramaswamy, T.B. Liverpool, J. Prost, M. Rao, R.A. Simha, Hydrodynamics of soft active matter. Rev. Modern Phys. 85(3), 1143 (2013)

    Article  ADS  Google Scholar 

  7. A.S. Yap, W.M. Brieher, B.M. Gumbiner, Molecular and functional analysis of cadherin-based adherens junctions. Ann. Rev. Cell Dev. Biol. 13(1), 119–146 (1997)

    Article  Google Scholar 

  8. Roberto Mayor, Carlos Carmona-Fontaine, Keeping in touch with contact inhibition of locomotion. Trends Cell Biol. 20(6), 319–328 (2010)

    Article  Google Scholar 

  9. Xavier Trepat, Erik Sahai, Mesoscale physical principles of collective cell organization. Nat. Phys. 14(7), 671–682 (2018)

    Article  Google Scholar 

  10. X. Trepat, M.R. Wasserman, T.E. Angelini, E. Millet, D.A. Weitz, J.P. Butler, J.J. Fredberg, Physical forces during collective cell migration. Nat. Phys. 5(6), 426–430 (2009)

    Article  Google Scholar 

  11. R. Sunyer, V. Conte, J. Escribano, A. Elosegui-Artola, A. Labernadie, L. Valon, D. Navajas, J.M. García-Aznar, J.J. Muñoz, P. Roca-Cusachs, X. Trepat. Collective cell durotaxis emerges from long-range intercellular force transmission. Science (New York, NY), 353(6304):1157–1161, September 2016

  12. X. Serra-Picamal, V. Conte, R. Vincent, E. Anon, D.T. Tambe, E. Bazellieres, J.P. Butler, J.J. Fredberg, X. Trepat, Mechanical waves during tissue expansion. Nat. Phys. 8(8), 628–634 (2012)

    Article  Google Scholar 

  13. C. Pérez-González, R. Alert, C. Blanch-Mercader, M. Gómez-González, T. Kolodziej, E. Bazellieres, J. Casademunt, X. Trepat, Active wetting of epithelial tissues. Nat. Phys. 8(2), 026014 (2019)

  14. Sham Tlili, Estelle Gauquelin, Brigitte Li, Olivier Cardoso, Benoît Ladoux, Hélène. Delanoë-Ayari, François Graner, Collective cell migration without proliferation: density determines cell velocity and wave velocity. R. Soc. Open Sci. 5(5), 20–172421 (2018)

    Article  Google Scholar 

  15. S. Jain, V.M.L. Cachoux, G.H.N.S. Narayana, S. de Beco, J. D’Alessandro, V. Cellerin, T. Chen, M.L. Heuzé, P. Marcq, R.-M. Mège, A.J Kabla, C.T. Lim, B. Ladoux, The role of single-cell mechanical behaviour and polarity in driving collective cell migration. Nat. Phys., 10:1–8 (2020)

  16. C. Blanch-Mercader, R. Vincent, E. Bazellières, X. Serra-Picamal, X. Trepat, J. Casademunt, Effective viscosity and dynamics of spreading epithelia: a solvable model. Soft Matter 13(6), 1235–1243 (2017)

    Article  ADS  Google Scholar 

  17. S. Banerjee, K.J.C. Utuje, M. Cristina Marchetti, Propagating stress waves during epithelial expansion. Phys. Rev. Lett. 114(22), 228101–228105 (2015)

    Article  ADS  Google Scholar 

  18. J. Zimmermann, B.A. Camley, W.-J. Rappel, H. Levine, Contact inhibition of locomotion determines cell-cell and cell-substrate forces in tissues. Proc. Natl. Acad. Sci. U S A 113(10), 2660–2665 (2016)

    Article  ADS  Google Scholar 

  19. J.J. Williamson, G. Salbreux, Stability and roughness of interfaces in mechanically regulated tissues. Phys. Rev. Lett. 121(23), 238102 (2018)

    Article  ADS  Google Scholar 

  20. Ricard Alert, Carles Blanch-Mercader, Jaume Casademunt, Active fingering instability in tissue spreading. Phys. Rev. Lett. 122(8), 088104 (2019)

    Article  ADS  Google Scholar 

  21. Y. Yang, H. Levine, Leader-cell-driven epithelial sheet fingering. Phys. Biol. 17, 046003 (2020)

    Article  Google Scholar 

  22. F. Graner, J.A. Glazier, Simulation of biological cell sorting using a two-dimensional extended Potts model. Phys. Rev. Lett. 69(13), 2013 (1992)

    Article  ADS  Google Scholar 

  23. Reza Farhadifar, Jens-Christian. Röper, Benoit Aigouy, Suzanne Eaton, Frank Jülicher, The influence of cell mechanics, cell-cell interactions, and proliferation on epithelial packing. Curr. Biol. 17(24), 2095–2104 (2007)

    Article  Google Scholar 

  24. B.A. Camley, Y. Zhang, Y. Zhao, B. Li, E. Ben-Jacob, H. Levine, W.-J. Rappel, Polarity mechanisms such as contact inhibition of locomotion regulate persistent rotational motion of mammalian cells on micropatterns. Proc. Natl. Acad. Sci. 111(41), 14770–14775 (2014)

    Article  ADS  Google Scholar 

  25. Sara Najem, Martin Grant, Phase-field model for collective cell migration. Phys. Rev. E 93(5), 052405 (2016)

    Article  MathSciNet  ADS  Google Scholar 

  26. Tamás Vicsek, András Czirók, Eshel Ben-Jacob, Inon Cohen, Ofer Shochet, Novel type of phase transition in a system of self-driven particles. Phys. Rev. Lett. 75(6), 1226 (1995)

    Article  MathSciNet  ADS  Google Scholar 

  27. Markus Basan, Jens Elgeti, Edouard Hannezo, Wouter-Jan. Rappel, Herbert Levine, Alignment of cellular motility forces with tissue flow as a mechanism for efficient wound healing. Proc. Natl. Acad. Sci. 110(7), 2452–2459 (2013)

    Article  ADS  Google Scholar 

  28. C.E. Chan, D.J. Odde, Traction dynamics of filopodia on compliant substrates. Sci. (N. Y. NY) 322(5908), 1687–1691 (2008)

    Article  ADS  Google Scholar 

  29. B.L. Bangasser, G.A. Shamsan, C.E. Chan, K.N. Opoku, E.T. Uuml Zel, B.W. Schlichtmann, J.A. Kasim, B.J. Fuller, B.R. McCullough, S.S. Rosenfeld, D.J. Odde, Shifting the optimal stiffness for cell migration. Nat. Commun. 8, 1–10 (2017)

    Article  ADS  Google Scholar 

  30. J. Escribano, R. Sunyer, M.T. Sánchez, X. Trepat, P. Roca-Cusachs, J.M. García-Aznar, A hybrid computational model for collective cell durotaxis. Biomech. Model. Mechanobiol. 17(4):1037–1052 (2018)

  31. N. Yamana, Y. Arakawa, T. Nishino, K. Kurokawa, M. Tanji, R.E. Itoh, J.M., Toshimasa Ishizaki, H. Bito, K. Nozaki, et al., The rho-mdia1 pathway regulates cell polarity and focal adhesion turnover in migrating cells through mobilizing apc and c-src. Mol. Cell. Biol., 26(18):6844–6858 (2006)

  32. Alex Mogilner, Mathematics of cell motility: have we got its number? J. Math. Biol. 58(1–2), 105–134 (2009)

    Article  MathSciNet  Google Scholar 

  33. M. Buenemann, H. Levine, W.-J. Rappel, L.M. Sander, The role of cell contraction and adhesion in dictyostelium motility. Biophys. J., 99(1):50–58 (2010)

  34. J. Feng, H. Levine, X. Mao, L.M. Sander, Cell motility, contact guidance, and durotaxis. Soft Matter 15, 4856–4864 (2019)

    Article  ADS  Google Scholar 

  35. Yanjun Yang, Herbert Levine, Role of the supracellular actomyosin cable during epithelial wound healing. Soft Matter 14(23), 4866–4873 (2018)

    Article  ADS  Google Scholar 

  36. A. William, Wells, does size matter? J. Cell Biol. 158(7), 1156–1159 (2002)

    Article  Google Scholar 

  37. Markus Basan, Jacques Prost, Jean-François. Joanny, Jens Elgeti, Dissipative particle dynamics simulations for biological tissues: rheology and competition. Phys. Biol. 8(2), 026014 (2011)

    Article  ADS  Google Scholar 

  38. S.J. Streichan, C.R. Hoerner, T. Schneidt, D. Holzer, L. Hufnagel, Spatial constraints control cell proliferation in tissues. Proc. Natl. Acad. Sci. 111(15), 5586–5591 (2014)

    Article  ADS  Google Scholar 

  39. Dhruv K. Vig, Alex E. Hamby, Charles W. Wolgemuth, Cellular contraction can drive rapid epithelial flows. Biophys. J. 113(7), 1613–1622 (2017)

    Article  ADS  Google Scholar 

  40. Somanna A. Kollimada, Ankur H. Kulkarni, Aniket Ravan, Namrata Gundiah, Advancing edge speeds of epithelial monolayers depend on their initial confining geometry. PLoS ONE 11(4), e0153471 (2016)

    Article  Google Scholar 

  41. P. Rodríguez-Franco, A. Brugués, A. Marín-Llauradó, V. Conte, G. Solanas, E. Batlle, J.J. Fredberg, P. Roca-Cusachs, R. Sunyer, X. Trepat, Long-lived force patterns and deformation waves at repulsive epithelial boundaries. Nat. Mater., 16(10):1029–1037 (2017)

  42. T.A. Ulrich, E.M. de Juan Pardo, S. Kumar, The mechanical rigidity of the extracellular matrix regulates the structure, motility, and proliferation of glioma cells. Cancer Res., 69(10):4167–4174 (2009)

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Acknowledgements

This work was supported in part by the National Science Foundation Center for Theoretical Biological Physics NSF PHY-2019745, and also by PHY-1605817 and NSF-EFRI-1741618.

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All authors designed and conducted the research, analyzed the data, and wrote the manuscript.

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Correspondence to Leonard M. Sander.

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Deng, Y., Levine, H., Mao, X. et al. Collective motility and mechanical waves in cell clusters. Eur. Phys. J. E 44, 137 (2021). https://doi.org/10.1140/epje/s10189-021-00141-7

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