Multicellular aggregates: a model system for tissue rheology

  • Tomita Vasilica Stirbat
  • Sham Tlili
  • Thibault Houver
  • Jean-Paul Rieu
  • Catherine Barentin
  • Hélène Delanoë-Ayari
Regular Article
Part of the following topical collections:
  1. Physical constraints of morphogenesis and evolution

Abstract

Morphogenetic processes involve cell flows. The mechanical response of a tissue to active forces is linked to its effective viscosity. In order to decouple this mechanical response from the complex genetic changes occurring in a developing organism, we perform rheometry experiments on multicellular aggregates, which are good models for tissues. We observe a cell softening behavior when submitting to stresses. As our technique is very sensitive, we were able to get access to the measurement of a yield point above which a creep regime is observed obtained for strains above 12%. To explain our rheological curves we propose a model for the cytoskeleton that we represent as a dynamic network of parallel springs, which will break under stress and reattach at null strain. Such a simple model is able to reproduce most of the important behavior of cells under strain. We highlight here the importance of considering cells as complex fluids whose properties will vary with time according to the history of applied stress.

Graphical abstract

Keywords

Topical issue: Physical constraints of morphogenesis and evolution 

References

  1. 1.
    B. Aigouy, R. Farhadifar, D.B. Staple, A. Sagner, J.C. Röper, F. Jülicher, S. Eaton, Cell 142, 773 (2010).CrossRefGoogle Scholar
  2. 2.
    F. Bosveld, I. Bonnet, B. Guirao, S. Tlili, Z. Wang, A. Petitalot, R. Marchand, P.L. Bardet, P. Marcq, F. Graner et al., Science 336, 724 (2012).ADSCrossRefGoogle Scholar
  3. 3.
    J. Ranft, M. Basan, J. Elgeti, J.F. Joanny, J. Prost, F. Jülicher, Proc. Natl. Acad. Sci. U.S.A. 107, 20863 (2010).ADSCrossRefGoogle Scholar
  4. 4.
    S. Douezan, K. Guevorkian, R. Naouar, S. Dufour, D. Cuvelier, F. Brochard-Wyart, Proc. Natl. Acad. Sci. U.S.A. 108, 7315 (2011).ADSCrossRefGoogle Scholar
  5. 5.
    P. Marmottant, A. Mgharbel, J. Käfer, B. Audren, J.P. Rieu, J. Vial, B. Van Der Sanden, A. Marée, F. Graner, H. Delanoë, Proc. Natl. Acad. Sci. U.S.A. 106, 17271 (2009).ADSCrossRefGoogle Scholar
  6. 6.
    M.S. Steinberg, Science 141, 401 (1963).ADSCrossRefGoogle Scholar
  7. 7.
    R.A. Foty, G. Forgacs, C. Pfleger, M.S. Steinberg, Phys. Rev. Lett. 72, 2298 (1994).ADSCrossRefGoogle Scholar
  8. 8.
    G. Forgacs, R.A. Foty, Y. Shafrir, M.S. Steinberg, Biophys. J. 74, 2227 (1998).ADSCrossRefGoogle Scholar
  9. 9.
    T. Wakatsuki, M.S. Kolodney, G.I. Zahalak, E.L. Elson, Biophys. J. 79, 2353 (2000).CrossRefGoogle Scholar
  10. 10.
    T.V. Stirbat, A. Mgharbel, S. Bodennec, K. Ferri, H.C. Mertani, J.P. Rieu, H. Delanoë, PLoS ONE 8, e52554 (2013).ADSCrossRefGoogle Scholar
  11. 11.
    B. Fabry, G.N. Maksym, J.P. Butler, M. Glogauer, D. Navajas, J.J. Fredberg, Phys. Rev. Lett. 87, 148102 (2001).ADSCrossRefGoogle Scholar
  12. 12.
    B.D. Hoffman, G. Massiera, K.M. Van Citters, J.C. Crocker, Proc. Natl. Acad. Sci. U.S.A. 103, 10259 (2006).ADSCrossRefGoogle Scholar
  13. 13.
    A. Palmer, J. Xu, S.C. Kuo, D. Wirtz, Biophys. J. 76, 1063 (1999).CrossRefGoogle Scholar
  14. 14.
    D. Wirtz, Annu. Rev. Biophys. 38, 301 (2009).CrossRefGoogle Scholar
  15. 15.
    D. Stamenović, N. Rosenblatt, M. Montoya-Zavala, B.D. Matthews, S. Hu, B. Suki, N. Wang, D.E. Ingber, Biophys. J. 93, L39 (2007).CrossRefGoogle Scholar
  16. 16.
    N. Wang, D.E. Ingber, Biophys. J. 66, 2181 (1994).ADSCrossRefGoogle Scholar
  17. 17.
    L. Deng, N.J. Fairbank, B. Fabry, P.G. Smith, G.N. Maksym, Am. J. Physiol. Cell Physiol. 287, C440 (2004).CrossRefGoogle Scholar
  18. 18.
    D. Icard-Arcizet, O. Cardoso, A. Richert, S. Hénon, Biophys. J. 94, 2906 (2008).CrossRefGoogle Scholar
  19. 19.
    P. Fernández, P.a. Pullarkat, A. Ott, Biophysical J. 90, 3796 (2006).ADSCrossRefGoogle Scholar
  20. 20.
    X. Trepat, M. Grabulosa, F. Puig, G.N. Maksym, D. Navajas, R. Farré, Am. J. Physiol. Lung Cell. Mol. Physiol. 287, L1025 (2004).CrossRefGoogle Scholar
  21. 21.
    P. Kollmannsberger, C.T. Mierke, B. Fabry, Soft Matter 7, 3127 (2011).ADSCrossRefGoogle Scholar
  22. 22.
    X. Trepat, L. Deng, S.S. An, D. Navajas, D.J. Tschumperlin, W.T. Gerthoffer, J.P. Butler, J.J. Fredberg, Nature 447, 592 (2007).ADSCrossRefGoogle Scholar
  23. 23.
    P. Sollich, Phys. Rev. E 58, 738 (1998) 9712001v2.ADSCrossRefGoogle Scholar
  24. 24.
    R. Krishnan, C.Y. Park, Y.c. Lin, J. Mead, R.T. Jaspers, X. Trepat, G. Lenormand, D. Tambe, A.V. Smolensky, A.H. Knoll et al., PloS one 4, e5486 (2009).ADSCrossRefGoogle Scholar
  25. 25.
    L. Wolff, P. Fernández, K. Kroy, P. Ferna, PloS one 7, e40063 (2012).ADSCrossRefGoogle Scholar
  26. 26.
    K.E. Kasza, A.C. Rowat, J. Liu, T.E. Angelini, C.P. Brangwynne, G.H. Koenderink, D.A. Weitz, Curr. Opin. Cell Biol. 19, 101 (2007).CrossRefGoogle Scholar
  27. 27.
    D. Robert, T.h. Nguyen, F. Gallet, C. Wilhelm, PloS one 5, e10046 (2010).ADSCrossRefGoogle Scholar
  28. 28.
    A.R. Harris, L. Peter, J. Bellis, B. Baum, A.J. Kabla, G.T. Charras, Proc. Natl. Acad. Sci. U.S.A. 29, 16449 (2012).ADSCrossRefGoogle Scholar
  29. 29.
    A. Nagafuchi, Y. Shirayoshi, K. Okazaki, K. Yasuda, M. Takeichi, Nature 329, 341 (1987).ADSCrossRefGoogle Scholar
  30. 30.
    M. Coué, S.L. Brenner, I. Spector, E.D. Korn, FEBS Lett. 213, 316 (1987).CrossRefGoogle Scholar
  31. 31.
    A. Bershadsky, A. Chausovsky, E. Becker, A. Lyubimova, B. Geiger, Curr. Biol. 6, 1279 (1996).CrossRefGoogle Scholar
  32. 32.
    J. Xu, Y. Tseng, D. Wirtz, Journal Biol. Chem. 275, 35886 (2000).CrossRefGoogle Scholar
  33. 33.
    R.H. Ewoldt, a.E. Hosoi, G.H. McKinley, Integr. Comp. Biol. 49, 40 (2009).CrossRefGoogle Scholar
  34. 34.
    C. Semmrich, T. Storz, J. Glaser, R. Merkel, A. Bausch, K. Kroy, Proc. Natl. Acad. Sci. U.S.A. 104, 20199 (2007).ADSCrossRefGoogle Scholar
  35. 35.
    C. Semmrich, R.J. Larsen, A.R. Bausch, Soft Matter 4, 1675 (2008).ADSCrossRefGoogle Scholar
  36. 36.
    C.P. Broedersz, K.E. Kasza, L.M. Jawerth, S. Münster, D.a. Weitz, F.C. MacKintosh, Soft Matter 6, 4120 (2010).ADSCrossRefGoogle Scholar
  37. 37.
    R.H. Ewoldt, G.H. Mckinley, Rheology Bull. 76, 4 (2007).Google Scholar
  38. 38.
    P. Fernández, A. Ott, Phys. Rev. Lett. 100, 2 (2008).Google Scholar
  39. 39.
    P. Bursac, G. Lenormand, B. Fabry, M. Oliver, D.A. Weitz, V. Viasnoff, J.P. Butler, J.J. Fredberg, Nat. Mater. 4, 557 (2005).ADSCrossRefGoogle Scholar
  40. 40.
    N. Desprat, A. Richert, J. Simeon, A. Asnacios, Biophys. J. 88, 2224 (2005).CrossRefGoogle Scholar
  41. 41.
    D.R. Overby, B.D. Matthews, E. Alsberg, D.E. Ingber, Acta Biomater. 1, 295 (2005).CrossRefGoogle Scholar
  42. 42.
    P. Sollich, F. Lequeux, P. Hébraud, M.M. Cates, Phys. Rev. Lett. 78, 2020 (1997).ADSCrossRefGoogle Scholar
  43. 43.
    B. Fabry, G.N. Maksym, J.P. Butler, M. Glogauer, D. Navajas, N.A. Taback, E.J. Millet, J.J. Fredberg, Phys. Rev. E. 68, 41914 (2003).ADSCrossRefGoogle Scholar
  44. 44.
    K.K. Mandadapu, S. Govindjee, M.R.K. Mofrad, J. Biomech. 41, 1467 (2008).CrossRefGoogle Scholar
  45. 45.
    H.A. Kramers, Physica 7, 284 (1940).ADSCrossRefMATHMathSciNetGoogle Scholar
  46. 46.
    E.A. Evans, Faraday Disc. 111, 1 (1998).ADSCrossRefGoogle Scholar
  47. 47.
    G.I. Bell, Science 200, 618 (1978).ADSCrossRefGoogle Scholar
  48. 48.
    M. Srinivasan, S. Walcott, Phys. Rev. E 80, 046124 (2009).ADSCrossRefGoogle Scholar
  49. 49.
    S. Walcott, S.X. Sun, Proc. Natl. Acad. Sci. U.S.A. 107, 7757 (2010).ADSCrossRefGoogle Scholar
  50. 50.
    S.M. Fielding, M.E. Cates, P. Sollich, Soft Matter 5, 2378 (2009) arXiv:0812.3300v1.ADSCrossRefGoogle Scholar
  51. 51.
    E. Ben-Isaac, Y. Park, G. Popescu, F.L.H. Brown, N.S. Gov, Y. Shokef, Phys. Rev. Lett. 106, 238103 (2011).ADSCrossRefGoogle Scholar
  52. 52.
    L. Wolff, K. Kroy, Phys. Rev. E 86, 040901 (2012).ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Tomita Vasilica Stirbat
    • 1
  • Sham Tlili
    • 2
  • Thibault Houver
    • 1
  • Jean-Paul Rieu
    • 1
  • Catherine Barentin
    • 1
  • Hélène Delanoë-Ayari
    • 1
  1. 1.Institut Lumière MatièreUMR5306 Université de Lyon 1-CNRS, Université de LyonVilleurbanne cedexFrance
  2. 2.Laboratoire Matière et Systèmes Complexes, Centre National de la Recherche ScientifiqueUnité Mixte de Recherche 7057, Université Paris 7 - Denis DiderotParis Cedex 13France
  3. 3.Physico-Chimie Curie, Institut CurieUMR168 CNRS, UPMCParis Cedex 05France

Personalised recommendations