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
Similar content being viewed by others
References
B. Aigouy, R. Farhadifar, D.B. Staple, A. Sagner, J.C. Röper, F. Jülicher, S. Eaton, Cell 142, 773 (2010).
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).
J. Ranft, M. Basan, J. Elgeti, J.F. Joanny, J. Prost, F. Jülicher, Proc. Natl. Acad. Sci. U.S.A. 107, 20863 (2010).
S. Douezan, K. Guevorkian, R. Naouar, S. Dufour, D. Cuvelier, F. Brochard-Wyart, Proc. Natl. Acad. Sci. U.S.A. 108, 7315 (2011).
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).
M.S. Steinberg, Science 141, 401 (1963).
R.A. Foty, G. Forgacs, C. Pfleger, M.S. Steinberg, Phys. Rev. Lett. 72, 2298 (1994).
G. Forgacs, R.A. Foty, Y. Shafrir, M.S. Steinberg, Biophys. J. 74, 2227 (1998).
T. Wakatsuki, M.S. Kolodney, G.I. Zahalak, E.L. Elson, Biophys. J. 79, 2353 (2000).
T.V. Stirbat, A. Mgharbel, S. Bodennec, K. Ferri, H.C. Mertani, J.P. Rieu, H. Delanoë, PLoS ONE 8, e52554 (2013).
B. Fabry, G.N. Maksym, J.P. Butler, M. Glogauer, D. Navajas, J.J. Fredberg, Phys. Rev. Lett. 87, 148102 (2001).
B.D. Hoffman, G. Massiera, K.M. Van Citters, J.C. Crocker, Proc. Natl. Acad. Sci. U.S.A. 103, 10259 (2006).
A. Palmer, J. Xu, S.C. Kuo, D. Wirtz, Biophys. J. 76, 1063 (1999).
D. Wirtz, Annu. Rev. Biophys. 38, 301 (2009).
D. Stamenović, N. Rosenblatt, M. Montoya-Zavala, B.D. Matthews, S. Hu, B. Suki, N. Wang, D.E. Ingber, Biophys. J. 93, L39 (2007).
N. Wang, D.E. Ingber, Biophys. J. 66, 2181 (1994).
L. Deng, N.J. Fairbank, B. Fabry, P.G. Smith, G.N. Maksym, Am. J. Physiol. Cell Physiol. 287, C440 (2004).
D. Icard-Arcizet, O. Cardoso, A. Richert, S. Hénon, Biophys. J. 94, 2906 (2008).
P. Fernández, P.a. Pullarkat, A. Ott, Biophysical J. 90, 3796 (2006).
X. Trepat, M. Grabulosa, F. Puig, G.N. Maksym, D. Navajas, R. Farré, Am. J. Physiol. Lung Cell. Mol. Physiol. 287, L1025 (2004).
P. Kollmannsberger, C.T. Mierke, B. Fabry, Soft Matter 7, 3127 (2011).
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).
P. Sollich, Phys. Rev. E 58, 738 (1998) 9712001v2.
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).
L. Wolff, P. Fernández, K. Kroy, P. Ferna, PloS one 7, e40063 (2012).
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).
D. Robert, T.h. Nguyen, F. Gallet, C. Wilhelm, PloS one 5, e10046 (2010).
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).
A. Nagafuchi, Y. Shirayoshi, K. Okazaki, K. Yasuda, M. Takeichi, Nature 329, 341 (1987).
M. Coué, S.L. Brenner, I. Spector, E.D. Korn, FEBS Lett. 213, 316 (1987).
A. Bershadsky, A. Chausovsky, E. Becker, A. Lyubimova, B. Geiger, Curr. Biol. 6, 1279 (1996).
J. Xu, Y. Tseng, D. Wirtz, Journal Biol. Chem. 275, 35886 (2000).
R.H. Ewoldt, a.E. Hosoi, G.H. McKinley, Integr. Comp. Biol. 49, 40 (2009).
C. Semmrich, T. Storz, J. Glaser, R. Merkel, A. Bausch, K. Kroy, Proc. Natl. Acad. Sci. U.S.A. 104, 20199 (2007).
C. Semmrich, R.J. Larsen, A.R. Bausch, Soft Matter 4, 1675 (2008).
C.P. Broedersz, K.E. Kasza, L.M. Jawerth, S. Münster, D.a. Weitz, F.C. MacKintosh, Soft Matter 6, 4120 (2010).
R.H. Ewoldt, G.H. Mckinley, Rheology Bull. 76, 4 (2007).
P. Fernández, A. Ott, Phys. Rev. Lett. 100, 2 (2008).
P. Bursac, G. Lenormand, B. Fabry, M. Oliver, D.A. Weitz, V. Viasnoff, J.P. Butler, J.J. Fredberg, Nat. Mater. 4, 557 (2005).
N. Desprat, A. Richert, J. Simeon, A. Asnacios, Biophys. J. 88, 2224 (2005).
D.R. Overby, B.D. Matthews, E. Alsberg, D.E. Ingber, Acta Biomater. 1, 295 (2005).
P. Sollich, F. Lequeux, P. Hébraud, M.M. Cates, Phys. Rev. Lett. 78, 2020 (1997).
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).
K.K. Mandadapu, S. Govindjee, M.R.K. Mofrad, J. Biomech. 41, 1467 (2008).
H.A. Kramers, Physica 7, 284 (1940).
E.A. Evans, Faraday Disc. 111, 1 (1998).
G.I. Bell, Science 200, 618 (1978).
M. Srinivasan, S. Walcott, Phys. Rev. E 80, 046124 (2009).
S. Walcott, S.X. Sun, Proc. Natl. Acad. Sci. U.S.A. 107, 7757 (2010).
S.M. Fielding, M.E. Cates, P. Sollich, Soft Matter 5, 2378 (2009) arXiv:0812.3300v1.
E. Ben-Isaac, Y. Park, G. Popescu, F.L.H. Brown, N.S. Gov, Y. Shokef, Phys. Rev. Lett. 106, 238103 (2011).
L. Wolff, K. Kroy, Phys. Rev. E 86, 040901 (2012).
Author information
Authors and Affiliations
Corresponding author
Additional information
Contribution to the Topical Issue “Physical constraints of morphogenesis and evolution”, edited by Vincent Fleury, Paul François and Marie Christine Ho Ba Tho.
Rights and permissions
About this article
Cite this article
Vasilica Stirbat, T., Tlili, S., Houver, T. et al. Multicellular aggregates: a model system for tissue rheology. Eur. Phys. J. E 36, 84 (2013). https://doi.org/10.1140/epje/i2013-13084-1
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epje/i2013-13084-1