The European Physical Journal E

, Volume 13, Issue 3, pp 247–259 | Cite as

Role of tensile stress in actin gels and a symmetry-breaking instability

  • K. Sekimoto
  • J. Prost
  • F. Jülicher
  • H. Boukellal
  • A. Bernheim-Grosswasser
Article

Abstract.

It has been observed experimentally that the actin gel grown from spherical beads coated with polymerization enzymes spontaneously breaks the symmetry of its spherical shape, and yields a “comet” pushing the bead forward. We propose a mechano-chemical coupling mechanism for the initialization of this symmetry breaking. Key assumptions are that the dissociation of the gel takes place mostly in the region of the external surface, and that the rates of the dissociation depend on the tensile stress in the gel. We analyze a simplified two-dimensional model with a circular substrate. Our analysis shows that the symmetric steady state is always unstable against the inhomogeneous modulation of the thickness of the gel layer, for any radius of the circular substrate. We argue that this model represents the essential feature of three-dimensional systems for a certain range of characteristic lengths of the modulation. The characteristic time of the symmetry-breaking process in our model depends linearly on the radius of curvature of the substrate surface, which is consistent with experimental results, using spherical latex beads as substrate. Our analysis of the symmetry-breaking phenomenon demonstrates aspects of mechano-chemical couplings that should be working in vivo as well as in vitro.

Keywords

Tensile Stress Symmetry Breaking Coupling Mechanism Latex Bead Spherical Bead 

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References

  1. 1.
    F. Gerbal, V. Laurent, A. Ott, P. Chaikin, J. Prost, Eur. Biophys. J. 29, 134 (2000).CrossRefGoogle Scholar
  2. 2.
    J. Taunton, B.A. Rowning, M.L. Coughlin, M. Wu, R.T. Moon, T.J. Mitchison, C.A. Larabell, J. Cell Biol. 148, 519 (2000).CrossRefGoogle Scholar
  3. 3.
    T.P. Loisel, R. Boujemaa, D. Pantaloni, M.F. Carlier, Nature 401, 613 (1999).CrossRefPubMedGoogle Scholar
  4. 4.
    L.A. Cameron, M.J. Footer, A. van Oudenaarden, J.A. Theriot, Proc. Natl. Acad. Sci. U.S.A. 96, 4908 (1999).CrossRefGoogle Scholar
  5. 5.
    V. Noireaux, R.M. Golsteyn, E. Friedrich, J. Prost, C. Antony, D. Louvard, C. Sykes, Biophys. J. 78, 1643 (2000).Google Scholar
  6. 6.
    D. Yarar, W. To, A. Abo, M.D. Welch, Curr. Biol. 9, 555 (1999).CrossRefGoogle Scholar
  7. 7.
    A. Bernheim-Grosswasser, S. Wiesner, R.M. Goldsteyn, M.-F. Carlier, C. Sykes, Nature 417, 308 (2002).CrossRefPubMedGoogle Scholar
  8. 8.
    S. Rafelski, P. Lauer, D. Portnoy, J. Theriot, http://cmgm.stanford.edu/theriot/movies.htm: Skidding moti-lity of mutant Listeria (2002).Google Scholar
  9. 9.
    A. van Oudenaarden, Julie A. Theriot, Nature Cell Biol. 1, 493 (1999).CrossRefGoogle Scholar
  10. 10.
    A. Mogilner, G. Oster, Biophys. J. 84, 1591 (2003).Google Scholar
  11. 11.
    F. Gerbal, P. Chaikin, Y. Rabin, J. Prost, Biophys. J. 79, 2259 (2000).Google Scholar
  12. 12.
    L. Landau, E. Lifchitz, The Theory of Elasticity (Mir, Moscow, 1967).Google Scholar
  13. 13.
    K. Sekimoto, F. Jülicher, J. Prost, unpublished (2001).Google Scholar
  14. 14.
    K. Kassner, C. Misbah, J. Muller, J. Kappey, P. Kohlert, Phys. Rev. E 63, 036117 (2001). (The original literatures on the crystal growth related to the stress concentration, such as R.J. Asaro, W.A. Tiller, Metall. Trans. 3, 1789 (1972) and M.A. Grinfeld, Dokl. Akad. Nauk USSR 265, 836 (1982) are cited and described therein.)CrossRefGoogle Scholar
  15. 15.
    F. Gerbal, V. Noireaux, C. Sykes, F. Jülicher, P. Chaikin, A. Ott, J. Prost, R.M. Golsteyn, E. Friederich, D. Louvard, V. Laurent, M.F. Carlier, Pramana 53, 155 (1999).Google Scholar
  16. 16.
    J. Prost, in Physics of Bio-molecules and Cells, Les Houches Session LXXV, 2-27 July 2001, edited by H. Flyvbjerg et al. , Les Houches Summer School Series, Vol. 75 (Springer, 2002).Google Scholar
  17. 17.
    M. Dogterom, B. Yurke, Science 278, 856 (1997).CrossRefPubMedGoogle Scholar
  18. 18.
    J. Plastino, I. Lelidis, J. Prost, C. Sykes, Eur. Biophys. J. (published on line, 09 December, 2003); DOI: 10.1007/s00249-003-0370-3.Google Scholar
  19. 19.
    K. Tawada, K. Sekimoto, J. Theor. Biol. 150, 193 (1991).Google Scholar
  20. 20.
    P.A. Giardini, D.A. Fletcher, J.A. Theriot, Proc. Natl. Acad. Sci. U.S.A. 100, 6493 (2003).CrossRefGoogle Scholar
  21. 21.
    A. Upadhyaya, J.R. Chabot, A. Andreeva, A. Samadani, A. van Oudenaarden, Proc. Natl. Acad. Sci. U.S.A. 100, 4521 (2003).CrossRefGoogle Scholar
  22. 22.
    O. Campas, J.-F. Joanny, J. Prost, unpublished.Google Scholar
  23. 23.
    L.A. Cameron, T.M. Svitkina, D. Vignjevic, J.A. Theriot, G.G. Borisy, Curr. Biol. 11, 130 (2001).CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin/Heidelberg 2004

Authors and Affiliations

  • K. Sekimoto
    • 1
  • J. Prost
    • 1
  • F. Jülicher
    • 1
  • H. Boukellal
    • 1
  • A. Bernheim-Grosswasser
    • 1
  1. 1.Physico-ChimieUMR168 Institut CurieParis Cedex 05France

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