The European Physical Journal E

, Volume 18, Issue 1, pp 41–54 | Cite as

Nonlinear competition between asters and stripes in filament-motor systems

Original Article

Abstract.

A model for polar filaments interacting via molecular motor complexes is investigated which exhibits bifurcations to spatial patterns. It is shown that the homogeneous distribution of filaments, such as actin or microtubules, may become either unstable with respect to an orientational instability of a finite wave number or with respect to modulations of the filament density, where long-wavelength modes are amplified as well. Above threshold nonlinear interactions select either stripe patterns or periodic asters. The existence and stability ranges of each pattern close to threshold are predicted in terms of a weakly nonlinear perturbation analysis, which is confirmed by numerical simulations of the basic model equations. The two relevant parameters determining the bifurcation scenario of the model can be related to the concentrations of the active molecular motors and of the filaments, respectively, which both could be easily regulated by the cell.

PACS.

87.16.-b Subcellular structure and processes 47.54.+r Pattern selection; pattern formation 89.75.-k Complex systems 

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References

  1. 1.
    B. Alberts , Molecular Biology of the Cell (Garland Publishing, New York, 2001).Google Scholar
  2. 2.
    J. Howard, Mechanics of Motor Proteins and the Cytoskeleton (Sinauer, Sunderland, 2001).Google Scholar
  3. 3.
    A. Hyman, E. Karsenti, Cell 45, 329 (1986).CrossRefPubMedGoogle Scholar
  4. 4.
    E. Karsenti, I. Vernos, Science 294, 543 (2001).CrossRefPubMedGoogle Scholar
  5. 5.
    D. Pantaloni, C. LeClainche, M.F. Carlier, Science 292, 1502 (2001).CrossRefPubMedGoogle Scholar
  6. 6.
    A.B. Verkhovsky, T.M. Svitkina, G.G. Borisy, Curr. Biol. 9, 11 (1999).CrossRefPubMedGoogle Scholar
  7. 7.
    R. Urrutia , Proc. Natl. Acad. Sci. U.S.A. 88, 6701 (1991).PubMedGoogle Scholar
  8. 8.
    F.J. Nedelec, T. Surrey, A.C. Maggs, S. Leibler, Nature 389, 305 (1997).CrossRefPubMedGoogle Scholar
  9. 9.
    T. Surrey , Proc. Natl. Acad. Sci. U.S.A. 95, 4293 (1998).CrossRefPubMedGoogle Scholar
  10. 10.
    D. Humphrey , Nature 416, 413 (2002).PubMedGoogle Scholar
  11. 11.
    D. Smith , Molecular motors in cells: A rapid switch of biopolymer organization, in preparation (2005).Google Scholar
  12. 12.
    T. Surrey, F. Nedelec, S. Leibler, E. Karsenti, Science 292, 116 (2001).CrossRefGoogle Scholar
  13. 13.
    F. Nédélec, J. Cell Biol. 158, 1005 (2002).CrossRefPubMedGoogle Scholar
  14. 14.
    B. Bassetti, M.C. Lagomarsino, P. Jona, Eur. Phys. J. B 15, 483 (2000).CrossRefGoogle Scholar
  15. 15.
    H.Y. Lee, M. Kardar, Phys. Rev. E 64, 056113 (2001).CrossRefGoogle Scholar
  16. 16.
    J. Kim , J. Korean Phys. Soc. 42, 162 (2003).Google Scholar
  17. 17.
    H. Nakazawa, K. Sekimoto, J. Physiol. Soc. Jpn. 65, 2404 (1996).CrossRefGoogle Scholar
  18. 18.
    K. Kruse, F. Jülicher, Phys. Rev. Lett. 85, 1778 (2000).CrossRefPubMedGoogle Scholar
  19. 19.
    K. Kruse, A. Zumdieck, F. Jülicher, Europhys. Lett. 64, 716 (2003).CrossRefGoogle Scholar
  20. 20.
    M. Doi, S.F. Edwards, The Theory of Polymer Dynamics (Clarendon Press, Oxford, 1986).Google Scholar
  21. 21.
    L. Onsager, Ann. N.Y. Acad. Sci. 51, 627 (1949).Google Scholar
  22. 22.
    P.G. de Gennes, J. Prost, The Physics of Liquid Crystals (Clarendon, Oxford, 1993).Google Scholar
  23. 23.
    Z.Y. Chen, Macromolecules 26, 3419 (1993).CrossRefGoogle Scholar
  24. 24.
    A.L. Hitt, A.R. Cross, J.R.C. Williams, J. Biol. Chem. 265, 1639 (1990).PubMedGoogle Scholar
  25. 25.
    A. Suzuki, T. Maeda, T. Ito, Biophys. J. 59, 25 (1991).PubMedGoogle Scholar
  26. 26.
    F. Ziebert, W. Zimmermann, Phys. Rev. E 70, 022902 (2004).CrossRefGoogle Scholar
  27. 27.
    T. Liverpool, M. Marchetti, Phys. Rev. Lett. 90, 138102 (2003).CrossRefPubMedGoogle Scholar
  28. 28.
    M.C. Cross, P.C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993).CrossRefGoogle Scholar
  29. 29.
    A.C. Newell, T. Passot, J. Lega, Annu. Rev. Fluid Mech. 25, 399 (1992).CrossRefGoogle Scholar
  30. 30.
    P. Manneville, Dissipative Structures and Weak Turbulence (Academic Press, London, 1990).Google Scholar
  31. 31.
    S. Ciliberto , Phys. Rev. Lett. 65, 2370 (1990).CrossRefPubMedGoogle Scholar
  32. 32.
    L.A. Segel, J. Fluid Mech. 21, 359 (1965).Google Scholar
  33. 33.
    J.P. Straley, Phys. Rev. A 8, 2181 (1973).CrossRefGoogle Scholar
  34. 34.
    F. Nédélec, T. Surrey, C. R. Acad. Sci. Paris, Série IV 6, 841 (2001). Google Scholar
  35. 35.
    F. Ziebert, W. Zimmermann, Phys. Rev. Lett. 93, 159801 (2004).CrossRefPubMedGoogle Scholar
  36. 36.
    F. Ziebert, W. Zimmermann, Oscillatory and density instabilities in filament-motor systems, in preparation (2005).Google Scholar
  37. 37.
    I. Teraoka, R. Hayakawa, J. Chem. Phys. 89, 6989 (1988)CrossRefGoogle Scholar
  38. 38.
    T. Liverpool, M. Marchetti, Europhys. Lett. 69, 846 (2005).CrossRefGoogle Scholar
  39. 39.
    K. Kruse, S. Camalet, F. Jülicher, Phys. Rev. Lett. 87, 138101 (2001).CrossRefPubMedGoogle Scholar
  40. 40.
    H.-G. Döbereiner , Phys. Rev. Lett. 93, 108105 (2004).CrossRefPubMedGoogle Scholar
  41. 41.
    F. Nédélec, T. Surrey, A.C. Maggs, Phys. Rev. Lett. 86, 3192 (2001).CrossRefPubMedGoogle Scholar
  42. 42.
    K. Kruse , Eur. Phys. J. E 16, 5 (2005).CrossRefPubMedGoogle Scholar
  43. 43.
    T. Shimada, M. Doi, K. Okano, J. Chem. Phys. 88, 7181 (1988).CrossRefGoogle Scholar

Copyright information

© EDP Sciences, Società Italiana di Fisica and Springer-Verlag 2005

Authors and Affiliations

  1. 1.Theoretische PhysikUniversität des SaarlandesSaarbrückenGermany
  2. 2.Theoretische PhysikUniversität BayreuthBayreuthGermany

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