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Journal of Biological Physics

, Volume 32, Issue 6, pp 497–506 | Cite as

RETRACTED ARTICLE: Nematic Ordering Pattern Formation in the Process of Self-Organization of Microtubules in a Gravitational Field

  • Hu Jian
  • Qiu Xijun
  • Li Ruxin
Research Paper

Abstract

Papaseit et al. (Proc. Natl. Acad. Sci. U.S.A. 97, 8364, 2000) showed the decisive role of gravity in the formation of patterns by assemblies of microtubules in vitro. By virtue of a functional scaling, the free energy for MT systems in a gravitational field was constructed. The influence of the gravitational field on MT’s self-organization process, that can lead to the isotropic to nematic phase transition, is the focus of this paper. A coupling of a concentration gradient with orientational order characteristic of nematic ordering pattern formation is the new feature emerging in the presence of gravity. The concentration range corresponding to a phase coexistence region increases with increasing g or MT concentration. Gravity facilitates the isotropic to nematic phase transition leading to a significantly broader transition region. The phase transition represents the interplay between the growth in the isotropic phase and the precipitation into the nematic phase. We also present and discuss the numerical results obtained for local MT concentration change with the height of the vessel, order parameter and phase transition properties.

Key words

microtubules gravitational field concentration gradient nematic ordering 

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References

  1. 1.
    Papaseit, C., Pochon, N., Tabony, J.: Microtubule self-organization is gravity-dependent. Proc. Natl. Acad. Sci. USA 97, 8364–8368 (2000)ADSCrossRefGoogle Scholar
  2. 2.
    de Pablo, P.J., Schaap, I.A.T., MacKintosh, F.C., Schmidt, C.F.: Deformation and collapse of microtubules on the nanometer scale. Phys. Rev. Lett. 91, 098101 (2003)Google Scholar
  3. 3.
    Athenstaedt, H.: Pyroelectric and piezoelectric properties of vertebrates. Ann. N.Y. Acad. Sci. 238, 68–94 (1974)ADSCrossRefGoogle Scholar
  4. 4.
    Margulis, L., To, L., Chase, D.: Microtubules in prokaryotes. Science 200, 1118–1124 (1978)ADSCrossRefGoogle Scholar
  5. 5.
    Hameroff, S.R., Watt, R.C.: Information processing in microtubules. J. Theor. Biol. 98, 549–561 (1982)CrossRefGoogle Scholar
  6. 6.
    Kis, A., Kasas, S., Babic, B., Kulik, A.J., Benoît, W., Briggs, G.A.D., Schönenberger, C., Catsicas, S., Forró, L.: Nanomechanics of microtubules. Phys. Rev. Lett. 89, 248101 (2002)Google Scholar
  7. 7.
    Spacelab I Reports. Science 225, 205–235 (1984)Google Scholar
  8. 8.
    Tabony, J., Job, D.: Gravitational symmetry breaking in microtubular dissipative structures. Proc. Natl. Acad. Sci. USA 89, 6948–6952 (1992)ADSCrossRefGoogle Scholar
  9. 9.
    Portet, S., Tuszyński, J.A., Dixon, J.M., Satarić, M.V.: Models of spatial and orientational self-organization of microtubules under the influence of gravitational fields. Phys. Rev. E 68, 021903 (2003)Google Scholar
  10. 10.
    Melton, D.A.: Pattern formation during animal development. Science 252, 234–241 (1991)ADSCrossRefGoogle Scholar
  11. 11.
    Gerhart, J., Keller, R.: Region-specific cell activities in amphibian gastrulation. Annu. Rev. Cell. Biol. 2, 201–229 (1986)CrossRefGoogle Scholar
  12. 12.
    Zisckind, N., Elinson, R.P.: Gravity and microtubules in dorsoventral polarization of the Xenopus Egg Develop. Growth Differ. 32, 575–581 (1990)CrossRefGoogle Scholar
  13. 13.
    Beetschen, J.C., Gautier, J.: Heat-shock-induced grey crescent formation in axolotl eggs and oocytes: the role of gravity. Development 100, 599–609 (1987)Google Scholar
  14. 14.
    Malacinski, G.M., Neff, A.W.: The amphibian egg as a model system for analyzing gravity effects. Adv. Space Res. 9, 169–176 (1989)ADSCrossRefGoogle Scholar
  15. 15.
    Elinson, R.P., Rowning, B.: A transient array of parallel microtubules in frog eggs: potential tracks for a cytoplasmic rotation that specifies the dorso-ventral axis. Dev. Biol. 128, 185–197 (1988)CrossRefGoogle Scholar
  16. 16.
    Driss-Ecole, D., Lefranc, A., Perbal, G.: A polarized cell: the root statocyte. Physiol. Plant. 118, 305–312 (2003)CrossRefGoogle Scholar
  17. 17.
    Himmelspach, R., Wymer, C.L., Lioyd, C.W., Nick, P.: Gravity-induced reorientation of cortical microtubules observed in vivo. Plant J. 18, 449–453 (1999)CrossRefGoogle Scholar
  18. 18.
    Fischer, K., Schopfer, P.: Physical strain-mediated microtubule reorientation in the epidermis of gravitropically or phototropically stimulated maize coleoptiles. Plant J. 15, 119–123 (1998)CrossRefGoogle Scholar
  19. 19.
    Parsons, J.D.: Nematic ordering in a system of rods. Phys. Rev. A 19, 1225–1230 (1979)ADSCrossRefGoogle Scholar
  20. 20.
    de Gennes, P.: Polymer Liquid Crystals. Academic Press, New York, (1982)Google Scholar
  21. 21.
    Baulin, V.A., Khokhlov, A.R.: Nematic ordering of rigid rods in a gravitational field. Phys. Rev. E 60, 2973–2977 (1999)ADSCrossRefGoogle Scholar
  22. 22.
    Sin-Doo, L.: A numerical investigation of nematic ordering based on a simple hard-rod model. J. Chem. Phys. 87, 4972–4974 (1987)ADSCrossRefGoogle Scholar
  23. 23.
    Satarić, M.V., Tuszyński, J.A.: Relationship between the nonlinear ferroelectric and liquid crystal models for microtubules. Phys. Rev. E 67, 011901 (2003)Google Scholar
  24. 24.
    Tuszyński, J.A., Satarić, M.V., Portet, S., Dixon, J.M.: Gravitational symmetry breaking leads to a polar liquid crystal phase of microtubules in vitro. J. Biol. Phys. 31, 477–486 (2005)CrossRefGoogle Scholar
  25. 25.
    Baulin, V.A.: Self-assembled aggregates in the gravitational field: growth and nematic order. J. Chem. Phys. 119, 2874–2885 (2003)ADSCrossRefGoogle Scholar
  26. 26.
    Stracke, R., Böhm, K.J., Wollweber, L., Tuszyński, J.A., Unger, E.: Analysis of the migration behaviour of single microtubules in electric fields. Biochem. Biophys. Res. Commun. 293, 602–609 (2002)CrossRefGoogle Scholar
  27. 27.
    Bras, W., Diakun, G.P., Diaz, J.F., Maret, G., Kramer, H., Bordas, J., Medrano, F.J.: The Susceptibility of pure tubulin to high magnetic fields: a magnetic birefringence and X-ray fiber diffraction study. Biophys. J. 74, 1509–1521 (1998)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.Department of PhysicsShanghai UniversityShanghaiChina
  2. 2.Shanghai Institute of Optics and Fine MechanicsChinese Academy of ScienceShanghaiChina

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