Advertisement

Squeezed helical elastica

  • Lila Bouzar
  • Martin Michael Müller
  • Pierre Gosselin
  • Igor M. Kulić
  • Hervé Mohrbach
Regular Article

Abstract.

We theoretically study the conformations of a helical semi-flexible filament confined to a flat surface. This squeezed helix exhibits a variety of unexpected shapes resembling circles, waves or spirals depending on the material parameters. We explore the conformation space in detail and show that the shapes can be understood as the mutual elastic interaction of conformational quasi-particles. Our theoretical results are potentially useful to determine the material parameters of such helical filaments in an experimental setting.

Graphical abstract

Keywords

Living systems: Biological Matter 

References

  1. 1.
    O. Kahraman, N. Stoop, M.M. Müller, New J. Phys. 14, 095021 (2012)ADSCrossRefGoogle Scholar
  2. 2.
    N. Stoop, J. Najafi, F.K. Wittel, M. Habibi, Phys. Rev. Lett. 106, 214102 (2011)ADSCrossRefGoogle Scholar
  3. 3.
    J. Guven, P. Vázquez-Montejo, Phys. Rev. E 85, 026603 (2012)ADSCrossRefGoogle Scholar
  4. 4.
    H.P. Hsu, P. Grassberger, J. Chem. Phys. 120, 2034 (2004)ADSCrossRefGoogle Scholar
  5. 5.
    T. Sanchez, I.M. Kulić, Z. Dogic, Phys. Rev. Lett. 104, 098103 (2010)ADSCrossRefGoogle Scholar
  6. 6.
    J. Guven, D.M. Valencia, P. Vázquez-Montejo, J. Phys. A: Math. Theor. 47, 355201 (2014)CrossRefGoogle Scholar
  7. 7.
    G.H.M. van der Heijden, Proc. R. Soc. London A 457, 695 (2001)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    G.H.M. van der Heijden, A.R. Champneys, J.M.T. Thompson, Int. J. Solids Struct. 39, 1863 (2002)CrossRefGoogle Scholar
  9. 9.
    G.H.M. van der Heijden, M.A. Peletier, R. Planqué, Arch. Ration. Mech. Anal. 182, 471 (2006)MathSciNetCrossRefGoogle Scholar
  10. 10.
    G.H.M. van der Heijden, A.R. Champneys, J.M.T. Thompson, J. Mech. Phys. Solids 47, 59 (1999)ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    J.H. Maddocks, Arch. Ration. Mech. Anal. 85, 311 (1984)MathSciNetCrossRefGoogle Scholar
  12. 12.
    H. Mohrbach, A. Johner, I.M. Kulić, Phys. Rev. Lett. 105, 268102 (2010)ADSCrossRefGoogle Scholar
  13. 13.
    H. Mohrbach, A. Johner, I.M. Kulić, Eur. Biophys. J. 41, 217 (2012)CrossRefGoogle Scholar
  14. 14.
    C. Lu, M. Reedy, H.P. Erickson, J. Bacteriol. 182, 164 (2000)CrossRefGoogle Scholar
  15. 15.
    S.M. Ferguson, P. De Camilli, Nat. Rev. Mol. Cell Biol. 13, 75 (2012)Google Scholar
  16. 16.
    S. Asakura, G. Eguchi, T. Iino, J. Mol. Biol. 16, 302 (1966)CrossRefGoogle Scholar
  17. 17.
    A. Volodin et al., Phys. Rev. Lett. 84, 3342 (2000)ADSCrossRefGoogle Scholar
  18. 18.
    S.M. Douglas, J.J. Chou, W.M. Shih, Proc. Natl. Acad. Sci. U.S.A. 104, 6644 (2007)ADSCrossRefGoogle Scholar
  19. 19.
    G.M. Nam, N.K. Lee, H. Mohrbach, A. Johner, I.M. Kulić, EPL 100, 28001 (2012)ADSCrossRefGoogle Scholar
  20. 20.
    M. Nizette, A. Goriely, J. Math. Phys. 40, 2830 (1999)ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    O. Kahraman, H. Mohrbach, M.M. Müller, I.M. Kulić, Soft Matter 10, 2836 (2014)ADSCrossRefGoogle Scholar
  22. 22.
    N. Chouaieb, A. Goriely, J.H. Maddocks, Proc. Natl. Acad. Sci. U.S.A. 103, 9398 (2006)ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions, 9th edition (Dover, Mineola, NY, 1970)Google Scholar
  24. 24.
    R.S. Manning, SIAM Rev. 51, 193 (2009)ADSMathSciNetCrossRefGoogle Scholar
  25. 25.
    J.F. Currie, J.A. Krumhans, A.R. Bishof, S.E. Trullinger, Phys. Rev. B 22, 477 (1980)ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    P. Gosselin, H. Mohrbach, I.M. Kulić, F. Ziebert, Physica D 318-319, 105 (2016)ADSCrossRefGoogle Scholar
  27. 27.
    G. Domokos, P. Holmes, B. Royce, J. Nonlinear Sci. 7, 281 (1997)MathSciNetCrossRefGoogle Scholar
  28. 28.
    R.S. Manning, G.B. Bulman, Proc. R. Soc. London A: Math. Phys. Eng. Sci. 461, 2423 (2005)ADSMathSciNetCrossRefGoogle Scholar
  29. 29.
    B. Nöding, S. Köster, Phys. Rev. Lett. 108, 088101 (2012)ADSCrossRefGoogle Scholar
  30. 30.
    J.H. Maddocks, Arch. Ration. Mech. Anal. 99, 301 (1987)MathSciNetCrossRefGoogle Scholar
  31. 31.
    I.M. Kulić, H. Mohrbach, V. Lobaskin, R. Thaokar, H. Schiessel, Phys. Rev. E 72, 041905 (2005)ADSCrossRefGoogle Scholar
  32. 32.
    I.M. Kulić, H. Mohrbach, R. Thaokar, H. Schiessel, Phys. Rev. E 75, 011913 (2007)ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Lila Bouzar
    • 1
    • 2
  • Martin Michael Müller
    • 3
    • 4
  • Pierre Gosselin
    • 5
  • Igor M. Kulić
    • 4
  • Hervé Mohrbach
    • 3
    • 4
  1. 1.Département de Physique Théorique, Faculté de PhysiqueUSTHBAlgerAlgeria
  2. 2.Laboratoire de Physique et Chimie QuantiqueUniversité Mouloud MammeriTizi-OuzouAlgeria
  3. 3.Equipe BioPhysStat, ICPMB-FR CNRS 2843Université de LorraineMetzFrance
  4. 4.Institut Charles Sadron, CNRS-UdSStrasbourg cedex 2France
  5. 5.Institut Fourier, UMR 5582 CNRS-UJFUniversité Grenoble ISaint-Martin d’HèresFrance

Personalised recommendations