The European Physical Journal E

, Volume 23, Issue 4, pp 375–388 | Cite as

Stretching dynamics of semiflexible polymers

Regular Article

Abstract.

We analyze the nonequilibrium dynamics of single inextensible semiflexible biopolymers as stretching forces are applied at the ends. Based on different (contradicting) heuristic arguments, various scaling laws have been proposed for the propagation speed of the backbone tension which is induced in response to stretching. Here, we employ a newly developed unified theory to systematically substantiate, restrict, and extend these approaches. Introducing the practically relevant scenario of a chain equilibrated under some prestretching force f pre that is suddenly exposed to a different external force f ext at the ends, we give a concise physical explanation of the underlying relaxation processes by means of an intuitive blob picture. We discuss the corresponding intermediate asymptotics, derive results for experimentally relevant observables, and support our conclusions by numerical solutions of the coarse-grained equations of motion for the tension.

PACS.

61.41.+e Polymers, elastomers, and plastics 87.15.La Biological and medical physics: Mechanical properties 87.15.He Dynamics and conformational changes 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A.R. Bausch, K. Kroy, Nat. Phys. 2, 231 (2006).CrossRefGoogle Scholar
  2. 2.
    M.L. Gardel, Proc. Natl. Acad. Sci. U.S.A. 103, 1762 (2006).CrossRefADSGoogle Scholar
  3. 3.
    R. Granek, J. Phys. I 7, 1761 (1997).CrossRefGoogle Scholar
  4. 4.
    N. Rosenblatt, Phys. Rev. Lett. 97, 168101 (2006).CrossRefADSGoogle Scholar
  5. 5.
    D. Mizuno, C. Tardin, C.F. Schmidt, F.C. MacKintosh, Science 315, 370 (2007).CrossRefADSGoogle Scholar
  6. 6.
    C. Bustamante, Z. Bryant, S.B. Smith, Nature 421, 423 (2003).CrossRefADSGoogle Scholar
  7. 7.
    J.-C. Meiners, S.R. Quake, Phys. Rev. Lett. 84, 5014 (2000).CrossRefADSGoogle Scholar
  8. 8.
    D. Lumma, S. Keller, T. Vilgis, J.O. Rädler, Phys. Rev. Lett. 90, 218301 (2003).CrossRefADSGoogle Scholar
  9. 9.
    R.E. Goldstein, S.A. Langer, Phys. Rev. Lett. 75, 1094 (1995).CrossRefADSGoogle Scholar
  10. 10.
    N.-K. Lee, D. Thirumalai, Biophys. J. 86, 2641 (2004).CrossRefADSGoogle Scholar
  11. 11.
    Y. Bohbot-Raviv, Phys. Rev. Lett. 92, 098101 (2004).CrossRefADSGoogle Scholar
  12. 12.
    T.B. Liverpool, Phys. Rev. E 72, 021805 (2005).CrossRefADSMathSciNetGoogle Scholar
  13. 13.
    U. Seifert, W. Wintz, P. Nelson, Phys. Rev. Lett. 77, 5389 (1996).CrossRefADSGoogle Scholar
  14. 14.
    A. Ajdari, F. Jülicher, A. Maggs, J. Phys. I 7, 823 (1997).CrossRefGoogle Scholar
  15. 15.
    R. Everaers, F. Jülicher, A. Ajdari, A.C. Maggs, Phys. Rev. Lett. 82, 3717 (1999).CrossRefADSGoogle Scholar
  16. 16.
    F. Brochard-Wyart, A. Buguin, P.G. de Gennes, Europhys. Lett. 47, 171 (1999).CrossRefADSGoogle Scholar
  17. 17.
    S. Manneville, Europhys. Lett. 36, 413 (1996).CrossRefADSGoogle Scholar
  18. 18.
    B. Maier, U. Seifert, J.O. Rädler, Europhys. Lett. 60, 622 (2002).CrossRefADSGoogle Scholar
  19. 19.
    O. Hallatschek, E. Frey, K. Kroy, Phys. Rev. Lett. 94, 077804 (2005).CrossRefADSGoogle Scholar
  20. 20.
    P.G. de Gennes, P. Pincus, R.M. Velasco, F. Brochard, J. Phys. (Paris) 37, 1461 (1976).Google Scholar
  21. 21.
    N. Saitô, K. Takahashi, Y. Yunoki, J. Phys. Soc. Jpn. 22, 219 (1967).CrossRefADSGoogle Scholar
  22. 22.
    P.A. Wiggins, Nat. Nanotechnol. 1, 137 (2006).CrossRefADSGoogle Scholar
  23. 23.
    A.K. Mazur, Phys. Rev. Lett. 98, 218102 (2007).CrossRefADSGoogle Scholar
  24. 24.
    J. Kierfeld, O. Niamploy, V. Sa-yakanit, R. Lipowsky, Eur. Phys. J. E 14, 17 (2004).CrossRefGoogle Scholar
  25. 25.
    O. Hallatschek, E. Frey, K. Kroy, Phys. Rev. E 75, 031905 (2007).CrossRefADSMathSciNetGoogle Scholar
  26. 26.
    F.C. MacKintosh, J. Käs, P.A. Janmey, Phys. Rev. Lett. 75, 4425 (1995).CrossRefADSGoogle Scholar
  27. 27.
    O. Hallatschek, E. Frey, K. Kroy, Phys. Rev. E 75, 031906 (2007).CrossRefADSMathSciNetGoogle Scholar
  28. 28.
    J.E. Dennis, R.B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Prentice-Hall, Englewood Cliffs, 1983).Google Scholar
  29. 29.
    M.J.D. Powell, in Numerical Methods for Nonlinear Algebraic Equations, edited by P. Rabinowitz (Gordon and Breach, London, 1970) Chapt. 6, p. 87.Google Scholar
  30. 30.
    U. Nowak, L. Weimann, Technical Report No. TR-91-10, Konrad-Zuse-Zentrum für Informationstechnik, Berlin (1991).Google Scholar
  31. 31.
    V. Pereyra, Numer. Math. 8, 376 (1966).MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© EDP Sciences, Società Italiana di Fisica and Springer-Verlag 2007

Authors and Affiliations

  • B. Obermayer
    • 1
  • O. Hallatschek
    • 2
  • E. Frey
    • 1
  • K. Kroy
    • 3
  1. 1.Arnold Sommerfeld Center and Center for NanoScienceLMU MünchenMünchenGermany
  2. 2.Lyman Laboratory of PhysicsHarvard UniversityCambridgeUSA
  3. 3.Institut für Theoretische PhysikUniversität LeipzigLeipzigGermany

Personalised recommendations