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Drift and diffusion of a confined semiflexible chain

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Abstract.

We study the transverse and longitudinal linear response function of rigid chains subjected to an external force. Our main concern are stiff polymers confined in narrow pores with diameter less than their persistence length. We explicitly consider confinement in a transverse harmonic potential and generalize results by scaling arguments. Our results describe the drift of the filament under an external force, time evolution of the filament shape, and filament diffusion. Diffusion of a confined filament resembles the celebrated reptation process for flexible chains, albeit with distinct kinetic exponents. The limiting case of stiff free filaments is also mentioned.

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References

  1. M.E. Jason, M. Dogterom, Biophys. J. 87, 2723 (2004)

    Article  ADS  Google Scholar 

  2. T. Sanchez, I.M. Kulić, Z. Dogic, Phys. Rev. Lett. 104, 098103 (2010)

    Article  ADS  Google Scholar 

  3. K.M. Tautel, F. Pampaloni, E. Frey, E.-L. Florin, Phys. Rev. Lett. 100, 028102 (2008)

    Article  ADS  Google Scholar 

  4. R. Granek, J. Phys. II 7, 1761 (1997)

    Article  Google Scholar 

  5. D. Morse, Macromolecules 31, 7030 (1998)

    Article  ADS  Google Scholar 

  6. D. Morse, Macromolecules 31, 7044 (1998)

    Article  ADS  Google Scholar 

  7. R. Evaraers, F. Jülicher, A. Ajdari, A.C. Maggs, Phys. Rev. Lett. 82, 3717 (1999)

    Article  ADS  Google Scholar 

  8. U. Seifert, W. Wintz, P. Nelson, Phys. Rev. Lett. 77, 5389 (1996)

    Article  ADS  Google Scholar 

  9. G. Nam, N.-K. Lee, J. Chem. Phys. 126, 164902 (2006)

    Article  ADS  Google Scholar 

  10. O. Hallatschek, E. Frey, K. Kroy, Phys. Rev. Lett. 94, 077804 (2005)

    Article  ADS  Google Scholar 

  11. C.P. Brangwynne, G.H. Koenderink, E. Barry, Z. Doric, F.C. MacKintosh, D.A. Weitz, Biophys. J. 93, 346 (2007)

    Article  ADS  Google Scholar 

  12. M.C. Choi et al., Macromolecules 38, 9882 (2005)

    Article  ADS  Google Scholar 

  13. Y.-L. Chen, M.D. Graham, J.J. de Pablo, G.C. Randall, M. Gupta, P.S. Doyle, Phys. Rev. E 70, 060901(R) (2004)

    ADS  Google Scholar 

  14. D.J. Bonthuis, C. Meyer, D. Stein, C. Dekker, Phys. Rev. Lett. 101, 108303 (2008)

    Article  ADS  Google Scholar 

  15. T. Odijk, Phys. Rev. E 77, 060901(R) (2008)

    Article  ADS  Google Scholar 

  16. E. Farge, A.C. Maggs, Macromolecules 26, 5041 (1993)

    Article  ADS  Google Scholar 

  17. G. Nam, N.-K. Lee, A. Johner, to be published in J. Chem. Phys. (2010)

  18. When hydrodynamic interactions are taken into account, the frictional coefficients per unit length, $\zeta_{\parallel}$ and $\zeta_{\perp}$, are similar to those for a rod and carry logarithmic corrections in free space, $\zeta_{\parallel} = 2\pi\eta_s/\log(S/b)$, $\zeta_{\perp} \approx 4\pi\eta_s/\log(S/b)$, with $\eta_s$ being the solvent viscosity and $b$ the chain thickness. In our case of fluctuating filaments, the upper cut-off length $S$ is replaced with the longitudinal/transverse dynamic correlation length, respectively. For confined filaments the details of hydrodynamic boundary conditions matter

  19. B. Obermayer, O. Hallatschek, Phys. Rev. Lett. 99, 098302 (2007)

    Article  ADS  Google Scholar 

  20. In principle, the expectation value can be always measured provided that enough statistics is accumulated

  21. T.B. Liverpool, A.C. Maggs, Macromolecules 34, 6064 (2001)

    Article  ADS  Google Scholar 

  22. I. Nyrkova, A.N. Semenov, Phys. Rev. E 76, 011802 (2007)

    Article  ADS  Google Scholar 

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Correspondence to N. -K. Lee.

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Nam, G., Johner, A. & Lee, N.K. Drift and diffusion of a confined semiflexible chain. Eur. Phys. J. E 32, 119–126 (2010). https://doi.org/10.1140/epje/i2010-10624-1

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  • DOI: https://doi.org/10.1140/epje/i2010-10624-1

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