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Polymer translocation across an oscillating nanopore: study of several distribution functions of relevant Brownian functionals

Brownian functionals of polymer translocation across oscillating nanopore
  • Ashutosh Dubey
  • Malay BandyopadhyayEmail author
Regular Article
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Abstract

In this paper, we study polymer translocation dynamics across an oscillating nanopore by proposing and inspecting several probability distribution functions (PDFs) of relevant Brownian functionals which specify the translocation across the nanopore. We model such translocation process by an overdamped Langevin equation of collective variable x. We introduce several probability distribution functions (PDFs) to identify the translocation process. We consider elegant backward Fokker-Planck method to derive analytically closed form expressions of several PDFs associated with such stochastic process. For instance, an important quantity for translocation processes is the first passage time, i.e. the time the molecule takes to cross the nanopore with initial collective value of the molecule x0. We derive analytical expressions for: (i) the PDF P(tf|x0) of the first passage time tf which specify the lifetime of protein translocation process, (ii) the PDF P(A|x0) of the area A till the first passage time and it provides us numerous valuable information about the average size and reactivity of the process, and (iii) the PDF P(M) associated with the maximum value of collective mode, M, of the translocation process before the first passage time. Our analysis is limited to a regime where both drift and diffusion have the same periodic time dependence with a constant ratio between them. We further confirm our analytical predictions by computing the same PDFs with direct numerical simulations of the corresponding Langevin equation. We obtain a very good agreement of our theoretical predictions with the numerically simulated results. Finally, several nontrivial scaling behaviour in the asymptotic limits for the above mentioned PDFs are predicted, which can be verified further from experimental observation.

Graphical abstract

Keywords

Statistical and Nonlinear Physics 

References

  1. 1.
    F. Cecconi, M.A. Shahzad, U.M.B. Marconi, A. Vulpiani, Phys. Chem. Chem. Phys. 19, 11260 (2017) CrossRefGoogle Scholar
  2. 2.
    R. Maillard, G. Chistol, M. Sen, M. Righini, J. Tan, C.M. Kaiser, C. Hodges, A. Martin, C. Bustamante, Cell 145, 459 (2011) CrossRefGoogle Scholar
  3. 3.
    T. Menais, S. Mossa, A. Buhot, Sci. Rep. 6, 38558 (2016) ADSCrossRefGoogle Scholar
  4. 4.
    K. Briggs, G. Madejski, M. Magill, K. Kastritis, H.W. de Haan, J.L. McGrath, V. Tabard-Coss, Nano Lett. 18, 660 (2018) ADSCrossRefGoogle Scholar
  5. 5.
    J.A. Cohen, A. Chaudhuri, R. Golestanian, J. Chem. Phys. 137, 204911 (2012) ADSCrossRefGoogle Scholar
  6. 6.
    J.A. Cohen, A. Chaudhuri, R. Golestanian, Phys. Rev. Lett. 107, 238102 (2011) ADSCrossRefGoogle Scholar
  7. 7.
    J. Wang, Y. Wang, K. Luo, J. Chem. Phys. 142, 084901 (2015) ADSCrossRefGoogle Scholar
  8. 8.
    T. Ikonen, J. Shin, W. Sung, T. Ala-Nissila, J. Chem. Phys. 136, 205104 (2012) ADSCrossRefGoogle Scholar
  9. 9.
    J. Sarabadani, T. Ikonen, T. Ala-Nissila, J. Chem. Phys. 143, 074905 (2015) ADSCrossRefGoogle Scholar
  10. 10.
    A. Fiasconaro, J.J. Mazo, F. Falo, Phys. Rev. E 91, 022113 (2015) ADSCrossRefGoogle Scholar
  11. 11.
    A. Meller, J. Phys.: Condens. Matter 15, R581 (203) Google Scholar
  12. 12.
    A. Milchev, J. Phys.: Condens. Matter 23, 103101 (2011) ADSGoogle Scholar
  13. 13.
    Z. Zhang, H. Chen, Z. Hou, J. Chem. Phys. 137, 044904 (2012) ADSCrossRefGoogle Scholar
  14. 14.
    D. Huh, K. Mills, X. Zhu, M.A. Burns, M.D. Thouless, S. Takayama, Nat. Mater. 6, 424 (2007) ADSCrossRefGoogle Scholar
  15. 15.
    P. Fanzio, C. Manneschi, E. Angeli, V. Mussi, G. Firpo, L. Ceseracciu, L. Repetto, U. Valbusa, Sci. Rep. 2, 791 (2012) ADSCrossRefGoogle Scholar
  16. 16.
    D. Fologea, J. Uplinger, B. Thomas, D.S. McNabb, J. Li, Nano Lett. 5, 1734 (2005) ADSCrossRefGoogle Scholar
  17. 17.
    I. Hulea, A. Pronin, H. Brom, Appl. Phys. Lett. 86, 252107 (2005) ADSCrossRefGoogle Scholar
  18. 18.
    C.C. Harrell, Y. Choi, L.P. Horne, L.A. Baker, Z.S. Siwy, C.R. Martin, Langmuir 22, 10837 (2006) CrossRefGoogle Scholar
  19. 19.
    Polymers in Confined Geometries, edited by S. Granick (Spring, 1999), Vol. 138 Google Scholar
  20. 20.
    M. Muthukumar,Polymer Translocation (CRC Press, Florida, 2011) Google Scholar
  21. 21.
    X. Shi, R.W. Hammond, M.D. Morris, Anal. Chem. 67, 3219 (1995) CrossRefGoogle Scholar
  22. 22.
    S.N. Majumdar, Curr. Sci. 89, 2076 (2005) Google Scholar
  23. 23.
    J. Randon-Furling, S.N. Majumdar, J. Stat. Mech.: Theory Exp. 2007, P10008 (2007) CrossRefGoogle Scholar
  24. 24.
    E. Urdapilleta, Phys. Rev. E 83, 021102 (2011) ADSCrossRefGoogle Scholar
  25. 25.
    J. Benda, L. Maler, A. Longtin, J. Neurophysiol. 104, 2806 (2010) CrossRefGoogle Scholar
  26. 26.
    B. Lindner, A. Longtin, J. Theor. Biol. 232, 505 (2005) CrossRefGoogle Scholar
  27. 27.
    S. Kumar, G. Mishra, Phys. Rev. Lett. 110, 258102 (2013) ADSCrossRefGoogle Scholar
  28. 28.
    S. Kumar, R. Kumar, W. Janke, Phys. Rev. E 93, 010402(R) (2016) ADSCrossRefGoogle Scholar
  29. 29.
    B.S. Alexandrov, V. Gelev, A.R. Bishop, A. Usheva, K.Ø. Rasmussen, Phys. Lett. A 374, 1214 (2010) ADSCrossRefGoogle Scholar
  30. 30.
    E.S. Swanson, Phys. Rev. E 83, 040901(R) (2011) ADSCrossRefGoogle Scholar
  31. 31.
    A. Molini, P. Talkner, G.G. Katul, A. Porporatoa, Physica A 390, 1841 (2011) ADSMathSciNetCrossRefGoogle Scholar
  32. 32.
    A. Dubey, M. Bandyopadhyay, Eur. Phys. J. B 91, 276 (2018) ADSCrossRefGoogle Scholar
  33. 33.
    A. Dubey, M. Bandyopadhyay, AIP Conf. Proc. 1942, 04001 (2018) Google Scholar
  34. 34.
    A. Dubey, M. Bandyopadhyay, AIP Conf. Proc. 2100, 020065 (2019) CrossRefGoogle Scholar
  35. 35.
    M. Bandyopadhyay, S. Gupta, D. Segal, Phys. Rev. E 83, 031905 (2011) ADSCrossRefGoogle Scholar
  36. 36.
    M. Kac, Trans. Am. Math. Soc. 65, 1 (1949) CrossRefGoogle Scholar
  37. 37.
    S.N. Majumdar, M.J. Kearney, Phys. Rev. E 76, 031130 (2007) ADSCrossRefGoogle Scholar
  38. 38.
    P.L. Krapivsky, S.N. Majumdar, A. Rosso, J. Phys. A 43, 315001 (2010) ADSMathSciNetCrossRefGoogle Scholar
  39. 39.
    A. Hanke, R. Metzler, J. Phys. A 36, L473 (2003) ADSCrossRefGoogle Scholar
  40. 40.
    A. Bar, Y. Kafri, D. Mukamel, Phys.: Rev. Lett. 98, 038103 (2007) ADSGoogle Scholar
  41. 41.
    A. Bar, Y. Kafri, D. Mukamel, J. Phys. Condens. Matter 21, 034110 (2009) CrossRefGoogle Scholar
  42. 42.
    W. Sung, P.J. Park, Phys. Rev. Lett. 77, 783 (1996) ADSCrossRefGoogle Scholar
  43. 43.
    J.M. Polson, A.C. McCaffrey, J. Chem. Phys. 138, 174902 (2013) ADSCrossRefGoogle Scholar
  44. 44.
    F. Cecconi, M. Bacci, M. Chinappi, Protein Pept. Lett. 21, 8665 (2014) CrossRefGoogle Scholar
  45. 45.
    H. Risken,The Fokker-Planck Equation: Methods of Solutions and Applications, 2nd edn. (Springer-Verlag, Berlin, 1989) Google Scholar
  46. 46.
    C.W. Gardiner,Handbook of Stochastic Methods: For Physics, Chemistry and the Natural Sciences, 2nd edn. (Springer-Verlag, Berlin, 1985) Google Scholar
  47. 47.
    N.G. van Kampen,Stochastic Processes in Physics and Chemistry (North-, Amsterdam, 2007) Google Scholar
  48. 48.
    O. Krichevsky, G. Bonnet, Rep. Prog. Phys. 65, 251 (2002) ADSCrossRefGoogle Scholar
  49. 49.
    G. Altan-Bonnet, A. Libchaber, O. Krichevsky, Phys. Rev. Lett. 90, 138101 (2003) ADSCrossRefGoogle Scholar
  50. 50.
    A.C. Branka, D.M. Heyes, Phys. Rev. E 58, 2611 (1998) ADSCrossRefGoogle Scholar
  51. 51.
    A. Meller, J. Phys.: Condens. Matter 15, R581 (2003) ADSGoogle Scholar
  52. 52.
    A. Meller, L. Nivon, D. Branton, Phys. Rev. Lett. 86, 3435 (2001) ADSCrossRefGoogle Scholar
  53. 53.
    S. Redner,A guide to first-passage processes (Cambridge University Press, Cambridge, UK, 2001) Google Scholar

Copyright information

© EDP Sciences / Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Basic Sciences, Indian Institue of Technology BhubaneswarBhubaneswarIndia

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