Geodesic
Bulk-mediated Surface Diffusion on a Cylinder in the Fast Exchange Limit
A. V. Chechkin1 ; I. M. Zaid2 ; M. A. Lomholt3 ; I. M. Sokolov4 ; R. Metzler5
1 Institute for Theoretical Physics NSC KIPT, Akademicheskaya st.1, 61108 Kharkov, Ukraine and Max-Planck Institute for Physics of Complex Systems, Nöthnitzer Str. 38, D-01187 Dresden, FRG
2 Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, United Kingdom
3 MEMPHYS - Center for Biomembrane Physics, Department of Physics, Chemistry, and Pharmacy, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
4 Institut für Physik, Humboldt Universität zu Berlin, Newtonstraße 15, D-12489 Berlin, FRG
5 Institute for Physics & Astronomy, University of Potsdam, D-14476 Potsdam-Golm, Germany and Department of Physics, Technical University of Tampere, FI-33101 Tampere, Finland
Mathematical modelling of natural phenomena, Tome 8 (2013) no. 2, pp. 114-126

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In various biological systems and small scale technological applications particles transiently bind to a cylindrical surface. Upon unbinding the particles diffuse in the vicinal bulk before rebinding to the surface. Such bulk-mediated excursions give rise to an effective surface translation, for which we here derive and discuss the dynamic equations, including additional surface diffusion. We discuss the time evolution of the number of surface-bound particles, the effective surface mean squared displacement, and the surface propagator. In particular, we observe sub- and superdiffusive regimes. A plateau of the surface mean-squared displacement reflects a stalling of the surface diffusion at longer times. Finally, the corresponding first passage problem for the cylindrical geometry is analysed.
DOI : 10.1051/mmnp/20138208

A. V. Chechkin 1 ; I. M. Zaid 2 ; M. A. Lomholt 3 ; I. M. Sokolov 4 ; R. Metzler 5

1 Institute for Theoretical Physics NSC KIPT, Akademicheskaya st.1, 61108 Kharkov, Ukraine and Max-Planck Institute for Physics of Complex Systems, Nöthnitzer Str. 38, D-01187 Dresden, FRG
2 Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, United Kingdom
3 MEMPHYS - Center for Biomembrane Physics, Department of Physics, Chemistry, and Pharmacy, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
4 Institut für Physik, Humboldt Universität zu Berlin, Newtonstraße 15, D-12489 Berlin, FRG
5 Institute for Physics & Astronomy, University of Potsdam, D-14476 Potsdam-Golm, Germany and Department of Physics, Technical University of Tampere, FI-33101 Tampere, Finland 
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     title = {Bulk-mediated {Surface} {Diffusion} on a {Cylinder} in the {Fast} {Exchange} {Limit}},
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A. V. Chechkin; I. M. Zaid; M. A. Lomholt; I. M. Sokolov; R. Metzler. Bulk-mediated Surface Diffusion on a Cylinder in the Fast Exchange Limit. Mathematical modelling of natural phenomena, Tome 8 (2013) no. 2, pp. 114-126. doi: 10.1051/mmnp/20138208

[1] O. V. Bychuk, B. O'Shaughnessy Phys. Rev. Lett. 1995 1795 1798

[2] O. V. Bychuk, B. O'Shaughnessy Langmuir 1994 3260 3267

[3] J. A. Revelli, C. E. Budde, D. Prato, H. S. Wio New J. Phys. 2005

[4] Yu. Georgievskii, E. S. Medvedev, A. A. Stuchebrukhov J. Chem. Phys. 2002 1692 Biophys. J. 2002 2833 2846 J. Math. Biol. 2006 209 239 J. Phys. Cond. Mat. 2011

[5] O. V. Bychuk, B. O'Shaugnessy J. Chem. Phys. 1994 772 780 Phys. Rev. E 1997 4371 4375

[6] G. Oshanin, M. Tamm, O. Vasilyev J. Chem. Phys. 2010

[7] O. Bénichou, D. Grebenkov, P. Levitz, C. Loverdo, R. Voituriez Phys. Rev. Lett. 2010 J. Stat. Phys. 2011 657 685

[8] M. E. Toimil-Molares, L. Roentsch, W. Sigle, K.-H. Heinig, C. Trautmann, R. Neumann Adv. Funct. Mater. 2012 695 701

[9] M. Coppey, O. Bénichou, J. Klafter, M. Moreau, G. Oshanin Phys. Rev. E 2004

[10] R. Kimmich, S. Stapf, P. Callaghan, A. Coy Magnet. Reson. Imaging 1994 339 343

[11] S. Stapf, R. Kimmich, R.-O. Seitter Phys. Rev. Lett. 1995 2855 2858

[12] P. Levitz, M. Zinsmeister, P. Davidson, D. Constantin, O. Poncelet Phys. Rev. E 2008

[13] M. V. Velosoa, A. G. Souza Filhoa, J. Mendes Filhoa, S. B. Faganb Chem. Phys. Lett. 2006 71 74

[14] P. H. Von Hippel, O. G. Berg J. Biol. Chem. 1989 675 678

[15] I. Bonnet, A. Biebricher, P.-L. Porté, C. Loverdo, O. Bénichou, R. Voituriez, C. Escudé, W. Wende, A. Pingoud, P. Desbiolles Nucl. Acids Res. 4118 2008 Biophys. J. 2005 895 902 Proc. Natl. Acad. Sci. USA 2008 15738 15742

[16] Y. M. Wang, R. H. Austin, E. C. Cox Phys. Rev. Lett. 2006

[17] C. Bustamante, Y. R. Chemla, N. R. Forde, D. Izhaky Ann. Rev. Biochem. 2004 705 748

[18] S. I. Coyne, N. H. Mendelson Infection and Immunity 1975 1189 1194

[19] A. V. Chechkin, I. M. Zaid, M. A. Lomholt, I. M. Sokolov, R. Metzler Phys. Rev. E 2009 J. Chem. Phys. 2011 Phys. Rev. E 2012

[20] M. A. Lomholt, I. M. Zaid, R. Metzler Phys. Rev. Lett. 2007 Biophys. J. 2009 710 721

[21] R. B. Winter, O. G. Berg, P. H. Von Hippel Biochem. 1981 6961 6977

[22] E. S. Medvedev, A. A. Stuchebrukhov FEBS Lett. 2013 345 349

[23] R. Metzler, J. Klafter Phys. Rep. 2000 1 77 J. Phys. A 2004 R161 R208

[24] A. V. Chechkin, V. Yu. Gonchar, J. Klafter, R. Metzler, L. V. Tanatarov J. Stat. Phys. 2004 1505 1535

[25] S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional Integrals and Derivatives, Theory and Applications. Gordon and Breach, New York, 1993.

[26] O. G. Berg, C. Blomberg Biophys. Chem. 1976 367 381

[27] S. Havlin, G. H. Weiss J. Stat. Phys. 1990 1267 1273

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