- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Dynamics of DNA breathing: Weak noise analysis, finite time singularity, and mapping onto the quantum Coulomb problem

Hans C. Fogedby*

Ralf Metzler†

  • Department of Physics and Astronomy, University of Aarhus, Ny Munkegade, 8000, Aarhus C, Denmark and Niels Bohr Institute for Astronomy, Physics, and Geophysics, Blegdamsvej 17, 2100, Copenhagen Ø, Denmark

  • Physik Department, Technical University of Munich, 85748 Garching, Germany

  • *fogedby@phys.au.dk
  • †metz@ph.tum.de
PDF

Phys. Rev. E 76, 061915 – Published 21 December, 2007

DOI: https://doi.org/10.1103/PhysRevE.76.061915

Abstract

We study the dynamics of denaturation bubbles in double-stranded DNA on the basis of the Poland-Scheraga model. We show that long time distributions for the survival of DNA bubbles and the size autocorrelation function can be derived from an asymptotic weak noise approach. In particular, below the melting temperature the bubble closure corresponds to a noisy finite time singularity. We demonstrate that the associated Fokker-Planck equation is equivalent to a quantum Coulomb problem. Below the melting temperature, the bubble lifetime is associated with the continuum of scattering states of the repulsive Coulomb potential; at the melting temperature, the Coulomb potential vanishes and the underlying first exit dynamics exhibits a long time power law tail; above the melting temperature, corresponding to an attractive Coulomb potential, the long time dynamics is controlled by the lowest bound state. Correlations and finite size effects are discussed.

View figure in article

Article Text

References (40)

  1. A. Kornberg, DNA Synthesis (W. H. Freeman, San Francisco, 1974).
  2. J. D. Watson and F. H. C. Crick, Cold Spring Harb. Symp. Quant. Biol. 18, 123 (1953).
  3. D. Poland and H. A. Scheraga, Theory of Helix-Coil Transitions in Biopolymers (Academic Press, New York, 1970).
  4. M. Guéron, M. Kochoyan, and J. L. Leroy, Nature (London) 328, 89 (1987).
  5. G. Altan-Bonnet, A. Libchaber, and O. Krichevsky, Phys. Rev. Lett. 90, 138101 (2003).
  6. A. Krueger, E. Protozanova, and M. D. Frank-Kamenetskii, Biophys. J. 90, 3091 (2006).
  7. M. D. Frank-Kamenetskii, Nature (London) 328, 17 (1987).
  8. M. Peyrard and A. R. Bishop, Phys. Rev. Lett. 62, 2755 (1989).
  9. T. Dauxois, M. Peyrard, and A. R. Bishop, Phys. Rev. E 47, R44 (1993).
  10. T. Hwa, E. Marinari, K. Sneppen, and L. H. Tang, Proc. Natl. Acad. Sci. U.S.A. 100, 4411 (2003).
  11. A. Hanke and R. Metzler, J. Phys. A 36, L473 (2003).
  12. S. K. Banik, T. Ambjörnsson, and R. Metzler, Europhys. Lett. 71, 852 (2005).
  13. T. Ambjörnsson and R. Metzler, Phys. Rev. E 72, 030901(R) (2005).
  14. T. Ambjörnsson, S. K. Banik, O. Krichevsky, and R. Metzler, Phys. Rev. Lett. 97, 128105 (2006).
  15. T. Ambjörnsson, S. K. Banik, O. Krichevsky, and R. Metzler, Biophys. J. 92, 2674 (2007).
  16. T. Ambjörnsson, S. K. Banik, O. Krichevsky, and R. Metzler, Phys. Rev. E 75, 021908 (2007).
  17. D. J. Bicout and E. Kats, Phys. Rev. E 70, 010902(R) (2004).
  18. T. Novotny, J. N. Pedersen, T. Ambjörnsson, M. S. Hansen, and R. Metzler, Europhys. Lett. 77, 48001 (2007).
  19. H. C. Fogedby, Phys. Rev. E 59, 5065 (1999).
  20. H. C. Fogedby, Phys. Rev. E 68, 026132 (2003).
  21. H. C. Fogedby and R. Metzler, Phys. Rev. Lett. 98, 070601 (2007).
  22. R. Metzler, T. Ambjörnsson, A. Hanke, Y. Zhang, and S. Levene, J. Comput. Theor. Nanosci. 4, 1 (2007).
  23. R. M. Wartell and A. S. Benight, Phys. Rep. 126, 67 (1985).
  24. D. Poland and H. A. Scheraga, J. Chem. Phys. 45, 1456 (1966).
  25. J. SantaLucia, Jr., Proc. Natl. Acad. Sci. U.S.A. 95, 1460 (1998).
  26. R. D. Blake, J. W. Bizarro, J. D. Blake, G. R. Day, S. G. Delcourt, J. Knowles, K. A. Marx, and J. SantaLucia, Jr., Bioinformatics 15, 370 (1999).
  27. C. Richard and A. J. Guttmann, J. Stat. Phys. 115, 925 (2004).
  28. E. Carlon, E. Orlandini, and A. L. Stella, Phys. Rev. Lett. 88, 198101 (2002).
  29. A. Bar, Y. Kafri, and D. Mukamel, Phys. Rev. Lett. 98, 038103 (2007).
  30. Y. Kafri, D. Mukamel, and L. Peliti, Phys. Rev. Lett. 85, 4988 (2000).
  31. Y. Kafri, D. Mukamel, and L. Peliti, Eur. Phys. J. B 27, 135 (2002).
  32. T. Garel, C. Monthus, and H. Orland, Europhys. Lett. 55, 132 (2001).
  33. H. Risken, The Fokker-Planck Equation (Springer-Verlag, Berlin, 1989).
  34. S. Redner, A Guide to First-Passage Processes (Cambridge University Press, Cambridge, England, 2001).
  35. R. Graham and T. Tél, J. Stat. Phys. 35, 729 (1984).
  36. H. C. Fogedby and V. Poutkaradze, Phys. Rev. E 66, 021103 (2002).
  37. N. N. Lebedev, Special Functions and Their Applications (Dover, New York, 1972).
  38. L. Landau and E. Lifshitz, Quantum Mechanics (Pergamon Press, Oxford, 1959).
  39. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals. Series, and Products (Academic Press, New York, 1965).
  40. G. Bonnet, O. Krichevsky, and A. Libchaber, Proc. Natl. Acad. Sci. U.S.A. 95, 8602 (1998).

Outline

Information

Phys. Rev. E 76, 061915– Published 21 December, 2007
  • Received 29 June 2007

© 2007 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation