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Master equation approach to DNA breathing in heteropolymer DNA

Tobias Ambjörnsson1,*, Suman K. Banik2, Michael A. Lomholt1,†, and Ralf Metzler1,‡

  • 1NORDITA (Nordic Institute for Theoretical Physics), Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark
  • 2Department of Physics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061-0435, USA

  • *Present address: Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA. Electronic address: ambjorn@mit.edu
  • †Present address: Department of Physics, University of Ottawa, 150 Louis Pasteur, Ottawa, Ontario, Canada, K1N 6N5.
  • ‡Present address: Department of Physics, University of Ottawa, 150 Louis Pasteur, Ottawa, Ontario, Canada K1N 6N5. Electronic address: metz@nordita.dk
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Phys. Rev. E 75, 021908 – Published 16 February, 2007

DOI: https://doi.org/10.1103/PhysRevE.75.021908

Abstract

After crossing an initial barrier to break the first base-pair (bp) in double-stranded DNA, the disruption of further bps is characterized by free energies up to a few kBT. Thermal motion within the DNA double strand therefore causes the opening of intermittent single-stranded denaturation zones, the DNA bubbles. The unzipping and zipping dynamics of bps at the two zipper forks of a bubble, where the single strand of the denatured zone joins the still intact double strand, can be monitored by single molecule fluorescence or NMR methods. We here establish a dynamic description of this DNA breathing in a heteropolymer DNA with given sequence in terms of a master equation that governs the time evolution of the joint probability distribution for the bubble size and position along the sequence. The transfer coefficients are based on the Poland-Scheraga free energy model. We derive the autocorrelation function for the bubble dynamics and the associated relaxation time spectrum. In particular, we show how one can obtain the probability densities of individual bubble lifetimes and of the waiting times between successive bubble events from the master equation. A comparison to results of a stochastic Gillespie simulation shows excellent agreement.

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Outline

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Phys. Rev. E 75, 021908– Published 16 February, 2007
  • Received 19 October 2006

© 2007 American Physical Society

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