Bubble coalescence in breathing DNA: Two vicious walkers in opposite potentials

¹  Nano-Science Center, University of Copenhagen - Universitetsparken 5, 2100 Copenhagen, Denmark
²  Department of Condensed Matter Physics, Faculty of Mathematics and Physics, Charles University - Ke Karlovu 5, 121 16 Prague, Czech Republic
³  Mathematical Physics, Lund University - Box 118, 22100 Lund, Sweden
⁴  Nordic Institute for Theoretical Physics (NORDITA) - Blegdamsvej 17, 2100 Copenhagen, Denmark
⁵  Department of Chemistry, Massachusetts Institute of Technology - 77 Massachusetts Avenue, Cambridge, MA 02139, USA
⁶  Department of Mathematics, Technical University of Denmark - Bldg. 303S, Matematiktorvet, 2800 Kgs. Lyngby, Denmark
⁷  Physics Department, University of Ottawa - 150 Louis Pasteur, Ottawa, ON, K1N 6N5, Canada

Received: 27 October 2006
Accepted: 12 December 2006

Abstract

We investigate the coalescence of two DNA bubbles initially located at weak segments and separated by a more stable barrier region in a designed construct of double-stranded DNA. The characteristic time for bubble coalescence and the corresponding distribution are derived, as well as the distribution of coalescence positions along the barrier. Below the melting temperature, we find a Kramers-type barrier crossing behaviour, while at high temperatures, the bubble corners perform drift-diffusion towards coalescence. The results are obtained by mapping the bubble dynamics on the problem of two vicious walkers in opposite potentials.