  We investigate the coalescence of two DNA-bubbles initially located at weak
domains and separated by a more stable barrier region in a designed construct
of double-stranded DNA. In a continuum Fokker-Planck approach, 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
behavior, while at high temperatures, the bubble corners perform
drift-diffusion towards coalescence. In the calculations, we map the bubble
dynamics on the problem of two vicious walkers in opposite potentials. We also
present a discrete master equation approach to the bubble coalescence problem.
Numerical evaluation and stochastic simulation of the master equation show
excellent agreement with the results from the continuum approach. Given that
the coalesced state is thermodynamically stabilized against a state where only
one or a few base pairs of the barrier region are re-established, it appears
likely that this type of setup could be useful for the quantitative
investigation of thermodynamic DNA stability data as well as the rate constants
involved in the unzipping and zipping dynamics of DNA, in single molecule
fluorescence experiments.
