  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 between less than one to a few kT. This causes the opening of
intermittent single-stranded bubbles. Their unzipping and zipping dynamics can
be monitored by single molecule fluorescence or NMR methods. We here establish
a dynamic description of this DNA-breathing in a heteropolymer DNA 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.
