Bubble Relaxation Dynamics in Double-Stranded DNA

The paper deals with the two-state (opening-closing of base pairs) model used to describe the fluctuation dynamics of a single bubble formation. We present an exact solution for the discrete and finite size version of the model that includes end effects and derive analytic expressions of the correlation function, survival probability and lifetimes for the bubble relaxation dynamics. It is shown that the continuous and semi-infinite limit of the model becomes a good approximation to exact result when a^N << 1, where N is bubble size and a, the ratio of opening to closing rates of base pairs, is the control parameter of DNA melting.