Strand diffusion-limited closure of denaturation bubbles in DNA

The closure dynamics of a pre-equilibrated DNA denaturation bubble is studied using both Brownian dynamics simulations and an analytical approach. The numerical model consists of two semi-flexible interacting single strands (ssDNA) and a bending modulus which depends on the base-pair state, with double-strand DNA (dsDNA) segments being 50 times stiffer than ssDNA ones. For DNA lengths from N=20 to 100 base-pairs (bp) and initial bubble sizes of N-6 bp, long closure times of 0.1 to 4 microseconds are found, following a scaling law in N^2.4. The bubble starts to close by a fast zipping which stops when the bubble reaches a highly bent metastable state of length around 10 bp. The limiting final step to complete closure is controlled by the dsDNA "arms" rotational diffusion, with closure occurring once they are nearly aligned. The central role of chain bending, which cannot be accounted for in one-dimensional models, is thus illuminated.