Slow closure of denaturation bubbles in DNA: twist matters

The closure of long equilibrated denaturation bubbles in DNA is studied using Brownian dynamics simulations. A minimal mesoscopic model is used where the double-helix is made of two interacting bead-spring freely rotating strands, with a non-zero torsional modulus in the duplex state, $\kappa_\phi=$200 to 300 kT. For DNAs of lengths N=40 to 100 base-pairs (bps) with a large initial bubble in their middle, long closure times of 0.1 to 100 microseconds are found. The bubble starts winding from both ends until it reaches a 10 bp metastable state. The final closure is limited by three competing mechanisms depending on $\kappa_\phi$ and N: arms diffusion until their alignment, bubble diffusion along the DNA until one end is reached, or local Kramers process (crossing over a torsional energy barrier). For clamped ends or long DNAs, the closure occurs via this latter temperature activated mechanism, yielding for the first time a good quantitative agreement with experiments.