Mean bubble formation time in DNA denaturation

Using the Poland-Scheraga free energy of the bubble size in a double-stranded DNA we propose a discrete stochastic dynamics for the number of base pairs N of an unzipped bubble. We derive a universal subdiffusive growth T_NA/(b+2)N^1+b for the mean formation time (MBFT) T_N of a bubble of size N. The amplitude A is determined by the bubble initiation rate and time spent in the denaturated state. We examine critically the significance of these results for experiments. We find: i) Our results provide a new method to determine whether the order of the denaturation transition is discontinuous (b>2) or not. ii) The asymptotic growth law of T_N is reached with 10% precision already for small bubbles of sizes >20. However, the amplitude is very sensitive to modeling details for small bubbles. iii) In an equilibrium sample of bubbles up to size N the averaged MBFT grows diffusively, T_N*N², irrespective of b. ©2011