Localization of denaturation bubbles in random DNA sequences

We study the thermodynamic and dynamic behaviors of twist-induced denaturation bubbles in a long, stretched random sequence of DNA. The small bubbles associated with weak twist are delocalized. Above a threshold torque, the bubbles of several tens of bases or larger become preferentially localized to AT-rich segments. In the localized regime, the bubbles exhibit "aging" and move around subdiffusively with continuously varying dynamic exponents. These properties are derived by using results of large-deviation theory together with scaling arguments and are verified by Monte Carlo simulations.