The time duration for DNA thermal denaturation

Motivated by the thermal denaturation of DNA, we consider two interacting three-dimensional macromolecular chains, bound to each other, in a medium at thermal equilibrium from about room temperature up to about the melting one (T-m), at which they become unbound. We outline models for the non-equilibrium evolution of the double-stranded system, based upon the Smoluchowski equation, and allow for heterogeneities, excluded-volume effects and hydrodynamic interactions. A moment method leads us to approximate the Smoluchowski equation by a one-dimensional differential equation for the lowest order moment, containing a global effective potential between the two strands. We concentrate on the time duration (tau) required for thermal denaturation to occur, for long times and temperature T similar or equal to T-m. Here tau is approximated by the so-called mean first passage time (MFPT) for the relative separation of the centres of mass of the two chains. An approximate formula for the MFPT is obtained and employed for estimates. The consistency of the MFPT with experimental results is discussed for both Rouse and Zimm regimes.