Statistical physics of the melting of inhomogeneous DNA

We studied how the inhomogeneity of a sequence affects the phase transition that takes place at DNA melting. Unlike previous works, which considered thermodynamic quantities averaged over many different inhomogeneous sequences, we focused on precise sequences and investigated the succession of local openings that lead to their dissociation. For this purpose, we performed transfer-integral-type calculations with two different dynamical models: namely, the heterogeneous Dauxois-Peyrard-Bishop model and the model based on finite stacking enthalpies we recently proposed. It appears that, for both models, the essential effect of heterogeneity is to let different portions of the investigated sequences open at slightly different temperatures. Besides this macroscopic effect, the local aperture of each portion indeed turns out to be very similar to that of a homogeneous sequence with the same length. Rounding of each local opening transition is therefore merely a size effect. For the Dauxois-Peyrard-Bishop model, sequences with a few thousand base pairs are still far from the thermodynamic limit, so that it is inappropriate, for this model, to discuss the order of the transition associated with each local opening. In contrast, sequences with several hundred to a few thousand base pairs are pretty close to the thermodynamic limit for the model we proposed. The temperature interval where a power law holds is consequently broad enough to enable the estimation of critical exponents. On the basis of the few examples we investigated, it seems that, for our model, disorder does not necessarily induce a decrease of the order of the transition.