  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 thousands 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 hundreds to a few thousands base
pairs are pretty close to the thermodynamic limit for the model we proposed.
The temperature interval where power laws 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.
