  The thermodynamical properties of heterogeneous DNA sequences are computed by
path integral techniques applied to a nonlinear model Hamiltonian. The base
pairs relative displacements are interpreted as time dependent paths whose
amplitudes are consistent with the model potential for the hydrogen bonds
between complementary strands. The portion of configuration space contributing
to the partition function is determined, at any temperature, by selecting the
ensemble of paths which fulfill the second law of thermodynamics. For a short
DNA fragment, the denaturation is signaled by a succession of peaks in the
specific heat plots while the entropy grows continuously versus $T$. Thus, the
opening of the double strand with bubble formation appears as a smooth
crossover due to base pair fluctuation effects which are accounted for by the
path integral method. The multistep transition is driven by the AT-rich regions
of the DNA fragment. The base pairs path ensemble shows an enhanced degree of
cooperativity at about the same temperatures for which the specific heat peaks
occur. These findings establish a link between microscopic and macroscopic
signatures of the transition. The fractions of mean base pair stretchings are
computed by varying the AT base pairs content and taking some threshold values
for the occurrence of the molecule denaturation.
