  The denaturation of the double helix is a template for fundamental biological
functions such as replication and transcription involving the formation of
local fluctuational openings. The denaturation transition is studied for
heterogeneous short sequences of DNA, i.e. $\sim 100$ base pairs, in the
framework of a mesoscopic Hamiltonian model which accounts for the helicoidal
geometry of the molecule. The theoretical background for the application of the
path integral formalism to predictive analysis of the molecule thermodynamical
properties is discussed. The base pair displacements with respect to the ground
state are treated as paths whose temperature dependent amplitudes are governed
by the thermal wavelength. The ensemble of base pairs paths is selected, at any
temperature, consistently with both the model potential and the second law of
thermodynamics. The partition function incorporates the effects of the base
pair thermal fluctuations which become stronger close to the denaturation. The
transition appears as a gradual phenomenon starting from the molecule segments
rich in adenine-thymine base pairs. Computing the equilibrium thermodynamics,
we focus on the interplay between twisting of the complementary strands around
the molecule axis and nonlinear stacking potential: it is shown that the latter
affects the melting profiles only if the rotational degrees of freedom are
included in the Hamiltonian. The use of ladder Hamiltonian models for the DNA
complementary strands in the pre-melting regime is questioned.
