  The paper uses mesoscopic, non-linear lattice dynamics based
(Peyrard-Bishop-Dauxois, PBD) modeling to describe thermal properties of DNA
below and near the denaturation temperature. Computationally efficient notation
is introduced for the relevant statistical mechanics. Computed melting profiles
of long and short heterogeneous sequences are presented, using a recently
introduced reparametrization of the PBD model, and critically discussed. The
statistics of extended open bubbles and bound clusters is formulated and
results are presented for selected examples.
