  We propose a new statistical mechanics model for the melting transition of
DNA. Base pairing and stacking are treated as separate degrees of freedom, and
the interplay between pairing and stacking is described by a set of local rules
which mimic the geometrical constraints in the real molecule. This microscopic
mechanism intrinsically accounts for the cooperativity related to the free
energy penalty of bubble nucleation. The model describes both the unpairing and
unstacking parts of the spectroscopically determined experimental melting
curves. Furthermore, the model explains the observed temperature dependence of
the effective thermodynamic parameters used in models of the nearest neighbor
(NN) type. We compute the partition function for the model through the transfer
matrix formalism, which we also generalize to include non local chain entropy
terms. This part introduces a new parametrization of the Yeramian-like transfer
matrix approach to the Poland-Scheraga description of DNA melting. The model is
exactly solvable in the homogeneous thermodynamic limit, and we calculate all
observables without use of the grand partition function. As is well known,
models of this class have a first order or continuous phase transition at the
temperature of complete strand separation depending on the value of the
exponent of the bubble entropy.
