  The Poland-Scheraga (PS) model for the helix-coil transition of DNA considers
the statistical mechanics of the binding (or hybridization) of two
complementary strands of DNA of equal length, with the restriction that only
bases with the same index along the strands are allowed to bind. In this paper,
we extend this model by relaxing these constraints: We propose a generalization
of the PS model which allows for the binding of two strands of unequal lengths
$N_{1}$ and $N_{2}$ with unrelated sequences. We study in particular (i) the
effect of mismatches on the hybridization of complementary strands (ii) the
hybridization of non complementary strands (as resulting from point mutations)
of unequal lengths $N_{1}$ and $N_{2}$. The use of a Fixman-Freire scheme
scales down the computational complexity of our algorithm from
$O(N_{1}^{2}N_{2}^{2})$ to $O(N_{1}N_{2})$.The simulation of complementary
strands of a few kbps yields results almost identical to the PS model. For
short strands of equal or unequal lengths, the binding displays a strong
sensitivity to mutations. This model may be relevant to the experimental
protocol in DNA microarrays, and more generally to the molecular recognition of
DNA fragments. It also provides a physical implementation of sequence
alignments.
