  At present, there have been suggested two types of physical mechanism that
may facilitate preferential pairing between DNA molecules, with identical or
similar base pair texts, without separation of base pairs. One solely relies on
base pair specific patterns of helix distortion being the same on the two
molecules, discussed extensively in the past. The other mechanism proposes that
there are preferential interactions between base pairs of the same composition.
We introduce a model, built on this second mechanism, where both thermal
stretching and twisting fluctuations are included, as well as the base pair
specific helix distortions. Firstly, we consider an approximation for weak
pairing interactions, or short molecules. This yields a dependence of the
energy on the square root of the molecular length, which could explain recent
experimental data. However, analysis suggests that this approximation is
no-longer valid at large DNA lengths. In a second approximation, for long
molecules, we define two adaptation lengths for twisting and stretching, over
which the pairing interaction can limit the accumulation of helix disorder.
When the pairing interaction is sufficiently strong, both adaptation lengths
are finite; however, as we reduce pairing strength, the stretching adaptation
length remains finite but the torsional one becomes infinite. This second state
persists to arbitrarily weak values of the pairing strength; suggesting that,
if the molecules are long enough, the pairing energy scales as length. To probe
differences between the two pairing mechanisms, we also construct a model of
similar form. However, now, pairing between identical sequences solely relies
on the intrinsic helix distortion patterns. Between the two models, we see
interesting qualitative differences. We discuss our findings, and suggest new
work to distinguish between the two mechanisms.
