  Homologous gene shuffling between DNA promotes genetic diversity and is an
important pathway for DNA repair. For this to occur, homologous genes need to
find and recognize each other. However, despite its central role in homologous
recombination, the mechanism of homology recognition is still an unsolved
puzzle. While specific proteins are known to play a role at later stages of
recombination, an initial coarse grained recognition step has been proposed.
This relies on the sequence dependence of the DNA structural parameters, such
as twist and rise, mediated by intermolecular interactions, in particular
electrostatic ones. In this proposed mechanism, sequences having the same base
pair text, or are homologous, have lower interaction energy than those
sequences with uncorrelated base pair texts; the difference termed the
recognition energy. Here, we probe how the recognition energy changes when one
DNA fragment slides past another, and consider, for the first time, homologous
sequences in antiparallel alignment. This dependence on sliding was termed the
recognition well. We find that there is recognition well for anti-parallel,
homologous DNA tracts, but only a very shallow one, so that their interaction
will differ little from the interaction between two nonhomologous tracts. This
fact may be utilized in single molecule experiments specially targeted to test
the theory. As well as this, we test previous theoretical approximations in
calculating the recognition well for parallel molecules against MC simulations,
and consider more rigorously the optimization of the orientations of the
fragments about their long axes. The more rigorous treatment affects the
recognition energy a little, when the molecules are considered rigid. However
when torsional flexibility of the DNA molecules is introduced, we find
excellent agreement between analytical approximation and simulation.
