  In this paper we consider a physical system in which two DNA molecules braid
about each other. The distance between the two molecular ends, on either side
of the braid, is held at a distance much larger than supercoiling radius of the
braid. The system is subjected to an external pulling force, and a moment that
induces the braiding. In a model, developed for understanding such a system, we
assume that each molecule can be divided into a braided and unbraided section.
We also suppose that the DNA is nicked so that there is no constraint of the
individual linking numbers of the molecules. Included in the model are steric
and electrostatic interactions, thermal fluctuations of the braided and
unbraided sections of the molecule, as well as the constraint on the braid
linking (catenation) number. We compare two approximations used in estimating
the free energy of the braided section. One is where the amplitude of
undulations of one molecule with respect to the other is determined only by
steric interactions. The other is a self-consistent determination of the mean
squared amplitude of these undulations. In this second approximation
electrostatics should play an important role in determining this quantity, as
suggested by physical arguments. We see that if the electrostatic interaction
is sufficiently large there are indeed notable differences between the two
approximations. We go on to test the self-consistent approximation, included in
the full model, against experimental data, for such a system, and we find good
agreement. However, there seems to by a slight left/right handed braid
asymmetry in some of the experimental results. We discuss what might be the
origin of this small asymmetry
