  This paper extends on a recent work where it was shown that forces dependent
on the helical structure may cause two DNA molecules to spontaneously braid [R.
Cortini et Al, Biophys. J. 101, 875 (2011)]. Here, bending fluctuations of DNA
centre lines about the braid axis are incorporated into the braiding theory.
The free energy of the pair of molecules is recalculated and compared to its
value without incorporating undulations. We find that the loss of
configurational entropy due to confinement of the molecules in the braid is
rather high. This contribution to the Free Energy pushes up the amount of
attraction needed for spontaneous braiding due to helix dependant forces. The
theory will be further developed for plectonemes and braids under mechanical
forces, in later work.
