Effect of undulations on spontaneous braid formation.

This paper is an extension of a recent study where it was shown that forces dependent on molecular helical structure may cause two DNA molecules to spontaneously braid [R. Cortini et al., Biophys. J. 101, 875 (2011)]. Here, bending fluctuations of molecular center lines about the braid axis are incorporated into the braiding theory, which may be generalized to other helix-dependent interactions and other helical molecules. 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 quite high. This contribution to the free energy increases the amount of attraction needed for spontaneous braiding due to helix-dependent forces. The theory will be further developed for plectonemes and braids under mechanical forces in later work.