The dependence of DNA tertiary structure on end conditions: Theory and implications for topological transitions

Explicit expressions are derived for the equilibrium configurations of long segments of a DNA double helix subject to boundary conditions of the type imposed by DNA-bending proteins at the ends of otherwise free segments. The expressions, which are exact within the framework of Kirchhoff s theory of elastic rods, show that, in appropriate ranges of parameters, small changes in end conditions can result in large changes in tertiary structure. A discussion is given of the implications of this observation for understanding the action of bending proteins and of proteins that induce topological transitions that change the linking number of closed loops of DNA.