A new analytical model for studying the energy of DNA with and without proteins*

We introduce a new analytical rod model to describe the configuration of DNA with and without proteins. The model incorporates any pathway of protein-bound DNA, including those found in high-resolution structures, and allows for the treatment of circular and looped molecules. We determined the mathematical equation for linkers that can smoothly connect two protein-bound DNA segments with arbitrary positions and orientations. The smooth linker is a quartic function with five coefficients which can be expressed in terms of its boundary values. We first considered ideal protein-bound DNA segments containing left-handed and right-handed helical supercoils with complete and partial turns.
We are using these supercoils and the smooth linkers as building blocks to study more complicated structures like the SV40 minichromosome. We are studying the effects of electrostatic and elastic energy on the stable configurations of these systems.