Supercoiling of DNA plasmids: mechanics of the generalized ply

In this paper we address the mechanics of ply formation in DNA supercoils. We extend the variable ply formulation of Coleman & Swigon to include end loads, and the derived constitutive relations of this generalized ply are shown to be in excellent agreement with experiments. We make a careful physical examination of the uniform ply in which two strands coil around one another in the form of a helix. We next address the problem of determining the link (Lk), twist (Tw) and writhe (Wr) of a closed DNA plasmid from an inspection of its electron micrograph. Previous work has made use of the topological relation, Lk = Tw + Wr, but we show how this kinematic result can be augmented by the mechanics solutions. A very precise result is achieved in a trial calculation.