Supercoiling of DNA plasmids: mechanics of the generalised ply

J.M.T. Thompson, G.H.M. van der Heijden & S. Neukirch

In this paper we address the mechanics of ply formation in DNA supercoils. We extend the variable ply formulation of Coleman and Swigon to include end loads, and the derived constitutive relations of this generalised 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.

keywords: supercoiling of DNA, DNA molecule, writhing, ply mechanics, writhing of DNA, electron micrograph, rod theory

Proc. R. Soc. Lond. A. 458, 959-985 (2002)