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