  The torsional elasticity of semiflexible polymers like DNA is of biological
significance. A mathematical treatment of this problem was begun by Fuller
using the relation between link, twist and writhe, but progress has been
hindered by the non-local nature of the writhe. This stands in the way of an
analytic statistical mechanical treatment, which takes into account thermal
fluctuations, in computing the partition function. In this paper we use the
well known analogy with the dynamics of tops to show that when subjected to
stretch and twist, the polymer configurations which dominate the partition
function admit a local writhe formulation in the spirit of Fuller and thus
provide an underlying justification for the use of Fuller's "local writhe
expression" which leads to considerable mathematical simplification in solving
theoretical models of DNA and elucidating their predictions. Our result
facilitates comparison of the theoretical models with single molecule
micromanipulation experiments and computer simulations.
