Tops and Writhing DNA

Abstract

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.

17 pages two figures

References in corpus (9)

• Geometry of Calugareanu's theorem
• Writhe formulas and antipodal points in plectonemic DNA configurations
• Molecular elasticity and the geometric phase
• DNA Elasticity : Topology of Self-Avoidance
• Comment on "Elasticity Model of a Supercoiled DNA Molecule"
• The Writhe Distribution Of Stretched Polymers
• DNA loop statistics and torsional modulus
• Free Energy of Twisted Semiflexible Polymers
• Comment on "Writhe formulas and antipodal points in plectonemic DNA configurations"