On the toroidal condensed state of closed circular DNA

The influence of double helix torsional elasticity on the compaction and structure of circular DNA compact form is studied theoretically in the case when the compact (globular) form has torus shape. For closed circular DNA the topological invariant, the linking number, yields a strict connection between conformation of the double helix considered as unifilar homopolymer and elastic energy of torsional twisting. The contribution of torsional elasticity to the free energy of the toruslike globule is calculated. This contribution is shown to be proportional to the square of superhelical density. Allowance of the torsional elasticity decreases the equilibrium radius of the toruslike globule formed by circular DNA. Closure of linear DNA into a ring widens the stability range of the relatively short DNA compact form and tightens it for long DNA.