Toroidal elastic supercoiling of DNA

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Abstract
Covalently closed circular DNA can exist in different configurations known as circular, toroidal, and interwound. Changes among these forms can be made in several ways, including the insertion of dye molecules between adjacent base pairs, which tends to untwist the double‐helical structure. The aim of this paper is to discuss these configurations, and the changes among them, in the context of classical elastomechanics. The concepts of twisting, linkage and writhing are explained. Simple experiments on a twisted linear‐elastic rod are described, and it is shown that although the circular and interwound forms may be modeled in this way, the toroidal form does not occur, being mechanically unstable. Theoretical energy calculations by Levitt on bent and twisted DNA show that DNA exhibits a particular kind of nonlinear elasticity in which there is an unusual coupling between bending and twisting. The aim of the paper is to show qualitatively that this special kind of elasticity can stabilize the toroidal form of closed circular DNA.