Relationship between the energy of superhelix formation, the shear modulus, and the torsional brownian motion of DNA

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Abstract
The torsional energy of a DNA is the energy involved when the average angle between adjacent base pairs is modified under applied constraints. A relationship is established between the energy of superhelix formation of a upercoiled DNA and its torsional energy. This relationship, valid when the number of the tertiary turns of the supercoiled DNA is small, contains the ratio of the bending to the torsional elastic paramaters of the DNA. From this relationship, the fluctations of the number of tertiary turns of the supercoiled DNA may be compared to those of the DNA with only one sinle‐strand scission. An expression for the shear modulus of the DNA is derived from the anisotropy of the fluorescnece of the intercalated ethidium [Wahl et al. (190) Proc. Natl. Acad. Sci. USA 65, 417–421.]. The value of te torsional elastic parameter deduced from these computations is very close to the parameter of the energy of the superhelix formation determined on supercoiled DNAs by different authors. The energy that must be given to twist it. Consequently, the number of crossovers determined using the EM technique should be much less than the value deduced from the amount of ethiium necessary words, the first ethidium cations intercalating into a relaxed, closed double‐standard DNA change the twist of the DNA but not its tertiary structure.