The flexibility of DNA. I. Thermal fluctuations

The theory of the flexibility of DNA makes use of a worm-like coil model which implies an isotropic bending potential. This paper investigates the influence of non-isotropic bending which is cased by the real, lower symmetry of a DNA molecule. Formulas are developed for the persistence and mean square length of a molecule in terms of DNA symmetry elements, i.e., a helical screw operation and perpendicular dyad axes. It is shown that the low symmetry of a DNA helix leads to mean propagation properties which differ from the static equilibrium properties. The worm-like coil model may be justified in terms of the mean, thermally averaged, properties of the DNA but not in terms of its equilibrium properties. Changes in helix angle and displacement with temperature and solvent are a natural result of the asymmetric potential of DNA.