The role of the stress resultant in determining mechanical equilibria of superhelical DNA

Duplex DNA has the mechanical properties of a hyperelastic symmetric Each secondary structure has an unstressed shape, which is usually straight with a helical twist characteristic of the secondary structure involved. Because DNA is hyperelastic, a free energy density W is associated to deformations away from the unstressed conformation. These deformations are expressed in terms of K ( s ) , the curvature at position s along the molecule, and T ( s ) , the local deviation from the unstressed helicity measured in radians per unit length. Because DNA is mechanically symmetric, bending has no preferred direction and the hyperelastic energy density is a function of three variables3: W = W( K , T, s). In most analyses of DNA superhelical tertiary structure the molecule is regarded as linearly elastic, homogeneous, and mechanically symmetric with constant cross s e c t i ~ n , ~ , ~ so that W has the form