The elastic properties of a molecule of duplex DNA are strongly dependent on nucleotide sequence. In the theory developed here the contriubtion psi~n of six kinematicalvariables,called tilt,roll,twist,shift,slide,and rise,that describe therelative orientation and displacement of the nth and (n+1)th base pairs. The sequence dependence of elastic properties is determined when one specifies the way psi~n depends on the nucleotides of the two base pairs of the nth step. Among the items discussed are thesymmetry relations imposed on psi~n by the complementarity of bases,i.e.,of A to T and C to G,the antiparallel nature of the DNA sugar-phosphate chains,and the requirement that psi~n be independent of the choice of the direction of increasing n. Variational equations of mechanical equilibrium are here derived without special assumptions about the form of the functions psi~n, and numerical solutions of those equations are shown for illustrative cases in which psi~n is,for each n,a quadratic form and the DNA forms a closed, 150 base-pair,minicircle that can be called a DNA o-ring because it has a nearly circular stress-free configuration. Examples are given of noncircular equilibrium configurations of naked DNA o-rings and of cases inwhich the interaction with ligands induces changes in configuration that are markedly different from those undergone by a minicircle of intrinsically straight DNA. When a minicircle of intrinsically straight DNA interacts with an intercalating agent that upon binding to DNA causes a locla reduction of intrinsic twist,the configuration that minimizes elastic energy depends on the number of intercalated molecules,but is independent of the spatial distribution of those molecules along the minicricle. In contrast,it is shown here that the configuration and elastic energy of a DNA o-ring can depend strongly on the spatial distribution of the intercalated molecules. As others have observed in calculations for Kirchhloff rods with intrinsic curvature,an o-ring that has its intrinsic twist reduced at a single base-pair step can undergolarge deformations with localized untwisting and bending at remote steps,even when the amount alpha of twist reduction is less than the amount required toinduce supercoiling in rings of intrinsically straight DNA. We here find that the presence in the function psi~n of cross-terms coupling twist to roll can amplify the configurational changes induced by local untwisting to the point where there can be a value of alpha at which a first-order transition occurs between two distinct stable noncircular configurations with equal elastic energy.
展开▼
