For many problems in the theory of DNA elasticity a DNA molecule in the familiar Watson-Crick double helical B form can be treated as though it is a rod-like structure obtained by stacking dominoes one on top of another with each rotated by approximately one-tenth of a full turn with respect to its immediate predecessor in the stack. In molecular biology these "dominoes" are called base pairs, because each is formed by joining together with hydrogen bonds two nearly planar complementary nucleotide bases (with type A complementary to type T, and type C complementary to type G). Both the intrinsic geometry (e.g., curvature in the stress free state) and the elastic properties (e.g., moduli governing bending, twisting, shearing, and coupling between such modes of deformation) are sensitive to the nucleotide sequence in the DNA molecule. Each base in a base pair is covalently attached to the sugar-phosphate backbone chain of one of the two DNA strands that have come together to form the Watson-Crick structure. As each phosphate group in the backbone chain bears one electronic charge, two such charges are associated with each base pair, and under physiological conditions the electrical force exerted at a base pair can be expected to be strongly dependent on the position in space of even remotely placed base pairs in the same DNA molecule. In this research we construct and explore the implications of nonlinear theories of the mechanics of such structures.
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