A Theory of DNA Elasticity That Takes Into Account Long Range Intramolecular Electrical Forces

Bernard D. Coleman, Rutgers University

Our group has been developing a mathematical theory of DNA elasticity that accounts for the dependence of the mechanical properties of a DNA molecule on its nucleotide sequence and the electrostatic forces between the members of that sequence. The theory permits us to calculate the dependence of the equilibrium configurations of an intrinsically curved DNA molecule on the concentration of salt in the medium.

For many problems in DNA elasticity a DNA molecule in the familiar Watson-Crick double helical 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. Both the intrinsic geometry (e.g., the curvature in the stress-free state) and the elastic properties (e.g., the moduli governing the bending, twisting, and shearing that occur at each base pair step) depend on the nucleotide sequence in the DNA molecule.

Each 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, and, as each phosphate group in the backbone chain bears one electronic charge, two such charges are associated with each base pair. Hence, the electrical force exerted at a base pair is dependent on the position in space of the other base pairs in the same molecule and, because and Debye-Huckle screening, on the concentration of salt in the medium. 

Our theory tells us that the influence of these electrostatic forces, and hence of salt concentration, on the configurations of intrinsically curved DNA molecules can be much larger than previously had been expected. Calculations to be presented in the talk suggest that circularized molecules of DNA formed from appropriate sequences of several hundred base-pairs can serve as mesoscale mechano-chemical switches that undergo striking changes in configuration when the salt concentration is changed. 

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