Bifurcations of Equilibria in DNA Elasticity

Rutgers University New Brunswick, New Brunswick NJ

Investigators

Abstract

For many problems in the theory of DNA elasticity, a DNA molecule 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., 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 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. The electrical force exerted on each base pair depends on the concentration of salt in the medium and the position in space of even remotely placed base pairs in the same DNA molecule. Calculations based on this model performed under a previous NSF grant indicate that the equilibrium configurations of an intrinsically curved DNA molecule in solution are very sensitive to the concentration c of salt in the medium. Bifurcation diagrams with c as the parameter can have great complexity and, under appropriate circumstances, contain regions in which several locally stable equilibrium configurations (each giving the molecule a distinct shape) occur at a single value of c. The goal of this project is to develop the mathematical theory of the model to the point where its conclusions are easily capable of experimental testing (e.g., by predicting that for particular DNA sequences experimentally detectable changes in configuration should occur at values of c near to calculated critical values). The attainment of a well developed theory of the influence of long-range electrostatic forces, and hence of changes in salt concentration, on the configurations of intrinsically curved (and in general non-homogeneous) DNA molecules is a matter of general interest in biophysics that has implications in bioengineering. The research in this project is expected to have applications to microdevices for imaging and sorting genomic-length DNA molecules. In one such device the DNA is elongated by confinement to a channel with a width of 0.1 microns, and the computational methods to be developed will aid in the attainment of an understanding of the way the amount of extension experienced by DNA confined in such a channel is related to the channel diameter, the concentration of salt, and the intrinsic curvature of the DNA. Another application of the theory is the investigation of the possibility that circularized molecules of DNA formed from appropriate sequences of several hundred base-pairs can serve as mesoscale mechano-chemical switches that undergo large changes in configuration upon small changes in salt concentration.