Bifurcations of equilibria in DNA elasticity

Yoav Biton
2007
DNA molecules in the familiar double helical B form are treated here as though they have rod-like structures obtained by stacking thenearly planar base pairs comprising them one on top of another with each rotated by approximately one-tenth of a full turn with respectto its immediate predecessor in the stack. As each base in a base pair is attached to the sugar-phosphate backbone chain of one of thetwo DNA strands that have come together to form the Watson-Crick structure, and each phosphate
more » ... up in a backbone chain bears one electronic charge, two such charges are associated with each base pair. Thus, each base pair is subject to not only the elastic forces and moments exerted on it by its neighboring base pairs but also to remote electrostatic forces that, because they are only partially screened out by positively charged counter ions, can render the molecule's equilibrium configurations sensitive to changes in the concentration c of salt in the medium.The observation that the step from one base pair to the next can be one of several distinct types, each having its own mechanical properties that depend on the nucleotide composition of the step, and the assumption that a base pair is rigid, led to the development of a theory of sequence dependent DNA elasticity [Coleman, Olson, and Swigon, J. Chem. Phys. 118 ,7127-7140, (2003)]. The theory of DNA molecules in aqueous solution developed here is based on but goes beyond that theory. It takes into account the intramolecular electrostatic interactions of the negatively charged phosphate groups in the molecule and the impenetrability of the DNA molecule for cases in which theelectrostatic repulsive forces do not suffice to avoid self penetration. The theory permits one to calculate equilibrium configurations, to determine their stability, and to study the dependence of them on salt concentration and on all kinds of end conditions.When the intramolecular electrostatic forces are taken into account, the equations of mechanical equilibrium for a DNA molecule with N+1 [...]
doi:10.7282/t3js9qwr fatcat:tp3axv4xefgqxeg3fbasasbtrm