Effect of salt-dependent stiffness on the conformation of a stressed DNA loop containing initially coplanar bends

Closed DNA loops containing one or more bent regions are important structures that occur in the regulation of gene expression. We analyze the response of structures of this type to a change in applied rotation (change in linking deficiency, ΔLk). Our results apply to a closed loop formed from an elastic rod that is intrinsically bent in Nb discrete, 20° steps up to a maximum of 240°, the bent regions being initially coplanar with the plane of the relaxed DNA loop. We determine the effect of changing the intrinsic elastic resistance of the DNA loop to bending and torsional deformations. This relative resistance is expressed by Poisson's ratio ν, which depends upon the ratio of bending stiffness to torsional rigidity. Poisson's ratio is primarily a function of salt type and concentration. We find that the tertiary structure of DNA loops changes with ΔLk, but that the geometric response can be either of two quite different types, depending upon the precise (Nb, ν) pair. For combinations of Nb and ν that are above a critical curve (the Fickel curve), the response to increasing ΔLk is nonmonotonic (NMT region): the distance between the loop closure point and its diametric opposite first decreases, then increases, as ΔLk increases. For combinations of Nb and ν that are below the Fickel curve (NMT region), the corresponding diameter never increases, but always decreases with increasing ΔLk. In addition to these results, we define and implement a new measure of tertiary structure in closed DNA: the absolute writhe, AWr. © 1999 John Wiley & Sons, Inc. Biopoly 49: 605–619, 1999