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 structur es 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 link ing deficiency, Delta Lk). Our results apply to a closed loop formed from a n elastic rod that is intrinsically bent in N-b discrete, 20 degrees steps tip to a maximum of 240 degrees, 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 nu, which depends upon the ratio of bending bending stiffness to torsional rigi dity. Poisson's ratio is primarily a function of salt type and concentratio n. We find that the tertiary structure of DNA loops changes with Delta Lk, but that the geometric response can be either of trio quite different types , depending upon the bending precise (N-b, nu) pair For combinations of N-b and nu that are above a critical curve (the Fickel curve), the response to increasing Delta Lk is nonmonotonic (NMT region): the distance between the loop closure point and its diametric opposite first decreases, then increa ses, as Delta Lk increases. For combinations of N-b and nu that nta below t he Fickel curve (NMT region), the corresponding diameter never increases, b ut always decreases with increasing Delta Lk. In addition to these results, we define and implement a new measure of tertiary structure in closed DNA: the absolute writhe, AWr. (C) 1999 John Wiley & Sons, Inc.