Finite-element analysis of the displacement of closed DNA loops under torsional stress.

Abstract

Closed DNA loops that contain intrinsic curvature occur in biologically important structures that are formed by bringing together proteins attached at distinct sites. Such loops constitute topological domains that are characterized by a linking number Delta Lk. We calculate, using finite-element analysis, the structural changes induced by small changes in this linking number, Delta Lk. Because of the intrinsic curvature, the slightest change in linking number induces writhe and the loop begins to fold in space. We previously studied the case in which the initial curvature is uniformly distributed along the DNA rod. We found that there are two different folding modes, depending on the amount of intrinsic curvature and the Poisson ratio, a quantity that measures the ratio of bending stiffness to torsional rigidity. For combinations of the Poisson ratio and curvature that lie below a critical curve, called the Fickel curve, the folding is monotonic in the sense that the writhe uniformly increases as Delta Lk increases, until self-contact occurs. For combinations below this curve, the folding is non-monotonic in the sense that as Delta Lk increases the writhe first increases, then decreases back to essentially zero, and then increases uniformly until self-contact occurs. The folding behaviour and the self-contact points in the two folding modes are completely different. In this paper we first review this previous work. We then extend those results to more-complex situations in which the curvature is initially distributed non-uniformly along the DNA rod. We show that the location of the Fickel curve depends upon both the extent of the initial curvature and upon its distribution along the rod. We also show that two DNAs with the same total intrinsic curvature will fold differently depending upon the distribution of that curvature along the DNA axis, and upon the point of the loop at which the applied rotation or change in Delta Lk is introduced.