Twist and writhe of a DNA loop containing intrinsic bends

The finite-element method of solid mechanics is applied to calculation of the three-dimensional structure of closed circular DNA, modeled as an elastic rod subject to large motions. The results predict the minimum elastic energy conformation of a closed loop of DNA as a function of relaxed equilibrium configuration and linking number (Lk). We apply the method to four different starting states: a straight rod, two rods containing either one or two 20 degrees bends, and a circular O-ring. The results, here at low superhelix density, show the changes in writhe (Wr) and in twist (Tw) as Lk is progressively lowered. The presence of even a single intrinsic bend reduces significantly the linking number change at which Wr first appears, compared to an initially straight, bend-free rod. The presence of two in-phase bends, situated at opposite ends of a diameter, leads to the formation of at least two distinct regions of different but relatively uniform Tw increment. The O-ring begins to writhe immediately upon reduction of Lk, and the Tw increment distribution is sinusoidal along the rod. The mechanics calculations, unlike other theoretical approaches, permit us to calculate Tw and Wr independent of the constraint of constant Lk.