Bauer W R, Lund R A, White J H
Department of Microbiology, School of Medicine, State University of New York, Stony Brook 11794-5222.
Proc Natl Acad Sci U S A. 1993 Feb 1;90(3):833-7. doi: 10.1073/pnas.90.3.833.
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.
固体力学的有限元方法被应用于计算闭合环状DNA的三维结构，该结构被建模为一个经历大幅运动的弹性杆。结果预测了作为松弛平衡构型和连接数（Lk）函数的闭合DNA环的最小弹性能构象。我们将该方法应用于四种不同的起始状态：一根直杆、两根分别含有一个或两个20度弯曲的杆以及一个圆形O环。在低超螺旋密度下的结果显示，随着Lk逐渐降低，螺旋数（Wr）和扭转数（Tw）的变化情况。与初始为直的、无弯曲的杆相比，即使存在单个固有弯曲也会显著降低Wr首次出现时的连接数变化。位于直径相对两端的两个同相弯曲的存在，导致形成至少两个不同但相对均匀的Tw增量的不同区域。Lk降低时，O环立即开始螺旋化，并且Tw增量沿杆呈正弦分布。与其他理论方法不同，力学计算使我们能够独立于恒定Lk的约束来计算Tw和Wr。
