Schlick T, Olson W K, Westcott T, Greenberg J P
Chemistry Department, New York University, New York 10012.
Biopolymers. 1994 May;34(5):565-97. doi: 10.1002/bip.360340502.
A combination of detailed energy minimization and molecular dynamics studies of closed circular DNA offers here new information that may be relevant to the dynamics of short DNA chains and/or low superhelical densities. We find a complex dependence of supercoiled DNA energies and geometries on the linking number difference delta Lk as physiological superhelical densities (magnitude of sigma approximately 0.06) are approached. The energy minimization results confirm and extend predictions of classical elasticity theory for the equilibria of elastic rods. The molecular dynamics results suggest how these findings may affect the dynamics of supercoiled DNA. The minimization reveals sudden higher order configurational transitions in addition to the well-known catastrophic buckling from the circle to the figure-8. The competition among the bending, twisting, and self-contact forces leads to different families of supercoiled forms. Some of those families begin with configurations of near-zero twist. This offers the intriguing possibility that nicked DNA may relax to low-twist forms other than the circle, as generally assumed. Furthermore, for certain values of delta Lk, more than one interwound DNA minimum exists. The writhing number as a function of delta Lk is discontinuous in some ranges; it exhibits pronounced jumps as delta Lk is increased from zero, and it appears to level off to a characteristic slope only at higher values of delta Lk. These findings suggest that supercoiled DNA may undergo systematic rapid interconversions between different minima that are both close in energy and geometry. Our molecular dynamics simulations reveal such transitional behavior. We observe the macroscopic bending and twisting fluctuations of interwound forms about the global helix axis as well as the end-over-end tumbling of the DNA as a rigid body. The overall mobility can be related to magnitude of sigma and to the bending, twisting, and van der Waals energy fluctuations. The general character of molecular motions is thus determined by the types of energy minima found at a given delta Lk. Different time scales may be attributed to each type of motion: The overall chain folding occurs on a time scale almost an order of magnitude faster than the end-over-end tumbling. The local bending and twisting of individual chain residues occur at an even faster rate, which in turn correspond to several cycles of local variations for each large-scale bending and straightening motion of the DNA.
对闭环圆形DNA进行详细的能量最小化和分子动力学研究相结合，在此提供了可能与短DNA链动力学和/或低超螺旋密度相关的新信息。我们发现，当接近生理超螺旋密度（σ的大小约为0.06）时，超螺旋DNA能量和几何形状对连接数差ΔLk存在复杂的依赖性。能量最小化结果证实并扩展了经典弹性理论对弹性杆平衡的预测。分子动力学结果表明这些发现可能如何影响超螺旋DNA的动力学。最小化揭示了除了从圆形到8字形的众所周知的灾难性弯曲之外，还有突然的高阶构型转变。弯曲、扭转和自接触力之间的竞争导致了不同的超螺旋形式家族。其中一些家族始于接近零扭转的构型。这提供了一种有趣的可能性，即带切口的DNA可能会松弛到除圆形之外的低扭转形式，而通常的假设是它会松弛到圆形。此外，对于特定的ΔLk值，存在不止一个相互缠绕的DNA能量最小值。缠绕数作为ΔLk的函数在某些范围内是不连续的；当ΔLk从零增加时，它会出现明显的跳跃，并且似乎只有在较高的ΔLk值时才趋于一个特征斜率。这些发现表明，超螺旋DNA可能在能量和几何形状都相近的不同最小值之间进行系统的快速相互转换。我们的分子动力学模拟揭示了这种过渡行为。我们观察到相互缠绕形式围绕全局螺旋轴的宏观弯曲和扭转波动，以及DNA作为刚体的端对端翻滚。整体迁移率可以与σ的大小以及弯曲、扭转和范德华能量波动相关。分子运动的一般特征因此由在给定的ΔLk处发现的能量最小值类型决定。不同的时间尺度可能归因于每种运动类型：整体链折叠发生的时间尺度比端对端翻滚快几乎一个数量级。单个链残基的局部弯曲和扭转以更快的速率发生，这反过来又对应于DNA每次大规模弯曲和伸直运动的几个局部变化周期。
