Liu Zhirong, Chan Hue Sun
Department of Biochemistry and Department of Molecular Genetics, Faculty of Medicine, University of Toronto, Toronto, Ontario M5S 1A8, Canada.
J Chem Phys. 2008 Apr 14;128(14):145104. doi: 10.1063/1.2899022.
We develop two classes of Monte Carlo moves for efficient sampling of wormlike DNA chains that can have significant degrees of supercoiling, a conformational feature that is key to many aspects of biological function including replication, transcription, and recombination. One class of moves entails reversing the coordinates of a segment of the chain along one, two, or three axes of an appropriately chosen local frame of reference. These transformations may be viewed as a generalization, to the continuum, of the Madras-Orlitsky-Shepp algorithm for cubic lattices. Another class of moves, termed T+/-2, allows for interconversions between chains with different lengths by adding or subtracting two beads (monomer units) to or from the chain. Length-changing moves are generally useful for conformational sampling with a given site juxtaposition, as has been shown in previous lattice studies. Here, the continuum T+/-2 moves are designed to enhance their acceptance rate in supercoiled conformations. We apply these moves to a wormlike model in which excluded volume is accounted for by a bond-bond repulsion term. The computed autocorrelation functions for the relaxation of bond length, bond angle, writhe, and branch number indicate that the new moves lead to significantly more efficient sampling than conventional bead displacements and crankshaft rotations. A close correspondence is found in the equilibrium ensemble between the map of writhe computed for pair of chain segments and the map of site juxtapositions or self-contacts. To evaluate the more coarse-grained freely jointed chain (random-flight) and cubic lattice models that are commonly used in DNA investigations, twisting (torsional) potentials are introduced into these models. Conformational properties for a given superhelical density sigma may then be sampled by computing the writhe and using White's formula to relate the degree of twisting to writhe and sigma. Extensive comparisons of contact patterns and knot probabilities of the more coarse-grained models with the wormlike model show that the behaviors of the random-flight model are similar to that of DNA molecules in a solution environment with high ionic strengths, whereas the behaviors of the cubic lattice model with excluded volume are akin to that of DNA molecules under low ionic strengths.
我们开发了两类蒙特卡罗移动方法，用于对具有显著超螺旋程度的类蠕虫状DNA链进行高效采样。超螺旋是一种构象特征，对包括复制、转录和重组在内的许多生物学功能方面都至关重要。一类移动方法是沿适当选择的局部参考系的一个、两个或三个轴反转链段的坐标。这些变换可以看作是针对立方晶格的马德拉斯 - 奥里茨基 - 谢泼算法在连续介质中的推广。另一类移动方法称为T + / - 2，通过向链中添加或从链中减去两个珠子（单体单元），实现不同长度链之间的相互转换。如先前晶格研究所示，长度改变移动通常对于给定位点并列的构象采样很有用。在此，连续介质中的T + / - 2移动旨在提高其在超螺旋构象中的接受率。我们将这些移动方法应用于一个类蠕虫状模型，其中通过键 - 键排斥项来考虑排除体积。计算得到的键长、键角、扭曲数和分支数弛豫的自相关函数表明，新的移动方法比传统的珠子位移和曲轴旋转导致更高效的采样。在平衡系综中，发现为链段对计算的扭曲数图与位点并列或自接触图之间存在密切对应关系。为了评估DNA研究中常用的更粗粒度的自由连接链（随机飞行）和立方晶格模型，将扭转（扭转）势引入这些模型。然后，通过计算扭曲数并使用怀特公式将扭转程度与扭曲数和超螺旋密度σ相关联，可以对给定超螺旋密度σ的构象性质进行采样。对更粗粒度模型与类蠕虫状模型的接触模式和结概率进行的广泛比较表明，随机飞行模型的行为类似于高离子强度溶液环境中DNA分子的行为，而具有排除体积的立方晶格模型的行为类似于低离子强度下DNA分子的行为。
