Knotting probability of self-avoiding polygons under a topological constraint.
Knotting probability of self-avoiding polygons under a topological constraint.
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拓扑约束下自回避多边形的结概率。
DOI：
10.1063/1.4996645
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
T. Deguchi
中科院分区：
文献类型：
--
作者：
Erica Uehara;T. Deguchi
我们通过具有结类型K的N个段的随机多边形或自避免多边形（SAP）的概率来定义结K的打结概率。我们显示的打结概率的基本和通用的属性，特别是它对排除量的依赖。我们调查他们的SAP组成的单位长度和半径雷克斯的硬圆柱段。对于各种素数和复合结，我们数值计算表明，一个紧凑的公式描述了打结的概率为圆柱形SAP作为段数N和半径雷克斯的函数。它将小N与大N行为联系起来，甚至在半径值较大的情况下与晶格结联系起来。除三叶结外，素结的最大打结概率随排除体积的增大而减小。如果它是大的，三叶结和它的后代是占主导地位的非平凡结中的SAP。从打结概率的因子分解性质，我们推导出一个求和规则之间的拟合参数的估计为所有的素数结，这表明当地的结图片和三叶结的情况下，大的排除体积的优势。在这里，我们注意到，圆柱形SAP给出了一个模型的环状DNA是带负电荷的和半柔性的，其中半径雷克斯对应的筛选长度。
We define the knotting probability of a knot K by the probability for a random polygon or self-avoiding polygon (SAP) of N segments having the knot type K. We show fundamental and generic properties of the knotting probability particularly its dependence on the excluded volume. We investigate them for the SAP consisting of hard cylindrical segments of unit length and radius rex. For various prime and composite knots, we numerically show that a compact formula describes the knotting probabilities for the cylindrical SAP as a function of segment number N and radius rex. It connects the small-N to the large-N behavior and even to lattice knots in the case of large values of radius. As the excluded volume increases, the maximum of the knotting probability decreases for prime knots except for the trefoil knot. If it is large, the trefoil knot and its descendants are dominant among the nontrivial knots in the SAP. From the factorization property of the knotting probability, we derive a sum rule among the estimates of a fitting parameter for all prime knots, which suggests the local knot picture and the dominance of the trefoil knot in the case of large excluded volumes. Here we remark that the cylindrical SAP gives a model of circular DNA which is negatively charged and semiflexible, where radius rex corresponds to the screening length.
DOI：
10.1016/s0021-9258(18)89168-2
发表时间：
1985-04
期刊：
The Journal of biological chemistry
影响因子：
--
作者：
F. Dean;A. Stasiak;T. Koller;N. Cozzarelli
通讯作者：
F. Dean;A. Stasiak;T. Koller;N. Cozzarelli
DOI：
10.1073/pnas.90.11.5307
发表时间：
1993-06-01
影响因子：
11.1
作者：
RYBENKOV, VV;COZZARELLI, NR;VOLOGODSKII, AV
通讯作者：
VOLOGODSKII, AV
影响因子：
2.4
作者：
Katritch, V;Olson, WK;Stasiak, A
通讯作者：
Stasiak, A