Characterising knotting properties of polymers in nanochannels
Characterising knotting properties of polymers in nanochannels
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DOI：
10.1039/c8sm00734a
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发表时间：
2018-07-28
期刊：
影响因子：
3.4
通讯作者：
Soteros, C. E.
中科院分区：
文献类型：
--
作者：
Beaton, N. R.;Eng, J. W.;Soteros, C. E.
使用一个晶格模型的聚合物在一个管中，我们定义了一种方法来计算一个给定的结的不同配置为本地或非本地的，基于一个标准的方法来测量一个结的聚合物链内的结的大小。该方法涉及将结类型与链的子弧相关联，然后识别具有最小弧长的打结子弧;该弧长然后是结大小。如果结的大小相对于链的整个长度是小的，那么结被认为是局部的或局部的;否则，它是非局部的。使用这个定义，我们建立，但指数很少足够长的自避免多边形（闭链）在一个管状的简单立方晶格的子格是非局部打结。这也适用于相同的多边形受到外部张力的情况，以及在极端情况下，当它们尽可能紧凑（没有空的晶格位点）。我们还提供了数值证据的小管尺寸，在平衡非局部打结是更可能比局部打结，无论拉伸或压缩力的强度。这些结果的相关性，其他模型和最近的实验涉及DNA结也进行了讨论。
Using a lattice model of polymers in a tube, we define one way to characterise different configurations of a given knot as either local or non-local, based on a standard approach for measuring the size of a knot within a knotted polymer chain. The method involves associating knot-types to subarcs of the chain, and then identifying a knotted subarc with minimal arclength; this arclength is then the knot-size. If the resulting knot-size is small relative to the whole length of the chain, then the knot is considered to be localised or local; otherwise, it is non-local. Using this definition, we establish that all but exponentially few sufficiently long self-avoiding polygons (closed chains) in a tubular sublattice of the simple cubic lattice are non-locally knotted. This is shown to also hold for the case when the same polygons are subject to an external tensile force, as well as in the extreme case when they are as compact as possible (no empty lattice sites). We also provide numerical evidence for small tube sizes that at equilibrium non-local knotting is more likely than local knotting, regardless of the strength of the stretching or compressing force. The relevance of these results to other models and recent experiments involving DNA knots is also discussed.