Phase transition of DNA knotting in spherical space
Phase transition of DNA knotting in spherical space
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球形空间中 DNA 打结的相变
DOI：
10.1088/1361-648x/ac808f
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发表时间：
2022-07
期刊：
影响因子：
--
通讯作者：
Yanhui Liu
中科院分区：
文献类型：
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作者：
Xiaolin Nie;Caiyun Xiong;Xun Zhou;Yanhui Liu
结已经在各种生物系统中被发现，例如DNA。DNA在自由空间中的打结概率与其弯曲刚度呈非单调关系，并有一个显著的峰值。目前的工作旨在了解DNA打结概率对弯曲刚度的非单调依赖性的潜在机制。分别用蠕虫链模型和柔性扭结模型对封闭的DNA分子进行了Monte Carlo模拟。封闭的DNA的轮廓长度和球形空间半径都增加了打结概率，但也改变了打结概率对弯曲刚度的单峰依赖性。这是使用基于这两个模型的通用相图来概括的。在柔性扭结模型下，当激发能较高时，闭合DNA的总打结几率明显增加。这支持了这样的预期，即结尺寸的熵效应有利于在相对低的弯曲刚度下形成结。在一个给定的球形空间中，由蠕虫状链模型描述的闭合DNA的轮廓长度的增加导致打结概率分布的可见移动。同时，非平凡的封闭DNA的回转半径变得与平凡的封闭DNA的回转半径相当，使得它们的比率与平均结长不反相关。对于不同轮廓长度的闭合DNA，平均结长与抗弯刚度之间的关系具有普遍的行为：平均结长在抗弯刚度为1.5时减小到局部最小值，然后逐渐增大到恒定值。局部极小值的存在由排斥Lennard-Jones势的截断距离决定。对应于恒定平均打结长度开始的弯曲刚度与打结分布峰值处的弯曲刚度一致。在这一点上，结尺寸效应与碎片自由能效应平衡，并且在更大的弯曲刚度下，结长度在平均结长度值附近呼吸。
Knots have been discovered in various biological systems, such as DNA. The knotting probability of DNA in free space depends non-monotonically on its bending rigidity and has a prominent peak. The current work aims to understand the underlying mechanism of the non-monotonic dependence of DNA knotting probability on bending rigidity. Monte Carlo simulations are performed on a closed DNA molecule confined in spherical space described by a worm-like chain model and a flexible kink model, respectively. The closed DNA’s contour length and the spherical space radius both increase knotting probability, but also alter the unimodal dependence of knotting probability on bending rigidity. This is generalized using universal phase diagrams based on the two models. Under the flexible kink model, the total knotting probability of closed DNA is obviously increased at a relatively high excited energy. This supports the expectation that the entropy effect of knot size favours knot formation at a relatively low bending rigidity. In a given spherical space, the increasing contour length of closed DNA described by the worm-like chain model results in a visible shift in the knotting probability distribution. At the same time, the gyration radius of non-trivial closed DNA becomes comparable to that of trivial closed DNA, so that their ratio is not anti-correlated with average knot length. For closed DNA of various contour lengths, the relationship between average knot length and bending rigidity has a universal behaviour: the average knot length decreases to a local minimum at a bending rigidity of ∼5 and then gradually increases to a constant value. The existence of the local minimum is determined by the cut-off distance in repulsive Lennard–Jones potential. The bending rigidity corresponding to the beginning of the constant average knot length is consistent with that at the peak in the knotting distribution. At this point, the knot-size effect balances with the fragment free-energy effect and, at an even greater bending rigidity, knot length breathes around the average knot length value.