弱螺旋比力闭环复丝的统计力学模型
Statistical Mechanical Model for a closed loop plectoneme with weak helix specific forces
摘要：
我们开发了一个统计力学框架，基于变分近似，描述闭环plectonemes。这个框架将弱螺旋结构依赖力的自由能和平均结构的plectoneme的确定。值得注意的是，由于它们的手性性质，螺旋结构依赖力打破了左手和右手超螺旋之间的对称性。本文提出的理论方法，也提供了一个系统的方法来加强闭环超螺旋的拓扑约束的变分近似。在大的缀素长度下，通过考虑关联函数在关于其热平均值的空间平均扭曲密度的展开式中的作用，可以论证拓扑约束可以用它们的热平均值代替扭曲和扭动来近似。在自由能上加一个拉格朗日乘子，即平均扭转和扭动之和，可以方便地加强这一结果。在变分近似下，通过高斯积分的热平均，可以计算出平均扭振。此外，这种方法允许一种可能的方式来计算由于拓扑约束的有限尺寸校正。使用平均场Kornyshev-Leikin理论的相互作用能量项，对于对应于弱螺旋依赖力的参数值，我们计算了plectoneme的自由能，波动幅度和平均几何参数。我们看到一个轻微的不对称，有趣的是，左手超线圈比右手超线圈有更松散的结构，尽管自由能更低，不像以前的基态计算所建议的那样。
英文摘要：
We develop a statistical mechanical framework, based on a variational approximation, to describe closed loop plectonemes. This framework incorporates weak helix structure dependent forces into the determination of the free energy and average structure of a plectoneme. Notably, due to their chiral nature, helix structure dependent forces break the symmetry between left and right handed supercoiling. The theoretical approach, presented here, also provides a systematic way of enforcing the topological constraint of closed loop supercoiling in the variational approximation. At large plectoneme lengths, by considering correlation functions in an expansion in terms of the spatial mean twist density about its thermally averaged value, it can be argued that topological constraint may be approximated with by replacing twist and writhe by their thermal averages. A Lagrange Multiplier, containing the sum of average twist and writhe, can be added to the free energy to conveniently inforce this result. The average writhe can be calculated through the thermal average of Gauss integral in the variational approximation. Furthermore, this approach allows for a possible way to calculate finite size corrections due to the topological constraint. Using interaction energy terms from the mean-field Kornyshev-Leikin theory, for parameter values that correspond to weak helix dependent forces, we calculate the free energy, fluctuation magnitudes and mean geometric parameters for the plectoneme. We see a slight asymmetry, where interestingly enough left handed supercoils have looser structure than right handed ones, although a lower free energy, unlike what previous ground state calculations would suggest.
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