蠕虫极限中的DNA环化和循环：正规模和调和近似的有效性
DNA cyclization and looping in the wormlike limit: normal modes and the validity of the harmonic approximation
摘要：
在过去三十年的大部分时间里，蒙特卡罗模拟方法一直是准确计算具有序列依赖性弯曲或不均匀弯曲柔性的DNA模型的环化概率、$J$或J因子的标准方法。然而，在过去的十年中，半柔性聚合物模型的谐波分析的基础上的方法已经推出，它提供了更大的计算效率比蒙特卡罗技术。这些方法考虑的是关于一个明确定义的弹性能量最小值的谐波波动方面的分子构象的合奏。然而，谐波近似仅适用于小系统，因为较大系统的可及构象空间越来越多地由非谐波贡献主导。在J因子的计算值的情况下，作为DNA长度的函数的$J$的精确值的谐波近似的偏差尚未被表征。使用最近，数值精确的方法，占非谐和谐波贡献$J$的蠕虫状链的任意大小，我们在这里报告的明显错误，结果从忽略非谐行为。对于蠕虫状链的轮廓长度小于四倍的持久性长度的误差$J$所产生的谐波近似一般是小的，相当于自由能小于热能，$k_B T$。然而，对于较大的系统，谐波和精确$J$值之间的偏差随着尺寸近似线性地增加。
英文摘要：
For much of the last three decades Monte Carlo-simulation methods have been the standard approach for accurately calculating the cyclization probability, $J$, or J factor, for DNA models having sequence-dependent bends or inhomogeneous bending flexibility. Within the last ten years, however, approaches based on harmonic analysis of semi-flexible polymer models have been introduced, which offer much greater computational efficiency than Monte Carlo techniques. These methods consider the ensemble of molecular conformations in terms of harmonic fluctuations about a well-defined elastic-energy minimum. However, the harmonic approximation is only applicable for small systems, because the accessible conformation space of larger systems is increasingly dominated by anharmonic contributions. In the case of computed values of the J factor, deviations of the harmonic approximation from the exact value of $J$ as a function of DNA length have not been characterized. Using a recent, numerically exact method that accounts for both anharmonic and harmonic contributions to $J$ for wormlike chains of arbitrary size, we report here the apparent error that results from neglecting anharmonic behavior. For wormlike chains having contour lengths less than four times the persistence length the error in $J$ arising from the harmonic approximation is generally small, amounting to free energies less than the thermal energy, $k_B T$. For larger systems, however, the deviations between harmonic and exact $J$ values increase approximately linearly with size.
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