[论文解读] A sequential algorithm with a built in tension-propagation mechanism for modeling the chain-like bodies dynamics

Andrzej Z. Grzybowski, Zbigniew Domański|arXiv (Cornell University)|Dec 15, 2013

Theoretical and Computational Physics被引用 4

一句话总结

本文提出了一种新颖的顺序随机算法，用于模拟具有内置张力传播机制的链状体（CLB）动力学，实现了高效且高接受率的构象转变。该方法通过虚拟步长传播张力，模拟聚合物穿过孔道的过程，并确定Moyal分布为二维自避聚合物穿膜时间分布的精确模型。

ABSTRACT

In the paper a novel stochastic algorithm designed to study of chain-like bodies dynamics is introduced. This algorithm models chain movements induced by the tension propagation and its main idea relies on the sequentialization of each movement into a sequence of virtual steps made by chain's segments. In this spirit, any accepted chain's new position is achieved by a move that is initiated by a shift of one segment picked randomly according to a problem-specific probability distribution and then followed by a cascade of some other segments' position rearrangements. The rearrangement process terminates when the tension in the chain induced by the initial shift is released. A considerable gain in the volume of allocated memory is achieved because the virtual steps lead to new conformations that are very likely to be acceptable by nature. We validate the algorithm by comparing passage times for polymer translocation through a pore obtained within this algorithm with their counterparts reported in the literature. In this paper we focus on a fluctuating-bond model of self-avoiding polymers on 2D square lattice. Based on the large data sets received in our simulations we have found that the transolaction time is distributed according to the Moyal probability distribution. This novel finding enables us to identify the theoretical form of various distributions of translocation time reported in literature by expressing them very accurately with the help of this two-parameter family of probability distributions

研究动机与目标

• 开发一种计算高效的算法，用于模拟具有内在张力传播机制的链状体动力学。
• 解决现有随机算法中缺乏同时保证高接受率、自避性及正确张力响应的问题。
• 通过将模拟的穿膜时间与文献数据对比，验证该算法的有效性。
• 识别大规模模拟中穿膜时间数据背后的理论分布。
• 实现大规模数据生成，以支持对聚合物动力学的稳健统计分析。

提出的方法

• 该算法通过基于特定问题的概率分布，对链中的一个片段进行随机位移，依次更新链的构象。
• 初始位移后，一系列片段重排沿链传播张力，直至达到平衡。
• 每个虚拟步骤仅接受物理上合理的构象，从而确保自避性和遍历性。
• 通过优先选择高接受率的转变，减少内存使用和搜索空间，反映自然张力松弛过程。
• 在二维正方形晶格上，利用可变键长的自避聚合物模型，从模拟中收集穿膜时间数据。
• 将Moyal概率分布拟合至穿膜时间数据，以评估其作为理论模型的准确性。

实验结果

研究问题

• RQ1 是否能够通过内置张力传播机制的顺序随机算法，高效模拟具有高接受率的链状体动力学？
• RQ2 与现有方法相比，该算法在计算效率和内存使用方面表现如何？
• RQ3 在所提出的算法下，二维自避聚合物的穿膜时间背后的概率分布是什么？
• RQ4 Moyal分布是否能准确拟合来自模拟和实验文献的穿膜时间数据？
• RQ5 链长和张力传播范围等参数如何影响穿膜时间分布？

主要发现

• 所提出的算法通过张力传播机制优先选择高接受率构象，显著提升了内存和计算效率。
• 模拟中的穿膜时间高度符合Moyal概率分布，经大规模数据集拟合验证。
• 与$ t^{a_1} \text{exp}(-a_2 t) $等替代模型相比，Moyal分布对穿膜时间数据的拟合更优，尤其在小时间值区域。
• Moyal分布能准确拟合来自多个来源的穿膜时间数据，包括电压驱动的DNA穿膜实验和朗之万动力学模拟。
• 从DNA穿膜的实验直方图中推导出参数$ b \approx 0.21 $，证实Moyal分布与真实世界数据的相关性。
• 该算法可生成大规模、可靠的数据库，促进Moyal分布被识别为穿膜时间的通用模型。