Section on Molecular Transport, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland 20892, USA.
J Chem Phys. 2017 Sep 14;147(10):104103. doi: 10.1063/1.5002127.
Recent experiments with single biological nanopores, as well as single-molecule fluorescence spectroscopy and pulling studies of protein and nucleic acid folding raised a number of questions that stimulated theoretical and computational investigations of barrier crossing dynamics. The present paper addresses a closely related problem focusing on trajectories of Brownian particles that escape from a cylindrical trap in the presence of a force F parallel to the cylinder axis. To gain new insights into the escape dynamics, we analyze the "fine structure" of these trajectories. Specifically, we divide trajectories into two segments: a looping segment, when a particle unsuccessfully tries to escape returning to the trap bottom again and again, and a direct-transit segment, when it finally escapes moving without touching the bottom. Analytical expressions are derived for the Laplace transforms of the probability densities of the durations of the two segments. These expressions are used to find the mean looping and direct-transit times as functions of the biasing force F. It turns out that the force-dependences of the two mean times are qualitatively different. The mean looping time monotonically increases as F decreases, approaching exponential F-dependence at large negative forces pushing the particle towards the trap bottom. In contrast to this intuitively appealing behavior, the mean direct-transit time shows rather counterintuitive behavior: it decreases as the force magnitude, |F|, increases independently of whether the force pushes the particles to the trap bottom or to the exit from the trap, having a maximum at F = 0.
最近的单生物纳米孔、单分子荧光光谱和蛋白质及核酸折叠的牵引研究实验提出了许多问题，这些问题激发了对势垒穿越动力学的理论和计算研究。本文针对一个密切相关的问题，重点研究了在平行于圆柱轴的力 F 作用下，从圆柱阱中逃逸的布朗粒子的轨迹。为了深入了解逃逸动力学，我们分析了这些轨迹的“精细结构”。具体来说，我们将轨迹分为两个部分：一个是循环部分，当粒子试图逃逸但一次又一次地返回阱底部时；另一个是直接穿越部分，当它最终逃脱并不再触及底部时。我们推导出了两个部分的持续时间概率密度的拉普拉斯变换的解析表达式。这些表达式用于找到两个平均时间作为偏置力 F 的函数的函数。结果表明，这两个平均时间的力依赖性在定性上是不同的。平均循环时间随着 F 的减小而单调增加，在将粒子推向阱底部的大负力下，趋近于指数 F 依赖性。与这种直观的吸引力行为相反，平均直接穿越时间表现出相当反直觉的行为：它随着力的大小|F|的增加而减小，而不管力是将粒子推向阱底部还是从阱中逸出，在 F = 0 时达到最大值。
