Berezhkovskii Alexander M, Makarov Dmitrii E
Section of Molecular Transport, Eunice Kennedy Shriver National Institute of Child health and Human Development, National Institutes of Health, Bethesda, Maryland 20819, USA.
Department of Chemistry and Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, Texas 78712.
ArXiv. 2024 May 27:arXiv:2405.17620v1.
A recent experimental study reports on measuring the temporal duration and the spatial extent of failed attempts to cross an activation barrier (i.e., "loops") for a folding transition in a single molecule and for a Brownian particle trapped within a bistable potential. Within the model of diffusive dynamics, however, both of these quantities are, on the average, exactly zero because of the recrossings of the barrier region boundary. That is, an observer endowed with infinite spatial and temporal resolution would find that finite loops do not exist (or, more precisely, form a set of measure zero). Here we develop a description of the experiment that takes finite experimental resolution into account and show how the experimental uncertainty of localizing the point, in time and space, where the barrier is crossed leads to observable distributions of loop times and sizes. Although these distributions generally depend on the experimental resolution, this dependence, in certain cases, may amount to a simple resolution-dependent factor and thus the experiments do probe inherent properties of barrier crossing dynamics.
最近的一项实验研究报告了对单个分子折叠转变以及被困在双稳势中的布朗粒子跨越激活势垒（即“环”）失败尝试的时间持续和空间范围的测量。然而，在扩散动力学模型中，由于势垒区域边界的重新穿越，这两个量平均而言恰好为零。也就是说，具有无限时空分辨率的观察者会发现不存在有限的环（或者更准确地说，形成一个测度为零的集合）。在这里，我们考虑有限的实验分辨率来描述该实验，并展示在时间和空间上确定势垒穿越点的实验不确定性如何导致环时间和大小的可观测分布。尽管这些分布通常取决于实验分辨率，但在某些情况下，这种依赖性可能相当于一个简单的与分辨率相关的因子，因此这些实验确实探测了势垒穿越动力学的固有特性。
