The significance of fuzzy boundaries of the barrier regions in single-molecule measurements of failed barrier crossing attempts

TL;DR

This paper investigates how finite experimental resolution affects measurements of barrier crossing attempts in single-molecule experiments, revealing that observed distributions of failed crossing attempts depend on resolution but can still reflect intrinsic dynamics.

Contribution

The authors develop a model incorporating finite resolution effects to interpret measurements of barrier crossing attempts, clarifying the relationship between observed data and true molecular dynamics.

Findings

Finite resolution causes observable distributions of loop times and sizes.

In certain cases, these distributions are resolution-dependent only by a simple factor.

Experiments can still probe intrinsic barrier crossing properties despite resolution limitations.

Abstract

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.