Abstract
This paper deals with transitions of diffusing point particles between the two ends of expanding and narrowing two-dimensional conical channels. The particle trajectory starts from the reflecting boundary and ends as soon as the absorbing boundary is reached for the first time. Any such trajectories can be divided into two segments: the looping segment and the transition path segment. The latter is the last part of the trajectory that leaves the reflecting boundary and goes to the absorbing boundary without returning to the reflecting one. The remaining portion of the trajectory is the looping part, where a number of loops that begin and end at the same reflecting boundary are made without touching the absorbing boundary. Because axial diffusion of a smoothly varying channel can be approximately described as one-dimensional diffusion in the presence of an entropy potential with position-dependent effective diffusivity, we approach the problem in terms of the modified Fick–Jacobs equation. This allows us to derive analytical expressions for mean first-passage time, as well as looping and transition path times. Comparison with results from Brownian dynamics simulations allows us to establish the domain of applicability of the one-dimensional description. We also compare our results with those obtained for three-dimensional conical tubes [A. M. Berezhkovskii, L. Dagdug, and S. M. Bezrukov, J. Chem. Phys. 147, 134104 (2017)].
Highlights
INTRODUCTIONTransport in systems of varying geometry has been studied in-depth at the theoretical level, given the ubiquitous nature of these systems in both nature and technology and how they control the dynamics of many physical, chemical, and biochemical processes. Examples include diffusion in artificially produced pores in thin solid films, proteins through a phase space funnellike region, transport in zeolites, and solid-state nanopores as single-molecule biosensors for the detection and structural analysis of individual molecules
In recent years, transport in systems of varying geometry has been studied in-depth at the theoretical level, given the ubiquitous nature of these systems in both nature and technology1–11 and how they control the dynamics of many physical, chemical, and biochemical processes.12 Examples include diffusion in artificially produced pores in thin solid films,13 proteins through a phase space funnellike region,14 transport in zeolites,15 and solid-state nanopores as single-molecule biosensors for the detection and structural analysis of individual molecules.16–18Recent experiments with single biological nanopores, studies of pulling proteins and nucleic acid folding, and single-molecule fluorescence spectroscopy have raised a number of questions that stimulated theoretical and computational investigation of barriercrossing dynamics.19 The fine structure of these trajectories has been analyzed in order to gain new insights into escape dynamics
The behavior observed by the curves can be understood using the entropy potential, which drives the particles to the absorbing boundary for expanding conical channels/tubes and pushes them back toward the reflecting boundary in the opposite case
Summary
Transport in systems of varying geometry has been studied in-depth at the theoretical level, given the ubiquitous nature of these systems in both nature and technology and how they control the dynamics of many physical, chemical, and biochemical processes. Examples include diffusion in artificially produced pores in thin solid films, proteins through a phase space funnellike region, transport in zeolites, and solid-state nanopores as single-molecule biosensors for the detection and structural analysis of individual molecules.. For conical 3D tubes, Berezhkovskii et al. derived analytical expressions for Laplace transforms of the probability densities of first-passage, transition path, and looping times, which they used to find the mean values of these random variables. (7) and (8) predict that the mean first-passage time goes to L2/2D0, as expected for a free particle diffusing into a cylindrical tube or along a 1D coordinate x.11. To such end, we begin by mapping the two-dimensional description of particle dynamics in the channel onto a one-dimensional description in terms of the modified Fick–Jacobs equation.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
