Counter-Intuitive Features of Particle Dynamics in Nanopores

Abstract

Using the framework of a continuous diffusion model based on the Smoluchowski equation, we analyze particle dynamics in the confinement of a transmembrane nanopore. We briefly review existing analytical results to highlight consequences of interactions between the channel nanopore and the translocating particles. These interactions are described within a minimalistic approach by lumping together multiple physical forces acting on the particle in the pore into a one-dimensional potential of mean force. Such radical simplification allows us to obtain transparent analytical results, often in a simple algebraic form. While most of our findings are quite intuitive, some of them may seem unexpected and even surprising at first glance. The focus is on five examples: (i) attractive interactions between the particles and the nanopore create a potential well and thus cause the particles to spend more time in the pore but, nevertheless, increase their net flux; (ii) if the potential well-describing particle-pore interaction occupies only a part of the pore length, the mean translocation time is a non-monotonic function of the well length, first increasing and then decreasing with the length; (iii) when a rectangular potential well occupies the entire nanopore, the mean particle residence time in the pore is independent of the particle diffusivity inside the pore and depends only on its diffusivity in the bulk; (iv) although in the presence of a potential bias applied to the nanopore the “downhill” particle flux is higher than the “uphill” one, the mean translocation times and their distributions are identical, i.e., independent of the translocation direction; and (v) fast spontaneous gating affects nanopore selectivity when its characteristic time is comparable to that of the particle transport through the pore.