Stochastic Gating as a Novel Mechanism for Channel Selectivity

Flux through membrane channel: linear transport vs. single-molecule approaches

One of the most subtle steps in the single-molecule approach to the flux through the membrane channel, which uses the one-dimensional Smoluchowski equation, is to describe the molecule's "behavior" at the contacts between the channel openings and the bulk. Earlier, to handle this issue, we introduced the so-called "radiation boundary conditions" that account for the interplay between the two types of trajectories of the molecules starting at the openings, specifically, the ones that eventually return to the channel and the ones that escape to infinity. The latter trajectories represent the true translocation events on the condition that initially the molecule entered the channel from the opposite side. Here, we demonstrate that the single molecule approach based on the one-dimensional Smoluchowski equation with radiation boundary conditions leads to the same expression for the flux through the channel as the conventional approach based on the linear transport theory.

Counter-Intuitive Features of Particle Dynamics in Nanopores

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.

The Puzzle of Metabolite Exchange and Identification of Putative Octotrico Peptide Repeat Expression Regulators in the Nascent Photosynthetic Organelles of Paulinella chromatophora

The endosymbiotic acquisition of mitochondria and plastids more than one billion years ago was central for the evolution of eukaryotic life. However, owing to their ancient origin, these organelles provide only limited insights into the initial stages of organellogenesis. The cercozoan amoeba Paulinella chromatophora contains photosynthetic organelles-termed chromatophores-that evolved from a cyanobacterium ∼100 million years ago, independently from plastids in plants and algae. Despite the more recent origin of the chromatophore, it shows tight integration into the host cell. It imports hundreds of nucleus-encoded proteins, and diverse metabolites are continuously exchanged across the two chromatophore envelope membranes. However, the limited set of chromatophore-encoded solute transporters appears insufficient for supporting metabolic connectivity or protein import. Furthermore, chromatophore-localized biosynthetic pathways as well as multiprotein complexes include proteins of dual genetic origin, suggesting that mechanisms evolved that coordinate gene expression levels between chromatophore and nucleus. These findings imply that similar to the situation in mitochondria and plastids, also in P. chromatophora nuclear factors evolved that control metabolite exchange and gene expression in the chromatophore. Here we show by mass spectrometric analyses of enriched insoluble protein fractions that, unexpectedly, nucleus-encoded transporters are not inserted into the chromatophore inner envelope membrane. Thus, despite the apparent maintenance of its barrier function, canonical metabolite transporters are missing in this membrane. Instead we identified several expanded groups of short chromatophore-targeted orphan proteins. Members of one of these groups are characterized by a single transmembrane helix, and others contain amphipathic helices. We hypothesize that these proteins are involved in modulating membrane permeability. Thus, the mechanism generating metabolic connectivity of the chromatophore fundamentally differs from the one for mitochondria and plastids, but likely rather resembles the poorly understood mechanism in various bacterial endosymbionts in plants and insects. Furthermore, our mass spectrometric analysis revealed an expanded family of chromatophore-targeted helical repeat proteins. These proteins show similar domain architectures as known organelle-targeted expression regulators of the octotrico peptide repeat type in algae and plants. Apparently these chromatophore-targeted proteins evolved convergently to plastid-targeted expression regulators and are likely involved in gene expression control in the chromatophore.

Theoretical insights into mechanisms of channel-facilitated molecular transport in the presence of stochastic gating

Molecular motion through pores plays a crucial role in various natural and industrial processes. One of the most fascinating features of biological channel-facilitated transport is a stochastic gating process, when the channels dynamically fluctuate between several conformations during the translocation. Although this phenomenon has been intensively investigated, many properties of translocation in a dynamically changing environment remain not well understood microscopically. We developed a discrete-state stochastic framework to analyze the molecular mechanisms of transport processes with stochastic gating by explicitly calculating molecular fluxes through the pores. Two scenarios are specifically investigated: (1) symmetry preserving stochastic gating with free-energy changes and (2) stochastic gating with symmetry changes but without modifications in the overall particle-pore interactions. It is found that stochastic gating can either accelerate or slow down the molecular translocation depending on the specific parameters of the system. We argue that biological systems might optimize their performance by utilizing conformational fluctuations of channels. Our theoretical analysis clarifies physical-chemical aspects of the molecular mechanisms of transport with stochastic gating.

Effect of stochastic gating on the flux through a membrane channel: a steady-state approach

This paper deals with the effect of stochastic gating on the flux of solute molecules through a membrane channel. According to the conventional approach, this flux is given by the product of the flux through the open channel and the probability of finding the channel in the open state. Recently we derived an expression for the flux through a stochastically gated channel (Berezhkovskii and Bezrukov 2017 J. Chem. Phys. 147 084109) that showed that the conventional approach may underestimate the flux at fast gating by orders of magnitude. The present work proposes a novel approach to the problem: while our initial derivation of the expression for the flux focuses on the molecule propagator in the channel, here we treat the problem by considering the steady-state flux through an ensemble of identical stochastically gated channels. We show now that the effect of gating on the flux is independent of the gate position, i.e. whether the gate is located at the channel entrance or exit.