Fluxes of non-interacting and strongly repelling particles through a single conical channel: Analytical results and their numerical tests

Abstract

Using a diffusion model of particle dynamics in the channel, we study entropic effects in channelfacilitated transport. We derive general expressions for the fluxes of non-interacting particles and particles that strongly repel each other through the channel of varying cross section area, assuming that the transport is driven by the difference in particle concentrations on the two sides of the membrane. For a special case of a right truncated cone expanding in the left-to-right direction, we show how the fluxes depend on the geometric parameters of the channel and on the particle concentrations. For non-interacting particles the flux is direction-independent in the sense that inversion of the concentration difference leads to the inversion of the direction of the flux without changing its magnitude. This symmetry is broken for repelling particles: The flux in the left-toright direction exceeds its right-to-left counterpart. Our theoretical predictions are supported by three-dimensional Brownian dynamics simulations.

Kinetics and thermodynamics of binding reactions as exemplified by anthrax toxin channel blockage with a cationic cyclodextrin derivative

“…Aðx; βÞexpð−βUðx; βÞÞ dx; [8] where β = 1=ðk B TÞ, x is a coordinate measured along the channel axis, 0 ≤ x ≤ L, Aðx; βÞ is the coordinate-dependent cross-sectional area of the channel, and Uðx; βÞ is the coordinate-dependent potential of mean force describing particle interaction with the channel (6-8). Both the cross-sectional area and the potential of mean force are, in general, functions of temperature.…”

“…Although these two estimates generally do not have to coincide, this impressive difference compelled us to take a detailed look at the assumptions that are often used in the thermodynamic analysis of blocking reactions as well as at the possible physical forces involved in the channel-blocker interaction. Our analysis is based on consideration of a simple model of particle interaction with the channel (6)(7)(8), which allows an explicit calculation of the involved thermodynamics. As might be expected, in the case of the temperatureindependent flat potential well, the enthalpy of the binding reaction is equal to the depth of the potential well.…”

Obstructing Toxin Pathways by Targeted Pore Blockage

“…Introduction of the effective pore radius, R eff = R ch – r , accounts for the entropic contribution discussed above. Analysis can be easily extended to noncylindrical, e.g., conical, channels by including the position-dependent entropic potential into U ( x ). , …”

Propagating Concentration Polarization and Ionic Current Rectification in a Nanochannel–Nanofunnel Device

“…For instance, the transport properties of asymmetric channels and the corresponding phenomenological coefficients (e.g., hydraulic and electroosmotic permeabilities, ionic electric conductivity, diffusion coefficient, and mean residence time) are dependent on the direction of macroscopic mass and charge transport. This kind of anisotropy results in a number of intriguing phenomena, such as asymmetric diffusive flux, − valveless hydraulic pumping, , asymmetric electroosmotic flow (EOF), , and ionic current rectification (ICR). − Particularly, the latter two phenomena are respectively encountered when the EOF velocity and ionic current through a channel depend on the polarity of the applied bias.…”