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

Using a diffusion model of particle dynamics in the channel, we study entropic effects in channel-facilitated 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.

Entropic effects in channel-facilitated transport: interparticle interactions break the flux symmetry.

We analyze transport through conical channels that is driven by the difference in particle concentrations on the two sides of the membrane. Because of the detailed balance, fluxes of noninteracting particles through the same channel, inserted into the membrane in two opposite orientations, are equal. We show that this flux symmetry is broken by particle-particle interactions so that one of the orientations can be much more efficient for transport under the same external conditions.

Relaxation and fluctuations of the number of particles in a membrane channel at arbitrary particle-channel interaction.

We analyze the relaxation of the particle number fluctuations in a membrane channel at arbitrary particle-channel interaction and derive general expressions for the relaxation time and low-frequency limit of the power spectral density. These expressions simplify significantly when the channel is symmetric. For a square-well potential of mean force that occupies the entire channel, we verify the accuracy of the analytical predictions by Brownian dynamics simulations.

Diffusion in a tube of varying cross section: numerical study of reduction to effective one-dimensional description.

Brownian dynamics simulations of the particle diffusing in a long conical tube (the length of the tube is much greater than its smallest radius) are used to study reduction of the three-dimensional diffusion in tubes of varying cross section to an effective one-dimensional description. The authors find that the one-dimensional description in the form of the Fick-Jacobs equation with a position-dependent diffusion coefficient, D(x), suggested by Zwanzig [J. Phys.

Analytical theory of hysteresis in ion channels: two-state model.

Channel-forming proteins in a lipid bilayer of a biological membrane usually respond to variation of external voltage by changing their conformations. Periodic voltages with frequency comparable with the inverse relaxation time of the protein produce hysteresis in the occupancies of the protein conformations. If the channel conductance changes when the protein jumps between these conformations, hysteresis in occupancies is observed as hysteresis in ion current through the channel.