Predictions of diffusion models for one-ion membrane channels

Transport and escape in a deformable channel driven by fractional Gaussian noise

Fractional Gaussian noise (FGN) with the Hurst exponent H is an important tool to model various phenomena in biophysical systems, like subdiffusion in a single protein molecule. Considering that there also exists a confined structure which can be modeled as a channel in these systems, transport and escape driven by FGN in a deformable channel are investigated in this paper. By calculating the mean velocity, and the mean first passage time (MFPT) for crossing the nearest bottleneck and the probability distribution of the final position, effects of FGN and channel structure on the system dynamics are illustrated. Our results indicate that FGN has a complex influence mechanism under different combinations of H and the noise intensity. For a persistence case (H>0.5), the mean velocity decreases but MFPT increases with the increase of the noise intensity and H. While for an antipersistence case (H<0.5), when H is small, the relationships among the mean velocity, MFPT and the noise intensity are exactly the opposite to persistence cases. When H has a large value, the mean velocity tends to first decrease and then increase. Moreover, effects of the bottleneck and channel asymmetry are investigated. It is shown that a small H and a large channel width can lead to a large mean velocity and fast crossing. Besides, a channel asymmetry can affect the system dynamics by inducing asymmetric structure and adjusting the width of bottleneck. However, the effect of the bottleneck is the main factor. Therefore, a combination of channel with wide bottleneck and FGN in an antipersistence regime is the optimal choice to promote the transport and escape. These results provide a basis for the explanation of molecular activity in living organisms and the design of particle mixture separators.

Diffusion over an entropic barrier: non-Arrhenius behavior

We have examined the temperature dependence of noise-induced escape rate of brownian particles between two distinct regions in a two-dimensional enclosure through a narrow bottleneck. Varying cross section of the confinement results in an effective entropic barrier in reduced dimension. The strong non-Arrhenius dependence of the escape rate is observed, which can be explained in terms of a crossover between entropy-dominated regime and energy-dominated regime in presence of an interplay of gravitational bias and thermal motion.

Phase shift induces currents in a periodic tube

The average current of an overdamped Brownian particle moving along the axis of a three-dimensional periodic tube is investigated in the presence of a symmetric potential and a temporally symmetric unbiased external force. Reduction of the spatial dimensionality from two or three physical dimensions to an effective one-dimensional system entails the appearance of not only an entropic barrier but also an effective diffusion coefficient. The authors find that the phase shift between the tube shape and the potential can break the symmetry of the effective potential and can induce net currents. Under optimal condition, the current as a function of temperature and the phase shift possesses many extrema of alternating signs. The current may reverse its direction several times when temperature or the phase shift is changed. The authors' model is to describe the movement of molecular motors along microtubule.

Current in a three-dimensional periodic tube with unbiased forces

Transport of a Brownian particle moving along the axis of a three-dimensional asymmetric periodic tube is investigated in the presence of asymmetric unbiased forces. The reduction of the coordinates may involve not only the appearance of entropic barrier but also the effective diffusion coefficient. It is found that in the presence of entropic barrier, the asymmetry of the tube shape and the asymmetry of the unbiased forces are the two ways of inducing a net current. The current is a peaked function of temperature which indicates that the thermal noise may facilitate the transport even in the presence of entropic barrier. An optimized radius exists at the bottleneck at which the current takes its maximum value. Competition between the two opposite driving factors may induce current reversal.

Kinetic equations for diffusion in the presence of entropic barriers

We use the mesoscopic nonequilibrium thermodynamics theory to derive the general kinetic equation of a system in the presence of potential barriers. The result is applied to a description of the evolution of systems whose dynamics is influenced by entropic barriers. We analyze in detail the case of diffusion in a domain of irregular geometry in which the presence of the boundaries induces an entropy barrier when approaching the exact dynamics by a coarsening of the description. The corresponding kinetic equation, named the Fick-Jacobs equation, is obtained, and its validity is generalized through the formulation of a scaling law for the diffusion coefficient which depends on the shape of the boundaries. The method we propose can be useful to analyze the dynamics of systems at the nanoscale where the presence of entropy barriers is a common feature.

A site accessible to extracellular TEA+ and K+ influences intracellular Mg2+ block of cloned potassium channels

The members of the RCK family of cloned voltage-dependent K+ channels are quite homologous in primary structure, but they are highly diverse in functional properties. RCK4 channels differ from RCK1 and RCK2 channels in inactivation and permeation properties, the sensitivity to external TEA, and to current modulation by external K+ ions. Here we show several other interesting differences: While RCK1 and RCK2 are blocked in a voltage and concentration dependent manner by internal Mg2+ ions, RCK4 is only weakly blocked at very high potentials. The single-channel current-voltage relations of RCK4 are rather linear while RCK2 exhibits an inwardly rectifying single-channel current in symmetrical K+ solutions. The deactivation of the channels, measured by tail current protocols, is faster in RCK4 by a factor of two compared with RCK2. In a search for the structural motif responsible for these differences, point mutants creating homology between RCK2 and RCK4 in the pore region were tested. The single-point mutant K533Y in the background of RCK4 conferred the properties of Mg2+ block, tail current kinetics, and inward ion permeation of RCK2 to RCK4. This mutant was previously shown to be responsible for the alterations in external TEA sensitivity and channel regulation by external K+ ions. Thus, this residue is expected to be located at the external side of the pore entrance. The data are consistent with the idea that the mutation alters the channel occupancy by K+ and thereby indirectly affects internal Mg2+ block and channel closing.

Electrostatic interactions in gramicidin channels. Three-dielectric model

A model based on the solution of the electrostatic potential for a geometry of three dielectric regions associated with a gramicidin A channel (GA) is presented. The model includes a cylindrical dielectric layer to represent the peptide backbone and dipole rings to account for dipolar side chains. Image potential and dipolar contributions for different orientations and positions along the channel are analyzed. The conductance of GA and two analogues obtained by substituting the amino acid at position 1 are studied. The numerical simulation reproduces experimental results (Barrett et al. 1986, Biophys J 49, 673-686) and supports the idea that electrostatic dipole-ion interactions are of primary importance in gramicidin channel function.

Permeation in ionic channels: a statistical rate theory approach

A novel way to model permeation through ionic channels is formulated. Our method does not require that equilibrium exists in the channel or at the channel interfaces. In addition, the potential profile does not need to be specified and the assumption of constant field across the membrane does not need to be made. Our formulation relies on statistical rate theory for its development and uses a form of the electrochemical potential which assumes that the ions are in solution. We show that the conductance and the degree of nonlinearity are dependent on the relative equilibrium exchange rates in the channel and at the interfaces. Nonlinear current-voltage plots can be obtained in symmetric solutions as well as a nonunity exponent for the Ussing flux ratio. Due to the dependence of the partition coefficient on solubility, it is highly unlikely that the intracellular and extracellular partition coefficients are the same. A manifestation of unequal partition coefficients is a current reversal at a membrane voltage that is different from the Nernst potential of the current-carrying ionic species.