Ion transport through confined ion channels in the presence of immobile charges

We study charge transport in an ionic solution in a confined nanoscale geometry in the presence of an externally applied electric field and immobile background charges. For a range of parameters, the ion current shows non-monotonic behavior as a function of the external ion concentration. For small applied electric field, the ion transport can be understood from simple analytic arguments, which are supported by Monte Carlo simulation. The results qualitatively explain measurements of ion current seen in a recent experiment on ion transport through a DNA-threaded nanopore (D. J. Bonthuis et. al., Phys. Rev. Lett, vol. 97, 128104 (2006)).Comment: 5 pages, 3 figure

On the Physics of Size Selectivity

We demonstrate that two mechanisms used by biological ion channels to select particles by size are driven by entropy. With uncharged particles in an infinite cylinder, we show that a channel that attracts particles is small-particle selective and that a channel that repels water from the wall is large-particle selective. Comparing against extensive density-functional theory calculations of our model, we find that the main physics can be understood with surprisingly simple bulk models that neglect the confining geometry of the channel completely.Comment: 4 pages, 3 figures, Phys. Rev. Lett. (accepted

Voltage sensing in ion channels: Mesoscale simulations of biological devices

Electrical signaling via voltage-gated ion channels depends upon the function of a voltage sensor (VS), identified with the S1-S4 domain in voltage-gated K+ channels. Here we investigate some energetic aspects of the sliding-helix model of the VS using simulations based on VS charges, linear dielectrics and whole-body motion. Model electrostatics in voltage-clamped boundary conditions are solved using a boundary element method. The statistical mechanical consequences of the electrostatic configurational energy are computed to gain insight into the sliding-helix mechanism and to predict experimentally measured ensemble properties such as gating charge displaced by an applied voltage. Those consequences and ensemble properties are investigated for two alternate S4 configurations, \alpha- and 3(10)-helical. Both forms of VS are found to have an inherent electrostatic stability. Maximal charge displacement is limited by geometry, specifically the range of movement where S4 charges and counter-charges overlap in the region of weak dielectric. Charge displacement responds more steeply to voltage in the \alpha-helical than the 3(10)-helical sensor. This difference is due to differences on the order of 0.1 eV in the landscapes of electrostatic energy. As a step toward integrating these VS models into a full-channel model, we include a hypothetical external load in the Hamiltonian of the system and analyze the energetic in/output relation of the VS.Comment: arXiv admin note: substantial text overlap with arXiv:1112.299

Entropic transport - A test bed for the Fick-Jacobs approximation

Biased diffusive transport of Brownian particles through irregularly shaped, narrow confining quasi-one-dimensional structures is investigated. The complexity of the higher dimensional diffusive dynamics is reduced by means of the so-called Fick-Jacobs approximation, yielding an effective one-dimensional stochastic dynamics. Accordingly, the elimination of transverse, equilibrated degrees of freedom stemming from geometrical confinements and/or bottlenecks cause entropic potential barriers which the particles have to overcome when moving forward noisily. The applicability and the validity of the reduced kinetic description is tested by comparing the approximation with Brownian dynamics simulations in full configuration space. This non-equilibrium transport in such quasi-one-dimensional irregular structures implies for moderate-to-strong bias a characteristic violation of the Sutherland-Einstein fluctuation-dissipation relation.Comment: 15 pages, 6 figures ; Phil. Trans. R. Soc. A (2009), in pres

Effect of Interactions on Molecular Fluxes and Fluctuations in the Transport Across Membrane Channels

Transport of molecules across membrane channels is investigated theoretically using exactly solvable one-dimensional discrete-state stochastic models. An interaction between molecules and membrane pores is modeled via a set of binding sites with different energies. It is shown that the interaction potential strongly influences the particle currents as well as fluctuations in the number of translocated molecules. For small concentration gradients the attractive sites lead to largest currents and fluctuations, while the repulsive interactions yield the largest fluxes and dispersions for large concentration gradients. Interaction energies that lead to maximal currents and maximal fluctuations are the same only for locally symmetric potentials, while they differ for the locally asymmetric potentials. The conditions for the most optimal translocation transport with maximal current and minimal dispersion are discussed. It is argued that in this case the interaction strength is independent of local symmetry of the potential of mean forces. In addition, the effect of the global asymmetry of the interaction potential is investigated, and it is shown that it also strongly affects the particle translocation dynamics. These phenomena can be explained by analyzing the details of the particle entering and leaving the binding sites in the channel.Comment: submitted to J. Chem. Phy

Optimization of the leak conductance in the squid giant axon

We report on a theoretical study showing that the leak conductance density, \GL, in the squid giant axon appears to be optimal for the action potential firing frequency. More precisely, the standard assumption that the leak current is composed of chloride ions leads to the result that the experimental value for \GL is very close to the optimal value in the Hodgkin-Huxley model which minimizes the absolute refractory period of the action potential, thereby maximizing the maximum firing frequency under stimulation by sharp, brief input current spikes to one end of the axon. The measured value of \GL also appears to be close to optimal for the frequency of repetitive firing caused by a constant current input to one end of the axon, especially when temperature variations are taken into account. If, by contrast, the leak current is assumed to be composed of separate voltage-independent sodium and potassium currents, then these optimizations are not observed.Comment: 9 pages; 9 figures; accepted for publication in Physical Review

Ab initio molecular dynamics calculations of ion hydration free energies

We apply ab initio molecular dynamics (AIMD) methods in conjunction with the thermodynamic integration or "lambda-path" technique to compute the intrinsic hydration free energies of Li+, Cl-, and Ag+ ions. Using the Perdew-Burke-Ernzerhof functional, adapting methods developed for classical force field applications, and with consistent assumptions about surface potential (phi) contributions, we obtain absolute AIMD hydration free energies (Delta G(hyd)) within a few kcal/mol, or better than 4%, of Tissandier 's [J. Phys. Chem. A 102, 7787 (1998)] experimental values augmented with the SPC/E water model phi predictions. The sums of Li+/Cl- and Ag+/Cl- AIMD Delta G(hyd), which are not affected by surface potentials, are within 2.6% and 1.2 % of experimental values, respectively. We also report the free energy changes associated with the transition metal ion redox reaction Ag++Ni+-> Ag+Ni2+ in water. The predictions for this reaction suggest that existing estimates of Delta G(hyd) for unstable radiolysis intermediates such as Ni+ may need to be extensively revised.Comment: 18 pages, 8 figures. This version is essentially the one published in J. Chem. Phy

Ion-channel-like behavior in lipid bilayer membranes at the melting transition

It is well known that at the gel-liquid phase transition temperature a lipid bilayer membrane exhibits an increased ion permeability. We analyze the quantized currents in which the increased permeability presents itself. The open time histogram shows a "-3/2" power law which implies an open-closed transition rate that decreases like $k(t) \propto t^{-1}$ as time evolves. We propose a "pore freezing" model to explain the observations. We discuss how this model also leads to the $1/f^{\alpha}$ noise that is commonly observed in currents across biological and artificial membranes.Comment: 5 pages, 4 figure

Asymmetry in shape causing absolute negative mobility

We propose a simple classical concept of nanodevices working in an absolute negative mobility (ANM) regime: The minimal spatial asymmetry required for ANM to occur is embedded in the geometry of the transported particle, rather than in the channel design. This allows for a tremendous simplification of device engineering, thus paving the way towards practical implementations of ANM. Operating conditions and performance of our model device are investigated, both numerically and analytically.Comment: 6 pages; accepted for publication in PR

Unidirectional hopping transport of interacting particles on a finite chain

Particle transport through an open, discrete 1-D channel against a mechanical or chemical bias is analyzed within a master equation approach. The channel, externally driven by time dependent site energies, allows multiple occupation due to the coupling to reservoirs. Performance criteria and optimization of active transport in a two-site channel are discussed as a function of reservoir chemical potentials, the load potential, interparticle interaction strength, driving mode and driving period. Our results, derived from exact rate equations, are used in addition to test a previously developed time-dependent density functional theory, suggesting a wider applicability of that method in investigations of many particle systems far from equilibrium.Comment: 33 pages, 8 figure