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

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

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

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

A nonlinear equation for ionic diffusion in a strong binary electrolyte

The problem of the one dimensional electro-diffusion of ions in a strong binary electrolyte is considered. In such a system the solute dissociates completely into two species of ions with unlike charges. The mathematical description consists of a diffusion equation for each species augmented by transport due to a self consistent electrostatic field determined by the Poisson equation. This mathematical framework also describes other important problems in physics such as electron and hole diffusion across semi-conductor junctions and the diffusion of ions in plasmas. If concentrations do not vary appreciably over distances of the order of the Debye length, the Poisson equation can be replaced by the condition of local charge neutrality first introduced by Planck. It can then be shown that both species diffuse at the same rate with a common diffusivity that is intermediate between that of the slow and fast species (ambipolar diffusion). Here we derive a more general theory by exploiting the ratio of Debye length to a characteristic length scale as a small asymptotic parameter. It is shown that the concentration of either species may be described by a nonlinear integro-differential equation which replaces the classical linear equation for ambipolar diffusion but reduces to it in the appropriate limit. Through numerical integration of the full set of equations it is shown that this nonlinear equation provides a better approximation to the exact solution than the linear equation it replaces.Comment: 4 pages, 1 figur

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

Diffusion of multiple species with excluded-volume effects

Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial differential equations. In this paper we consider multiple interacting subpopulations/species and study how the inter-species competition emerges at the population level. Each individual is described as a finite-size hard core interacting particle undergoing Brownian motion. The link between the discrete stochastic equations of motion and the continuum model is considered systematically using the method of matched asymptotic expansions. The system for two species leads to a nonlinear cross-diffusion system for each subpopulation, which captures the enhancement of the effective diffusion rate due to excluded-volume interactions between particles of the same species, and the diminishment due to particles of the other species. This model can explain two alternative notions of the diffusion coefficient that are often confounded, namely collective diffusion and self-diffusion. Simulations of the discrete system show good agreement with the analytic results

Sensing of Fluctuating Nanoscale Magnetic Fields Using NV Centres in Diamond

New magnetometry techniques based on Nitrogen-Vacancy (NV) defects in diamond allow for the imaging of static (DC) and oscillatory (AC) nanoscopic magnetic systems. However, these techniques require accurate knowledge and control of the sample dynamics, and are thus limited in their ability to image fields arising from rapidly fluctuating (FC) environments. We show here that FC fields place restrictions on the DC field sensitivity of an NV qubit magnetometer, and that by probing the dephasing rate of the qubit in a magnetic FC environment, we are able to measure fluctuation rates and RMS field strengths that would be otherwise inaccessible with the use of DC and AC magnetometry techniques. FC sensitivities are shown to be comparable to those of AC fields, whilst requiring no additional experimental overheads or control over the sample.Comment: 5 pages, 4 figure