Ion transport between two baths of fixed ionic concentrations and applied electrostatic (ES) potential is analysed using a one-dimensional drift-diffusion (Poisson–Nernst–Planck, PNP) transport system designed to model biological ion channels. The ions are described as charged, hard spheres with excess chemical potentials computed from equilibrium density functional theory (DFT). The method of Rosenfeld (Rosenfeld Y 1993 J. Chem. Phys. 98 8126) is generalized to calculate the ES excess chemical potential in channels. A numerical algorithm for solving the set of integral–differential PNP/DFT equations is described and used to calculate flux through a calcium-selective ion channel.

L-type calcium channels are Ca(2+) binding proteins of great biological importance. They generate an essential intracellular signal of living cells by allowing Ca(2+) ions to move across the lipid membrane into the cell, thereby selecting an ion that is in low extracellular abundance. Their mechanism of selection involves four carboxylate groups, containing eight oxygen ions, that belong to the side chains of the "EEEE" locus of the channel protein, a setting similar to that found in many Ca(2+)-chelating molecules. This study examines the hypothesis that selectivity in this locus is determined by mutual electrostatic screening and volume exclusion between ions and carboxylate oxygens of finite diameters. In this model, the eight half-charged oxygens of the tethered carboxylate groups of the protein are confined to a subvolume of the pore (the "filter"), but interact spontaneously with their mobile counterions as ions interact in concentrated bulk solutions. The mean spherical approximation (MSA) is used to predict ion-specific excess chemical potentials in the filter and baths. The theory is calibrated using a single experimental observation, concerning the apparent dissociation constant of Ca(2+) in the presence of a physiological concentration of NaCl. When ions are assigned their independently known crystal diameters and the carboxylate oxygens are constrained, e.g., to a volume of 0.375 nm(3) in an environment with an effective dielectric coefficient of 63.5, the hypothesized selectivity filter produces the shape of the calcium binding curves observed in experiment, and it predicts Ba(2+)/Ca(2+) and Na(+)/Li(+) competition, and Cl(-) exclusion as observed. The selectivities for Na(+), Ca(2+), Ba(2+), other alkali metal ions, and Cl(-) thus can be predicted by volume exclusion and electrostatic screening alone. Spontaneous coordination of ions and carboxylates can produce a wide range of Ca(2+) selectivities, depending on the volume density of carboxylate groups and the permittivity in the locus. A specific three-dimensional structure of atoms at the binding site is not needed to explain Ca(2+) selectivity.

Nanotubes can selectively conduct ions across membranes to make ionic devices with transport characteristics similar to biological ion channels and semiconductor electron devices. Depending on the surface charge profile of the nanopore, ohmic resistors, rectifiers, and diodes can be made. Here we show that a uniformly charged conical nanopore can have all these transport properties by changing the ion species and their concentrations on each side of the membrane. Moreover, the cation vs. anion selectivity of the pores can be changed. We find that polyvalent cations like Ca 2+ and the trivalent cobalt sepulchrate produce localized charge inversion to change the effective pore surface charge profile from negative to positive. These effects are reversible so that the transport and selectivity characteristics of ionic devices can be tuned, much as the gate voltage tunes the properties of a semiconductor.

L-type Ca channels contain a cluster of four charged glutamate residues (EEEE locus), which seem essential for high Ca specificity. To understand how this highly charged structure might produce the currents and selectivity observed in this channel, a theory is needed that relates charge to current. We use an extended Poisson-Nernst-Planck (PNP2) theory to compute (mean) Coulombic interactions and thus to examine the role of the mean field electrostatic interactions in producing current and selectivity. The pore was modeled as a central cylinder with tapered atria; the cylinder (i.e., "pore proper") contained a uniform volume density of fixed charge equivalent to that of one to four carboxyl groups. The pore proper was assigned ion-specific, but spatially uniform, diffusion coefficients and excess chemical potentials. Thus electrostatic selection by valency was computed self-consistently, and selection by other features was also allowed. The five external parameters needed for a system of four ionic species (Na, Ca, Cl, and H) were determined analytically from published measurements of thre limiting conductances and two critical ion concentrations, while treating the pore as a macroscopic ion-exchange system in equilibrium with a uniform bath solution. The extended PNP equations were solved with these parameters, and the predictions were compared to currents measured in a variety of solutions over a range of transmembrane voltages. The extended PNP theory accurately predicted current-voltage relations, anomalous mole fraction effects in the observed current, saturation effects of varied Ca and Na concentrations, and block by protons. Pore geometry, dielectric permittivity, and the number of carboxyl groups had only weak effects. The successful prediction of Ca fluxes in this paper demonstrates that ad hoc electrostatic parameters, multiple discrete binding sites, and logistic assumptions of single-file movement are all unnecessary for the prediction of permeation in Ca channels over a wide range of conditions. Further work is needed, however, to understand the atomic origin of the fixed charge, excess chemical potentials, and diffusion coefficients of the channel. The Appendix uses PNP2 theory to predict ionic currents for published "barrier-and-well" energy profiles of this channel.

An approximate electrostatic (ES) excess free energy functional for charged, hard sphere fluids is presented. This functional is designed for systems with large density variations, but may also be applied to systems without such variations. Based on the Rosenfeld method of perturbation about a bulk (homogeneous) reference fluid [Y. Rosenfeld, J. Chem. Phys. 98, 8126 (1993)], the new ES functional replaces the reference fluid densities with a functional of the particle densities, called the RFD functional. The first-order direct correlation function (DCF) in the particle densities is computed using as input the first- and second-order DCFs in [rho(i)(x)], the inhomogeneous densities defined by the RFD functional. Because this formulation imposes no a priori constraints on the form of the RFD functional-it is valid for any choice of [rho(i)(x)]-the RFD functional may be chosen (1) so that the input DCFs (that is, DCFs in [rho(i)(x)]) may be approximated and (2) so the combination of [rho(i)(x)] and input DCFs yields a good estimate of the first-order DCF in the particle densities. In this way, the general problem of finding the excess free energy functional has been replaced by the specific problem of choosing a RFD functional. We present a particular RFD functional that, together with bulk formulations for the input DCFs, accurately reproduces the results of Monte Carlo simulations.