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.

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.

A model of the ryanodine receptor (RyR) calcium channel is used to study the energetics of binding selectivity of Ca(2+) versus monovalent cations. RyR is a calcium-selective channel with a DDDD locus in the selectivity filter, similar to the EEEE locus of the L-type calcium channel. While the affinity of RyR for Ca(2+) is in the millimolar range (as opposed to the micromolar range of the L-type channel), the ease of single-channel measurements compared to L-type and its similar selectivity filter make RyR an excellent candidate for studying calcium selectivity. A Poisson-Nernst-Planck/density functional theory model of RyR is used to calculate the energetics of selectivity. Ca(2+) versus monovalent selectivity is driven by the charge/space competition mechanism in which selectivity arises from a balance of electrostatics and the excluded volume of ions in the crowded selectivity filter. While electrostatic terms dominate the selectivity, the much smaller excluded-volume term also plays a substantial role. In the D4899N and D4938N mutations of RyR that are analyzed, substantial changes in specific components of the chemical potential profiles are found far from the mutation site. These changes result in the significant reduction of Ca(2+) selectivity found in both theory and experiments.

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.

Calcium-selective ion channels are known to have carboxylate-rich selectivity filters, a common motif that is primarily responsible for their high Ca(2+) affinity. Different Ca(2+) affinities ranging from micromolar (the L-type Ca channel) to millimolar (the ryanodine receptor channel) are closely related to the different physiological functions of these channels. To understand the physical mechanism for this range of affinities given similar amino acids in their selectivity filters, we use grand canonical Monte Carlo simulations to assess the binding of monovalent and divalent ions in the selectivity filter of a model Ca channel. We use a reduced model where the electolyte is modeled by hard-sphere ions embedded in a continuum dielectric solvent, while the interior of protein surrounding the channel is allowed to have a dielectric coefficient different from that of the electrolyte. The induced charges that appear on the protein/lumen interface are calculated by the induced charge computation method [Boda et al., Phys. Rev. E 69, 046702 (2004)]. It is shown that decreasing the dielectric coefficient of the protein attracts more cations into the pore because the protein's carboxyl groups induce negative charges on the dielectric boundary. As the density of the hard-sphere ions increases in the filter, Ca(2+) is absorbed into the filter with higher probability than Na(+) because Ca(2+) provides twice the charge to neutralize the negative charge of the pore (both structural carboxylate oxygens and induced charges) than Na(+) while occupying about the same space (the charge/space competition mechanism). As a result, Ca(2+) affinity is improved an order of magnitude by decreasing the protein dielectric coefficient from 80 to 5. Our results indicate that adjusting the dielectric properties of the protein surrounding the permeation pathway is a possible way for evolution to regulate the Ca(2+) affinity of the common four-carboxylate motif.

Biological L-type calcium channels selectively accumulate Ca 2+ , even when there is 10 5 more Na + in the surrounding electrolyte solution. Like other Ca 2+ -chelating molecules, the L-type calcium channel has four carboxylate groups that contain eight oxygen ions. In this modeling study, these oxygens are confined to a small subvolume of the channel protein (the "filter") that is embedded in a bulk electrolyte solution (the "bath"). With the system in equilibrium, the concentrations of the ions and water in the filter are computed, given their concentrations in the bath. The excess thermodynamic properties are calculated using the mean spherical approximation (MSA), with water modeled as an uncharged hard sphere [the so-called solvent primitive model (SPM)] and a dielectric coefficient. Use of the SPM is an extension of previous work, where water was modeled as an amorphous dielectric. Other new aspects included in this study are changing the volume of the filter in response to the pressure generated by the water and ions in the filter and modeling solvation effects in more detail. The model is calibrated with a single experimental measurement. Predictions are compared to experimental results, where available, and future experiments are suggested. Finally, the model is considered as a Ca 2+ signal transducer able to perform substantial mechanical work in a Ca 2+ regulated protein.

Biological ion channels are proteins that passively conduct ions across membranes that are otherwise impermeable to ions. Here, we present a model of ion permeation and selectivity through a single, open ryanodine receptor (RyR) ion channel. Combining recent mutation data with electrodiffusion of finite-sized ions, the model reproduces the current/voltage curves of cardiac RyR (RyR2) in KCl, LiCl, NaCl, RbCl, CsCl, CaCl(2), MgCl(2), and their mixtures over large concentrations and applied voltage ranges. It also reproduces the reduced K(+) conductances and Ca(2+) selectivity of two skeletal muscle RyR (RyR1) mutants (D4899N and E4900Q). The model suggests that the selectivity filter of RyR contains the negatively charged residue D4899 that dominates the permeation and selectivity properties and gives RyR a DDDD locus similar to the EEEE locus of the L-type calcium channel. In contrast to previously applied barrier models, the current model describes RyR as a multi-ion channel with approximately three monovalent cations in the selectivity filter at all times. Reasons for the contradicting occupancy predictions are discussed. In addition, the model predicted an anomalous mole fraction effect for Na(+)/Cs(+) mixtures, which was later verified by experiment. Combining these results, the binding selectivity of RyR appears to be driven by the same charge/space competition mechanism of other highly charged channels.

Monte Carlo simulations of equilibrium selectivity of Na channels with a DEKA locus are performed over a range of radius R and protein dielectric coefficient epsilon(p). Selectivity arises from the balance of electrostatic forces and steric repulsion by excluded volume of ions and side chains of the channel protein in the highly concentrated and charged (approximately 30 M) selectivity filter resembling an ionic liquid. Ions and structural side chains are described as mobile charged hard spheres that assume positions of minimal free energy. Water is a dielectric continuum. Size selectivity (ratio of Na+ occupancy to K+ occupancy) and charge selectivity (Na+ to Ca2+) are computed in concentrations as low as 10(-5) M Ca2+. In general, small R reduces ion occupancy and favors Na+ over K+ because of steric repulsion. Small epsilon(p) increases occupancy and favors Na+ over Ca2+ because protein polarization amplifies the pore's net charge. Size selectivity depends on R and is independent of epsilon(p); charge selectivity depends on both R and epsilon(p). Thus, small R and epsilon(p) make an efficient Na channel that excludes K+ and Ca2+ while maximizing Na+ occupancy. Selectivity properties depend on interactions that cannot be described by qualitative or verbal models or by quantitative models with a fixed free energy landscape.