Anomalous Mole Fraction Effect Research Articles

Mechanisms of ion selectivity and throughput in the mitochondrial calcium uniporter.

The mitochondrial calcium uniporter, which regulates aerobic metabolism by catalyzing mitochondrial Ca2+ influx, is arguably the most selective ion channel known. The mechanisms for this exquisite Ca2+ selectivity have not been defined. Here, using a reconstituted system, we study the electrical properties of the channel's minimal Ca2+-conducting complex, MCU-EMRE, from Tribolium castaneum to probe ion selectivity mechanisms. The wild-type TcMCU-EMRE complex recapitulates hallmark electrophysiological properties of endogenous Uniporter channels. Through interrogation of pore-lining mutants, we find that a ring of glutamate residues, the "E-locus," serves as the channel's selectivity filter. Unexpectedly, a nearby "D-locus" at the mouth of the pore has diminutive influence on selectivity. Anomalous mole fraction effects indicate that multiple Ca2+ ions are accommodated within the E-locus. By facilitating ion-ion interactions, the E-locus engenders both exquisite Ca2+ selectivity and high ion throughput. Direct comparison with structural information yields the basis for selective Ca2+ conduction by the channel.

Calcium versus potassium selectivity in a nanopore: The effect of charge inversion at localized pore charges

The Anomalous Mole Fraction Effect (AMFE) in negatively charged pores has been considered as a signature of Ca2+ vs.monovalent ion (K+, in this study) selectivity. Increasing the mole fraction of CaCl2 in the KCl/CaCl2 mixture, the total conductance first declines as Ca2+ ions replace K+ ions inside the pore, then it increases as Ca2+ becomes the main charge carrier. While the AMFE was first pointed out in calcium selective ion channels, in a previous study (Gillespie et al., Biophys. J. 95 (2008) 609–619.) we showed that it is also present in synthetic nanopores. Here we use the Local Equilibrium Monte Carlo method coupled to the Nernst-Planck transport equation to study a simple model of a finite nanopore in a membrane with ions being explicitly modeled as charged hard spheres and water as an implicit continuum. The novel component of the model is the treatment of the pore charges that are present in localized COO− groups on the wall of the nanopore. Therefore, we study the effect of localizing the pore charges instead of smearing them as a continuous surface charge. Localized charges profoundly influence Ca2+ vs.K+ selectivity because they enhance charge inversion at the pore wall. Ca2+ ions overcharge the pore wall at which the K+ ions have a disadvantage in the K+ vs.Ca2+ competition because the overcharged pore wall does not attract them so strongly.

Extended kinetic lattice grand canonical Monte Carlo simulation method for transport of multicomponent ion mixtures through a model nanopore system

AbstractAn extended version of the original kinetic lattice grand canonical Monte Carlo simulation method combined with mean field theory (KLGCMC/MF) (J. Chem. Phys. 2007, 127, 024706) is presented for the study of transport of multicomponent ion mixtures through a model nanopore. Comparison of the extended KLGCMC/MF (eKLGCMC/MF) simulation results with Poisson–Nernst–Planck (PNP) calculations is also made to confirm the validity of the extended simulation approach. Unlike the original version of KLGCMC/MF simulation method that treats only a binary ionic solution with one cation and one anion species, this extended version can deal with a system that includes ternary ion mixtures. A diffusion probability algorithm is also added to the extended version of the simulation method to describe the inhomogeneous diffusivity of ions that is often observed in the ion permeation through nanopores. Both Legendre and Chebyshev polynomials of the second kind were tested as a basis set for the basis set expansion (BSE) method with which to calculate the reaction field energy in the eKLGCMC/MF simulation. It turned out that the Legendre polynomials perform better than the Chebyshev polynomials, and as a result, the Legendre polynomials were implemented in the current version of eKLGCMC/MF simulation algorithm. The presented eKLGCMC/MF simulation method with new features finds its potential applications in nanopore systems where the correlation between ion species with the same sign of charges plays a key role such as oscillating ion currents or anomalous mole fraction effects.

Transport mechanisms of SARS-CoV-E viroporin in calcium solutions: Lipid-dependent Anomalous Mole Fraction Effect and regulation of pore conductance

The envelope protein E of the SARS-CoV coronavirus is an archetype of viroporin. It is a small hydrophobic protein displaying ion channel activity that has proven highly relevant in virus-host interaction and virulence. Ion transport through E channel was shown to alter Ca2+ homeostasis in the cell and trigger inflammation processes. Here, we study transport properties of the E viroporin in mixed solutions of potassium and calcium chloride that contain a fixed total concentration (mole fraction experiments). The channel is reconstituted in planar membranes of different lipid compositions, including a lipid mixture that mimics the endoplasmic reticulum-Golgi intermediate compartment (ERGIC) membrane where the virus localizes within the cell. We find that the E ion conductance changes non-monotonically with the total ionic concentration displaying an Anomalous Mole Fraction Effect (AMFE) only when charged lipids are present in the membrane. We also observe that E channel insertion in ERGIC-mimic membranes – including lipid with intrinsic negative curvature – enhances ion permeation at physiological concentrations of pure CaCl2 or KCl solutions, with a preferential transport of Ca2+ in mixed KCl-CaCl2 solutions. Altogether, our findings demonstrate that the presence of calcium modulates the transport properties of the E channel by interacting preferentially with charged lipids through different mechanisms including direct Coulombic interactions and possibly inducing changes in membrane morphology.

Theory and Experiments on Multi-Ion Permeation and Selectivity in the NaChBac Ion Channel

The highly selective permeation of ions through biological ion channels is an unsolved problem of noise and fluctuations. In this paper, we motivate and introduce a non-equilibrium and self-consistent multi-species kinetic model, with the express aims of comparing with experimental recordings of current versus voltage and concentration and extracting important permeation parameters. For self-consistency, the behavior of the model at the two-state, i.e., selective limit in linear response, must agree with recent results derived from an equilibrium statistical theory. The kinetic model provides a good fit to data, including the key result of an anomalous mole fraction effect.

Potassium channel selectivity filter dynamics revealed by single-molecule FRET.

Potassium (K) channels exhibit exquisite selectivity for conduction of K+ ions over other cations, particularly Na+. High resolution structures reveal an archetypal selectivity filter (SF) conformation in which dehydrated K+, but not Na+, ions are perfectly coordinated. Using single molecule FRET (smFRET), we show that the SF-forming loop (SF-loop) in KirBac1.1 transitions between constrained and dilated conformations as a function of ion concentrations. The constrained conformation, essential for selective K+ permeability, is stabilized by K+ but not Na+ ions. Mutations that render channels non-selective result in dilated and dynamically unstable conformations, independent of the permeant ion. Further, while wild type KirBac1.1 channels are K+-selective in physiological conditions, Na+ permeates in the absence of K+. Moreover, while K+ gradients preferentially support 86Rb+ fluxes, Na+ gradients preferentially support 22Na+ fluxes. This suggests differential ion selectivity in constrained versus dilated states, potentially providing a structural basis for this anomalous mole fraction effect.

Permeation Mechanisms in the TMEM16B Calcium-Activated Chloride Channels.

TMEM16A and TMEM16B encode for Ca2+-activated Cl− channels (CaCC) and are expressed in many cell types and play a relevant role in many physiological processes. Here, I performed a site-directed mutagenesis study to understand the molecular mechanisms of ion permeation of TMEM16B. I mutated two positive charged residues R573 and K540, respectively located at the entrance and inside the putative channel pore and I measured the properties of wild-type and mutant TMEM16B channels expressed in HEK-293 cells using whole-cell and excised inside-out patch clamp experiments. I found evidence that R573 and K540 control the ion permeability of TMEM16B depending both on which side of the membrane the ion substitution occurs and on the level of channel activation. Moreover, these residues contribute to control blockage or activation by permeant anions. Finally, R573 mutation abolishes the anomalous mole fraction effect observed in the presence of a permeable anion and it alters the apparent Ca2+-sensitivity of the channel. These findings indicate that residues facing the putative channel pore are responsible both for controlling the ion selectivity and the gating of the channel, providing an initial understanding of molecular mechanism of ion permeation in TMEM16B.

Ionic Coulomb blockade and anomalous mole fraction effect in the NaChBac bacterial ion channel and its charge-varied mutants

Background. The selectivity of biological cation channels is defined by a short, narrow selectivity filter, having a negative net fixed charge Qf . Voltage gated bacterial channels (NaChBac and some others) are frequently used in biophysics as simplified models of mammalian calcium and sodium channels. We report an experimental, analytic and numerical study of the effects of Qf and bulk ionic concentrations of Ca2+ and Na+ on conduction and selectivity of NaChBac channels, wild type and Qf -varied mutants. Methods. Site-directed mutagenesis and voltage clamp recordings were used to investigate the Na+ /Ca2+ selectivity, divalent blockade and anomalous mole fraction effect (AMFE) for different NaChBac wild type/mutants channels and the properties dependence on Qf . Experimental results were compared with Brownian dynamics simulations and with analytic predictions of the ionic Coulomb blockade (ICB) model, which was extended to encompass bulk concentration effects. Results. It was shown that changing of Qf from –4e (for LESWAS wild type) to –8e (for LEDWAS mutant) leads to strong divalent blockade of the Na+ current by micromolar amounts of Ca2+ ions, similar to the effects seen in mammalian calcium channels. The BD simulations revealed a concentration-related logarithmic shift of the conduction bands. These results were shown to be consistent with ICB model predictions. Conclusions. The extended ICB model explains the experimental (divalent blockade and AMFE) and simulated (multi-ion bands and their concentration-related shifts) selectivity phenomena of NaChBac channel and its charge-varied mutants. These results extend the understanding of ion channel selectivity and may also be applicable to biomimetic nanopores with charged walls.

On the selectivity of the NaChBac channel: an integrated computational and experimental analysis of sodium and calcium permeation.

Ion channel selectivity is essential for their function, yet the molecular basis of a channel's ability to select between ions is still rather controversial. In this work, using a combination of molecular dynamics simulations and electrophysiological current measurements we analyze the ability of the NaChBac channel to discriminate between calcium and sodium. Our simulations show that a single calcium ion can access the Selectivity Filter (SF) interacting so strongly with the glutamate ring so as to remain blocked inside. This is consistent with the tiny calcium currents recorded in our patch-clamp experiments. Two reasons explain this scenario. The first is the higher free energy of ion/SF binding of Ca2+ with respect to Na+. The second is the strong electrostatic repulsion exerted by the resident ion that turns back a second potentially incoming Ca2+, preventing the knock-on permeation mechanism. Finally, we analyzed the possibility of the Anomalous Mole Fraction Effect (AMFE), i.e. the ability of micromolar Ca2+ concentrations to block Na+ currents. Current measurements in Na+/Ca2+ mixed solutions excluded the AMFE, in agreement with metadynamics simulations showing the ability of a sodium ion to by-pass and partially displace the resident calcium. Our work supports a new scenario for Na+/Ca2+ selectivity in the bacterial sodium channel, challenging the traditional notion of an exclusion mechanism strictly confining Ca2+ ions outside the channel.

Ion-Ion Interaction at the Multi-Ion TRPV1 Pore

Proton released upon tissue injury, inflammation, or ischemia produces sustained pain that may be mediated by nociceptor TRPV1. Our previous study demonstrated that extracellular H+ not only activates the channel but also inhibits ion permeation. Voltage-dependence of H+ inhibition suggested that H+ moves halfway into the transmembrane electric field. The location of inhibitory H+ and the mechanism underlying H+ inhibition, however, remain unclear. To investigate the role of H+ in ion permeation, we examined the behavior of TRPV1 permeant ions using anomalous mole fraction effect (AMFE). For the experiment, two types of permeant ions mixed at a constant total concentration but at varying ratio were used to measure conductance of TRPV1. An AMFE exists when one of the mixed solutions yields the minimum conductance compared to pure solutions. We found that TRPV1 exhibits AMFE in mixtures of Na+ and Rb+, suggesting the presence of multiple permeant ions in the pore. This result is interesting given that the structure of TRPV1 ion selectivity filter appears much shorter than that of potassium channels, which is known to hold multiple ions in a single file. The AMFE under acidic conditions will be measured to test whether H+ interferes with permeant ions in the TRPV1 pore to produce inhibition.

Coulomb blockade model of permeation and selectivity in biological ion channels

Biological ion channels are protein nanotubes embedded in, and passing through, the bilipid membranes of cells. Physiologically, they are of crucial importance in that they allow ions to pass into and out of cells, fast and efficiently, though in a highly selective way. Here we show that the conduction and selectivity of calcium/sodium ion channels can be described in terms of ionic Coulomb blockade in a simplified electrostatic and Brownian dynamics model of the channel. The Coulomb blockade phenomenon arises from the discreteness of electrical charge, the strong electrostatic interaction, and an electrostatic exclusion principle. The model predicts a periodic pattern of Ca2+ conduction versus the fixed charge Qf at the selectivity filter (conduction bands) with a period equal to the ionic charge. It thus provides provisional explanations of some observed and modelled conduction and valence selectivity phenomena, including the anomalous mole fraction effect and the calcium conduction bands. Ionic Coulomb blockade and resonant conduction are similar to electronic Coulomb blockade and resonant tunnelling in quantum dots. The same considerations may also be applicable to other kinds of channel, as well as to charged artificial nanopores.

Molecular Dynamics Study of Ion Conduction and Selectivity in a Prokaryotic Ion Channel

Since the publication of crystal structure of NavAb, the first of a (prokaryotic) voltage gated sodium channel, several computational studies have been aimed at determining the mechanisms of ion selectivity and ion conduction in voltage gated sodium channels. We provide a two-part study, well-converged free energy surfaces involving one, two and three ions provide results consistent with microsecond timescale simulations of ion conduction over concentration and voltages. The position of ions in the pore and cavity correlate to coordination number and side chain orientation, showing, as suggested by Chakrabarti et al. (PNAS (2013) 110, 11331). More surprising, presence of an ion in the aqueous cavity beneath the selectivity filter was sufficient to influence glutamate conformation.Because the crystal structure of NavAb was in a closed pore conformation, we truncated the S5 and S6 helices and restrained these outer helices harmonically in a membrane represented by supporting lattice of neon. The turrets, pore helices and selectivity filter were free to move. Conductances were in the range of the experimental values; however, our studies show no preference for sodium conduction over potassium conduction at physiological conditions (−200mV, 0.15 M salt). While sodium conductance varied little with respect to concentration and presence of potassium in solution, stronger potassium selectivity is observed at 1 M and in mixed solutions. Our results are consistent with the observation of anomalous mole fraction effect in NaChBac by Finol-Urdaneta et al. (JGP (2014) 143, 157-171), though not sufficient to confirm such an effect. Additionally, we provide mechanisms for ion conduction showing a greater variety of states and transitions occupied during potassium conduction, and note that at higher concentrations of salt the mechanism of conduction is not as clearly cut.

Poisson-Nernst-Planck-Fermi theory for modeling biological ion channels.

A Poisson-Nernst-Planck-Fermi (PNPF) theory is developed for studying ionic transport through biological ion channels. Our goal is to deal with the finite size of particle using a Fermi like distribution without calculating the forces between the particles, because they are both expensive and tricky to compute. We include the steric effect of ions and water molecules with nonuniform sizes and interstitial voids, the correlation effect of crowded ions with different valences, and the screening effect of water molecules in an inhomogeneous aqueous electrolyte. Including the finite volume of water and the voids between particles is an important new part of the theory presented here. Fermi like distributions of all particle species are derived from the volume exclusion of classical particles. Volume exclusion and the resulting saturation phenomena are especially important to describe the binding and permeation mechanisms of ions in a narrow channel pore. The Gibbs free energy of the Fermi distribution reduces to that of a Boltzmann distribution when these effects are not considered. The classical Gibbs entropy is extended to a new entropy form - called Gibbs-Fermi entropy - that describes mixing configurations of all finite size particles and voids in a thermodynamic system where microstates do not have equal probabilities. The PNPF model describes the dynamic flow of ions, water molecules, as well as voids with electric fields and protein charges. The model also provides a quantitative mean-field description of the charge/space competition mechanism of particles within the highly charged and crowded channel pore. The PNPF results are in good accord with experimental currents recorded in a 10(8)-fold range of Ca(2+) concentrations. The results illustrate the anomalous mole fraction effect, a signature of L-type calcium channels. Moreover, numerical results concerning water density, dielectric permittivity, void volume, and steric energy provide useful details to study a variety of physical mechanisms ranging from binding, to permeation, blocking, flexibility, and charge/space competition of the channel.

Analytical models of calcium binding in a calcium channel.

The anomalous mole fraction effect of L-type calcium channels is analyzed using a Fermi like distribution with the experimental data of Almers and McCleskey [J. Physiol. 353, 585 (1984)] and the atomic resolution model of Lipkind and Fozzard [Biochemistry 40, 6786 (2001)] of the selectivity filter of the channel. Much of the analysis is algebraic, independent of differential equations. The Fermi distribution is derived from the configuration entropy of ions and water molecules with different sizes, different valences, and interstitial voids between particles. It allows us to calculate potentials and distances (between the binding ion and the oxygen ions of the glutamate side chains) directly from the experimental data using algebraic formulas. The spatial resolution of these results is comparable with those of molecular models, but of course the accuracy is no better than that implied by the experimental data. The glutamate side chains in our model are flexible enough to accommodate different types of binding ions in different bath conditions. The binding curves of Na(+) and Ca(2+) for [CaCl2] ranging from 10(-8) to 10(-2) M with a fixed 32 mM background [NaCl] are shown to agree with published Monte Carlo simulations. The Poisson-Fermi differential equation-that includes both steric and correlation effects-is then used to obtain the spatial profiles of energy, concentration, and dielectric coefficient from the solvent region to the filter. The energy profiles of ions are shown to depend sensitively on the steric energy that is not taken into account in the classical rate theory. We improve the rate theory by introducing a steric energy that lumps the effects of excluded volumes of all ions and water molecules and empty spaces between particles created by Lennard-Jones type and electrostatic forces. We show that the energy landscape varies significantly with bath concentrations. The energy landscape is not constant.

Voltage control of Ca²⁺ permeation through N-type calcium (Ca(V)2.2) channels.

Voltage-gated calcium (Ca(V)) channels deliver Ca(2+) to trigger cellular functions ranging from cardiac muscle contraction to neurotransmitter release. The mechanism by which these channels select for Ca(2+) over other cations is thought to involve multiple Ca(2+)-binding sites within the pore. Although the Ca(2+) affinity and cation preference of these sites have been extensively investigated, the effect of voltage on these sites has not received the same attention. We used a neuronal preparation enriched for N-type calcium (Ca(V)2.2) channels to investigate the effect of voltage on Ca(2+) flux. We found that the EC50 for Ca(2+) permeation increases from 13 mM at 0 mV to 240 mM at 60 mV, indicating that, during permeation, Ca(2+) ions sense the electric field. These data were nicely reproduced using a three-binding-site step model. Using roscovitine to slow Ca(V)2.2 channel deactivation, we extended these measurements to voltages <0 mV. Permeation was minimally affected at these hyperpolarized voltages, as was predicted by the model. As an independent test of voltage effects on permeation, we examined the Ca(2+)-Ba(2+) anomalous mole fraction (MF) effect, which was both concentration and voltage dependent. However, the Ca(2+)-Ba(2+) anomalous MF data could not be reproduced unless we added a fourth site to our model. Thus, Ca(2+) permeation through Ca(V)2.2 channels may require at least four Ca(2+)-binding sites. Finally, our results suggest that the high affinity of Ca(2+) for the channel helps to enhance Ca(2+) influx at depolarized voltages relative to other ions (e.g., Ba(2+) or Na(+)), whereas the absence of voltage effects at negative potentials prevents Ca(2+) from becoming a channel blocker. Both effects are needed to maximize Ca(2+) influx over the voltages spanned by action potentials.

Synthetic anionophores for basic anions as "presumably, OH⁻/Cl⁻ antiporters": from the synthetic ion channels to multi-ion hopping, anti-Hofmeister selectivity, and strong positive AMFE.

We describe application of theory and kinetic modeling to study transport of basic anions by the small synthetic molecules. The findings should equip researchers in the particular field with a tool necessary to address an essential question: whether a given anion transporter facilitates permeation of F(-), CH3COO(-), N3(-), and SCN(-) across biological membrane or it does not. The basic anions undergo hydrolysis and conjugate acids (HAnion) are permeant species. However, because methods to quantitatively account for HAnion transport do not exist, traditionally, the phenomenon is also treated as non-existing. When the relative activities and selectivity of the synthetic anionophores are evaluated, basic and non-basic anions are regarded in the same exact way. Here, we show that HAnion and H(+)/OH(-) transport proceed on the same time scale as the anion exchange, nevertheless, comprehensive kinetic study could provide solution to the problems at hands, such as selective transport of HCO3(-) or F(-) anions. We also use theory and modeling to study other questions of particular concern: transport of OH(-) and H(+) ions, facilitated by the small synthetic anionophore, origin of modified anti-Hofmeister selectivity, multi-ion hopping, and anomalous mole-fraction effect in the synthetic ion channels. We do not need to model kinetics in a synthetic channel with multiple ion binding sites. Instead, we "test" the most simple anionophore, a lipophilic electroneutral carrier with Hofmeister-like selectivity, in the classical assays as "presumably, Cl(-)/OH(-) antiporter." The implications of findings to the particular field and beyond are discussed.

Poisson-Fermi Model of a Calcium Channel: Correlations and Dielectric Coefficient are Computed Outputs

We derive a continuum model of biological calcium channels, called the Poisson-Fermi equation, designed to deal with crowded systems in which ionic species and side chains nearly fill space. The model is evaluated in three dimensions. It includes steric and correlation effects and is derived from classical hard-sphere lattice models of the configurational entropy of spherical ions and solvent molecules. Formulae are given for all ionic species with different sizes and valences. Unphysical overcrowding does not occur with Fermi distributions, unlike with Boltzmann distributions. We provide an analytical description of the implicit dielectric (‘primitive’) model of electrolytes that yields global and local formulae for chemical potential. Poisson-Fermi equations are local, with different correlations at different places. Correlations produce spatial variations of dielectric permittivity as an output of analysis. Computations of binding are consistent with Monte Carlo binding curves. They have anomalous mole fraction effects, an effective blockage of sodium binding by a tiny concentration of calcium ions. Symbols and details in J.Computational Physics 2013, 15, 88; J Phys Chem B 2013 doi:10.1021/jp408330fView Large Image | View Hi-Res Image | Download PowerPoint Slide

Energetics of discrete selectivity bands and mutation-induced transitions in the calcium-sodium ion channels family

We use Brownian dynamics (BD) simulations to study the ionic conduction and valence selectivity of a generic electrostatic model of a biological ion channel as functions of the fixed charge Q(f) at its selectivity filter. We are thus able to reconcile the discrete calcium conduction bands recently revealed in our BD simulations, M0 (Q(f)=1e), M1 (3e), M2 (5e), with a set of sodium conduction bands L0 (0.5e), L1 (1.5e), thereby obtaining a completed pattern of conduction and selectivity bands vs Q(f) for the sodium-calcium channels family. An increase of Q(f) leads to an increase of calcium selectivity: L0 (sodium-selective, nonblocking channel) → M0 (nonselective channel) → L1 (sodium-selective channel with divalent block) → M1 (calcium-selective channel exhibiting the anomalous mole fraction effect). We create a consistent identification scheme where the L0 band is putatively identified with the eukaryotic sodium channel The scheme created is able to account for the experimentally observed mutation-induced transformations between nonselective channels, sodium-selective channels, and calcium-selective channels, which we interpret as transitions between different rows of the identification table. By considering the potential energy changes during permeation, we show explicitly that the multi-ion conduction bands of calcium and sodium channels arise as the result of resonant barrierless conduction. The pattern of periodic conduction bands is explained on the basis of sequential neutralization taking account of self-energy, as Q(f)(z,i)=ze(1/2+i), where i is the order of the band and z is the valence of the ion. Our results confirm the crucial influence of electrostatic interactions on conduction and on the Ca(2+)/Na(+) valence selectivity of calcium and sodium ion channels. The model and results could be also applicable to biomimetic nanopores with charged walls.

Correlated Ions in a Calcium Channel Model: A Poisson–Fermi Theory

We derive a continuum model, called the Poisson-Fermi equation, of biological calcium channels (of cardiac muscle, for example) designed to deal with crowded systems in which ionic species and side chains nearly fill space. The model is evaluated in three dimensions. It includes steric and correlation effects and is derived from classical hard-sphere lattice models of configurational entropy of finite size ions and solvent molecules. The maximum allowable close packing (saturation) condition is satisfied by all ionic species with different sizes and valences in a channel system, as shown theoretically and numerically. Unphysical overcrowding ("divergence") predicted by the Gouy-Chapman diffuse model (produced by a Boltzmann distribution of point charges with large potentials) does not occur with the Fermi-like distribution. Using probability theory, we also provide an analytical description of the implicit dielectric model of ionic solutions that gives rise to a global and a local formula for the chemical potential. In this primitive model, ions are treated as hard spheres and solvent molecules are described as a dielectric medium. The Poisson-Fermi equation is a local formula dealing with different correlations at different places. The correlation effects are apparent in our numerical results. Our results show variations of dielectric permittivity from bath to channel pore described by a new dielectric function derived as an output from the Poisson-Fermi analysis. The results are consistent with existing theoretical and experimental results. The binding curve of Poisson-Fermi is shown to match Monte Carlo data and illustrates the anomalous mole fraction effect of calcium channels, an effective blockage of permeation of sodium ions by a tiny concentration (or number) of calcium ions.

Asp residues of the Glu-Glu-Asp-Asp pore filter contribute to ion permeation and selectivity of the Cav3.2 T-type channel

Voltage-activated Ca2+ channels are membrane protein machinery performing selective permeation of external calcium ions. The main Ca2+ selective filters of all high-voltage-activated Ca2+ channel isoforms are commonly composed of four Glu residues (EEEE), while those of low-voltage-activated T-type Ca2+ channel isoforms are made up of two Glu and two Asp residues (EEDD). We here investigate how the Asp residues at the pore loops of domains III and IV affect biophysical properties of the Cav3.2 channel. Electrophysiological characterization of the pore mutant channels in which the pore Asp residue(s) were replaced with Glu, showed that both Asp residues critically control the biophysical properties of Cav3.2, including relative permeability between Ba2+ and Ca2+, anomalous mole fraction effect (AMFE), voltage dependency of channel activation, Cd2+ blocking sensitivity, and pH effects, in distinctive ways.