Ionic selectivity, saturation, and block in sodium channels. A four- barrier model

Ionic fluxes in Na channels of myelinated axons show ionic competition, block, and deviations from simple flux independence. These phenomena are particularly evident when external Na+ ions are replaced by other permeant or impermeant ions. The observed currents require new flux equations not based on the concepts of free diffusion. A specific permeability model for the Na channel is developed from Eyring rate theory applied to a chain of saturable binding sites. There are four energy barriers in the pore and only one ion is allowed inside at a time. Deviations from independence arise from saturation. The model shows that ionic permeability ratios measured from zero-current potentials can differ from those measured from relative current amplitudes or conductances. The model can be fitted to experiments with various external sodium substitutes by varying only two parameters: For each ion the height of the major energy barrier (the selectivity filter) determines the biionic zero-current potential and the depth of the energy well (binding site) just external to that barrier then determines the current amplitudes. Voltage clamp measurements with myelinated nerve fibers are given showing numerous examples of deviations from independence in ionic fluxes. Strong blocks of ionic currents by guanidinium compounds and Tl+ ions are fitted by binding within the channel with apparent dissociation constants in the range 50-122 mM. A small block with high Na+ concentrations can be fitted by Na+ ion binding with a dissociation constant of 368 mM. The barrier model is given a molecular interpretation that includes stepwise dehydration of the permeating ion as it interacts with an ionized carboxylic acid.     

Barrier permeability at cut axonal ends progressively decreases until an ionic seal is formed

After axonal severance, a barrier forms at the cut ends to rapidly restrict bulk inflow and outflow. In severed crayfish axons we used the exclusion of hydrophilic, fluorescent dye molecules of different sizes (0.6-70 kDa) and the temporal decline of ionic injury current to levels in intact axons to determine the time course (0-120 min posttransection) of barrier formation and the posttransection time at which an axolemmal ionic seal had formed, as confirmed by the recovery of resting and action potentials. Confocal images showed that the posttransection time of dye exclusion was inversely related to dye molecular size. A barrier to the smallest dye molecule formed more rapidly (<60 min) than did the barrier to ionic entry (>60 min). These data show that axolemmal sealing lacks abrupt, large changes in barrier permeability that would be expected if a seal were to form suddenly, as previously assumed. Rather, these data suggest that a barrier forms gradually and slowly by restricting the movement of molecules of progressively smaller size amid injury-induced vesicles that accumulate, interact, and form junctional complexes with each other and the axolemma at the cut end. This process eventually culminates in an axolemmal ionic seal, and is not complete until ionic injury current returns to baseline levels measured in an undamaged axon.     

Semiconductor theory of ion transport in thin lipid membranes: II. Surface recombination

Following the theory of surface recombination in semiconductors, we have derived an expression for the rate of ion recombination at the membrane surface. The surface recombination rate is used in the boundary conditions of current flows at the interfaces. Expressions for the ion fluxes are then derived as functions of environmental variables and membrane parameters. Our analysis strongly suggests that the ion flow through a thin lipid membrane consists of two major components: the surface barrier jumping current and the surface recombination current that are controlled decisively by surface barrier height, surface trap density and surface recombination rates. These general formulations are useful not only for the calculation but also for the understanding of ion transport in thin lipid membranes under a variety of experimental conditions. The implications of this theory to biological membranes and its possible extensions are discussed.     

Surface charge and lanthanum block of calcium current in bullfrog sympathetic neurons.

The density of surface charge associated with the calcium channel pore was estimated from the effect of extracellular ionic strength on block by La3+. Currents carried by 2 mM Ba2+ were recorded from isolated frog sympathetic neurons by the whole-cell patch-clamp technique. In normal ionic strength (120 mM N-methyl-D-glucamine, NMG), La3+ blocked the current with high affinity (IC50 = 22 nM at 0 mV). La3+ block was relieved by strong depolarization in a time- and voltage-dependent manner. After unblocking, open channels reblocked rapidly at 0 mV, allowing estimation of association and dissociation rates for La3+: k(on) = (7.2 +/- 0.7) x 10(8) M(-1) s(-1), k(off) = 10.0 +/- 0.5 s(-1). To assess surface charge effects, La3+ block was also measured in low ionic strength (12.5 mM NMG) and high ionic strength (250 mM NMG). La3+ block was higher affinity and faster by two- to threefold in 12.5 mM NMG, with little effect of 250 mM NMG. The data could be described by Gouy-Chapman theory with a surface charge density of approximately 1 e-/3000-4000 A2. These results indicate that there is a small but detectable surface charge associated with the pore of voltage-dependent calcium channels.     

Gating pore currents in DIIS4 mutations of NaV1.4 associated with periodic paralysis: saturation of ion flux and implications for disease pathogenesis

S4 voltage–sensor mutations in CaV1.1 and NaV1.4 channels cause the human muscle disorder hypokalemic periodic paralysis (HypoPP). The mechanism whereby these mutations predispose affected sarcolemma to attacks of sustained depolarization and loss of excitability is poorly understood. Recently, three HypoPP mutations in the domain II S4 segment of NaV1.4 were shown to create accessory ionic permeation pathways, presumably extending through the aqueous gating pore in which the S4 segment resides. However, there are several disparities between reported gating pore currents from different investigators, including differences in ionic selectivity and estimates of current amplitude, which in turn have important implications for the pathological relevance of these aberrant currents. To clarify the features of gating pore currents arising from different DIIS4 mutants, we recorded gating pore currents created by HypoPP missense mutations at position R666 in the rat isoform of Nav1.4 (the second arginine from the outside, at R672 in human NaV1.4). Extensive measurements were made for the index mutation, R666G, which created a gating pore that was permeable to K⁺ and Na⁺. This current had a markedly shallow slope conductance at hyperpolarized voltages and robust inward rectification, even when the ionic gradient strongly favored outward ionic flow. These characteristics were accounted for by a barrier model incorporating a voltage-gated permeation pathway with a single cation binding site oriented near the external surface of the electrical field. The amplitude of the R666G gating pore current was similar to the amplitude of a previously described proton-selective current flowing through the gating pore in rNaV1.4-R663H mutant channels. Currents with similar amplitude and cation selectivity were also observed in R666S and R666C mutant channels, while a proton-selective current was observed in R666H mutant channels. These results add support to the notion that HypoPP mutations share a common biophysical profile comprised of a low-amplitude inward current at the resting potential that may contribute to the pathological depolarization during attacks of weakness.     

Charge modification of the endothelial surface layer modulates the permeability barrier of isolated rat mesenteric small arteries

We hypothesized that modulation of the effective charge density of the endothelial surface layer (ESL) results in altered arterial barrier properties to transport of anionic solutes. Rat mesenteric small arteries (diameter approximately 190 microm) were isolated, cannulated, perfused, and superfused with MOPS-buffered physiological salt solutions. MOPS-solutions were of normal ionic strength (162 mM, MOPS), low ionic strength (81 mM, LO-MOPS), or high ionic strength (323 mM, HI-MOPS), to modulate ESL charge density (normal, high, or low ESL charge, respectively). Osmolarity of MOPS, LO-MOPS, and HI-MOPS was kept constant at 297 mosmol/l, using additional glucose when necessary. Perfusate solutions were supplemented with 1% BSA. Arteries were cannulated with a double-barreled theta-pipet on the inlet side and a regular pipet on the outlet side. After infusion of FITC-labeled dextran of 50 kDa (FITC-Delta50) and the endothelial membrane dye 1,1'-dioctadecyl-3,3,3',3'-tetramethylindocarbocyanine perchlorate, the dynamics of arterial dye filling were determined with confocal microscopy. ESL thickness, as determined from the initial exclusion zone for FITC-Delta50 on the luminal endothelial surface, was 6.3 +/- 1.4 microm for LO-MOPS, 2.7 +/- 1.0 microm for MOPS, and 1.1 +/- 1.3 microm for HI-MOPS. At low ionic strength, FITC-Delta50 permeated into the ESL with a total ESL permeation time (tauESL) of 26 min, and at normal ionic strength with a tauESL of 20 min. No apparent exclusion of FITC-Delta50 from the ESL could be observed at high ionic strength. In conclusion, we demonstrate that the modulation of solvent ionic strength influences the thickness and barrier properties of the ESL.     

Optimization of label-free DNA detection with electrochemical impedance spectroscopy using PNA probes

DNA biosensors, especially those based upon detection of the intrinsic negative charge of target DNA, can be greatly improved by the use of uncharged peptide nucleic acid (PNA) probes. Hybridization causes an increased electrostatic barrier for the negatively charged ferri/ferrocyanide redox couple, resulting in an increase in charge transfer resistance R(ct) that is measured using electrochemical impedance spectroscopy. We report on the optimization of PNA probe surface density by the simultaneous co-immobilization of thiol-modified probes and mercaptohexanol, with the PNA surface density controlled by the thiol mole ratio in solution. Maximum R(ct) change upon hybridization is obtained with 10% PNA mole fraction. The effect of the measurement buffer ionic strength is investigated. The electrostatic barrier for charge transfer to the ferri/ferrocyanide redox couple is approximately independent of ionic strength with PNA probes, but greatly increases with decreasing ionic strength, after hybridization with target DNA. This significantly enhances the R(ct) change upon hybridization. The optimization of PNA surface density and measurement buffer ionic strength leads to a 385-fold increase in R(ct) upon hybridization, a factor of 100 larger than previously reported results using either PNA or DNA probes.     

Permeation and interaction of monovalent cations with the cGMP-gated channel of cone photoreceptors

We measured the ion selectivity of cGMP-dependent currents in detached membrane patches from the outer segment of cone photoreceptors isolated from the retina of striped bass. In inside-out patches excised from either single or twin cones the amplitude of these currents, under symmetric ionic solutions, changed with the concentration of cGMP with a dependence described by a Hill equation with average values, at +80 mV, of Km = 42.6 microM and n = 2.49. In the absence of divalent cations, and under symmetric ionic solutions, the I-V curves of the currents were linear over the range of -80 to +80 mV. The addition of Ca altered the form of the I-V curve to a new function well described by an empirical equation that also describes the I-V curve of the photocurrent measured in intact photoreceptors. The monovalent cation permeability sequence of the cGMP-gated channels in the absence of divalent ions was PK > PNa = PLi = PRb > PCs (1.11 > 1.0 = 0.99 = 0.96 > 0.82). The conductance selectivity sequence at +80 mV was GNa = GK > GRb > GCs > GLi (1.0 = 0.99 > 0.88 > 0.74 > 0.60). The organic cations tetramethylammonium (TMA) and arginine partially blocked the current, but the larger ion, arginine, was permeant, whereas the smaller ion, TMA, was not. The amplitude of the outward current through the channels increased with the concentration of monovalent cations on the cytoplasmic membrane surface, up to a saturating value. The increase was well described by the adsorption isotherm of a single ion binding site within the channel with average binding constants, at +80 mV, of 104 mM for Na and 37.6 mM for Li. By assuming that the ion channel contains a single ion binding site in an energy trough separated from each membrane surface by an energy barrier, and using Eyring rate theory, we simulated I-V curves that fit the experimental data measured under ionic concentration gradients. From this fit we conclude that the binding site interacts with one ion at a time and that the energy barriers are asymmetrically located within the membrane thickness. Comparison of the quantitative features of ion permeation and interaction between the cGMP-gated channels of rod and cone photoreceptors reveals that the ion binding sites are profoundly different in the two types of channels. This molecular difference may be particularly important in explaining the differences in the transduction signal of each receptor type.     

How electrolyte shielding influences the electrical potential in transmembrane ion channels.

The electrical potential due to fixed charge distributions is strongly altered in the vicinity of a membrane and notably dependent on aqueous electrolyte concentration. We present an efficient way to solve the nonlinear Poisson-Boltzmann equation applicable to general cylindrically symmetric dielectric geometries. It generalizes Gouy-Chapman theory to systems containing transmembrane channels. The method is applied to three channel systems: gramicidin, gap junction, and porin. We find that for a long, narrow channel such as gramicidin concentration variation has little influence on the electrical image barrier to ion permeation. However, electrolyte shielding reduces the image induced contribution to the energy required for multiple occupancy. In addition, the presence of electrolyte significantly affects the voltage profile due to an applied potential, substantially compressing the electric field to the immediate vicinity of the pore itself. In the large diameter channels, where bulk electrolyte may be assumed to enter the pore, the electrolyte greatly reduces the image barrier to ion permeation. At physiological ionic strengths this barrier is negligible and the channel may be readily multiply occupied. At all ionic strengths considered (l greater than 0.005 M) the image barrier saturates rapidly and is essentially constant more than one channel radius from the entrance to the pore. At lower ionic strengths (l less than 0.016 M) there are noticeable (greater than 20 mV) energy penalties associated with multiple occupancy.     

Perineurium in the Drosophila (Diptera : Drosophilidae) embryo and its role in the blood-brain/nerve barrier

A monolayer of perineurial cells overlies glia and neurons, and this stratum of the central nervous system is the principal site of the Drosophila (Diptera : Drosophilidae) blood-brain barrier. Perineurial cells are bonded together by pleated-sheet septate junctions that are the anatomical correlate of the vertebrate tight junction. The blood-brain barrier maintains the ionic homeostasis necessary for proper nerve function. It was known that a functioning blood-brain barrier is present in mature (Stage 17) Drosophila embryos, but the genesis of this barrier was not known. We surveyed the central nervous system of late stage embryos (15 through 17) to determine when perineurial cells could first be detected. These cells take their place in (on) the central nervous system and are joined together by pleated-sheet septate junctions, during Stage 17. Those septate junctions are quickly occlusive to lanthanum tracer. This development step occurs during the same time as when chemical synapses first become functional. Such concurrent maturation is far from coincidental, because partitioning nerves and their synapses from hemolymph (with its variable ionic constitution) are essential for normal electrophysiology. We discuss details of the germ line derivation of perineurial cells, their first detection in the embryonic central nervous system, their functional properties, and the polygonal cell-packing pattern seen in the larval central nervous system.     

Surface charge and calcium channel saturation in bullfrog sympathetic neurons

Currents carried by Ba2+ through calcium channels were recorded in the whole-cell configuration in isolated frog sympathetic neurons. The effect of surface charge on the apparent saturation of the channel with Ba2+ was examined by varying [Ba2+]o and ionic strength. The current increased with [Ba2+]o, and the I-V relation and the activation curve shifted to more positive voltages. The shift of activation could be described by Gouy-Chapman theory, with a surface charge density of 1 e- /140 A2, calculated from the Grahame equation. Changes in ionic strength (replacing N-methyl-D-glucamine with sucrose) shifted the activation curve as expected for a surface charge density of 1 e-/85 A2, in reasonable agreement with the value from changing [Ba2+]o. The instantaneous I-V for fully activated channels also changed with ionic strength, which could be described either by a low surface charge density (less than 1 e-/1,500 A2), or by block by NMG with Kd approximately 300 mM (assuming no surface charge). We conclude that the channel permeation mechanism sees much less surface charge than the gating mechanism. The peak inward current saturated with an apparent Kd = 11.6 mM for Ba2+, while the instantaneous I-V saturated with an apparent Kd = 23.5 mM at 0 mV. This discrepancy can be explained by a lower surface charge near the pore, compared to the voltage sensor. After correction for a surface charge near the pore of 1 e-/1,500 A2, the instantaneous I-V saturated as a function of local [Ba2+]o, with Kd = 65 mM. These results suggest that the channel pore does bind Ba2+ in a saturable manner, but the current-[Ba2+]o relationship may be significantly affected by surface charge.     

Surface potentials measure ion concentrations near lipid bilayers during rapid solution changes.

We describe a puffing method for changing solutions near one surface of lipid bilayers that allows simultaneous measurement of channel activity and extent of solution change at the bilayer surface. Ion adsorption to the lipid headgroups and screening of the bilayer surface charge by mobile ions provided a convenient probe for the ionic composition of the solution at the bilayer surface. Rapid ionic changes induced a shift in bilayer surface potential that generated a capacitive transient current under voltage-clamp conditions. This depended on the ion species and bilayer composition and was accurately described by the Stern-Gouy-Chapman theory. The time course of solute concentrations during solution changes could also be modeled by an exponential exchange of bath and puffing solutions with time constants ranging from 20 to 110 ms depending on the flow pressure. During changes in [Cs+] and [Ca2+] (applied separately or together) both the mixing model and capacitive currents predicted [Cs+] and [Ca2+] transients consistent with those determined experimentally from: 1) the known Cs(+)-dependent conductance of open ryanodine receptor channels and 2) the Ca(2+)-dependent gating of ryanodine receptor Ca2+ channels from cardiac and skeletal muscle.     

A three-barrier model for the hemocyanin channel

Keyhole limpet hemocyanin forms ion-conducting channels in planar lipid bilayer membranes. Ionic current through the open hemocyanin channel presents the following characteristics: (a) it is carried mainly by cations; (b) it is a nonlinear function of membrane potential; (c) channel conductance is a saturating function of ion activity; (d) it shows ionic competition. A model for the open hemocyanin channel is developed from absolute reaction rate theory. The model calls for three energy barriers in the channel. Two energy barriers represent the entrance and exit of the ion into and out of the channel. The third barrier separates two energy minima that represent two binding sites. Furthermore, only one ion is allowed inside the channel at a given time. This model is able to recreate all the hemocyanin characteristics found experimentally in negatively charged and neutral membranes.     

Forces involved in adhesion of Bacillus cereus spores to solid surfaces under different environmental conditions

The adhesion of Bacillus cereus spores (NCTC 2599) to hydrophobic and hydrophilic glass surfaces was studied when environmental conditions were varied. The spores were exposed in media of different polarities as well as different pH and ionic concentrations. With increasing ethanol concentrations, the polarity of the medium was decreased and the predominant force of attraction was found to be hydrophobic. The spore surface was uncharged at a pH around 3, at which value the spore was most adhesive to both hydrophobic and hydrophilic glass. This could be attributable to the absence of electrostatic repulsion. An increased ionic concentration of the bulk increased the degree of adhesion especially to the hydrophilic surfaces. This indicates the suppression of a solvation barrier at high ionic concentrations, when the polymers of the spore surface become dehydrated.     

A transition state theory approach to the kinetics of conductance changes in excitable membranes

Summary The kinetics of ionic current mechanisms in excitable membranes are analyzed. It is assumed that there are voltage-dependent reactions occurring in the membrane which are independent of the flow of ionic current. The experimental evidence for this assumption is reviewed in the light of more recent results on the kinetics of conductance changes in cardiac membranes. Rate equations are then obtained using transition state theory and assuming that each reaction is rate limited by only one energy barrier. These equations give simple exponential functions for the voltage dependence of the rates. More complex functions may be obtained by assuming that more than one energy barrier is rate limiting. The single-barrier equations are used to estimate the energies of formation of the transition state. In most cases, the entropy of formation is positive but there is no systematic order in the estimated enthalpies. These results are contrasted with those for the ion permeation process itself which normally has a negative entropy of activation. This contrast reinforces the assumption that the reactions controlling membrane permeability are distinct from the ion permeation process itself. The significance of the positive entropy of formation of the transition state in the permeability reactions is discussed, and it is suggested that the membrane structures underlying these reactions may change their degree of hydration during the formation of the transition state.     

Estimation of ionic channel surface density from relaxation ionic and gating currents

It is shown that excitable membrane surface density of channels can be estimated from ionic and gating current relaxations. The gating currents are determined thermodynamically from a multistate kinetic model. The parameters of the kinetic model are derived from ionic current relaxations. The assumptions regarding the gating process made here are the same as those made in fluctuation analysis previously regarded as the only method that may yield channel density from membrane currents.     

Interactions between motile Escherichia coli and glass in media with various ionic strengths, as observed with a three-dimensional-tracking microscope.

Escherichia coli bacteria have been observed to swim along a glass surface for several minutes at a time. Settling velocities of nonmotile cells and a computer simulation of motile cells confirmed that an attractive force kept the bacteria near the surface. The goal of this study was to evaluate whether this attractive force could be explained by reversible adhesion of E. coli to the surface in the secondary energy minimum, according to the theory of Derjaguin, Landan, Verwey, and Overbeek (DLVO theory). This theory describes interactions between colloidal particles by combining attractive van der Waals forces with repulsive electrostatic forces. A three-dimensional-tracking microscope was used to follow both wild-type and smooth-swimming E. coli bacteria as they interacted with a glass coverslip in media of increasing ionic strengths, which corresponded to increasing depths of the secondary energy minimum. We found no quantifiable changes with ionic strength for either the tendencies of individual bacteria to approach the surface or the overall times bacteria spent near the surface. One change in bacterial behavior which was observed with the change in ionic strength was that the diameters of the circles which the smooth-swimming bacteria traced out on the glass increased in low-ionic-strength solution.     

Hydrodynamic model of temperature change in open ionic channels.

Most theories of open ionic channels ignore heat generated by current flow, but that heat is known to be significant when analogous currents flow in semiconductors, so a generalization of the Poisson-Nernst-Planck theory of channels, called the hydrodynamic model, is needed. The hydrodynamic theory is a combination of the Poisson and Euler field equations of electrostatics and fluid dynamics, conservation laws that describe diffusive and convective flow of mass, heat, and charge (i.e., current), and their coupling. That is to say, it is a kinetic theory of solute and solvent flow, allowing heat and current flow as well, taking into account density changes, temperature changes, and electrical potential gradients. We integrate the equations with an essentially nonoscillatory shock-capturing numerical scheme previously shown to be stable and accurate. Our calculations show that 1) a significant amount of electrical energy is exchanged with the permeating ions; 2) the local temperature of the ions rises some tens of degrees, and this temperature rise significantly alters for ionic flux in a channel 25 A long, such as gramicidin-A; and 3) a critical parameter, called the saturation velocity, determines whether ionic motion is overdamped (Poisson-Nernst-Planck theory), is an intermediate regime (called the adiabatic approximation in semiconductor theory), or is altogether unrestricted (requiring the full hydrodynamic model). It seems that significant temperature changes are likely to accompany current flow in the open ionic channel.     

Electrical responses to amputation of the eye in the mystery snail

Immediately following amputation through the eyestalk of the mystery snail (Pomacea), a persistent ionic current enters the apical amputation surface of the eyestalk stump. The circuit is completed by current driven from undamaged integument of the eyestalk stump and other body regions. The current is relatively steady during the first 10 hours following amputation. Currents subsequently begin a slow decline to base line levels by 60 hours postamputation--a time coincident with wound healing processes. The "battery" driving this ionic current is the internally negative transepidermal potential existing across the snail integument--perhaps the result of a net inward pumping of chloride across the skin. This system is compared to other regeneration models such as the amphibian limb, bone fracture repair, and skin wound healing. We suggest that ionic current may be a control of eye regeneration in the snail.     

Conductance channels in neutral lipid bilayers

Summary A model channel for the conduction of ions (positive or negative but not both) through a lipid bilayer is presented. The transition-state theory is used to relate the current with voltage and ionic concentrations. Sites within the channel are considered to act cooperatively so that the ion is subjected to a ligand field in which it has complete freedom along the channel axis. The ions in the channel are treated as an ionic gas. Effects due to space-charges within the channel arising from the conducting ions are considered whereas surface-charge effects are neglected.The ionic specificity of the channel is indicated and the theory compared to that in which equilibrium free energy changes are the dominant influence.