Mechanism of anion-cation selectivity of amphotericin B channels

Summary Zero current potential and conductance of ionic channels formed by polyene antibiotic amphotericin B in a lipid bilayer were studied in various electrolyte solutions. Nonpermeant magnesium and sulphate ions were used to independently vary the concentration of monovalent anions and cations as well as to maintain the high ionic strength of the two solutions separated by the membrane. Under certain conditions the channels select very strongly for anions over cations. They are permeable to small inorganic anions. However, in the absence of these anions the channels are practically impermeable to any cation. In the presence of a permeant anion the contribution of monovalent cations to channel conductance grows with an increase in the anion concentration. The ratio of cation-to-anion permeability coefficients is independent of the membrane potential and cation concentration, but it does depend linearly on the sum of concentrations of a permeant anion in the two solutions. These results are accounted for on the assumption that a cation can enter only an anion-occupied channel to form an ionic pair at the center of the channel. The cation is also assumed to slip past the anion and then to leave the channel for the opposite solution. This model with only few parameters can quantitatively describe the concentration dependences of conductance and zero current potential under various conditions.     

Ion-channel entrances influence permeation. Net charge, size, shape, and binding considerations.

Many ion channels have wide entrances that serve as transition zones to the more selective narrow region of the pore. Here some physical features of these vestibules are explored. They are considered to have a defined size, funnel shape, and net-negative charge. Ion size, ionic screening of the negatively charged residues, cation binding, and blockage of current are analyzed to determine how the vestibules influence transport. These properties are coupled to an Eyring rate theory model for the narrow length of the pore. The results include the following: Wide vestibules allow the pore to have a short narrow region. Therefore, ions encounter a shorter length of restricted diffusion, and the channel conductance can be greater. The potential produced by the net-negative charge in the vestibules attracts cations into the pore. Since this potential varies with electrolyte concentration, the conductance measured at low electrolyte concentrations is larger than expected from measurements at high concentrations. Net charge inside the vestibules creates a local potential that confers some cation vs. anion, and divalent vs. monovalent selectivity. Large cations are less effective at screening (diminishing) the net-charge potential because they cannot enter the pore as well as small cations. Therefore, at an equivalent bulk concentration the attractive negative potential is larger, which causes large cations to saturate sites in the pore at lower concentrations. Small amounts of large or divalent cations can lead to misinterpretation of the permeation properties of a small monovalent cation.     

Anion-cation permeability correlates with hydrated counterion size in glycine receptor channels

The functional role of ligand-gated ion channels depends critically on whether they are predominantly permeable to cations or anions. However, these, and other ion channels, are not perfectly selective, allowing some counterions to also permeate. To address the mechanisms by which such counterion permeation occurs, we measured the anion-cation permeabilities of different alkali cations, Li⁺ Na⁺, and Cs⁺, relative to either Cl⁻ or anions in both a wild-type glycine receptor channel (GlyR) and a mutant GlyR with a wider pore diameter. We hypothesized and showed that counterion permeation in anionic channels correlated inversely with an equivalent or effective hydrated size of the cation relative to the channel pore radius, with larger counterion permeabilities being observed in the wider pore channel. We also showed that the anion component of conductance was independent of the nature of the cation. We suggest that anions and counterion cations can permeate through the pore as neutral ion pairs, to allow the cations to overcome the large energy barriers resulting from the positively charged selectivity filter in small GlyR channels, with the permeability of such ion pairs being dependent on the effective hydrated diameter of the ion pair relative to the pore diameter.     

Cationic and anionic channels of apical receptive membrane in a taste cell contribute to generation of salt-induced receptor potential

• 1.1. After ionic composition of superficial fluid (ISF) and interstitial fluid (ISF) of the frog Rana catesbeiana) tongue had mostly been changed with a low Na⁺ saline solution, the relations between membrane potentials and receptor potentials in a frog taste cell evoked by various concentrations of NaCl and various types of salts were analyzed to examine permeability of the taste receptive membrane to cations and anions.
• 2.2. The mean reversal potentials for depolarizing potentials of a taste cell in response to 0.05 M, 0.2 M and 0.5 M Nad were -40.0, 6.4 and 28.8 mV, respectively.
• 3.3. When adding an anion channel blocker, SITS, to a NaCl solution the reversal potential for receptor potential with NaCl plus SITS became about twice as large than with NaCl alone.
• 4.4. Reversal potentials for 0.2 M NaCl, LiCl, KCl and NaSCN were 6.4, 25.4, −1.0 and −7.8 mV, respectively, indicating that permeability of the apical taste receptive membrane to cations of Cl⁻ salts is arranged in the order of Li⁺ > Na⁺ > K⁺ and that the permeability to anions of Na⁺ salts is arranged as SCN⁻ > Cl⁻
• 5.5. It is concluded that in the case of NaCl stimulation, Na⁺ and Cl⁻ of NaCl stimulus permeate NaCl-gated cationic and anionic channels at the apical taste receptive membrane in generating receptor potentials.

     

Background osmolyte current involved in cell volume regulation of neuroblastoma x glioma hybrid NG108-15 cells.

Recently, we showed that at constant extracellular osmolarity, the volume of NG108-15 cells was dependent on the external NaCl concentration and we assumed that the responsible mechanism was mediated by background channels (Rouzaire-Dubois et al. 1999). In order to confirm this view, the mean cell volume and the background current of NG108-15 cells were measured under different experimental conditions, after blockade of specific volume regulating mechanisms and ion channels. When the external NaCl concentration was decreased, the reversal potential of the background current was shifted toward negative values and the membrane conductance decreased. Opposite effects were observed when the NaCl concentration was increased. Substitution of external Na+ with various monovalent cations altered the mean cell volume by: Rb+, +17%; Cs+, +15%; K+, +10%; Li+, -6%; choline, -9%; N-methylglucamine, -25% . The reversal potential of the background current and the membrane conductance were altered by these Na+ substitutes in such a way that the cell volume increased linearly with the background current at -60 mV. Substitution of external Cl- with various monovalent anions altered the mean cell volume by: I-, +4%; Br-, 0%; NO-, -3%; F-, -5%; isethionate, -30%; gluconate, -50%. Cl- substitutes did not significantly alter the background current at -60 mV, except F- which increased it by 39%. These results suggest that 1. the cell volume is dependent on ion fluxes through background channels; 2. electrogenic cation fluxes are larger than anionic ones and the background current is proportional to the difference between these fluxes; 3. whereas external cations do not interfere with anion fluxes, external anions alter cation fluxes.     

Interfacial pH modulation of membrane protein function in vivo. Effect of anionic phospholipids.

In yeast cells, the magnitude of the membrane surface potential (phi) is determined to a large extent by the relative amount of anionic phospholipids (Cerbón and Calderón (1990) Biochim. Biophys. Acta 1028, 261-267). When a significant surface potential exists, the pH at the membrane surface (interfacial pH) will be different to that in the bulk suspending medium. We now report that: (1) In cells with higher phi (phosphatidylinositol-rich cells (PI-rich) and phosphatidylserine-rich cells (PS-rich) a 10-times lower proton concentration in the bulk was enough to achieve the maximum transport activity of H(+)-linked transport systems when compared to normal cells. (2) When the phi was reduced by increasing the concentration of cations in the medium, more protons were required to achieve maximum transport, that is, the pH activity curves shifted downwards to a more acidic pH. (3) The magnitude of the downward pH shift was around 2.5-times higher for the more charged membranes. (4) Around 10-times more KCl than MgCl2 was necessary to give an equivalent pH shift, in agreement with their capacity to reduce the phi of artificial bilayers. The interfacial pH calculated from the values of phi indicates that it was 0.4 pH units lower in the anionic phospholipid rich cells as compared to normal cells. The results indicate that membrane surface potential may explain the complex relationship between pH, ionic strength and membrane protein function. Maximum transport activities were found for glutamate at interfacial pH of 4.2-4.8 and were inhibited at interfacial pH = 3.2-3.4, suggesting that surface groups of the carrier proteins with pK values in the region 3.8-4.2 (aspartyl and glutamyl) are involved in binding and/or release of charged substrates.     

Permeation of both cations and anions through a single class of ATP-activated ion channels in developing chick skeletal muscle.

Micromolar concentrations of extracellular adenosine 5'-triphosphate (ATP) elicit a rapid excitatory response in developing chick skeletal muscle. Excitation is the result of a simultaneous increase in membrane permeability to sodium, potassium, and chloride ions. In the present study we quantify the selectivity of the ATP response, and provide evidence that a single class of ATP-activated ion channels conducts both cations and anions. Experiments were performed on myoballs using the whole-cell patch-clamp technique. We estimated permeability ratios by measuring the shift in reversal potential when one ion was substituted for another. We found that monovalent cations, divalent cations, and monovalent anions all permeate the membrane during the ATP response, and that there was only moderate selectivity between many of these ions. Calcium was the most permeant ion tested. To determine if ATP activates a single class of channels that conducts both cations and anions, or if ATP activates separate classes of cation and anion channels, we analyzed the fluctuations about the mean current induced by ATP. Ionic conditions were arranged so that the reversal potential for cations was +50 mV and the reversal potential for anions was -50 mV. Under these conditions, if ATP activates a single class of channels, ATP should not evoke an increase in noise at the reversal potential of the ATP current. However, if ATP activates separate classes of cation and anion channels, ATP should evoke a significant increase in noise at the reversal potential of the ATP current. At both +40 and -50 mV ATP elicited a clear increase in noise, but at the reversal potential of the ATP current (-5 mV), no increase in noise above background was seen. These results indicate that there is only a single class of excitatory ATP-activated channels, which do not select by charge. Based on analysis of the noise spectrum, the conductance of individual channels is estimated to be 0.2-0.4 pS.     

Electrochemical Properties of Hydrated Cation-Selective Glass Membrane: A Model of K+ and Na+ Transport

Electrochemical properties of cation-selective glass microelectrodes made from NAS_27-04 were studied. There was a marked fall in electrical resistance of the microelectrodes stored in 3 M KCl solution (aging). The resistance was in the range of 2 × 10⁷ to 10⁹ Ω, which were much lower than those estimated from the electrical resistivity of dry glass for the equivalent dimensions of microelectrode working tips. This fall in resistance was accompanied by an increase in microelectrode selectivity for K⁺. The low resistance and increased K⁺ selectivity are desirable features that make the microelectrode more suitable for application to biologic studies. The changes in microelectrode resistance and selectivity were interpreted to be due to hydration of the entire thickness of the glass membrane, resulting in a change in the field strength of anionic sites and formation of ionic channels in the glass membrane. Thus, the fall in resistance is explained by decrease in energy barrier, which is equivalent to the activation energy of interaction between the cations and anionic sites in the glass membrane. Some of the microelectrodes showed a transient depolarization that resembled the action potential of a biological membrane. This transient depolarization was associated with the changes in microelectrode resistance and selectivity. The transient depolarizations suggest the temporary development of wide channels in the membrane permitting free movement of hydrated cations according to the bulk electrochemical gradient.     

Helical alpha-synuclein forms highly conductive ion channels

Alpha-synuclein (alphaS) is a cytosolic protein involved in the etiology of Parkinson's disease (PD). Disordered in an aqueous environment, alphaS develops a highly helical conformation when bound to membranes having a negatively charged surface and a large curvature. It exhibits a membrane-permeabilizing activity that has been attributed to oligomeric protofibrillar forms. In this study, monomeric wild-type alphaS and two mutants associated with familial PD, E46K and A53T, formed ion channels with well-defined conductance states in membranes containing 25-50% anionic lipid and 50% phosphatidylethanolamine (PE) in the presence of a trans-negative potential. Another familial mutant, A30P, known to have a lower membrane affinity, did not form ion channels. Ca2+ prevented channel formation when added to membranes before alphaS and decreased channel conductance when added to preformed channels. In contrast to the monomer, membrane permeabilization by oligomeric alphaS was not characterized by formation of discrete channels, a requirement for PE lipid, or a membrane potential. Channel activity, alpha-helical content, thermal stability of membrane-bound alphaS determined by far-UV CD, and lateral mobility of alphaS bound to planar membranes measured by fluorescence correlation spectroscopy were correlated. It was inferred that discrete ion channels with well-defined conductance states were formed in the presence of a membrane potential by one or several molecules of monomeric alphaS in an alpha-helical conformation and that such channels may have a role in the normal function and/or pathophysiology of the protein.     

Improved 3D continuum calculations of ion flux through membrane channels

A continuum model, based on the Poisson–Nernst–Planck (PNP) theory, is applied to simulate steady-state ion flux through protein channels. The PNP equations are modified to explicitly account (1) for the desolvation of mobile ions in the membrane pore and (2) for effects related to ion sizes. The proposed algorithm for a three-dimensional self-consistent solution of PNP equations, in which final results are refined by a focusing technique, is shown to be suitable for arbitrary channel geometry and arbitrary protein charge distribution. The role of the pore shape and protein charge distribution in formation of basic electrodiffusion properties, such as channel conductivity and selectivity, as well as concentration distributions of mobile ions in the pore region, are illustrated by simulations on model channels. The influence of the ionic strength in the bulk solution and of the externally applied electric field on channel properties are also discussed.     

Anomalous permeabilities of the egg cell membrane of a starfish in K(+)-Tl(+) mixtures

The electrical properties of “inward” rectifying egg cell membranes of the starfish mediastera aequalis have been studied in the presence of K(+)-Tl(+) mixtures. When the ratio of the external concentrations of these ions is changed while their sum is kept constant, both the conductance and the zero-current membrane potential go through a minimum, showing clear discrepancies from theoretical results based on conventional electrodiffusion models (E.g., Goldman’s equation). By contrast, when the ration of the two concentrations is fixed and their sum varied, the potential follows an ideal Nernst slope, consistent with Goldman’s equation. The membrane conductance which, according to previous studies on similar membranes, is to be viewed as a function of the displacement of the membrane potential from its resting value δV, shows marked differences between the cases in which K(+) or Tl(+) are the predominant ions: when K(+) is the predominant permeant ion in solution, the addition of small amounts of Tl(+) inhibits the current, while corresponding blocking effects of K(+) on the current are not observed when Tl(+) is the predominant permeant ion. Also, the time course of the conductance during voltage clamp is different in the two cases, being much faster in Tl(+) than in K(+) solution for comparable values of δV. Most of the above features are accounted for by a model in which it is assumed that the ionic channels have external binding sites for cations and that their permeability properties depend on the species of the cation bound (K(+)or Tl(+) in the present experiments).     

The effect of multivalent cations on adhesion time for cellular adhesion to solid surfaces

The dynamic behavior of the adhesion of a charge-regulated cell to a solid surface of constant potential is investigated. In particular, the effect of the presence of multivalent cations in the suspension medium on adhesion time is discussed. By neglecting the effect of hydrodynamic retardation and assuming that the bulk liquid phase is stagnant, we show that the presence of multivalent cations has the effect of retarding cell adhesion. At a fixed level of ionic strength, the adhesion time increases with the increase of the concentration of multivalent cations in the suspension medium, and decreases with the increase in magnitude of the Hamaker constant. For a fixed concentration of cations, the adhesion time decreases with the increase of ionic strength. The effect of the magnitude of Hamaker constant on adhesion time is appreciable if both the ionic strength and the concentration of cations are high.     

Cloud-point temperatures for lysozyme in electrolyte solutions: effect of salt type, salt concentration and pH

Liquid-liquid phase-separation data were obtained for aqueous saline solutions of hen egg-white lysozyme at a fixed protein concentration (87 g/l). The cloud-point temperature (CPT) was measured as a function of salt type and salt concentration to 3 M, at pH 4.0 and 7.0. Salts used included those from mono and divalent cations and anions. For the monovalent cations studied, as salt concentration increases, the CPT increases. For divalent cations, as salt concentration rises, a maximum in the CPT is observed and attributed to ion binding to the protein surface and subsequent water structuring. Trends for sulfate salts were dramatically different from those for other salts because sulfate ion is strongly hydrated and excluded from the lysozyme surface. For anions at fixed salt concentration, the CPT decreases with rising anion kosmotropic character. Comparison of CPTs for pH 4.0 and 7.0 revealed two trends. At low ionic strength for a given salt, differences in CPT can be explained in terms of repulsive electrostatic interactions between protein molecules, while at higher ionic strength, differences can be attributed to hydration forces. A model is proposed for the correlation and prediction of the CPT as a function of salt type and salt concentration. NaCl was chosen as a reference salt, and CPT deviations from that of NaCl were attributed to hydration forces. The Random Phase Approximation, in conjunction with a square-well potential, was used to calculate the strength of protein-protein interactions as a function of solution conditions for all salts studied.     

Bacterial osmosensing: roles of membrane structure and electrostatics in lipid-protein and protein-protein interactions

Bacteria act to maintain their hydration when the osmotic pressure of their environment changes. When the external osmolality decreases (osmotic downshift), mechanosensitive channels are activated to release low molecular weight osmolytes (and hence water) from the cytoplasm. Upon osmotic upshift, osmoregulatory transporters are activated to import osmolytes (and hence water). Osmoregulatory channels and transporters sense and respond to osmotic stress via different mechanisms. Mechanosensitive channel MscL senses the increasing tension in the membrane and appears to gate when the lateral pressure in the acyl chain region of the lipids drops below a threshold value. Transporters OpuA, BetP and ProP are activated when increasing external osmolality causes threshold ionic concentrations in excess of about 0.05 M to be reached in the proteoliposome lumen. The threshold activation concentrations for the OpuA transporter are strongly dependent on the fraction of anionic lipids that surround the cytoplasmic face of the protein. The higher the fraction of anionic lipids, the higher the threshold ionic concentrations. A similar trend is observed for the BetP transporter. The lipid dependence of osmotic activation of OpuA and BetP suggests that osmotic signals are transmitted to the protein via interactions between charged osmosensor domains and the ionic headgroups of the lipids in the membrane. The charged, C-terminal domains of BetP and ProP are important for osmosensing. The C-terminal domain of ProP participates in homodimeric coiled-coil formation and it may interact with the membrane lipids and soluble protein ProQ. The activation of ProP by lumenal, macromolecular solutes at constant ionic strength indicates that its structure and activity may also respond to macromolecular crowding. This excluded volume effect may restrict the range over which the osmosensing domain can electrostatically interact. A simplified version of the dissociative double layer theory is used to explain the activation of the transporters by showing how changes in ion concentration could modulate interactions between charged osmosensor domains and charged lipid or protein surfaces. Importantly, the relatively high ionic concentrations at which osmosensors become activated at different surface charge densities compare well with the predicted dependence of 'critical' ion concentrations on surface charge density. The critical ion concentrations represent transitions in Maxwellian ionic distributions at which the surface potential reaches 25.7 mV for monovalent ions. The osmosensing mechanism is qualitatively described as an "ON/OFF switch" representing thermally relaxed and electrostatically locked protein conformations.     

The Non-Steady-State Membrane Potential of Ion Exchangers with Fixed Sites

A system of equations, based upon the assumption that the only force acting on each ionic species is due to the gradient of its electrochemical potential, is used to deduce, in the non-steady state for zero net current, the expression of the difference of electric potential between two solutions separated by an ion exchange membrane with fixed monovalent sites. The membrane is assumed to be solely permeable to cations or anions, depending on whether the charge of the sites is -1 or +1, and not to permit any flow of solvent. Under the assumptions that the difference of standard chemical potentials of any pair of permeant monovalent species and the ratio of their mobilities are constant throughout the membrane, even when the spacing of sites is variable, explicit expressions are derived for the diffusion potential and total membrane potential as functions of time and of solution activities. The expressions are valid for any number of permeant monovalent species having ideal behavior and for two permeant monovalent species having “n-type” non-ideal behavior. The results show that for a step change in solution composition the observable potential across a membrane having fixed, but not necessarily uniformly spaced, sites becomes independent of time once equilibria are established at the boundaries of the membrane and attains its steady-state value even while the ionic concentration profiles and the electric potential profile within the membrane are changing with time.     

Dependence of ion flow through channels on the density of fixed charges at the channel opening. Voltage control of inverse titration curves

Model calculations were done to investigate the effect of titratable fixed charges at channel openings on ion flow through open channels. The current titration curves (channel current vs. bulk pH) can assume the shape expected from the change of the ionic surface concentration with pH (c-control), or be inverted, i.e., follow the change of the electrical field within the membrane (V-control). The relationships were explored pars pro toto for Goldman-Hodgkin-Katz channels, two-barrier one-site channels and six-barrier five-site channels. With net current flowing in the direction of the concentration gradient and from the titrated fixed charge layer into the channel, c-control is the sign of low channel occupancy (entrance-step limitation) and V-control the sign of high channel occupancy (exit-step limitation). At intermediate occupancy, the current titration curve can be nearly invariant to pH.     

Alternative splicing switches the divalent cation selectivity of TRPM3 channels

TRPM3 is a poorly understood member of the large family of transient receptor potential (TRP) ion channels. Here we describe five novel splice variants of TRPM3, TRPM3alpha1-5. These variants are characterized by a previously unknown amino terminus of 61 residues. The differences between the five variants arise through splice events at three different sites. One of these splice sites might be located in the pore region of the channel as indicated by sequence alignment with other, better-characterized TRP channels. We selected two splice variants, TRPM3alpha1 and TRPM3alpha2, that differ only in this presumed pore region and analyzed their biophysical characteristics after heterologous expression in human embryonic kidney 293 cells. TRPM3alpha1 as well as TRPM3alpha2 induced a novel, outwardly rectifying cationic conductance that was tightly regulated by intracellular Mg(2+). However, these two variants are highly different in their ionic selectivity. Whereas TRPM3alpha1-encoded channels are poorly permeable for divalent cations, TRPM3alpha2-encoded channels are well permeated by Ca(2+) and Mg(2+). Additionally, we found that currents through TRPM3alpha2 are blocked by extracellular monovalent cations, whereas currents through TRPM3alpha1 are not. These differences unambiguously show that TRPM3 proteins constitute a pore-forming channel subunit and localize the position of the ion-conducting pore within the TRPM3 protein. Although the ionic selectivity of ion channels has traditionally been regarded as rather constant for a given channel-encoding gene, our results show that alternative splicing can be a mechanism to produce channels with very different selectivity profiles.     

How pore mouth charge distributions alter the permeability of transmembrane ionic channels.

This paper investigates the effects that surface dipole layers and surface charge layers along the pore mouth-water interface can have on the electrical properties of a transmembrane channel. Three specific molecular sources are considered: dipole layers formed by membrane phospholipids, dipole layers lining the mouth of a channel-forming protein, and charged groups in the mouth of a channel-forming protein. We find, consistent with previous work, that changing the lipid-water potential difference only influences channel conduction if the rate-limiting step takes place well inside the channel constriction. We find that either mouth dipoles or mouth charges can act as powerful ion attractors increasing either cation or anion concentration near the channel entrance to many times its bulk value, especially at low ionic strengths. The effects are sufficient to reconcile the apparently contradictory properties of high selectivity and high conductivity, observed for a number of K+ channel systems. We find that localizing the electrical sources closer to the constriction entrance substantially increases their effectiveness as ion attractors; this phenomenon is especially marked for dipolar distributions. An approximate treatment of electrolyte shielding is used to discriminate between the various mechanisms for increasing ionic concentration near the constriction entrance. Dipolar potentials are far less sensitive to ionic strength variation than potentials due to fixed charges. We suggest that the K+ channel from sarcoplasmic reticulum does not have a fixed negative charge near the constriction entrance; we suggest further that the Ca+2-activated K+ channel from transverse tubule does have such a charge.     

Ca2+ buffer sites in intact bovine rod outer segments: Introduction to a novel optical probe to measure ionic permeabilities in suspensions of small particles

Summary The nature of the Ca²⁺ buffer sites in intact rod outer segments isolated from bovine retinas (ROS) was investigated. The predominant Ca²⁺ buffer in intact ROS was found to be negatively charged groups confined to the surface of the disk membranes. Accordingly, Ca²⁺ buffering in ROS was strongly influenced by the electrostatic surface potential. The concentration of Ca²⁺ buffer sites was about 30mm, 80% of which were located at the membrane surface in the intradiskal space. A comparison with observations in model systems suggests that phosphatidylserine is the major Ca²⁺ buffer site in ROS. Protons and alkali cations could replace Ca²⁺ as mobile counterions for the fixed negatively charged groups. At physiological ionic strength, the total number of these diffusible, but osmotically inactive, counterions was as large as the number of osmotically active cations in ROS. The surface potential is dependent on the concentration of cations in ROS and can be measured with the optical dye neutral red. Addition of cations to the external solution led to the release of the internally bound dye as the cations crossed the outer membrane. The chemical and spectral properties of the dye enable its use as a real-time indicator of cation transport across the outer envelope of small particles in suspension. In this study, the dye method is illustrated by the use of well-defined ionophores in intact ROS and in liposomes. In the companion paper this method is used to describe the cation permeabilities native to ROS.     

The steady-state properties of an ion exchange membrane with mobile sites

A study of the properties of the steady states of a system composed of two solutions separated by an ion exchange membrane having mobile sites is presented. It is assumed that the membrane is impermeable to coions; the solutions contain no more than two species of counterions, both of the same valence; and no flow of bulk solution occurs. Assuming that all ions are completely dissociated, behave ideally, and have constant mobilities throughout the membrane, explicit expressions are derived for the steady states of the electric current, individual fluxes, and concentration profiles as functions of the compositions of the solutions and of the difference of electric potential between them. The derived expressions are compared with those for an ion exchange membrane having fixed sites; and it is found that the expressions of certain quantities, such as the difference of electric potential between the two solutions for zero current or the ratio of the fluxes of the counterions as functions of the external parameters of the system, are the same for both types of membranes. On the other hand, differences in the behavior of the two types of membranes are found from other expressions-for example, the current-voltage relationship. In the mobile site ion exchanger the current asymptotically approaches finite limiting values for high positive and negative voltages while in the fixed site ion exchanger it is the conductance which approaches finite limiting values.