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.     

Effect of ionic polarizability on electrodiffusion in lipid bilayer membranes.

Ion-carrier complexes and organic ions of similar size and shape have mobilities in lipid bilayer membranes which span several orders of magnitude. In this communication, an examination is made of the hypothesis that the basis for this unusually wide range of ionic mobilities is the potential energy barrier arising from image forces which selectively act on ions according to their polarizability. Using Poisson's equation to evaluate the electrostatic interaction between an ion and its surroundings, the potential energy barrier to ion transport due to image effects is computed, with the result that the potential energy barrier height depends strongly on ionic polarizability. Theoretical membrane potential energy profile calculations are used in conjunction with Nernst-Planck electrodiffusion equation to analyze the available mobility data for several ion-carrier complexes and lipid-soluble ions in lipid bilayer membranes. The variation among the mobilities of different ions is shown to be in agreement with theoretical predictions based on ionic polarizability and size. Furthermore, the important influence exerted by image forces on ion transport in lipid bilayer membranes compared to the frictional effect of membrane viscosity is established by contrasting available data on the activation energy of ionic conductivity with that for membrane fluidity.     

CONTRIBUTION TO THE THEORY OF PERMEABILITY OF MEMBRANES FOR ELECTROLYTES

From experiments on such membranes as apple skin, parchment paper membrane, and a membrane of completely dry collodion, results have been obtained which could be interpreted by the assumption that these membranes are less permeable for anions than for cations. In parchment paper there is only a relative diminution of the mobility of the anions, in the apple skin and in the dry collodion membrane there is practically no permeability for anions at all. The theory is developed which explains how the decrease or complete lack of mobility of anions influences the electromotive effects of the membrane and the diffusibility of electrolytes across a membrane. The results of the theory are compared with the experimental results. In membranes impermeable for anions the permeability for cations gives the same order of cations as for the mobilities in a free aqueous solution. But the differences of the mobilities are enormously magnified, e.g. the mobilities of H^• and Li^•, which are in the proportion of about 1:10 in aqueous solution, are in proportion of about 1:900 in the collodion membrane. The general cause for the retardation of ionic mobility within the membrane may be supposed to be the increased friction of the water envelope dragged along by the ion in the capillary canals of the membrane. The difference of the effect on the cations and on the anions may be attributed to the electric charge of the walls of the canals.     

Kinetics of Excitable Membranes : Voltage amplification in a diffusion regime

An understanding of the properties of excitable membranes requires the calculation of ion flow through the membrane, including the effects of nonuniformity in the transverse membrane properties (mobilities, fixed charge, electric field). Permeability is apparently controlled at the external interface. Two factors may be involved here: the statistical blocking of pores by divalent cations, and activation energy. Only the former is included in the present treatment. When the total transmembrane voltage is varied, a redistribution in ionic concentration occurs. This can cause a change in boundary (zeta) potential, large in comparison with the applied voltage change—"voltage amplification." The result is a steep change in membrane conductance. The calculated flow curves are compared with experimental results. The Appendix gives an outline of the numerical method used for solving the boundary value problem with several diffusible ions, across a nonuniform regime.     

a-c electrical properties of bipolar membranes: Experiments and a model

Summary The a-c electrical properties of bipolar membranes separating equal strength solutions of the same uni-univalent electrolyte are analyzed for the case where both ions have equal mobilities. Two membrane models are treated. In one, the fixed-charge density is assumed to be constant throughout the membrane. In the other, the membrane is regarded as comprising an array of pores separated by walls through which the fixed charge is spread uniformly. Experimental results are reported for the a-c electrical properties of a bipolar membrane prepared from a single polyolephine sheet and immersed in KCl solutions of various concentrations. It is found that the data can be interpreted using the pore model.     

Different Permeability of Potassium Salts across the Blood-Brain Barrier Follows the Hofmeister Series

The passage of ions across biological membranes is regulated by passive and active mechanisms. Passive ion diffusion into organs depends on the ion-pairing properties of salts present in the serum. Potassium ions could affect brain activity by crossing the blood-brain barrier (BBB) and its accumulation in the extracellular cerebral space could precipitate seizures. In the present study, we analyze passive diffusion of a series of potassium salts in the in vitro isolated guinea pig brain preparation. Different potassium counter-anions confer ion-pairing and lipophilicity properties that modulate membrane diffusion of the salt. Extracellular recordings in different cortical areas demonstrated the presence of epileptiform activities that strongly relate to anion identity, following the qualitative order of the Hofmeister series. Indeed, highly lipophilic salts that easily cross the BBB enhanced extracellular potassium concentration measured by ion-selective electrodes and were the most effective pro-epileptic species. This study constitutes a novel contribution for the understanding of the potential epileptogenicity of potassium salts and, more generally, of the role of counter-anions in the passive passage of salts through biological membranes.     

Effects of unstirred layers or transport number discontinuities on the transient and steady-state current-voltage relationships of membranes

The effects of current-induced electrolyte accumulation and depletion on the electrical properties of a two-layered membrane system have been examined. The membrane consisted of a charged, ion permselective layer and an uncharged, non-selective layer. The model was designed to reveal the properties of membranes possessing long pores with ionic charges at one end or of ion-selective membranes bounded by highly unstirred aqueous layers. Electrolyte concentration profiles in the inert layer and their time-dependent changes were obtained from solutions of the diffusion equation under the condition of constant current. The profiles were then used to calculate the voltage developed across the membrane at various times after the current is switched on. The theoretical results are presented in the form of $\text{i-V}$ curves with reduced coordinates that can be used to obtain time-current-voltage relationships for membranes of the type considered having any thickness of the non-selective layer and bathed in any concentration of any 1:1 electrolyte. Experimental results on a model composite membrane were in good agreement with calculations that assume that ion transport occurs only under the influence of electrical potential and concentration gradients, suggesting that in such systems, the combined effects of convection, osmosis, electro-osmosis, and concentration-dependence of diffusion coefficients, activity coefficients, and transference numbers are small. Voltage fluctuations in the form of periodic spikes were observed experimentally at the limiting current density (the current density at which the electrolyte concentration at one surface of the selective layer goes to 0). These phenomena were not seen when the current was in the direction leading to accumulation of electrolyte in the non-selective (unstirred) layer. Such composite membranes can exhibit S-shaped and N-shaped $\text{i-V}$ curves under ramp-voltage and ramp-current clamps, respectively.     

A method to relate steady-state ionic currents, conductances, and membrane potential in ion exchange membranes with unknown thermodynamic properties

A method is presented by which the steady-state properties of an homogeneous, permselective membrane at uniform temperature can be predicted without knowledge of its thermodynamic properties other than assuming that they are functions only of local mole fractions in the membrane. By making this assumption, it is shown how the ionic conductances can be calculated at any point in the membrane from two sets of measurements, (a) R(symm), the steady-state resistance of the membrane measured between identical solutions and (b) V(0), the potential difference between nonidentical solutions for zero current. These two parameters are measured at different external solution compositions (e.g. a varying sodium-potassium ratio ranging from zero to infinity). From these measurements it is shown how the flux equations may be integrated without a knowledge of mobilities, activity coefficients, and other interior membrane parameters. The application of the method to fixed site membranes with variable mobilities is described and the theory for this particular case has also been verified experimentally in glass membranes.1 A possible application to biological membranes is discussed and a comparison is made between the present treatment and previous treatments used to calculate the steady-state properties of cell membranes, notably the theory of Teorell, Meyer, and Sievers and the constant field theory.     

Monte Carlo studies on potentiometric titration of poly(glutamic acid)

The potentiometric titration of poly(glutamic acid) with special attention to its helix-coil transition is investigated in terms of the previously developed Monte Carlo method. The simulations of the potentiometric titration are carried out for helical and coiled form of the peptide, separately. A cylindrical rod with spherical ionizable groups is adopted as each conformational model of poly(glutamic acid) molecule. A spherical charge with a hard core potential is assumed as a mobile hydrated ion. The helix-coil transition curves are analyzed by the Zimm-Bragg theory. A satisfactory agreement is achieved for the titration curves with the experimental data in most cases. The significance and the limitations of the simulation method are discussed.     

Effects of cations and polyamines on the aggregation and fusion of phosphatidylserine membranes

Effects of various metal cations and polyamines on aggregation and fusion of phosphatidylserine vesicles and their associated physicochemical properties (such as surface tension and vesicle electrophoretic mobility) have been studied. It was found that metal polycations and hydrogen ion caused an increase in the surface tension of a phosphatidylserine monolayer, whereas the polyamines and other monovalent cations did not increase the surface tension of the membrane appreciably. All cations used affected the vesicle mobility roughly in the order of the number of their valencies and linearly with respect to the logarithm of their concentrations of ions; vesicle surface charge densities are reduced by adsorption and screening of the counter ions depending on their valencies and concentrations. The degree of aggregation of lipid vesicles parallels somewhat that of the reduction of vesicle electrophoretic mobilities. However, the degree of membrane fusion induced by these cations parallels that of the increase in surface tension of the membranes induced by these cations.     

IONIC TRANSFERENCE NUMBERS IN CELLOPHANE MEMBRANES

The "apparent" cation transference number within cellophane is determined for HCl, KCl, NH₄Cl, NaCl, and LiCl. The method consists in measuring the E.M.F. in a concentration chain employing Ag:AgCl electrodes or calomel electrodes and calculating from formulas derived for cases of simple, unconstrained diffusion. The transference numbers and the cation mobilities relative to the chloride ion were found to be higher in the cellophane (relative cation mobilities increased about 40 per cent). The effect of the membrane is discussed. It is emphasized that with the introduction of a membrane as a liquid junction new factors are introduced, which are not considered in the formulas ordinarily used. Such factors may be activity changes due to dimensional or other reasons and particularly electrical effects exhibited by the membrane upon the ionic diffusion. Accordingly the transference number, as determined, may lack well defined physical significance.     

Activity of toxins produced by Pseudomonas syringae pv. syringae in model and cell membranes

We studied effects of toxins produced by a bacterium Pseudomonas syringae pv. syringae on the conductance of bilayer lipid membranes (BLM). The used toxins were as follows: syringopeptin 22A (SP22A), syringomycin E (SPE), syringostatin A (SSA), syringotoxin B (STB), and methylated syringomycin E (CH3-SRE). All toxins demonstrated channel-forming activity. The threshold sequence for toxin activity was SP22A > SRE approximately equal to SSA > STB > CH3-SRE, and this sequence was independent of lipid membrane composition, and NaCl concentration (pH 6) in the membrane bathing solution (in the range of 0.1-1.0 M). This sequence correlated with relative bioactivities of toxins. In addition, SRE demonstrated a more potent antifungal activity than CH3-SRE. These findings suggest that ion channel formation may underlie the bioactivities of the above toxins. The properties of single ion channels formed by the toxins in BLMs were found to be similar, which points to the similarity in the channel structures. In negatively charged membranes, bathed with diluted electrolyte solutions (0.1 M NaCl), the channels were seen to open with positive transmembrane potentials (V) (from the side of toxin addition), and close with negative potentials. In uncharged membranes the opposite response to a voltage sign was observed. Increasing the NaCl concentration up to 1 M unified the voltage sensitivity of channels in charged and uncharged membranes: channels opened with negative V, and closed with positive V. With all systems, the voltage current curves of single channels were similarly superlinear in the applied voltage and asymmetric in its sign. It was found that the single channel conductance of STB and SSA was higher than that of other toxin channels. All the toxins formed at least two types of ion channels that were multiple by a factor of either 6 or 4 in their conductance. The results are discussed in terms of the structural features of toxin molecules.     

Influence of counterions on the interaction of pyridinium salts with model membranes

The interaction of pyridinium salts (PS) with red blood cells and planar lipid membranes was studied. The aim of the work was to find whether certain cationic surfactant counterion influence its possible biological activity. The counterions studied were Cl-, Br-, I-, ClO4-, BF4- and NO3-. The model membranes used were erythrocyte and planar lipid membranes (BLM). At high concentration the salts caused 100% erythrocyte hemolysis (C100) or broke BLMs (CC). Both parameters describe mechanical properties of model membranes. It was found that the efficiency of the surfactant to destabilize model membranes depended to some degree on its counterion. In both, erythrocyte and BLM experiments, the highest efficiency was observed for Br-, the lowest for NO3-. The influence of all other anions on surfactant efficiency changed between these two extremities; that of chloride and perchlorate ions was similar. Some differences were found in the case of BF4- ion. Its influence on hemolytic possibilities of PS was significant while BLM destruction required relatively high concentration of this anion. Apparently, the influence of various anions on the destructive action of PS on the model membrane used may be attributed to different mobilities and radii of hydrated ions and hence, to different possibilities of particular anions to modify the surface potential of model membranes. This can lead to a differentiated interaction of PS with modified bilayers. Moreover, the effect of anions on the water structure must be taken into account. It is important whether the anions can be classified as water ordering kosmotropes that hold the first hydration shell tightly or water disordering chaotropes that hold water molecules in that shell loosely.     

A light scattering study on the ion permeabilities of dark-adapted bovine rod outer segment disk membranes

The ion permeability properties of dark adapted bovine rod outer segment disk membranes were studied using light scattering to monitor osmotic responses of disks to various salts and ionophores. A preparation procedure is presented which provides very fresh rod outer segment material with mostly intact stacked disks, but with perforated plasma membrane. It is shown that in this preparation the disks (or rod sacs) are the only osmotically responding compartments and that these responses can be readily monitored by means of light-scattering techniques. The disk membrane is found under the conditions tested, to possess no measurable permeability to cations Na+, Ca2+, Mg2+ nor the the anions Cl-, Br-, NO3-, SO4(2-), H2PO4- and HPO4(2-). There is a considerable K+ permeability, which can be completely abolished by millimolar amounts of divalent cations. The proton permeability of the disk membrane is found to depend dramatically upon the preparation procedure and duration. The fresher the material used the lower is the proton permeability measured. In our freshest preparations, even after freeze-thawing in liquid nitrogen, the disks exhibit an H+ permeability which is so low that it cannot be measured with the techniques used in this study. Even in mitochondrial or chloroplast membmranes, in which proton gradients and therefore a low proton conductance play an essential role, such low proton permeabilities have not been found. This would suggest that proton gradients across the disk membrane could play an important role in the physiological function of the photoreceptor cell. In summary it can be said that the disk membrane, apparently more than any other natural membrane system studied so far, is capable of retaining ion gradients for extended periods of time.     

Bi-ionic potentials of bovine lens capsules and collodion membranes

Concentration dependencies of bi-ionic potentials of well-cleaned bovine lens capsules in vitro, of collodion and of modified collodion membranes were studied. The lens capsules have positively fixed charges, and collodion membranes have negatively fixed charges. As these membranes are partially selectively permeable, both co-ions and counter-ions exist in the membrane. However, many studies on bi-ionic potentials have been limited to systems in which the membrane has extreme ionic selectivity and co-ions are completely excluded from the membrane. Experimental results agreed with theoretical values obtained by assuming the common ion concentration to be constant throughout the membrane for systems such as KCl(C)-membrane (θ>0, or θ<0)-NaCl(C), NaNO₃(C)-membrane (θ>0)-NaCl(C) and CaCl₂(C₁)-membrane (θ>0)-NaCl(C₂) (C₂/C₁ = 2), where C is the bulk concentration. The theoretical reliability of this assumption was checked. When both electrolytes in solution were uni-univalent, the ratio of ionic mobilities of two counter-ions (or two co-ions) in all of these membranes was almost the same as the ratio obtained in bulk solution, while the ratio of ionic mobilities of the counter-ion and the co-ion was almost the same as the ratio obtained in bulk solution for the lens capsule, but different in the case of the collodion and modified collodion membranes.     

Filipin-induced lesions in planar phospholipid bilayers imaged by atomic force microscopy.

Filipin is a macrolide polyene with antifungal activity belonging to the same family of antibiotics as amphotericin B and nystatin. Despite the spectroscopy and electron microscopy studies of its interaction with natural membranes and membrane model systems, several aspects of its biochemical action, such as the role of membrane sterols, remain to be completely understood. We have used atomic force microscopy (AFM) to study the effect of filipin on dipalmitoylphosphatidylethanolamine bilayers in the presence and absence of cholesterol. The bilayers were prepared by Langmuir-Blodgett deposition over mica and imaged under water. It was shown that filipin-induced lesions could only be found in membranes with cholesterol. In close agreement with electron microscopy results, we have reported the presence of densely packed circular protrusions in the membrane with a mean diameter of 19 nm (corrected for convolution with AFM tip) and 0.4 nm height. Larger circular protrusions (90 nm diameter and 2.5 nm height) and doughnut-shaped lesions were also detected. These results demonstrate that filipin-induced lesions in membranes previously observed by electron microscopy are not biased by artifacts resulting from sample preparation. Filipin aggregates in aqueous solution could also be imaged for the first time. These polydisperse spherical structures were observed in samples with and without cholesterol.     

Photoionization used as a tool for the study of biomembranes: fate of tetramethylbenzidine photocation in purple membrane

Photoionization of hydrophobic probes has been developed in micelles or synthetic vesicles. Studies of the yields, compartmentation, and lifetimes of the photo-produced charged species have gathered reliable information on the interfacial and structural properties of these assemblies. Such an approach has never been applied to biological membranes. The present system is tetramethylbenzidine as the probe in native or modified (deionized and/or bleached) purple membrane from halobacteria. The data on photocation formation yields (phi ion) and lifetimes (tau 1/2) allow two main conclusions to be made: (1) tetramethylbenzidine, as the cation, is buried in the membrane core, and (2) its incorporation does not alter the biological activity of the protein. In this biological membrane the photocation lifetime and yield present the same trend of variation with the surface potential but to less of an extent than in model membranes. Bleaching of purple membrane completely modifies the photoionization process and the photocation decay. In addition, these experiments reveal a tight correlation between membrane structure and probe photoionization. Further evidence for structural modification of purple membrane, either by deionization or by bleaching is pointed out.     

Influence of plasmalogen deficiency on membrane fluidity of human skin fibroblasts: a fluorescence anisotropy study

The influence of plasmalogen deficiency on membrane lipid mobility was determined by measuring fluorescence anisotropy of trimethylammoniumdiphenylhexatriene (TMA-DPH) and diphenylhexatrienylpropanoylhydrazylstachyose (glyco-DPH) inserted in the plasma membranes of human skin fibroblasts deficient in plasmalogens. The cells used were from patients affected with cerebrohepatorenal (Zellweger) syndrome (CHRS) or rhizomelic chondrodysplasia punctata. Their plasmalogen content (0-5% of total phospholipid) is significantly reduced compared with that of control cells from healthy donors (13-15% of total phospholipid) or of CHRS fibroblasts supplemented with the plasmalogen precursor, hexadecylglycerol. Plasmalogen-deficient cells consistently showed lower fluorescence anisotropies of membrane-bound DPH fluorophores corresponding to higher membrane lipid mobilities as compared to controls. However, very similar lipid mobilities were found for sonicated aqueous dispersions of phospholipids extracted either from CHRS or control cells. Therefore, the differences observed with living cells are not due to differences in the overall physical properties of the membrane lipid constituents. Other phenomena such as lipid asymmetry and/or plasmalogen-protein interactions may be responsible for the effects observed in the biomembranes.     

Real-time fluorimetric analysis of gramicidin D- and alamethicin-induced K+ efflux from Sf9 and Cf1 insect cells.

Gramicidin D and alamethicin are pore-forming peptides which exhibit lethal properties against a large spectrum of cells. Despite a wealth of experimental data from artificial membranes, the time course and quantitative analysis of the activity of these ionophores are not well described in living cells. In the present study, the newly described fluorescent dye CD-222 was used to monitor extracellular potassium ion concentration and report the effects of these antibiotics on the K+ permeability of the plasma membrane of Spodoptera frugiperda (Sf9) and Choristoneura fumiferana (Cf1) insect cells. Both peptides induced a rapid efflux of intracellular K+ as a consequence of ion channel formation in the cell membrane. K+ efflux began without any measurable delay. While the final extracellular K+ concentration was unaffected by ionophore concentration, the rate of K+ efflux was dose dependent. Using a model describing the partition of the peptides in lipid membranes, the K+ efflux kinetic parameters were determined for both cell types and both pore formers. The proposed stoichiometry for the channel formed by gramicidin in living cells is in good agreement with the two-monomers model based on data from artificial membrane systems. The K+-permeable channel formed by alamethicin in insect cells appears to involve three monomers.     

A theory of ion permeation through membranes with fixed neutral sites

Summary Some model membranes and biological membranes behave as if ion permeation were controlled by fixed neutral sites, i.e., by groups that are polar but lack net charge. By solving the boundary conditions and Nernst-Planck flux equations, this paper derives the expected properties of four types of membranes with fixed neutral sites: model 1, a membrane thick enough that microscopic electroneutrality is obeyed; model 2, same as model 1 but with a free-solution shunt in parallel; model 3, a membrane thin enough that microscopic electroneutrality is violated; and model 4, same as model 3 but with a free-solution shunt in parallel. The conductance-concentration relation and the current-voltage relation in symmetrical solutions are approximately linear for all four models. Partial ionic conductances are independent of each other for a thin membrane but not for a thick membrane. Sets of permeability ratios derived from conductances, dilution potentials, or biionic potentials agree with each other in a thin membrane but not in a thick membrane. The current-voltage relation in asymmetrical single-salt solutions is linear for a thick membrane but nonlinear for a thin membrane. Examples of potential and concentration profiles in a thin membrane are calculated to illustrate the meaning of space charge and the electroneutrality condition. The experimentally determined properties (by A. Cass, A. Finkelstein & V. Krespi) of thin lipid membranes containing “pores” of the anion-selective antibiotic nystatin are in reasonable agreement with model 3. Tests are suggested for deciding if a membrane of unknown structure has neutral sites, whether it is thick or thin, and whether the sites are fixed or mobile.