Mechanism of ion transport through lipid bilayer-membranes mediated by peptide cyclo-(d-Val-l-Pro-l-Val-d-Pro)3

The cyclic dodecapeptide PV, cyclo-(d-Val-l-Pro-l-Val-d-Pro)₃, a structural analogue of the ion-carier valinomycin, increase the cation permeability of lipid bilayer membranes. This paper reports the results of two types of relaxation experiments, namely relaxation of the membrane current after a voltage jump and decay of the membrane voltage after a charge pulse in lipid bilayer membranes exposed to PV. From the relaxation data, the rate constant for the translocation of the ion carrier complex across the membrane, as well as the partition coefficient of the complex between water and membrane solution interface were computed and found to be about one order of magnitude less than the comparable values for valinomycin (Val). Furthermore, the dependence of the initial membrane conductivity on ion concentration was used to evaluate the equilibrium constant, K, of complexation between PV and some monovalent cations in water. The values of K yield the following selectivity sequence of PV: Na⁺ < NH₄⁺ < K⁺ < Cs⁺ < Rb⁺. These and earlier results are consistent with the idea that PV promotes cation movement across membranes by the solution complexation mechanism which involves complexation between ion and carrier in the aqueous phase and transport of the carrier across the membrane. In the particular form of the solution complexation mechanism operating here, the PV present in the PV-cation complex carrying charge across the membrane derives from the side from which the current is flowing (cis-mechanism). As shown previously, valinomycin, in contrast to PV, acts by an interfacial complexation mechanism in which the Val in the Val-cation complex derives from the side toward which current is flowing (trans-mechanims). The comparison of the kinetic properties of these two closely related compounds yields interesting insights into the relationship between chemical structure and function of ion carriers.     

Effects of unstirred layers on the steady-state zero-current conductance of bilayer membranes mediated by neutral carriers of ions

Some effects of diffusion polarization and chemical reactions on the steady-state zero-current conductance of lipid bilayers mediated by neutral carriers of ions have been studied theoretically and experimentally. Assuming that ion permeation across the interfaces occurs via a heterogeneous reaction between ions in the solution and carriers in the membrane, the relationship between the conductance and the aqueous concentration of carriers is shown to be linear only in a limited range of sufficiently low concentrations. At higher carrier concentrations, which for the most strongly bound cations are within the range of the experimentally accessible values, the conductance is expected to become limited by diffusion of the carried ion in the unstirred layers and therefore reach an upper limiting value independent of the membrane properties. This expectation has been successfully verified for glyceryl-monooleate membranes in the presence of the ions K+, Rb+ and NH+4 and carriers such as valinomycin and trinactin. The experimental results support, at least for the present system, the generally accepted view that complexation between ions and the macrocyclic antibiotics occurs at the membrane surface; it is shown, in fact, that for a different mechanism, such as that by which the complexes would form in the aqueous solutions and cross the interfaces as lipid-soluble ions, the same type of saturation would be expected to be observable only for unrealistically high values of the rate constants of the ion-carrier association. A previously proposed criterion to distinguish between these two mechanisms, based on the dependence of the conductance on the ion concentration, is discussed from the viewpoint of this more comprehensive model.     

Theory for carrier-mediated zero-current conductance of bilayers extended to allow for nonequilibrium of interfacial reactions,spatially dependent mobilities and barrier shape

Summary A generalized form of the electrodiffusion equation, allowing for any shape of symmetrical energy barrier and any spatial dependence of the diffusion coefficient, is used to deduce theoretically the carrier-mediated conductance for thin (e.g., bilayer) membranes in the limit of low applied current. Both the Nernst-Planck and the Eyring single-barrier treatments are special cases of this more general approach, which allows for the effect of non-uniform properties of the lipid and non-uniform profiles of the forces acting within the membrane interior. Two independent mechanisms for ions to cross the membrane-solution interfaces are considered; namely, (1) the reaction at the interface between ions from solution and carriers from the membrane, and (2) the partition across the interfaces of complexes already formed in the solution. The rates of these reactions are taken into account using the rate equations of chemical kinetics; and the Poisson-Boltzmann equation is integrated in the aqueous solutions to evaluate the effect of charged polar head groups of the lipid. The analysis leads to an expression for the conductance, which, in the approximation of constant field, is an explicit function of such experimentally variable parameters as the concentrations and types of permeant ions and carriers in the aqueous phases, the total ionic strength and the nature of the polar head groups of the lipid. The functional relationship observable in an unknown membrane can, in principle, enable one to deduce such information as the mechanism of ion permeation across the interfaces, the magnitude of the surface charge, and the degree of ion-carrier complexation in the aqueous solutions.     

A laser-temperature-jump method for the study of the rate of transfer of hydrophobic ions and carriers across the interface of thin lipid membranes

The first application of a laser-temperature-jump apparatus for the study of ion transport through planar (artificial) lipid membranes is described. The relaxation of the electric current is detected, either continuously at a constant applied voltage or discontinuously by a series of short voltage pulses. The second technique, a combined voltage- and temperature-jump method, is especially appropriate to investigate the kinetics of the adsorption/desorption process of hydrophobic ions and neutral carriers of cations at the membrane interface and to separate this phenomenon from the diffusion process through the unstirred aqueous layers adjacent to the membrane. The aim is to determine the rate-limiting step of transport. The permeation rate of the hydrophobic anion 2,4,6-trinitrophenolate is limited by the inner membrane barrier. For tetraphenylberate the rate constant of translocation across the inner barrier and that of desorption from the membrane into water are found to be of comparable magnitude. The membrane permeability of the neutral macrocyclic ion carrier enniatin B is strongly interface limited by its comparatively small rate of desorption into water. These results show that the frequently used a priori assumption of partition equilibrium at the membrane interfaces during transport is not justified.     

Complexation and ionophoric properties of taxol and colchicine: complex formation and transport of sodium, potassium, magnesium and calcium ions across a liquid membrane

We report the activities of taxol (an anticancer drug) and colchicine, which are inhibitors of microtubule organization, on the complexation and transport of Na+, K+, Mg2+ and Ca2+ ions across a liquid membrane, using a spectrophotometric procedure. Taxol, a diterpenoid compound, that has been demonstrated to possess a potent antitumour activity, is shown to extract Na+, K+, Mg2+ and Ca2+ ions from the aqueous solution to the organic phase with preference for Ca2+ ions. A kinetic study of the transport and complexation of Na+, K+, Mg2+ and Ca2+ ions through a liquid membrane revealed that the K+ ion is more rapidly transported and the Ca2+ ion is more rapidly complexed than other ions. However, colchicine, another alkaloid compound, extracted and transported only the divalent ions tested, Mg2+ and Ca2+. In both complexation and transport, the flux of the ions increases with the concentration of taxol or colchicine. Complexation and ionophoric properties of taxol and colchicine sheds new lights on therapeutic properties of these drugs. The treatment of disease states by the administration of these drugs to alter membrane permeability will prove to be a valuable therapeutic concept.     

Ion transport and displacement currents with membrane-bound carriers

Summary The standard carrier model for ion transport by a one-to-one mechanism is developed to predict the time-dependent currents for systems that are symmetrical at zero applied potential. The complete solution for ions and carriers bearing any charge is derived by assuming that the concentration of ions in the membrane is low and either that the applied potential is small or that the applied potential affects equally all of the association and dissociation reactions between the ions and the carriers. The response to an abruptly applied potential is then given by the sum of a constant and two declining exponential terms. The time constants of these relaxations are described by the equations derived for neutral carriers by Stark, Ketterer, Benz and Läuger in 1971 (Biophys. J. 11:981). The sum of the amplitudes of the exponentials for small applied potentials obeys a relation like that first derived by Markin and Liberman in 1973 (Biofizika 18:453). For small applied potentials expressions are also provided for the voltage transients in charge-pulse experiments and for the membrane admittance.     

The transport of potassium through lipid bilayer membranes by the neutral carriers valinomycin and monactin

Summary Stationary conductance experiments on neutral and negatively charged bilayer membranes in the presence of valinomycin or monactin agree with a recently proposed carrier transport model, which is common to both carrier types. This model assumes an interface reaction between a cation from the aqueous solution and a carrier molecule from the membrane phase to establish charge transport across the interface. The transport across the membrane interior is described by some kind of Eyring model. The discussion of the current-voltage characteristic, the dependence of membrane conductance on the carrier and K⁺ concentrations, and the comparison with appropriate experiments allow correlation of the different rate constants of the transport model. The results show that the rate constants partly depend on the surface charge of the membranes. This dependency can be described by introducing the Gouy-Chapman theory for charged surfaces into the transport model.It was found that the carrier molecules could be added either to the aqueous phase or to the membrane-forming solution. The quantitative treatment of this phenomenon gives an evaluation of the partition coefficient of the carrier molecules between the membrane bulk phase and water.     

Carrier Model for Active Transport of Ions across a Mosaic Membrane

The central purpose of this paper is to elucidate in a well defined system the meaning of certain phenomena and concepts associated with the active transport of ions. To this end a specific model for a carrier system which actively transports a single ionic species is analyzed and discussed in detail. It is assumed in this model that the carrier-mediated ionic transport occurs in regions of the membrane physically separate from those regions in which free ionic movement takes place,—coupling between the active and passive regions of the membrane occurring through local current flows. The model is seen to display the following characteristics: (a) Starting from identical solutions on the two sides of the membrane, there is produced a redistribution of ions; (b) with identical solutions on the two sides of the membrane there exists a potential difference across the membrane, i.e., the “pump” is electrogenic; (c) the “short circuit” current for symmetrical solutions is equal to the flux of the neutral ion carrier complex; (d) the rate of active transport (and hence of metabolism) is dependent on the ionic concentrations in the surrounding solutions. Throughout the paper comparison is made between features of the model and properties displayed by biological active transport systems, but there is no claim of an identity between the two.     

Kinetics of the iodine- and bromine-mediated transport of halide ions: demonstration of an interfacial complexation mechanism.

Stationary and kinetic experiments were performed on lipid bilayer membranes to study the mechanism of iodine- and bromine-mediated halide transport in detail. The stationary conductance data suggested that four different 1:1 complexes between I2 and Br2 and the halides I- and Br- were responsible for the observed conductance increase by iodine and bromine (I3-, I2Br-, Br2I-, and Br3-). Charge pulse experiments allowed the further elucidation of the transport mechanism. Only two of three exponential voltage relaxations predicted by the Läuger model could be resolved under all experimental conditions. This means that either the heterogeneous complexation reactions kR (association) and kD (dissociation) were too fast to be resolved or that the neutral carriers were always in equilibrium within the membrane. Experiments at different carrier and halide concentrations suggested that the translocation of the neutral carrier is much faster than the other processes involved in carrier-mediated ion transport. The model was modified accordingly. From the charge pulse data at different halide concentrations, the translocation rate constant of the complexed carriers, kAS, the dissociation constant, kD, and the total surface concentration of charged carriers, NAS, could be evaluated from one single charge pulse experiment. The association rate of the complex, kR, could be obtained in some cases from the plot of the stationary conductance data as a function of the halide concentration in the aqueous phase. The translocation rate constant, kAS, of the different complexes is a function of the image force and of the Born charging energy. It increases 5000-fold from Br3- to I3- because of an enlarged ion radius.     

How erythrocyte volume is regulated, or what mathematical models can and cannot do for biology

Modern concepts of the red blood cell (RBC) volume regulation are considered. It is shown that the system of ion pumps and channels in the cell membrane ensures the physiological value of volume with a precision of about 10% even at 5- to 7-fold variations of passive membrane permeability for ions. Particular attention is paid to mathematical models for evaluation of the role of different molecular mechanisms in the RBC volume control. It is shown that many questions, for example, ‘why the Na⁺,K⁺-ATPase pumps the ions in opposite directions’ or ‘what is the physiological role of Ca²⁺-activated K⁺-channels’, cannot be answered without adequate mathematical models of such complex control systems as cell volume control.     

The Properties of Ion Channels in Lipid Membranes Modified by the Aromatic Antibiotic Levorin А2

It has been shown that the main components of levorin A, that is, A₀, A₁, A₂, or A₃, that contain an aromatic group increase the permeability of membranes in the series A₃ > A₂ > A₁ > A₀ when they are on the same side of the membrane. All levorin components have cationic selectivity. The most studied levorin, А₂, promotes the almost ideal permeability of membranes to potassium ions. The membrane potential for a ten-fold change in the KCl concentration gradient is 56 ± 2 mV. It has been shown that the injection of the same concentration of levorin А₂ into one side of the membrane and then, after achieving the typical membrane permeability, into the other side of the membrane generates a two-fold increase in the total membrane permeability. This means that independent levorin-induced conductive semi-pores are formed on each side of the membrane. It has been found that the injection of levorin А₂ only into one side of the membrane enhances the membrane permeability to monosaccharides and other neutral molecules. The presence of levorin А₂ in cholesterol-, ergosterol-, and stigmasterol-containing phospholipid membranes has been shown to lead to the single-channel conductivity of typical ion channels of 0.2–0.5 pS. The properties of these channels have been studied. The levorin channels exist in two states, open and closed. Most of the time, the channel remains in the open state in the KBr solution. In solutions of different salts of the same concentration, the conductivity value of the levorin channels is approximately the same (0.4–0.5 pS). An increase in the dimethyl sulfoxide concentration in aqueous solutions facilitates the transition of polyene antibiotic molecules from dispersed to monomolecular form. The molecules of polyene antibiotics in the associated form exhibit high membrane activity.

     

The effects of pH and calcium concentrations on gill potentials in the Brown Trout,Salmo trutta

Summary Measurements of the transepithelial potential (V_int-V_ext) across the gills of Brown Trout,Salmo trutta, were made in solutions of a range of pH and calcium concentrations. The potential was strongly dependent on external pH, being negative in neutral solutions but positive in acid solutions. The addition of calcium to the external medium produced a positive shift in potential in all but very acid media (pH 4.0–3.5), where very little change was seen. The gill membrane appears to act as a hydrogen electrode having a very high permeability to H⁺ ions, and the potential behaves as a diffusion potential. The presence of calcium reduced the permeability to both H⁺ and Na⁺ ions but even at a calcium concentration of 8.0 mM/l the permeability ratio H⁺/Na⁺ was still more than 900. The transepithelial potential is shown to be diffusional in origin and is discussed in terms of the relative permeability of the gill to H⁺, Na⁺ and Cl^– ions. Sodium fluxes across the gills were measured and provide the basis for a theoretical consideration of Na⁺, Cl^– and H⁺ fluxes across the gills in neutral and acid solutions. The positive potential at low pH largely accounts for the increased loss of sodium from fish in these conditions.     

Oscillation of electrical potential in a porous-membrane doped with triolein induced by an Na+/K+ concentration gradient

The electrical potential across a fine pore membrane doped with trioleoyl glyceride (triolein) and separating aqueous solutions of 0.5M NaCl and 0.5M KCl, respectively, was studied. It was found that this system showed rhythmic and sustained oscillations of electrical potential between the two aqueous solutions. These oscillations were attributed to the change of permeability of Na+ and K+ ions across the membrane, which originated from the phase-transition of triolein molecules within the fine pores.     

Molecular Model of a Cell Plasma Membrane With an Asymmetric Multicomponent Composition: Water Permeation and Ion Effects

We present molecular dynamics simulations of a multicomponent, asymmetric bilayer in mixed aqueous solutions of sodium and potassium chloride. Because of the geometry of the system, there are two aqueous solution regions in our simulations: one mimics the intracellular region, and one mimics the extracellular region. Ion-specific effects are evident at the membrane/aqueous solution interface. Namely, at equal concentrations of sodium and potassium, sodium ions are more strongly adsorbed to carbonyl groups of the lipid headgroups. A significant concentration excess of potassium is needed for this ion to overwhelm the sodium abundance at the membrane. Ion-membrane interactions also lead to concentration-dependent and cation-specific behavior of the electrostatic potential in the intracellular region because of the negative charge on the inner leaflet. In addition, water permeation across the membrane was observed on a timescale of ∼100 ns. This study represents a step toward the modeling of realistic biological membranes at physiological conditions in intracellular and extracellular environments.     

‘Naked-eye’ quinoline-based ‘reactive’ sensor for recognition of Hg2+ ion in aqueous solution

A new ‘naked-eye’ quinoline-based ‘reactive’ ratiometric fluorescent probe was prepared. The reactive stoichiometry of the probe with Hg²⁺ ion was 2:1. The probe exhibited high selectivity towards Hg²⁺ ion to other metal ions with a 410-fold increase in absorbance intensity ratio (A₄₀₂/A₃₄₀) in aqueous solution over a wide-range pH value (2–12), accompanied by a resonance color change from colorless to pale yellow visible to naked-eye.     

Modification of valinomycin-mediated bilayer membrane conductance by 4,5,6,7-tetrachloro-2-methylbenzimidazole

Summary The compound, 4,5,6,7-tetrachloro-2-methylbenzimidazole (TMB), has been found to markedly modify the steady-state valinomycin-mediated conductance of potassium (K⁺) ions through lipid bilayer membranes. TMB alone does not contribute significantly to membrane conductance, being electrically neutral in solution. In one of two classes of experiments (I), valinomycin is first added to the aqueous phases then changes of membrane conductance accompanying stepwise addition of TMB to the water are measured. In a second class of experiments (II), valinomycin is added to the membrane-forming solution, follwed by TMB additions to the surrounding water. In both cases membrane conductance shows an initial increase with increasing TMB concentration which is more pronounced at lower K⁺ ion concentration. At TMB concentrations in excess of 10^–5 m, membrane conductance becomes independent of K⁺ ion concentration, in contrast to the linear dependence observed at TMB concentrations below 10^–7 m. This transition is accompanied by a change of high field current-voltage characteristics from superlinear (or weakly sublinear) to a strongly sublinear form. All of these observations may be correlated by the kinetic model for carriermedicated transport proposed by Läuger and Stark (Biochim. Biophys. Acta 211:458, 1970) from which it may be concluded that valinomycin-mediated ion transport is limited by back diffusion of the uncomplexed carrier at high TMB concentrations. Experiments of class I reveal a sharp drop of conductance at high (>10^–5 m) TMB concentration, not seen in class II experiments, which is attributed to blocked entry of uncomplexed carrier from the aqueous phases. Valinomycin initially in the membrane is removed by lateral diffusion to the surrounding torus. The time dependence of this removal has been studied in a separate series of experiments, leading to a measured coefficient of lateral diffusion for valinomycin of 5×10^–6 cm²/sec at 25°C. This value is about two orders of magnitude larger than the corresponding coefficient for transmembrane carrier diffusion, and provides further evidence for localization of valinomycin in the membrane/solution interfaces.     

Effect of peptide PV on the ionic permeability of lipid bilayer membranes

This paper reports the effects of peptide PV (primary structure: cyclo-(D-val-L-pro-L-val-D-pro)_δ) on the electrical properties of sheep red cell lipid bilayers. The membrane conductance (G_m) induced by PV in either Na⁺ or K⁺ medium is proportional to the concentration of PV in the aqueous phase. The PV concentration required to produce a comparable increase in G_m in K⁺ medium is about 10⁴ times greater than for its analogue, valinomycin (val). Although the selectivity sequence for PV and val is similar, K⁺ ≳ Rb⁺ > Cs⁺ > NH₄ ⁺ > TI⁺ > Na⁺ > Li⁺; the ratio of GGm in K⁺ to that in Na⁺ is about 10 for PV compared to > 10³ for val. When equal concentrations of PV are added to both sides of a bilayer, the membrane current approaches a maximum value independent of voltage when the membrane potential exceeds 100 mV. When PV is added to only one side of a bilayer separating identical salt solutions of either Na⁺ or K⁺ salts, rectification occurs such that the positive current flows more easily away rather than toward the side containing the carrier. Under these conditions, a large, stable, zero-current potential (VVm) is also observed, with the side containing PV being negative. The magnitude of this VVm is about 90 mV and relatively independent of PV concentration when the latter is larger than 2 Times; 10^–5 M. From a model which assumes that V_m equals the equilibrium potential for the PV-cation complexes (MS ⁺) and that the reaction between PV and cations is at equilibrium on the two membrane surfaces, we compute the permeability of the membrane to free PV to be about 10^–5 cm s^–1, which is about 10^–7 times the permeability of similar membranes to free val. This interpretation is supported by the fact that the observed values of V_m are in agreement with the calculated equilibrium potential for MS⁺ over a wide range of ratios of concentrations of total PV in the two bathing solutions, if the unstirred layers are taken into account in computing the MS⁺ concentrations at the membrane surfaces.     

Robust multiple-input-multiple-output control of non-linear continuous fermentation processes

In this study, the removal of nitrate (NO₃^m) ions from aqueous streams with liquid membrane technique has been investigated. Among the other parameters (temperature, pH, acceptor phase type and medium concentration), the stirring speed was chosen as process parameter. From the experimental results, it has been determined that the reaction was diffusion controlled. The transport efficiency of nitrate ions increased with increasing stirring speed. The membrane entrance and exit rate constants (k_1d, k_2m and k_2a respectively) were linearly dependent on the stirring speed ratios of 100 to 250 rpm. Coupled transport of nitrate ions through a liquid membrane in 85% n-hexane-15% tricloromethane as diluent, containing tetraoctyl ammonium chloride (TOACl) as a carrier was examined at various stirring speeds. Membrane entrance (k_1d) and exit rates (k_2m and k_2a) increase with increasing the stirring speeds. The diffusion of the nitrate ion-carrier complex through the narrow stagnant layers was found to be rate determining step. The membrane was stable during the transport experiments. There is no leakage of carrier or nitrate ion-carrier complex to both aqueous phases and also, no supplementary water penetration into the membrane. This favours interfacial reaction of nitrate ion and carrier.     

Ionic Blockage of Sodium Channels in Nerve

Increasing the hydrogen ion concentration of the bathing medium reversibly depresses the sodium permeability of voltage-clamped frog nerves. The depression depends on membrane voltage: changing from pH 7 to pH 5 causes a 60% reduction in sodium permeability at +20 mV, but only a 20% reduction at +180 mV. This voltage-dependent block of sodium channels by hydrogen ions is explained by assuming that hydrogen ions enter the open sodium channel and bind there, preventing sodium ion passage. The voltage dependence arises because the binding site is assumed to lie far enough across the membrane for bound ions to be affected by part of the potential difference across the membrane. Equations are derived for the general case where the blocking ion enters the channel from either side of the membrane. For H⁺ ion blockage, a simpler model, in which H⁺ enters the channel only from the bathing medium, is found to be sufficient. The dissociation constant of H⁺ ions from the channel site, 3.9 x 10^-6 M (pK_a 5.4), is like that of a carboxylic acid. From the voltage dependence of the block, this acid site is about one-quarter of the way across the membrane potential from the outside. In addition to blocking as described by the model, hydrogen ions also shift the responses of sodium channel "gates" to voltage, probably by altering the surface potential of the nerve. Evidence for voltage-dependent blockage by calcium ions is also presented.     

Electrolyte permeability and electromotive action of mosaic membranes composed of porous and liquid parts of high ionic selectivity for ions of opposite signs

Summary A theory is presented of the electromotive and ion permeability properties of membranes which consist of a mosaic of highly ion selectiveporous membrane areas of ion exchanger nature and of areas of highly ion selectiveliquid ion exchanger membranes, the two types of areas being exclusively permeable to ions of opposite sign. It is demonstrated that, with properly chosen membranes, the preferential permeability of such porous-liquid mosaic membranes for ions of one sign of charge will be the opposite of that apparently indicated by their electromotive action.The theory is based on the fact that the movement of ions across the porous membranes occurs in the dissociated state and in most instances is quantitatively linked to the resistance according to the Nernst-Einstein equation. The penetration of ions across liquid ion exchanger membranes, however, takes place essentially in a nondissociated state, and, as determined by self-exchange studies with radioactive tracers and stirred membranes, occurs at rates far in excess of those across porous membranes of the same resistance.For the theoretical treatment the simplest case, two-membrane macro-model concentration cells, is discussed in detail. Qualitatively, it is evident that the ratio of the permeability of anions and cations across such porous-liquid mosaic membranes ordinarily will be strongly in favor of the ions which penetrate across its liquid parts; contrariwise, the electromotive actions of the mosaic membranes ordinarily are dominated by its porous parts.Electric currents flow through all mosaic membranes; the strenghth of the current in a model cell may be calculated from the concentration potentials arising separately across the two membranes, and the resistances of the membranes and of the two solutions. From the strength of the current, the sign and the magnitude of the concentration potential arising in the model cell may be computed; in many instances it should closely approach the concentration potential across the porous membrane.For the test of this theory with two-membrane macro-mosaic models, the electrolyte of choice for experimental reasons was RbSCN, tagged with⁸⁶Rb⁺ and S¹⁴CN^–. The porous membranes were polystyrene sulfonic acid collodion matrix membranes; the liquid membranes consisted of 0.02m trioctyl propyl ammonium thiocyanate in 1-decanol. The ratios of the permeabilities across the model mosaic membranes determined by conventional rate of self-exchange measurements showed, as expected, that the permeability of the SCN^– ions is larger, up to 3600 times larger, than that of the Rb⁺ ions. The potentials arising in these models agreed within the limits of experimental error with those predicted by theory, closely approaching that arising at the cation selective porous membranes.