The Electrical Conductance of Semipermeable Membranes: II. Unipolar Flow, Symmetric Electrolytes

A general formulation of the problem of stationary ion flow through semipermeable membranes was presented in the first paper of this series. The formalism is applied here to the evaluation of membrane conductance for the special case of unipolar ion flow between symmetric electrolytes. Thus it is assumed that the permeant ions carry one sign of charge only. Furthermore, the valences of all ions in solution on both sides of the membrane are taken to be of equal absolute magnitude. Conductance results obtained by numerical methods are presented for several representative sets of the parameters which characterize the membrane system in equilibrium. These results are discussed qualitatively with emphasis upon the contribution of particular system parameters to the non-linearities observed. Approximate analytic conductance relations, valid for high current levels, are also given.     

The Electrical Conductance of Semipermeable Membranes: I. A Formal Analysis

A kinetic analysis of membrane conductance under conditions of stationary flow is presented. The semipermeable membrane is idealized as a homogeneous laminar phase separating ionic solutions on either side. It is assumed, without consideration of the mechanisms involved, that some ion species permeate the membrane while others do not. The flux of a given species is taken to be linearly related to the gradient of its concentration and to the electric field. The resulting flow equations, when combined with Poisson's equation, permit the formulation of the conductance problem in terms of a set of non-linear differential equations. They describe the spatial variation of the electric displacement and contain the ion current densities as parameters. Their integration, subject to appropriate boundary conditions, fixes the values of these parameters and of the corresponding transmembrane potential. The solution of the conductance problem cannot, however, be carried through in analytic form. The numerical analysis of a number of special cases will be presented in subsequent publications.     

Computation of the Electrical Double Layer Properties of Semipermeable Membranes in Multicomponent Electrolytes

A methodology is presented for calculating of the surface potential, Donnan potential, and ion concentration profiles for semipermeable microbial membranes that is valid for an arbitrary electrolyte composition. This model for surface potential, Donnan potential, and charge density was applied to recently reported experimental data for gram-positive bacteria, including Bacillus brevis, Rhodococcus opacus, Rhodococcus erythropolis, and Corynebacterium species. These calculations show that previously unconsidered trace amounts of divalent and trivalent cations at very low concentrations (10⁻⁶ M) can have significant effects on the calculated surface and Donnan potentials, at ionic strengths of I ≤ 0.01 M, and that these effects need to be considered in accurate modeling of microbial surface. In addition, the calculated ion concentration profiles show that owing to the relatively high surface charges that can develop in microbial membranes, electrostatic effects can act to significantly concentrate divalent (factors of 5 × 10³) and trivalent (factors of 2 × 10⁴) cations within the bacterial cell wall. Comparison of the calculated concentration factors with those derived from experiments shows that a significant fraction of the uptake of metal by bacteria can be explained by the proposed electrostatic model.     

Nonlinear Electrical Effects in Lipid Bilayer Membranes: III. The Dissociation Field Effect

In the course of an analysis of nonlinear electrical effects in lipid bilayer membranes, the influence of the dissociation field (or Wien) effect on the membrane conductivity is investigated. It is shown that the theory of Onsager for the Wien effect in a macroscopic phase can be applied to a thin membrane when the proper boundary conditions at the membrane-solution interface are introduced. It is assumed that an activation energy is associated with the passage of the ion across the interface. The mathematical treatment of the model is restricted to the case for which cations and anions have identical properties except for the charge sign. The resulting differential equations for the ion concentration within the membrane are integrated numerically. The analysis shows that the influence of the Wien effect on the membrane conductivity is appreciable only if the energy barrier at the interface is sufficiently high, i.e. if the rate limiting step for the ion transport is the passage of the ion across the interface.     

The Electrical Capacitance of Phospholipid Membranes

As one of the methods of finding out the structural change of lipid bilayers due to change of environmental solution, the capacitances of phosphatidyl choline (egg lecithin) and phosphatidyl serine (bovine brain) bilayer membranes in solutions of various pH and salt contents were measured. It was found that the capacitance of the bilayer depended upon pH and salt content. The capacitance had a minimum value around pH 4 for phosphatidyl choline and around pH 3-4 for phosphatidyl serine bilayers, respectively. The value of the capacitance increased as the pH of the solution became lower or higher. As the concentration of cholesterol in the phosphatidyl choline bilayer increased, the capacitance increased and reached a saturation value. A DC voltage across the phosphatidyl choline bilayer did not affect the value of the capacitance practically.     

Kinetic Theory Model for Ion Movement through Biological Membranes: III. Steady-State Electrical Properties with Solution Asymmetry

An electrodiffusion model for plasma membrane ion transport, which takes into account the influence of high electric field strengths and ion-membrane molecule interactions, is presented and analyzed. A generalized Nernst-Planck equation for steady-state situations is derived which has electric field-dependent mobility and diffusion coefficients. Under the assumption of a constant electric field within the membrane, this equation is integrated to give a more general form of the Goldman equation. Based on this equation numerical computations of ionic chord conductance as a function of applied electric field strength were carried out for several permeant ion concentration ratios. The model is capable of yielding significantly larger rectification ratios than is the Goldman equation. Further, high field asymptotes to the current vs. electric field strength curve do not generally intersect at the origin.     

Bipolar Lipid Vesicles: A Model for Archaeobacteria Membranes

Abstract

In this work we report the results of experiments performed on vesicles of bipolar lipids extracted from the thermophilic archaeobacterium Sulfolobus solfataricus These results are compared with similar data obtained with synthetic compounds which mimic the structure of natural archaeobacterial lipid molecules.     

Electrical Properties of Mitochondrial Membranes

The electrical capacity of the membrane of rat liver mitochondria is 0.5 to 0.6 µ./cm². This membrane capacity is obtained from the analysis of the frequency dependence of the admittance of a suspension of swollen mitochondria. In potassium chloride media the mitochondrial membrane capacity does not depend on the ion concentration. The internal conductance of the mitochondria was approximately one-half that of the external medium; the same applies if the mitochondria are equilibrated in a medium with a 10-fold difference in potassium chloride concentration. Hence the swollen mitochondria investigated here appear to be able to adjust their internal ion concentration in proportion with that of the external phase. The similarity of the membrane capacity of isolated mitochondria with the range of values known for other membranes suggests a common molecular structure. The analysis of experimental data suggests an anisotropic electrical behavior of the interior of mitochondria. This anisotropy is readily explained by the existence of internal membranes.     

Studies with Composite Membranes: III. Measurement of Water Permeability

The permeability of tritiated water (THO) across simple and layer-type composite membranes of collodion containing different amounts of polystyrenesulfonic acid has been measured and corrected for the effects of aqueous stationary layers present at the membrane-solution interfaces. It was found that the water permeabilities in the two opposite directions across the composite membranes were different, whereas they were the same across simple membranes. The theoretical permeability value for the composite membrane (formed by putting one simple membrane on top of another simple membrane of increasing charge density and gently pressing them together), calculated from the values due to simple membranes, was found to be always greater than the two measured values. It was shown that the aqueous layers trapped between membranes were not responsible for the low measured values. The factor causing this was ascribed to the mechanism which produced rectification of water flow in the composite membranes. Establishment of the THO concentration profile in the layered membranes showed that accumulation and depletion of THO in the membrane phase when the THO was flowing from the high charge density side to the low charge density side and vice versa, respectively, were responsible for the unequal flows observed across the composite membrane in the two directions.     

Effects of Different Semipermeable Membranes on In Vitro and In Vivo Performance of Microdialysis Probes

The in vitro and in vivo performance of three different semipermeable microdialysis membranes was compared: a proprietary polycarbonate-ether membrane made by Carnegie Medecin; cuprophan, a regenerated cellulose membrane; and polyacrylonitrile. When microdialysis probes were tested in a stirred in vitro solution, large and statistically significant differences among the three membranes in extraction of acid metabolites (3,4-dihydroxyphenylacetic acid, 5-hydroxyindoleacetic acid, and homovanillic acid) and acetaminophen were found. Polyacrylonitrile had the highest extractions in vitro. In contrast, when microdialysis probes were implanted in vivo (in rat striatum), extraction of acid metabolites and acetaminophen did not differ significantly among the different membranes. These results are consistent with predictions made by a mathematical model of microdialysis and can be explained by the fact that in vitro the main factor limiting extraction is membrane resistance to diffusion, whereas tissue resistance to diffusion plays a more dominant role in vivo. These findings suggest that (aside from differences in surface area), the choice of semipermeable membrane will generally have little effect on in vivo microdialysis results. Furthermore, in vitro measurements of microdialysis probe extractions are not a reliable way of calibrating in vivo performance.     

Changes in Electrical Conductance of Rhodopsin on Photolysis

The change in electrical conductance of rhodopsin solutions was studied with flash-photolysis techniques. The whole pattern of the conductance change on illumination consists of three different processes: (I) the initial decrease, (II) the increase, and (III) the slow decrease, which are in decreasing order of reaction rate. The processes I, II, and III can be most distinctly recognized on flash illumination of acid, slightly acid, and alkaline rhodopsins, respectively. On the other hand, the bleaching of rhodopsin also shows at least three successive phases of different rates, but none of them corresponds in reaction rate to any of the processes of the conductance change. The conductance change may be related to conformational changes of opsin following photoisomerization of retinene, being due to hydrogen or hydroxyl ions and some other inorganic electrolytes. The amount of the change, especially the initial decrease, is proportional to the amount of rhodopsin bleached, even when the photochemical back reaction towards rhodopsin and isorhodopsin occurs in the chromophore depending on the intensity of illumination. Of the three processes, the slow decrease is most severely affected by aging, but the initial decrease and increase are slightly affected. These two processes promptly caused by illumination are connected closely to the conformational changes during the conversion of rhodopsin to metarhodopsin, and perhaps to the initial stage of excitation of rod cells.     

Electrical Characteristics of Sphingomyelin Bilayer Membranes

Current-voltage characteristics and the conductivity temperature dependence of sphingomyelin bilayer membranes have been determined. The resistances were of the order of 10(8) Omega-cm(2) and exhibited ohmic behavior up to approximately 25 mv followed by increasing conductivity with applied voltage. The current is found to be proportional to a hyperbolic sine function of the voltage. The temperature dependence indicates a thermally activated conduction mechanism. The observed behavior closely follows a kinetic model involving a barrier modified by the applied electric field, the rate-limiting process being the surmounting of the barrier by the impinging ions. The model allows predictions to be made over a wide range of conditions.     

The Electrical Characteristics of Fixed Charge Membranes: Solution of the Field Equations

A theoretical analysis is made of the electrical characteristics of a membrane containing two fixed charge regions, of opposite sign, in contact. Profiles of ion concentrations, electrostatic potential, space charge density, as well as the voltage-current characteristics were obtained by numerical integration of the field equations on a computer. Comparison with the predictions of an earlier analysis of this system (Coster, 1965) shows that the latter is valid to a good approximation for membranes > 70 A in thickness. In particular the form of the electrical characteristics, including the punch-through effect, have been verified by the computer analysis. The range of useful validity of the earlier analysis, the use of Boltzmann statistics when currents are present, and variation of membrane capacitance with applied potential, are discussed in the light of the results obtained.     

Electrical Properties and Ultrastructure of Mycoplasma Membranes

Mycoplasma, in particular species laidlawii and gallisepticum, are found to have a very small, low frequency conductivity as would be predicted by the dielectric model for bacteria and their apparent lack of cell wall structure. Membrane capacitance values for the two organisms are both about 0.9 μF/cm², although electron micrographs show that the membrane of M. gallisepticum is 20-40 A thicker than that of M. laidlawii.     

The Electrical Resistance and Capacitance of the Membranes of Nitella translucens

The resistance and capacitance of the membranes of Nitella translucenshave been measured by direct current and alternating currentmethods. Current of the order of 10^-7 amp. was injected intothe cell by means of a conventional Ag, AgCl_-3N KCl glass microelectrodeinserted into the vacuole of the cell. The change of potentialacross the membrane was recorded by two other internal microelectrodeswhich had been inserted into the cell at known distances fromthe current-injecting electrode. In the direct-current experimentsthe input current was in the form of a square pulse, while sinusoidalcurrents of frequency 25 cycles per second were used in thealternating current experiments. The cell was treated as a shortlength of coaxial cable and from the measurements the followingparameters could be obtained: the space constant (), the membraneresistance (R_m) and the membrane capacitance (C_m). The valuesof R_m ranged from 6.7 to 36 K ohm cm.² (mean of 21.4 K ohm cm.²)and those of ranged from 1.5 to 5.7 cm. (mean of 2.6 cm.).The capacitance value was about I µF cm.^-2 These results are discussed within the framework of our knowledgeof these parameters for other cells, particularly plant cells.The measured electrical resistance is shown to be at least tentimes less than the value estimated from the passive fluxesof the principal ions K, Na, and Cl. It is suggested that thisdiscrepancy, which is usually attributed to non-independentmovement of these ions, could be partially explained on electro-osmoticgrounds. The value of the capacitance is very close to thatwhich is usually obtained for other cell membranes. One exceptionallylow value for Nitella has been quoted in the literature. Thereason for the gross error in this particular measurement isgiven.     

Single-Channel Characterization of a Nonselective Cation Channel from Human Placental Microvillous Membranes. Large Conductance, Multiplicity of Conductance States, and Inhibition by Lanthanides

The rate-limiting step for the maternofetal exchange of low molecular-weight solutes in humans is constituted by transport across a single epithelial layer (syncytiotrophoblast) of the placenta. Other than the well-established presence of a large-conductance, multisubstate Cl⁻ channel, the ionic channels occurring in this syncytial tissue are, for the most part, unknown. We have found that fusion of apical plasma membrane-enriched vesicle fractions with planar lipid bilayers leads, mainly (96% of 353 reconstitutions), to the reconstitution of nonselective cation channels. Here we describe the properties of this novel placental conductance at the single-channel level. The channel has a large (>200 pS) and variable conductance, is cation selective (P _Cl /P _K ≅ 0.024), is reversibly inhibited (presumably blocked) by submillimolar La³⁺, has very unstable kinetics, and displays a large number (>10) of current sublevels with a ``promiscuous' connectivity pattern. The occurrence of both ``staircaselike' and ``all-or-nothing' transitions between the minimum and maximum current levels was intriguing, particularly considering the large number of conductance levels spanned at a time during the concerted current steps. Single-channel data simulated according to a multistate linear reaction scheme, with rate constants that can vary spontaneously in time, reproduce many aspects of the recorded subconductance behavior. The channel's sensitivity to lanthanides is reminiscent of stretch-sensitive channels which, in turn, suggests a physiological role for this ion channel as a mechanotransducer during syncytiotrophoblast-volume regulation. Received: 30 August 1999/Revised: 12 November 1999     

The Effect of Surface Charge on the Voltage-Dependent Conductance Induced in Thin Lipid Membranes by Monazomycin

Differences in the behavior of phosphatidylethanolamine (PE) and phosphatidylglycerol (PG) thin lipid membranes treated with monazomycin are shown to be due to the negative surface charge on PG membranes. We demonstrate that shifts of the conductance-voltage (g-V) characteristic of PG films produced by changes of univalent or divalent cation concentrations result from changes of the membrane surface potential on one or both sides. In particular, if divalent cations are added to the aqueous phase not containing monazomycin, the resulting asymmetry of the surface potentials results in an intramembrane potential difference not recordable by electrodes in the bulk phases. Nevertheless, this intramembrane potential difference is "seen" by the monazomycin, and consequently the g-V characteristic is shifted along the voltage axis. These changes are accounted for by diffuse double layer theory. Thus we find it unnecessary to invoke specific binding of Mg⁺⁺ or Ca⁺⁺ to the negative charges of PG membranes to explain the observation that concentrations of these ions some 100-fold lower than that of the univalent cation present produce large shifts of the g-V characteristic. We suggest that analogous shifts of g-V characteristics in axons produced by changes of divalent cation concentration are also best explained by diffuse double layer theory.     

Conductance Properties of Artificial Lipidic Membranes Containing a Proteolipid from Electrophorus : Response to cholinergic agents

Previous studies have shown that a special proteolipid extract from the electric organ of Electrophorus showed high affinity binding for acetylcholine and other cholinergic agents. This proteolipid has now been incorporated into ultrathin lipidic membranes, and the membrane resistance was studied. The resistance decreased from 7.27 ± 0.82 x 10⁵ ohm cm² in the control membrane to 1.83 x 10⁵ ohm cm² with addition of 72 µg/ml proteolipid. The decrease in resistance followed a potential function of order four with the proteolipid concentration in the membrane-forming solution. The presence of this proteolipid determined some type of cationic selectivity which was not observed in the control. At a critical point of proteolipid concentration the conductance spontaneously fluctuated between two levels. The membrane current jumped from one state to another by way of single discrete steps, reminiscent of those obtained with the excitatory inducing material or the macrocyclic antibiotics. In membranes containing another proteolipid having no cholinergic binding properties, the increase in conductance was smaller, and had a linear function with the concentration. In this case the "flip flop" fluctuation and the cationic selectivity were not observed. The membranes containing the cholinergic proteolipid reacted to the addition of acetylcholine by a rapid and transient increase in conductance that was considerably reduced or abolished by a previous application of d-tubocurarine. These membranes also interacted with other cholinergic agents, such as gallamine triethiodide, hexamethonium, and α-bungarotoxin. These results suggest that this special proteolipid, when added to the artificial membranes, induces a "chemical excitability" toward cholinergic ligands.