Permeability of lipid bilayers to water and ionic solutes

The lipid bilayer moiety of biological membranes is considered to be the primary barrier to free diffusion of water and solutes. This conclusion arises from observations of lipid bilayer model membrane systems, which are generally less permeable than biological membranes. However, the nature of the permeability barrier remains unclear, particularly with respect to ionic solutes. For instance, anion permeability is significantly greater than cation permeability, and permeability to proton-hydroxide is orders of magnitude greater than other monovalent inorganic ions. In this review, we first consider bilayer permeability to water and discuss proposed permeation mechanisms which involve transient defects arising from thermal fluctuations. We next consider whether such defects can account for ion permeation, including proton-hydroxide flux. We conclude that at least two varieties of transient defects are required to explain permeation of water and ionic solutes.     

Energy of an ion crossing a low dielectric membrane: the role of dispersion self-free energy

The Born charging equation predicts that the permeability of a cell membrane to ions by the solubility-diffusion mechanism depends on the ionic radius and on the dielectric constant of the membrane. However, experiments, for example, on red blood cells and on lysosome membranes, show that the permeability depends strongly on the choice of salt anion in a way that cannot be accommodated by differences in ionic size. We demonstrate that one step towards understanding this ion specificity is to take account of the previously ignored dispersion self-free energy of the ion. This is the quantum electrodynamic analogue of the (electrostatic) Born self-energy of an ion. We show that the dispersion self-free energy contribution can be and often is of the same order of magnitude as the Born contribution. To understand the observed specificity, it is essential to take into account of both ionic size and ionic polarizability. In parallel and to reinforce these observations, we also give simple estimates for how self-free energy changes that occur when an ion moves into the air-water interface region (which has a density profile for water molecules) can influence the surface tension of salt solutions. Consistency can be found between the Hofmeister sequences observed in ion permeation and in surface tension of electrolytes when these previously ignored self-free energies are included properly.     

Energetics of permeation of thin lipid membranes by ions

The energy of an ion in a thin hydrocarbon membrane relative to its energy in a bulk aqueous phase is considered in terms of the electrostatic and surface components that may be expected to be involved. Except when diffusion activation energies are large compared to partition free energies, the latter will control permeation rate and the state of an ion having the lowest partition energy will be critical for its permeability. This minimum is found when an ion is surrounded with a thin layer of water. All ions of the same charge will tend to be at their lowest state in a sphere of water of the same size. It is concluded, therefore, that all ions of a given charge will have about the same permeability in lipid membranes.     

Amphotericin B-induced changes in renal membrane permeation: a model of nephrotoxicity

As part of an investigation into the nephrotoxic effects of the polyene antibiotic Amphotericin B we have studied its effects on the ion permeability of purified renal brush border membrane vesicles. Membrane potentials were measured using a potential sensitive carbocyanine dye, and ion permeabilities were calculated from the constant field equation. Amphotericin B significantly altered the ionic permeability sequence of isolated membranes and caused a selectivity for increasing the permeation of anions. Permeability changes induced by 2.0 micrograms/ml Amphotericin B resulted in an estimated hyperpolarization of the membrane from -50 mV to -72 mV. In addition, the kinetic parameters of Na+ dependent transport of organic metabolites were examined. The maximum change in fluorescence was decreased significantly in the presence of Amphotericin B. These results suggest that the ionic state of the renal cell membrane is significantly altered by the presence of Amphotericin B.     

Influence of dolichyl phosphate on permeability and stability of bilayer lipid membranes

The ionic permeability coefficients, ionic transference numbers, activation energy of ion transport and breakdown voltage of bilayer lipid membranes made from dioleoylphosphatidylcholine or its mixtures with dolichyl 12-phosphate have been studied. The electrical measurements showed that dolichyl phosphate in phospholipid bilayers decreases membrane permeability, changes membrane ionic selectivity and increases membrane stability. These results are discussed in light of the aggregation behavior and the intramolecular clustering of a dolichyl phosphate molecule in phospholipid membranes. From our data we suggest that the hydrophilic part of dolichyl phosphate molecules regulates their behavior in membranes.     

Measurement of the glucose permeation rate across phospholipid bilayers using small unilamellar vesicles. Effect of membrane composition and temperature

Small unilamellar vesicles were used to measure the permeability of saturated phosphatidylcholine bilayers to glucose. The presented method circumvents most of the common restriction of classical permeability experiments. Increasing the fatty acid chain length of the lipids reduced the permeation rate significantly. Raising the temperature above that of the lipid phase transition drastically increased membrane permeability. Arrhenius plots demonstrated the activation energy to be independent of membrane composition and the phase-state of the lipids. The permeation process is discussed in terms of a constant energy to disrupt all hydrogen bonds between permeant and aqueous solvent prior to penetrating the membrane. The magnitude of the permeability coefficient is partly determined by a unfavourable change in entropy of activation on crossing the water/lipid interface. All results indicate that the penetration of the dehydrated permeant into the hydrophobic barrier is the rate-limiting step in the permeation of glucose.     

Measurement of the glucose permeation rate across phospholipid bilayers using small unilamellar vesicles Effect of membrane composition and temperature

Small unilamellar vesicles were used to measure the permeability of saturated phosphatidylcholine bilayers to glucose. The presented method circumvents most of the common restrictions of classical permeability experiments. Increasing the fatty acid chain length of the lipids reduced the permeation rate significantly. Raising the temperature above that of the lipid phase transition drastically increased membrane permeability. Arrhenius plots demonstrated the activation energy to be independent of membrane composition and the phase-state of the lipids. The permeation process is discussed in terms of a constant energy to disrupt all hydrogen bonds between permeant and aqueous solvent prior to penetrating the membrane. The magnitude of the permeability coefficient is partly determined by a unfavourable change in entropy of activation on crossing the water/lipid interface. All results indicate that the penetration of the dehydrated permeant into the hydrophobic barrier is the rate-limiting step in the permeation of glucose.     

The Temperature Dependence of Lipid Membrane Permeability, its Quantized Nature, and the Influence of Anesthetics

We investigate the permeability of lipid membranes for fluorescence dyes and ions. We find that permeability reaches a maximum close to the chain melting transition of the membranes. Close to transitions, fluctuations in area and compressibility are high, leading to an increased likelihood of spontaneous lipid pore formation. Fluorescence correlation spectroscopy reveals the permeability for rhodamine dyes across 100-nm vesicles. Using fluorescence correlation spectroscopy, we find that the permeability of vesicle membranes for fluorescence dyes is within error proportional to the excess heat capacity. To estimate defect size we measure the conductance of solvent-free planar lipid bilayer. Microscopically, we show that permeation events appear as quantized current events very similar to those reported for channel proteins. Further, we demonstrate that anesthetics lead to a change in membrane permeability that can be predicted from their effect on heat capacity profiles. Depending on temperature, the permeability can be enhanced or reduced. We demonstrate that anesthetics decrease channel conductance and ultimately lead to blocking of the lipid pores in experiments performed at or above the chain melting transition. Our data suggest that the macroscopic increase in permeability close to transitions and microscopic lipid ion channel formation are the same physical process.     

Monolayer and interfacial permeation

Transport across physical-chemical interfaces is considered in connection with three particular problems of biological interfaces: the structure and properties of cell membranes, the properties of the lung surfactant, and the effects of ionic currents across excitable membranes. With regard to cell membranes, studies of monolayer permeation suggest that permselectivity on the basis of size is a property of bilayer structure and probably gives rise to the observed dependence of the permeability on partition coefficients. The permeabilities of lipid and protein monolayers are consistent with the bimolecular leaflet (BML) model of the membrane and not with mosaic models. Experiments with the lung surfactant indicate that, in addition to its surface tension-lowering properties, it is unusual in its ability to form a strong two-dimensional network, which probably contributes to alveolar stability. Finally, the results of studies of interfacial ionic transference suggest a new way of accounting for the ionic fluxes in excitable membranes during an action potential without assuming ion-selective pores or carriers. In the suggested mechanism, it is possible to account for the change in ionic selectivity and the proper phasing of the fluxes, as well as other aspects of excitation in natural membranes.     

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.     

The permeability of liposomes to nonelectrolytes. I. Activation energies for permeation.

The effect of temperature on the permeability of nonelectrolytes across liposomal membranes above and below their transition temperature has been studied by using an osmotic method. Below their transition temperature, liposomes are osmotically insensitive structures but, on addition of gramicidin A, the water permeability so increased that the permeability of solutes could be studied. The measured activation energies for permeation of a variety of nonelectrolytes has been found to increase when a) there is an increase in the capability of the solutes to form hydrogen bonds in water, b) the cholesterol concentration in the membranes increases and c) the membranes pass from a liquid-crystalline to a solid-crystalline state. The change in the activation energy for permeation per hydrogen bond is about 1.8 kcal/mole for all the different liposome systems investigated; the only solute tested that deviated from this correlation was urea, whose activation energy for permeation across a gramicidin-containing system was much lower than expected from its hydrogen-bonding capacity. This finding suggests that urea is permeating across the gramicidin pore. Although the literature contains only incomplete data relating the activation energies for permeation of nonelectrolytes across biological membranes to their hydrogen-bonding capacity, the available evidence suggests that there is a similar correlation to that found in liposomes. Thus, the average increase in the activation energy per hydrogen bond for permeation across ox red cell membranes (Jacobs, Glassman & Parpart, J. Cell. Comp. Physiol. 7:197, 1935) is 2.2 plus or minus 0.4 kcal/mole, a value that is similar to that obtained in liposomes. However, the activation energies for water and urea are - in such a system - very much lower than expected, suggesting that they, too, are permeating by some parallel route such as an aqueous pore.     

Chloride channels in toad skin

A study of the voltage and time dependence of a transepithelial Cl- current in toad skin (Bufo bufo) by the voltage-clamp method leads to the conclusion that potential has a dual role for Cl- transport. One is to control the permeability of an apical membrane Cl-pathway, the other is to drive Cl- ions through this pathway. Experimental analysis of the gating kinetics is rendered difficult owing to a contamination of the gated currents by cellular ion redistribution currents. To obtain insight into the effects of accumulation-depletion currents on voltage clamp currents of epithelial membranes, a mathematical model of the epithelium has been developed for computer analysis. By assuming that the apical membrane Cl- permeability is governed by a single gating variable (Hodgkin-Huxley kinetics), the model predicts fairly well steady-state current-voltage curves, the time course of current activations from a closed state, and the dependence of unidirectional fluxes on potential. Other predictions of the model do not agree with experimental findings, and it is suggested that the gating kinetics are governed by rate coefficients that also depend on the holding potential. Evidence is presented that Cl- transport through open channels does not obey the constant-field equation.     

On the nature of ion leaks in energy-transducing membranes

Diffusion is the implicit null hypothesis for ion transport across biological membranes. A proper model of ionic diffusion across the permeability barrier is needed to distinguish among leaks, channels and carriers and to determine whether changes in flux reflect changes in permeability (regulation) or merely changes in the driving force. These issues arise in all biomembranes, but they are particularly confounding in energy-transducing membranes on account of their characteristically high electrical gradients. This paper examines the nature of the barrier to ion leaks, using the classical Eyring rate theory. We introduce new practical procedures for estimating permeability coefficients from ion flux data. We also reach some general conclusions regarding ion leaks across energy-transducing membranes. (1) The dependence of ion flux on the electrical membrane potential is invariably non-linear (non-ohmic). (2) Non-ohmic behavior does not imply variable permeability. (3) Ohmic behavior is exceptional and its occurrence should alert us to the possibility of an underlying carrier or channel. (4) Leak pathways are very likely localized to protein-lipid interfaces and will exhibit quasi-specific properties such as saturation and competition. (5) The inherent non-ohmicity of leaks and the requirement for efficient energy transduction impose constraints upon the magnitude of allowable Gibbs free-energy changes in biological systems. (6) Nature adapts to these constraints by devising mechanisms for step-wise splitting of the partial reactions of energy transduction.     

The localization of transport properties in the frog lens.

The selectivity of fiber-cell membranes and surface-cell membranes in the frog lens is examined using a combination of ion substitutions and impedance studies. We replace bath sodium and chloride, one at a time, with less permeant substitute ions and we increase bath potassium at the expense of sodium. We then record the time course and steady-state value of the intracellular potential. Once a new steady state has been reached, we perform a small signal-frequency-domain impedance study. The impedance study allows us to separately determine the values of inner fiber-cell membrane conductance and surface-cell membrane conductance. If a membrane is permeable to a particular ion, we presume that the conductance of that membrane will change with the concentration of the permeant ion. Thus, the impedance studies allow us to localize the site of permeability to inner or surface membranes. Similarly, the time course of the change in intracellular potential will be rapid if surface membranes are the site of permeation whereas it will be slow if the new solution has to diffuse into the intercellular space to cause voltage changes. Lastly, the value of steady-state voltage change provides an estimate of the lens' permeability, at least for chloride and potassium. The results for sodium are complex and not well understood. From the above studies we conclude: (a) surface membranes are dominated by potassium permeability; (b) inner fiber-cell membranes are permeable to sodium and chloride, in approximately equal amounts; and (c) inner fiber-cell membranes have a rather small permeability to potassium.     

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.     

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.     

Molecular origin of biphasic response of main phase-transition temperature of phospholipid membranes to long-chain alcohols

A statistical mechanical theory is proposed which explains the molecular mechanism of the nonlinear response of the phase-transition temperature of phospholipid vesicle membranes to added 1-alkanols. By assuming that the free energy of transfer of 1-alkanols from the aqueous phase to the membrane and the interaction energy between 1-alkanol molecules are linear functions of alkanol alkyl chain-length, the nonlinear behavior is explained in the Bragg-Williams approximation. For dipalmitoylphosphatidylcholine vesicle membranes, the theory reveals a larger free energy of transfer of 1-alkanols from the aqueous phase to the solid-gel membrane than to the liquid-crystalline membrane when the number of carbon atoms of 1-alkanol exceeds 12. When the intermolecular interaction force between 1-alkanol molecules residing in the gel phase is stronger than the interaction force between those residing in the liquid-crystalline phase, the ligand effect is to tighten the lipid matrix structure, causing the transition temperature to rise. The interaction force is a quadratic function of 1-alkanol concentration; hence, the response of the transition temperature to the 1-alkanol concentration is nonlinear. At low concentrations of the long-chain 1-alkanols that predominantly elevate the transition temperature, this intermolecular interaction force is negligible. In this case, the entropic effect of the incorporated ligand molecules, which loosens the lipid matrix, predominates, and the transition temperature decreases. The biphasic action of long-chain 1-alkanols originates from the balance of these two opposing effects: entropy and intermolecular interaction.     

Dynamic property of membrane formation in a protoplasmic droplet of Nitella

A theory is presented to explain the dynamic characteristics of an electric potential and the resistance of a surface membrane during the formation of a protoplasmic droplet isolated from Nitella. Basic equations are coupled ones for describing ion concentrations near the surface of the droplet, active and passive ion fluxes on the surface, and kinetics of membrane-constituting molecules diffusing from the inside of the protoplasm. The present results give a good explanation of the observed kinetics of electric properties throughout the formative process of surface membranes after the ion concentrations are replaced by lower ones. The results can also explain well the observed data on the steady state. Oscillatory changes in the membrane potential induced by ions strongly adsorbed on the surface membrane are discussed in relation to growth and regeneration phenomena in biological systems such as bean roots and Acetabularia.