Some Peculiarities of Water Transport through Plasticized Nonporous Membranes

“Liquid” and “plasticized” solvent membranes are of interest as possible analogues of biological systems. Semipermeable homogeneous films are prepared by plasticizing polyvinylchloride with organic phosphates. Water permeability of such films is relatively high. For a material containing 70% of 1.4-dihydroxyphenyl-bis(dibutylphosphate), the diffusion coefficient of water at room temperature was estimated to be about 1 × 10^-6 cm²/sec. Conditioning of a plasticized membrane, under the osmotic gradient of solution of sodium nitrate, leads to profound changes in its morphology and to a drastic increase of its water permeability. The induced changes are reversible to a large extent. Their reversibility in various solutions may be correlated with the respective differences in permselectivity. The structure of expanded membranes and the mechanism of changes taking place under the osmotic gradients are discussed.     

The independence principle. A reconsideration

The electrodiffusion model presented in the previous paper, which specifically excludes ion-ion interactions, is analyzed for the ratio of one-way fluxes (flux ratio) as a function of the ionic driving force across the membrane. Significant deviations from the behavior expected on the basis of the Ussing relation are found. These are sufficient to explain the “nonindependent” ion movement noted in some biological flux ratio data. One-way fluxes are dependent on the ionic concentration on both sides of the membrane. The coupling of these fluxes to ionic concentrations comes from the dependence of ionic mobility and the diffusion coefficient on the equilibrium potential. It is concluded that nonindependent behavior in experimental data is not sufficient to implicate ion-ion interaction as the source of the discrepancy.     

High membrane permeability for melatonin

The pineal gland, an endocrine organ in the brain, synthesizes and secretes the circulating night hormone melatonin throughout the night. The literature states that this hormone is secreted by simple diffusion across the pinealocyte plasma membrane, but a direct quantitative measurement of membrane permeability has not been made. Experiments were designed to compare the cell membrane permeability to three indoleamines: melatonin and its precursors N-acetylserotonin (NAS) and serotonin (5-HT). The three experimental approaches were (1) to measure the concentration of effluxing indoleamines amperometrically in the bath while cells were being dialyzed internally by a patch pipette, (2) to measure the rise of intracellular indoleamine fluorescence as the compound was perfused in the bath, and (3) to measure the rate of quenching of intracellular fura-2 dye fluorescence as indoleamines were perfused in the bath. These measures showed that permeabilities of melatonin and NAS are high (both are uncharged molecules), whereas that for 5-HT (mostly charged) is much lower. Comparisons were made with predictions of solubility-diffusion theory and compounds of known permeability, and a diffusion model was made to simulate all of the measurements. In short, extracellular melatonin equilibrates with the cytoplasm in 3.5 s, has a membrane permeability of ∼1.7 µm/s, and could not be retained in secretory vesicles. Thus, it and NAS will be “secreted” from pineal cells by membrane diffusion. Circumstances are suggested when 5-HT and possibly catecholamines may also appear in the extracellular space passively by membrane diffusion.     

Correlation of Electrical and Permeability Properties of Ion-Selective Membranes

The linear phenomenological equations giving particle and practical fluxes of a single electrolyte across an ion-selective membrane are stated and interrelated. It is shown that the experimental measurements commonly made in biological and synthetic membrane studies may be used, with minor modification, to obtain the phenomenological transport coefficients and their concentration dependences. It is demonstrated that the electrical properties of a homogeneous membrane may be obtained as functions of the bathing solution concentration by combining fluxes measured under open and short circuit. Attention is paid to the use of radiotracers when measuring ionic fluxes. To obtain all the phenomenological coefficients at least one measurement must be made under a pressure gradient. The experimental difficulties in such measurements are discussed and the merits and demerits of various experiments considered. The problems of measuring potentials and concentrations at the low pressure face of a supported membrane make several mathematically simple approaches experimentally unattractive. The best methods appear to be either the measurement of a succession of “apparent osmotic pressures” under concentration differences sufficiently small that the membrane does not require support or the study of “reverse osmosis”. Sets of equations are given which enable the phenomenological coefficients to be evaluated from convenient experiments. With a stable homogeneous membrane nine coefficients may be obtained thus enabling either the applicability of the reciprocal relations or the applicability of linear theory under the conditions of the experiments to be tested. For a discontinuous system the six independent coefficients may be obtained from experiments in a single membrane cell.     

The Intracellular Transport and Distribution of Cysteamine Phosphate Derivatives

Radioautography and extractive techniques were used to analyze the transport of cysteamine phosphate and its derivatives in salamander oocytes. The quantitative relations among the processes involved — membrane permeation, enzymatic dephosphorylation, binding through mixed disulfide formation, and cytoplasmic diffusion — were elucidated. Within the detection limits, all of the intracellular material is present as dephosphorylated derivatives. Cytoplasmic diffusion is effectively slowed by binding (the “chromatographic” effect) and makes an appreciable contribution to cellular flux rates. As a consequence, one can observe by radioautography a cortical diffusion ring which spreads inward as a function of influx time, while also increasing in peak density because of the finite membrane permeability. Good agreement was found between the transport parameters determined by radioautography and those from influx data for the whole oocyte. The ratio of nuclear to cytoplasmic concentrations of the cysteamine phosphate derivatives at equilibrium is about 0.4. The nuclear membrane is, however, a negligible barrier to transport, and the asymmetry appears to arise primarily from the quantity and sulfhydryl content of the binding proteins in the two compartments.     

Direct effects on the membrane potential due to "pumps" that transfer no net charge

The effects of active ionic transport are included in the derivation of a general expression for the zero current membrane potential. It is demonstrated that an active transport system that transfers no net charge (nonrheogenic) may, nevertheless, directly alter the membrane potential. This effect depends upon the exchange of matter within the membrane between the active and passive diffusion regimes. Furthermore, in the presence of such exchange, the transmembrane active fluxes measured by the usual techniques and the local pumped fluxes are not identical. Several common uses of the term “electrogenic pump” are thus shown to be inconsistent with each other. These inconsistencies persist when the derivation is extended to produce a Goldman equation modified to account for active transport; however, that equation is shown to be limited by less narrow constraints on membrane heterogeneity and internal electric field than those previously required. In particular, it is applicable to idealized mosaic membranes limited by these requirements.     

Studies on the Movement of Water through the Isolated Toad Bladder and Its Modification by Vasopressin

Measurements of diffusion permeability and of net transfer of water have been made across the isolated urinary bladder of the toad, Bufo marinus, and the effects thereon of mammalian neurohypophyseal hormone have been examined. In the absence of a transmembrane osmotic gradient, vasopressin increases the unidirectional flux of water from a mean of 340 to a mean of 570 µl per cm² per hour but the net water movement remains essentially zero. In the presence of an osmotic gradient but without hormone net transfer of water remains very small. On addition of hormone large net fluxes of water occur; the magnitude of which is linearly proportional to the osmotic gradient. The action of the hormone on movement of water is not dependent on the presence of sodium or on active transport of sodium. Comparison of the net transport of water and of unidirectional diffusion permeability of the membrane to water indicates that non-diffusional transport must predominate as the means by which net movement occurs in the presence of an osmotic gradient. An action of the hormone on the mucosal surface of the bladder wall is demonstrated. The effects of the hormone on water movement are most simply explained as an action to increase the permeability and porosity of the mucosal surface of the membrane.     

The State of Water in Human and Dog Red Cell Membranes

The apparent activation energy for the water diffusion permeability coefficient, P_d, across the red cell membrane has been found to be 4.9 ± 0.3 kcal/mole in the dog and 6.0 ± 0.2 kcal/mole in the human being over the temperature range, 7° to 37°C. The apparent activation energy for the hydraulic conductivity, L_p, in dog red cells has been found to be 3.7 ± 0.4 kcal/mole and in human red cells, 3.3 ± 0.4 kcal/mole over the same temperature range. The product of L_p and the bulk viscosity of water, η, was independent of temperature for both dog and man which indicates that the geometry of the red cell membrane is not temperature-sensitive over our experimental temperature range in either species. In the case of the dog, the apparent activation energy for diffusion is the same as that for self-diffusion of water, 4.6–4.8 kcal/mole, which indicates that the process of water diffusion across the dog red cell membrane is the same as that in free solution. The slightly, but significantly, higher activation energy for water diffusion in human red cells is consonant with water-membrane interaction in the narrower equivalent pores characteristic of these cells. The observation that the apparent activation energy for hydraulic conductivity is less than that for water diffusion across the red cell membrane is characteristic of viscous flow and suggests that the flow of water across the membranes of these red cells under an osmotic pressure gradient is a viscous process.     

The Validity of the Ussing Flux Ratio Equation in a Three-Dimensionally Inhomogeneous Membrane

Derivations of the Ussing flux ratio equation have, until now, required the membrane to be both bounded by parallel planes and homogeneous, except in the transmembrane direction. These constraints have been necessary for the theoretical demonstration that the equation is independent of membrane parameters in the absence of carriers, coupling, solvent drag, or “single-file” diffusion. In a new derivation, the flux ratio equation is shown to be valid in this kind of diffusion regime without regard to the three-dimensional structure of the membrane. Thus the constraints on both membrane homogeneity and membrane geometry are shown to be unnecessary. The general use of this equation to differentiate between simple, uncoupled diffusion and other membrane transport phenomena is thus placed on a firmer base. However, as in earlier derivations, it is necessary that isopotential, isobaric, constant concentration surfaces exist sufficiently close to the membrane on both of its sides.     

On the large error introduced in the estimate of the density of membrane pores from permeability measurements when diffusion in "unstirred layer" within the cells is disregarded

After the development of the "black lipid membrane" techniques, studies of the permeability of labeled water and nonelectrolytes across these artificial membranes have yielded permeability constants comparable in magnitude to those obtained from tracer studies of living cell membranes. This general agreement has affirmed the belief that the living cell membranes are indeed closely similar to these bilayer phospholipid membranes. In this report, we draw attention to a hidden assumption behind such comparisons made: the assumption that labeled material passing through the cell membrane barriers instantly reaches diffusion equilibrium inside the cell. The permeability constants to labeled water (and nonelectrolytes) across lipid layers were obtained using setups in which the lipid membrane was sandwiched between aqueous compartments both of which were vigorously stirred. In studies of permeability of living cell membranes only the outside solution was stirred, the intracellular water remained stationary. Yet the calculations of permeability constants of the cell membrane were made with the tacit assumption, that once the labeled materials pass through the cell membrane, they were instantly mixed with the entire cell contents as if a stirrer operating at infinite speed had been present inside the cells. Ignoring this unstirred condition of the intracellular water, in fact, lumped all the real-life delay due to diffusion in the cytoplasm and added it to the resistance to diffusion of the membrane barrier. The result is an estimated membrane permeability to labeled water (and nonelectrolytes) many times slower than it actually is. The present report begins with a detailed analysis of a specific case: tritiated water diffusion from giant barnacle muscle fibers and two non-living models, one real, one imagined.(ABSTRACT TRUNCATED AT 250 WORDS)     

Equivalent Circuits as Related to Ionic Systems

The purpose of this paper is to clarify the relationship between certain “equivalent circuits” and the fundamental flux equations of Nernst and Planck. It is shown that as a direct algebraic consequence of these equations one may construct two types of equivalent circuits for a homogeneous (charged or uncharged) membrane. The one, which we term the “pure electrical equivalent circuit,” correctly predicts all of the electrical properties of the membrane for both steady and transient states. The other, which we call the “mixed equivalent circuit,” predicts the steady state I, Ψ characteristics of the membrane and the steady state ionic fluxes; it is not applicable to non-steady state properties or measurements. We emphasize that with regard to the portrayal of the physical basis of the properties of a homogeneous membrane, the mixed equivalent circuit can be misleading. This is particularly significant because this same circuit can also be used to depict a mosaic membrane, in which case the circuit gives a realistic pictorialization of the physical origin of the membrane properties. It is hoped that our analysis will be of aid to workers in electrophysiology who make use of equivalent circuit terminology in discussing the behavior of the plasma membrane.     

The volume dependence of the erythrocyte water diffusion permeability

The product of the water diffusion permeability and the membrane area of a human erythrocyte has been found to be nearly independent of the cell volume. The product was measured by an NMR technique. This result conflicts with previous flow tube determinations but is in accord with recent measurements of the hydraulic permeability and various solute permeabilities. The results are consistent with the major part of the water fllux traversing the membrane through a fixed number of pores. There may also be a minor non-pore flux. It appears to be practicable to follow volume changes in the red blood cell by an NMR technique.     

Effect of villosity and distension on the absorptive and secretory flux in the small intestine

The effects of villosity and distension on the absorptive and secretory flux in the small intestine were investigated theoretically in a simplified model. In the case of low epithelial permeability, villosity increases both fluxes by surface enlargement, but in the case of high epithelial permeability, this occurred only if the intervillous spaces are very narrow. Otherwise, the flux is reduced due to the intervillous diffusion resistance, which is more effective than the enlargement of the surface area in that case. Distension increases the fluxes due to the additional surface exposed, by opening the intervillous spaces. In the case of low epithelial permeability this increase exceeds that expected from the enlargement of the smooth inner cylindrical surface area. In the case of high epithelial permeability, however, the increase of the fluxes exceeds surface enlargement only in the first phase, just after opening the intervillous spaces. Otherwise, the increase of the flux is less, since the hindrance by the intervillous diffusion resistance is more effective than the increase of the smooth inner cylindrical surface area. In the intervillous spaces the concentration gradient is non-linear with the steepest slope at the entrance due to the permeation through the lateral surfaces of the villi. The gradient approaches linearity in the center of broad intervillous spaces and becomes steeper when the width decreases and the epithelial permeability increases. In rat small intestine broad intervillous spaces are formed at the front sides of the trapezoidal villi by the predominant circular distension. The diffusion resistance in these spaces and the increase of the supravillous diffusion resistance weaken the increase of the absorptive and secretory flux by distension, especially in the case of high epithelial permeability.     

Rb fluxes in Chinese hamster ovary cells as a function of membrane cholesterol content

Steady-state fluxes of ⁸⁶Rb⁺ (as a tracer for K⁺) were measured in Chinese hamster ovary cells (CHO-K1) and a mutant (CR1) defective in the regulation of cholesterol biosynthesis; the membrane cholesterol content of this mutant was varied by growing it on a range of cholesterol supplements to lipid-free medium (Sinensky, M. (1978) Proc. Natl. Acad. Sci. U.S. 75, 1247–1249).Analogous to previous findings in ascites tumor cells, ⁸⁶Rb⁺ influx in the parent strain was differentiated into a ouabain-inhibitable ‘pump’ flux, furosemide-sensitive, chloride-dependent exchange diffusion, and a residual ‘leak’ flux.On the basis of this flux characterization, ⁸⁶Rb⁺ pump and leak fluxes were measured in the mutant as a function of membrane cholesterol content. Pump and leak fluxes, when expressed per ml cell water, were independent of the cholesterol content of the mutant. Moreover, ⁸⁶Rb⁺ fluxes in the mutant were equal to those in the parent strain. Our data imply that the flux behavior of K⁺ in the steady state is independent of the ordering of membrane lipid acyl chains.     

A theory of membrane permeability: II. Diffusion in the presence of water-flow

The author's earlier treatment of diffusion through a membrane is extended to include the case in which there is a mass motion of water through the membrane. Water flows through the membrane in the direction from lower to higher concentrations of the solute. This water carries a part of the solute by convection. Thus in this general case there is a transport of solute through the membrane both in the direction from higher to lower concentration, and in the opposite direction. If the latter effect prevails, the net result is a flow of solute from lower to higher concentrations. Mathematically this corresponds to negative values of the permeability. The effect of hydrostatic pressure is considered also.     

A Physical Interpretation of the Phenomenological Coefficients of Membrane Permeability

A "translation" of the phenomenological permeability coefficients into friction and distribution coefficients amenable to physical interpretation is presented. Expressions are obtained for the solute permeability coefficient ω and the reflection coefficient σ for both non-electrolytic and electrolytic permeants. An analysis of the coefficients is given for loose membranes as well as for dense natural membranes where transport may go through capillaries or by solution in the lipoid parts of the membrane. Water diffusion and filtration and the relation between these and capillary pore radius of the membrane are discussed. For the permeation of ions through the charged membranes equations are developed for the case of zero electrical current in the membrane. The correlation of σ with ω and L_p for electrolytes resembles that for non-electrolytes. In this case ω and σ depend markedly on ion concentration and on the charge density of the membrane. The reflection coefficient may assume negative values indicating anomalous osmosis. An analysis of the phenomena of anomalous osmosis was carried out for the model of Teorell and Meyer and Sievers and the results agree with the experimental data of Loeb and of Grim and Sollner. A set of equations and reference curves are presented for the evaluation of ω and σ in the transport of polyvalent ions through charged membranes.     

Pathway for the movement of water and cryoprotectants in bovine oocytes and embryos

The permeability of cells is important for cryopreservation. Previously, we showed in mice that the permeability to water and cryoprotectants of oocytes and embryos at early cleavage stages (early embryos) is low because these molecules move across the plasma membrane predominantly by simple diffusion through the lipid bilayer, whereas permeability of morulae and blastocysts is high because of a water channel, aquaporin 3 (AQP3). In this study, we examined the pathways for the movement of water and cryoprotectants in bovine oocytes/embryos and the role of AQP3 in the movement by determining permeability, first in intact bovine oocytes/embryos, then in bovine morulae with suppressed AQP3 expression, and finally in mouse oocytes expressing bovine AQP3. Results suggest that water moves through bovine oocytes and early embryos slowly by simple diffusion, as is the case in mice, although channel processes are also involved in the movement. On the other hand, water appears to move through morulae and blastocysts predominantly by facilitated diffusion via channels, as in mice. Like water, cryoprotectants appear to move through bovine oocytes/early embryos mostly by simple diffusion, but channel processes could also be involved in the movement of glycerol and ethylene glycol, unlike that in mice. In bovine morulae, although glycerol and ethylene glycol would move predominantly by facilitated diffusion, mostly through AQP3, as in mice, dimethylsulfoxide appears to move predominantly by simple diffusion, unlike in mice. These results indicate that permeability-related properties of bovine oocytes/embryos are similar to those of mouse oocytes/embryos, but species-specific differences do exist.     

The Role of Paracellular Pathways in Isotonic Fluid Transport

Paracellular pathways across “leaky” epithelia are the major route for transepithelial ionic diffusion. The permselective properties of these pathways suggest that they offer a watery environment through which ions diffuse in their hydrated forms. There is also suggestive evidence that, at least in some tissues, paracellular pathways provide a significant route for transepithelial water flow in response to an osmotic pressure difference; however, this has not as yet been definitively established. The effect of junctional complexes that are permeable to ions and water on the predictions of the standing-osmotic gradient model for isotonic water absorption is considered.     

Water permeability of chlorella cell membranes by nuclear magnetic resonance: measured diffusion coefficients and relaxation times

Measurement by two nuclear magnetic resonance (NMR) techniques of the mean residence time τ_a of water molecules inside Chlorella vulgaris (Beijerinck) var. “viridis” (Chodot) is reported. The first is the Conlon and Outhred (1972 Biochim Biophys Acta 288: 354-361) technique in which extracellular water is doped with paramagnetic Mn²⁺ ions. Some complications in application of this technique are identified as being caused by the affinity of Chlorella cell walls for Mn²⁺ ions which shortens the NMR relaxation times of intra- and extracellular water. The second is based upon observations of effects of diffusion on the spin echo of intra- and extracellular water. Echo attenuation of intracellular water is distinguished from that of extracellular water by the extent to which diffusive motion is restricted. Intracellular water, being restricted to the cell volume, suffers less echo attenuation. From the dependence of echo amplitude upon gradient strength at several values of echo time, the mean residence time of intracellular water can be determined. From the mean residence time of intracellular water, the diffusional water permeability coefficient of the Chlorella membrane is calculated to be 2.1 ± 0.4 × 10⁻³ cm sec⁻¹.