Coupling of Solute and Solvent Flows in Porous Lipid Bilayer Membranes

The present experiments were designed to evaluate coupling of water and nonelectrolyte flows in porous lipid bilayer membranes (i.e., in the presence of amphotericin B) in series with unstirred layers. Alterations in solute flux during osmosis, with respect to the flux in the absence of net water flow, could be related to two factors: first, changes in the diffusional component of solute flux referable to variations in solute concentrations at the membrane interfaces produced by osmotic flow through the unstirred layers; and second, coupling of solute and solvent flows within the membrane phase. Osmotic water flow in the same direction as solute flow increased substantially the net fluxes of glycerol and erythritol through the membranes, while osmotic flow in the opposite direction to glycerol flow reduced the net flux of that solute. The observed effects of osmotic water flow on the fluxes of these solutes were in reasonable agreement with predictions based on a model for coupling of solute and solvent flows within the membrane phase, and considerably in excess of the prediction for a diffusion process alone.     

Theoretical Analysis of Net Tracer Flux Due to Volume Circulation in a Membrane with Pores of Different Sizes : Relation to solute drag model

When osmotic pressure across an artificial membrane, produced by a permeable electrically neutral solute on one side of it, is balanced by an external pressure difference so that there is no net volume flow across the membrane, it has been found that there will be a net flux of a second electrically neutral tracer solute, present at equal concentrations on either side of the membrane, in the direction that the "osmotic" solute diffuses. This has been ascribed to solute-solute interaction or drag between the tracer and the osmotic solutes. An alternative model, presented here, considers the membrane to have pores of different sizes. Under general assumptions, this "heteroporous" model will account for both the direction of net tracer flux and the observed linear dependence of unidirectional tracer fluxes on the concentration of the osmotic solute. The expressions for the fluxes of solutes and solvent are mathematically identical under the two models. An inequality is derived which must be valid if the solute interaction model and/or the heteroporous model can account for the data. If the inequality does not hold, then the heteroporous model alone cannot explain the data. It was found that the inequality holds for most published observations except when dextran is the osmotic solute.     

Epithelial water transport in a balanced gradient system.

The relationship between epithelial fluid transport, standing osmotic gradients, and standing hydrostatic pressure gradients has been investigated using a perturbation expansion of the governing equations. The assumptions used in the expansion are: (a) the volume of lateral intercellular space per unit volume of epithelium is small; (b) the membrane osmotic permeability is much larger than the solute permeability. We find that the rate of fluid reabsorption is set by the rate of active solute transport across lateral membranes. The fluid that crosses the lateral membranes and enters the intercellular cleft is driven longitudinally by small gradients in hydrostatic pressure. The small hydrostatic pressure in the intercellular space is capable of causing significant transmembrane fluid movement, however, the transmembrane effect is countered by the presence of a small standing osmotic gradient. Longitudinal hydrostatic and osmotic gradients balance such that their combined effect on transmembrane fluid flow is zero, whereas longitudinal flow is driven by the hydrostatic gradient. Because of this balance, standing gradients within intercellular clefts are effectively uncoupled from the rate of fluid reabsorption, which is driven by small, localized osmotic gradients within the cells. Water enters the cells across apical membranes and leaves across the lateral intercellular membranes. Fluid that enters the intercellular clefts can, in principle, exit either the basal end or be secreted from the apical end through tight junctions. Fluid flow through tight junctions is shown to depend on a dimensionless parameter, which scales the resistance to solute flow of the entire cleft relative to that of the junction. Estimates of the value of this parameter suggest that an electrically leaky epithelium may be effectively a tight epithelium in regard to fluid flow.     

Experimental study of osmosis through a collodion membrane

Experiments were carried out on a collodion membrane in order to study the factors that determine direction and magnitude of net flow of water across a membrane permeable to the solvent and to some of the solutes present. The solutes used were all non-ionic. When only one solute was present and there was no difference of hydrostatic pressure across the membrane, water flowed toward the side where its vapor pressure was lower, but the rate of transfer depended upon the nature of the solute: for a given difference in osmolality across the membrane, the rate increased with the molecular volume of the solute and reached its maximum with the solute to which the membrane was impermeable. These results led to the experimental demonstration that in the presence of two or more solutes of different molecular volumes, of which one at least can diffuse through the barrier, the net transfer of water can take place against its vapor pressure gradient. Some of the physicochemical and physiological implications of the data are discussed.     

The osmotic flow of an electrolyte through a charged porous membrane

A pore model in which the pore wall has a continuous distribution of electrical charge is used to investigate the osmotic flow through a charged permeable membrane separating electrolyte solutions of unequal concentrations. The pore is treated as a long, circular, cylindrical duct. The analysis is based on a continuum formulation in which a dilute electrolyte solution is described by the coupled Nernst-Planck/Poisson creeping flow equations. Account is taken of the significant size of the electrolyte ions (assumed to be rigid spheres) when compared with the diameter of the membrane pores. Analytical solutions for the ion concentrations, hydrostatic pressure and electrostatic potential in the electrolyte solutions are given and an intra-pore flow solution is derived. A mathematical expression for the osmotic reflection coefficient as a function of the solute ion: pore diameter ratio λ and the solute fluxes is obtained. Approximate solutions are quoted which relate the solute fluxes and the solution electrostatic potentials at the membrane surfaces to the bulk solution concentrations, the membrane pore charge and pore geometry. The osmotic reflection coefficient is thus determined as a function of these parameters.     

Influence of membrane heterogeneity on kinetics of nonelectrolyte tracer flows

Summary In a composite membrane with heterogeneous channels, prevention of net volume flow with hydrostatic pressure differences and/or impermeant osmotic solutes may induce positive isotope interaction (coupling of isotope flows) consequent to circulation of volume flow. The permeability coefficient for net flow will then exceed the tracer permeability coefficient. A permeant osmotic solute will induce either positive or negative isotope interaction, according to whether membrane heterogeneity is more marked for the test solute or the osmotic solute, respectively. Thus membrane heterogeneity may account for phenomena commonly attributed to single file diffusion or exchange diffusion. For sufficiently small flows the general flux ratio relationship for homogeneous membranes will continue to apply.     

Fluid mechanical and electrostatic study on the osmotic flow through cylindrical pores

When two solutions differing in solute concentration are separated by a porous membrane, the osmotic pressure will generate a net volume flux of the suspending fluid across the membrane; this is termed osmotic flow. We consider the osmotic flow across a membrane with circular cylindrical pores when the solute and the pore walls are electrically charged, and the suspending fluid is an electrolytic solution containing small cations and anions. Under the condition in which the radius of the pores and that of the solute molecules greatly exceed those of the solvent as well as the ions, a fluid mechanical and electrostatic theory is introduced to describe the osmotic flow in the presence of electric charge. The interaction energy, including the electrostatic interaction between the solute and the pore wall, plays a key role in determining the osmotic flow. We examine the electrostatic effect on the osmotic flow and discuss the difference in the interaction energy determined from the nonlinear Poisson-Boltzmann equation and from its linearized equation (the Debye-Hückel equation).     

The physico-chemical mechanism of mediated transport. II. Osmotic and isosmotic volume flow

The process of volume change of cells subject to osmotic shocks or isosmotic entrance of permeant solute is formulated on the basis of the accepted structure for the plasma membrane and a physico-chemical approach similar to that recently developed. The effect of relevant parameters is discussed and theoretical equilibrium values for the variables are calculated in connection with water and permeant solute permeability determinations. Although a sorption-diffusional mechanism for solute and/or water volume flow within the membrane is assumed in both cases, the kinetics of volume change is shown to be totally different between them. In the isosmotic process a fixed relationship, given by the total solute concentration, is shown to exist between the permeant solute and volume fluxes to the cell, thereby implying a definite value for the volume fraction of water in the migration pathway, higher than 90%. The bi-phase osmotic regulatory response caused by permeant solute is simulated on the basis of an osmotic and isosmotic processes in series, showing good agreement with general behavior. Finally, an explanation to the problem of volume flow and forces in connection with a diffusional mechanism in biological and artificial membranes, is presented.     

Membrane stress causes inhibition of water channels in brush border membrane vesicles from kidney proximal tubule

Brush border membrane vesicles (BBMV) from rabbit kidney proximal tubule cells, prepared with different internal solute concentrations (cellobiose buffer 13, 18 or 85 mosM) developed an hydrostatic pressure difference across the membrane of 18.7 mosM, that causes a membrane tension close to 5 × 10⁻⁵ N cm⁻¹. When subjected to several hypertonic osmotic shocks an initial delay of osmotic shrinkage (a lag time), corresponding to a very small change in initial volume was apparent. This initial osmotic response, which is significantly retarded, was correlated with the initial period of elevated membrane tension, suggesting that the water permeability coefficient is inhibited by membrane stress. We speculate that this inhibition may serve to regulate cell volume in the proximal tubule.     

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.     

Pressure-induced water transport in membrane channels studied by molecular dynamics

A method is proposed to measure the water permeability of membrane channels by means of molecular dynamics simulations. By applying a constant force to the bulk water molecules and a counter force on the complementary system, a hydrostatic pressure difference across the membrane can be established, producing a net directional water flow. The hydraulic or osmotic permeability can then be determined by the ratio of the water flux and the pressure difference. The method is applied and tested on an aquaglyceroporin channel through a series of simulations totaling 5 ns in duration.     

Reflection coefficients of homopore membranes: effect of molecular size and configuration

Osmotic water flow through membranes with uniform defined pores was measured for a variety of macromolecular solutes. Water flow increased linearly with applied hydrostatic pressure, allowing the effective osmotic pressure of the solutes to be estimated by extrapolation. Reflection coefficients for each solute-membrane combination were calculated and correlated with the ratio of solute size to pore size. For the same mean molecular size, proteins were found to have larger reflection coefficients than dextrans. Molecular rigidity may play a role in this difference in behavior.     

The Interaction between Osmotic- and Pressure-induced Water Flow in Plant Roots

This paper presents a general model for coupled solute and water flow through plant roots based on the thermodynamics of irreversible processes. The model explains in a straight-forward manner such experimentally observed phenomena as changes in root resistance, increased solute flux, and apparent negative resistance, which have been reported for root systems under the influence of a hydrostatic pressure gradient. These apparent anomalies are explained on the basis of the interaction between the osmotic and hydrostatic driving forces and the well known “sweeping away” or dilution effect. We show that with a constant hydraulic conductivity the only features necessary to explain these phenomena are some type of membrane or membranelike structure and a mechanism for actively accumulating solutes.     

A model for sieving of macromolecules by the glomerular membrane of the kidney.

The transport of water and of macromolecules across the glomerular membrane of the kidney depends on the membrane parameters (radius, length and number of pores) as well as on the hydrostatic and oncotic pressures on either side of the membrane. The filtration pressure decreases along the capillary loops from afferent to efferent end. Water and solute flows are thus given by a system of two differential equations. The sieving coefficient of the macromolecules is the ratio of solute to water flow. In the program described the differential equations are solved by the Runge-Kutta method (fourth order). Rosenbrock's method of minimization is used to adjust the theoretical to the experimental sieving coefficients. The pore radius, total pore area per unit of path length and conductance of the membrane, as well as the intracapillary hydrostatic pressure and its gradient can thus be determined.     

New method to measure water permeability in emptied-out Xenopus oocytes controlling conditions on both sides of the membrane

Membrane water permeability is habitually calculated from volume changes in Xenopus laevis oocytes during external osmotic challenges. Nevertheless, this approach is limited by the uncertainty on the oocyte internal composition. To circumvent this limitation a new experimental set up is introduced where the cell membrane of an emptied-out oocyte was mounted as a diaphragm between two chambers. In its final configuration the oocyte membrane was part of a closed compartment and net water movements induced swelling or shrinking of it. Volume changes were followed by video-microscopy and digitally recorded. In this manner, water movements could be continuously monitored while controlling chemical composition and hydrostatic pressure on both sides of the membrane. Using this novel experimental approach an increasing hydrostatic pressure gradient was applied to both mature (stage VI) and immature (stage IV) oocytes. The relative maximal volume change tolerated before disruption was similar in both cases (1.26+/-0.07 and 1.27+/-0.03 respectively) and similar to those previously reported under maximal osmotic stress. Nevertheless the osmotic permeability coefficient (P(OSM)) in mature oocytes ((1.72+/-0.58) x 10(-3) cm s(-1); n=6) was significantly lower than in immature oocytes ((5.18+/-0.59) x 10(-3) cm s(-1), n=5; p<0.005).     

Cellular volume homeostasis

All cells face constant challenges to their volume either through changes in intracellular solute content or extracellular osmolality. Cells respond to volume perturbations by activating membrane transport and/or metabolic processes that result in net solute loss or gain and return of cell volume to its normal resting state. This paper provides a brief overview of fundamental concepts of osmotic water flow across cell membranes, mechanisms of cell volume perturbation, the role of inorganic ions and organic osmolytes in cell volume regulation and the signaling mechanisms that regulate the activity of cell volume-sensitive transport and metabolic pathways.     

A Mathematical Treatment of Munch's Pressure-Flow Hypothesis of Phloem Translocation

The steady state solutions of two mathematical models are used to evaluate Münch's pressure-flow hypothesis of phloem translocation. The models assume a continuous active loading and unloading of translocate but differ in the site of loading and unloading and the route of water to the sieve tube. The dimensions of the translocation system taken are the average observed values for sugar beet and are intended to simulate translocation from a mature source leaf to an expanding sink leaf. The volume flow rate of solution along the sieve tube, water flow rate into the sieve tube, hydrostatic pressure, and concentration of sucrose in the sieve tube are obtained from a numerical computer solution of the models. The mass transfer rate, velocity of translocation, and osmotic and hydrostatic pressures are consistent with empirical findings. Owing to the resistance to water flow offered by the lateral membranes, the hydrostatic pressure generated by the osmotic pressure can be considerably less than would be predicted by the solute concentration. These models suggest that translocation at observed rates and velocities can be driven by a water potential difference between the sieve tube and surrounding tissue and are consistent with the pressure-flow hypothesis of translocation.     

Theoretical study of flow,pressure and solute concentration in double membrane systems

A model system consisting of two rigidly held membranes in series was investigated through the application of the Kedem and Katchalsky thermodynamic single membrane flow equations. This analysis results in predictions of the steady state flow properties as well as values for the solute concentration and pressure of the internal compartment when the system is under the influence of a constant solute concentration or hydrostatic pressure gradient. It is demonstrated that although the flow properties and internal compartment pressure are complicated functions of the membrane permeability coefficients and driving gradient across the system, the relationships are greatly simplified by the explicit appearance of the internal compartment steady state solute concentration in the equations. It is shown that the steady state volume flow rate depends on the absolute value of the solute concentration in the external compartments, as well as the solute concentration gradient across the system. The properties of non-linear dependence of volume flow on concentration gradient, and rectification of volume flow are discussed and shown to be independent properties of the system. For the system under the influence of a solute concentration gradient, the internal compartment pressure can be greater or less than the ambient pressure, and depends mainly on the order in which the membranes are encountered by the volume flow. These properties are qualitatively correlated with certain available experimental observations in biological systems.     

Isotonic Water Transport in Secretory Epithelia ,

The model proposed by Diamond and Bossert [1] for isotonic water transport has received wide acceptance in recent years. It assumes that the local driving force for water transport is a standing osmotic gradient produced in the lateral intercellular spaces of the epithelial cell layer by active solute transport. While this model is based on work done in absorptive epithelia where the closed to open direction of the lateral space and the direction of net transport are the same, it has been proposed that the lateral spaces could also serve as the site of the local osmotic gradients for water transport in secretory epithelia, where the closed to open direction of the lateral space and net transport are opposed, by actively transporting solute out of the space rather than into it. Operation in the backward direction, however, requires a lower than ambient hydrostatic pressure within the lateral space which would seem more likely to cause the space to collapse with loss of function. On the other hand, most secretory epithelia are characterized by transport into a restricted ductal system which is similar to the lateral intercellular space in the absorptive epithelia in that its closed to open direction is the same as that of net transport. In vitro micropuncture studies on the exocrine pancreas of the rabbit indicate the presence of a small but statistically significant increase in juice osmolality, 6 mOsm/kg H₂O, at the site of electrolyte and water secretion in the smallest extralobular ducts with secretin stimulation which suggests that the ductal system in the secretory epithelia rather than the lateral intercellular space is the site of the local osmotic gradients responsible for isotonic water transport.     

Permeability and the hidden area of lipid bilayers

The passive water permeability of a lipid vesicle membrane was studied, related to the hydrostatic (not osmotic) pressure difference between the inner and the outer side of the vesicle in a water environment without additives. Each pressure difference was created by sucking a vesicle into a micropipette at a given sucking pressure. The part of the membrane sucked into the micropipette (the projection length) was measured as a function of time. The time dependence can be divided into two intervals. We put forward the idea that smoothing of membrane defects, accompanied by an increase of the membrane area, takes place during the initial time interval, which results in a faster increase of the projection length. In the second time interval the volume of the vesicle decreases due to the permeability of its membrane and the increase of the projection length is slower. The hidden area and the water permeability of a typical lipid bilayer were estimated. The measured permeability, conjugated to the hydrostatic pressure difference, is an order of magnitude higher than the known value of the permeability, conjugated to the osmotic pressure difference. A hypothesis, based on pore formation, is proposed as an explanation of this experimental result.