Solute Flux Coupling in a Homopore Membrane

Our previous studies on solute drag on frog skin and synthetic heteropore membranes have been extended to a synthetic homopore membrane. The 150-Å radius pores of this membrane are formed by irradiation and etching of polycarbonate films. The membrane is 6-µm thick and it has 6 x 10⁸ pores cm^–2. In this study, sucrose has been used as the driver solute with bulk flow blocked by hydrostatic pressure. As before on heteroporous membranes, the transmembrane asymmetry of tracer solute is dependent on the concentration of the driver solute. Tracer sucrose shows no solute drag while maltotriose shows appreciable solute drag at 1.5 M sucrose. With tracer inulin and dextran, solute drag is detectable at 0.5 M sucrose. These results are in keeping with the previous findings on heteropore membranes. Transmembrane solute drag is the result of kinetic and frictional interaction of the driver and tracer solutes as the driver flows down its concentration gradient. The magnitude of the tracer flux asymmetry is also dependent on the size of the transmembrane pores.     

Role of solute drag in intestinal transport

This study presents experiments related to the role of solvent drag and solute drag in the transmembrane movement of nonelectrolytes in a perfused rat intestine preparation. Conditions were chosen to simulate the effects of luminal hyperosmolarity on the permeability of tracer solutes. Data are presented on net water flux, transepithelial potentials, and lumen-to-blood and blood-to-lumen tracer solute movements during control electrolyte perfusion and after making the perfusate hyperosmotic. The results indicate that both solvent drag and solute drag can play significant roles in the transepithelial movement of solute and solute permeabilities in the rat ileum preparation. It is suggested that the potential roles of solvent drag and solute drag should be accounted for or considered during the characterization of the mechanisms of biological membrane function.     

Use of the paracellular way for the intestinal absorption of sugars

Passive absorption of D-Galactose (in the presence of 0.5 mM phlorizin), 2-deoxy-D-glucose and D-Mannitol by rat jejunum has been measured in vivo by perfusion of an intestinal segment with recirculation, along successive absorption periods of 5 or 10 min duration. In the range of 1 to 40 mM concentrations, the three solutes were absorbed at a very similar rate that varied as a lineal function of the concentrations in the perfusion solution. Absorption of 1 mM solute was not modified by the presence of 40 mM glucose or galactose. Passive absorption kinetics suggests processes of simple diffusion or solvent drag. The use of paracellular way for the passive absorption is supported by the fact that triaminopyrimidine (TAP) and protamine, which decrease the permeability through the tight junctions, also inhibit the absorption, with similar characteristics for both actions: TAP inhibition (53%) is very rapid and can be easily reversed, while that of protamine (30%) requires some time of previous exposure, lasts longer and can be reversed by heparin. The same analogy is shown by two actions that enhance the paracellular permeability: theophylline increases (30%) the passive absorption with lasting effect, while luminal hypertony enhances absorption transitorily. The passive absorption of the assayed solutes could be estimated to take place by the paracellular way in at least 50% and probably 70% or even more. The measure of net fluid fluxes reveals that solute fluxes must be prevailingly explained by simple diffusion, as the solvent drag can only play a very minor role.     

A note on the diffusion drag forces

A formal derivation of the expression for the diffusion drag force is given. The expression involves the coefficient of diffusion of the solute through the solvent and the coefficient of diffusion which the solute would posses if it diffused through itself in the form of a gas, in the absence of the solvent.     

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.     

Passive Asymmetric Transport through Biological Membranes

The magnitude of passive diffusional solute transfer through artificial membranes is usually considered to be independent of the direction of the concentration gradient driving force. It can be shown, however, that a composite membrane, having as one component a membrane with a chemical reaction-facilitated diffusion transport mechanism, can result in an asymmetrical flux. An asymmetric flux caused by this type of structural heterogeneity may be one mechanism contributing to the asymmetric properties of biological membranes. Similar vectorial fluxes can be generated in interfacial solute transfer through membranes if hydrodynamic boundary layers occur at the membrane interface and reversible chemical reactions with the permeant species are involved in either phase.     

Further Observations on Asymmetrical Solute Movement across Membranes

The permeability of frog skin under the influence of urea hyperosmolarity has been studied. Flux ratio asymmetry has been demonstrated again for tracer mannitol. The inhibitors DNP, CN^-, and ouabain have been used to eliminate active sodium transport and it was found that urea hyperosmolarity produces asymmetrical mannitol fluxes on frog skins having no short-circuit current. These findings suggest that flux ratio asymmetry is due to solute interaction and is unrelated to sodium transport. Studies with a synthetic membrane show clearly that bulk flow of fluid can produce a "solvent drag" effect and change flux ratios. When bulk flow is blocked and solute gradients allowed their full expression, then solute interaction "solute drag" is easily demonstrable in a synthetic system.     

A kinetic theory of diffusion forces in metabolizing systems

The development of a molecular theory of the diffusion drag forces in liquids is attempted by considering the liquids as limiting cases of very dense gases. An expression is derived for the force on a small particle suspended in a nonuniform mixture of such gases on the basis of kinetic theory. Another expression for the order of magnitude of the force on a larger particle is obtained by introducing certain hydrodynamical considerations. These results are compared with an expression previously derived by N. Rashevsky, and estimates are made of the order of magnitude of the volume force on the granules and particles within a typical cell due to the diffusion of metabolites. It is found that the drag forces, exerted by a diffusing solute, depend to a very large extent on the physical properties of the solvent.     

Transport across homoporous and heteroporous membranes in nonideal, nondilute solutions. II. Inequality of phenomenological and tracer solute permeabilities.

The phenomenological solute permeability (omega p) of a membrane measures the flux of solute across it when the concentrations of the solutions on the two sides of the membrane differ. The relationship between omega p and the the conventionally measured tracer permeability (omega T) is examined for homoporous and heteroporous (parallel path) membranes in nonideal, nondilute solutions and in the presence of boundary layers. In general, omega p and omega T are not equal; therefore, predictions of transmembrane solute flux based on omega T are always subject to error. For a homoporous membrane, the two permeabilities become equal as the solutions become ideal and dilute. For heteroporous membranes, omega p is always greater than omega T. An upper bound on omega p- omega T is derived to provide an estimate of the maximum error in predicted solute flux. This bound is also used to show that the difference between omega P and omega T demonstrated earlier for the sucrose-Cuprophan system can be explained if the membrane is heteroporous. The expressions for omega P developed here support the use of a modified osmotic driving force to describe membrane transport in nonideal, nondilute solutions.     

Transmembrane Protein Diffusion in Gel-Supported Dual-Leaflet Membranes

Tools to measure transmembrane-protein diffusion in lipid bilayer membranes have advanced in recent decades, providing a need for predictive theoretical models that account for interleaflet leaflet friction on tracer mobility. Here we address the fully three-dimensional flows driven by a (nonprotruding) transmembrane protein embedded in a dual-leaflet membrane that is supported above and below by soft porous supports (e.g., hydrogel or extracellular matrix), each of which has a prescribed permeability and solvent viscosity. For asymmetric configurations, i.e., supports with contrasting permeability, as realized for cells in contact with hydrogel scaffolds or culture media, the diffusion coefficient can reflect interleaflet friction. Reasonable approximations, for sufficiently large tracers on low-permeability supports, are furnished by a recent phenomenological theory from the literature. Interpreting literature data, albeit for hard-supported membranes, provides a theoretical basis for the phenomenological Stokes drag law as well as strengthening assertions that nonhydrodynamic interactions are important in supported bilayer systems, possibly leading to overestimates of the membrane/leaflet viscosity. Our theory provides a theoretical foundation for future experimental studies of tracer diffusion in gel-supported membranes.     

A mathematical model of solute coupled water transport in toad intestine incorporating recirculation of the actively transported solute

A mathematical model of an absorbing leaky epithelium is developed for analysis of solute coupled water transport. The non-charged driving solute diffuses into cells and is pumped from cells into the lateral intercellular space (lis). All membranes contain water channels with the solute passing those of tight junction and interspace basement membrane by convection-diffusion. With solute permeability of paracellular pathway large relative to paracellular water flow, the paracellular flux ratio of the solute (influx/outflux) is small (2-4) in agreement with experiments. The virtual solute concentration of fluid emerging from lis is then significantly larger than the concentration in lis. Thus, in absence of external driving forces the model generates isotonic transport provided a component of the solute flux emerging downstream lis is taken up by cells through the serosal membrane and pumped back into lis, i.e., the solute would have to be recirculated. With input variables from toad intestine (Nedergaard, S., E.H. Larsen, and H.H. Ussing, J. Membr. Biol. 168:241-251), computations predict that 60-80% of the pumped flux stems from serosal bath in agreement with the experimental estimate of the recirculation flux. Robust solutions are obtained with realistic concentrations and pressures of lis, and with the following features. Rate of fluid absorption is governed by the solute permeability of mucosal membrane. Maximum fluid flow is governed by density of pumps on lis-membranes. Energetic efficiency increases with hydraulic conductance of the pathway carrying water from mucosal solution into lis. Uphill water transport is accomplished, but with high hydraulic conductance of cell membranes strength of transport is obscured by water flow through cells. Anomalous solvent drag occurs when back flux of water through cells exceeds inward water flux between cells. Molecules moving along the paracellular pathway are driven by a translateral flow of water, i.e., the model generates pseudo-solvent drag. The associated flux-ratio equation is derived.     

Effect of solute permeability in determination of elastic modulus using the vesicular swelling method.

The modulus of elasticity of artificial and biological membranes can be determined in membrane vesicles by monitoring the limitation of vesicular swelling during a slow decrease in medium tonicity. The higher the elastic modulus of the membrane, the more effectively the vesicles will resist swelling. This method assumes that the solutes in the system are impermeant, so that the final volume of the vesicles is determined solely by a balance of osmotic and hydrostatic forces. In this paper, we present the results of computer simulation of vesicular swelling in which the solute permeability of the membrane was varied. We find that even a small permeability will lead to a loss of solute from the vesicle that will retard the increase in vesicular volume during dilution of the medium, and thereby cause the apparent modulus of elasticity to be much greater than the true value. For example, if one takes the mannitol permeability in brush border membrane vesicles from small intestine to be 0.004 micron/s (a reasonable estimate), one finds that a vesicular swelling study using mannitol as the principal solute will show the apparent elastic modulus of the vesicles to be greater than 10 times larger than the true value. With higher permeabilities, the effect is even more dramatic. We conclude that determination of impermeance of solutes is a critical prerequisite for making valid determinations of membrane elastic modulus using the vesicular swelling method.     

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.     

Permeability of composite chondrocyte-culture-millipore membranes to solutes of varying size and shape.

A model connective-tissue system was developed that is amenable to the determination of permeability coefficients of diffusing solutes. The system involves the culture of 13-day chick-embryo chondrocytes on a Millipore filter (HA:0.45 micron pore size) to form what is, in effect, a confluent, extremely thin cartilage slice of uniform thickness. These cultured chondrocyte membranes were used to measure the steady-state flux of radioactively labelled low-molecular-weight solutes and micro-ions. Similarly, the permeability coefficients of either radioactively labelled or enzymically active proteins across the membranes were determined. The membrane was found to have no marked effects on the diffusional behaviour of low-molecular-weight non-electrolytes (water, proline, ribose, glucose, sorbitol, raffinose). For micro-ions (Na+, SO42-, Cl-, glutamate, glucuronate,), the diffusive behaviour was found to be markedly affected by the ionic strength of the solvent used in a manner which was consistent with a Donnan distribution resulting from the immobilized proteoglycans. Globular proteins permeated the membrane at rates which decreased as the molecular size of the diffusing solute increased. The apparent diffusion rates of fibrinogen and of collagen through the membranes were greater than would be expected on the basis of their diffusion coefficients in free solution. Reasons for this behaviour are discussed.     

Mechanical force characterization in manipulating live cells with optical tweezers

Laser trapping with optical tweezers is a noninvasive manipulation technique and has received increasing attentions in biological applications. Understanding forces exerted on live cells is essential to cell biomechanical characterizations. Traditional numerical or experimental force measurement assumes live cells as ideal objects, ignoring their complicated inner structures and rough membranes. In this paper, we propose a new experimental method to calibrate the trapping and drag forces acted on live cells. Binding a micro polystyrene sphere to a live cell and moving the mixture with optical tweezers, we can obtain the drag force on the cell by subtracting the drag force on the sphere from the total drag force on the mixture, under the condition of extremely low Reynolds number. The trapping force on the cell is then obtained from the drag force when the cell is in force equilibrium state. Experiments on numerous live cells demonstrate the effectiveness of the proposed force calibration approach.     

Permeability of Lipid Bilayer Membranes to Organic Solutes

A sensitive fluorescence technique was used to measure transport of organic solutes through lipid bilayer membranes and to relate permeability to the functional groups of the solute, lipid composition of the membrane, and pH of the medium. Indole derivatives having ethanol, acetate, or ethylamine in the 3-position, representing neutral, acidic, and basic solutes, respectively, were the primary models. The results show: (a) Neutral solute permeability is not greatly affected by changes in lipid composition but presence or absence of cholesterol in the membranes could greatly alter permeability of the dissociable substrates. (b) Indole acetate permeability was reduced by introduction of phosphatidylserine into membranes to produce a net negative charge on the membranes. (c) Permeability response of dissociable solutes to variation in pH was in the direction predicted but not always of the magnitude expected from changes in the calculated concentrations of the undissociated solute in the bulk aqueous phase. Concentration gradients of amines across the membranes caused substantial diffusion potentials, suggesting that some transport of the cationic form of the amine may occur. It is suggested that factors such as interfacial charge and hydration structure, interfacial polar forces, and lipid organization and viscosity, in addition to the expected solubility-diffusion relations, may influence solute flux.     

Forces causing osmotic pressure.

An analysis of forces acting on a simple system that includes a solvent, solute, and a semipermeable membrane shows the basic mechanism of osmotic pressure can be expressed as any of three forces: that due to the interaction of solute particles with the semipermeable membrane; that due to the cohesiveness of the solvent; or that due to the solute particles interacting with the free surface of the solvent.     

Diffusional solute flux during osmotic water flow across the human red cell membrane

The effect of solvent drag on the unidirectional efflux of labeled water, urea, and chloride from human red cells was studied by means of the continuous flow tube method under conditions of osmotic equilibrium and net volume flow. Solvent (water) flow out of cells was created by mixing cells equilibrated in 100 mM salt solution with a 200-mM or 250-mM salt solution, while flow of water into cells was obtained by equilibrating the cells in the higher concentration and mixing them with the 100-mM solution. Control experiments constitute measurements of efflux of [14C]ethanol in normal cells and 3H2O in cells treated with p-chloromercuribenzosulfonate under the conditions described above. In both instances, the solute is known to penetrate the membrane through nonporous pathways. As anticipated, the tracer flux of neither urea nor chloride showed any dependence on net solvent flow, regardless of the direction. If one assumes the recently reported reflection coefficient for urea of 0.7, the urea tracer flux should change by at least 24% under volume flow conditions. Since such changes would be easily detected with our method, we conclude that the pathways for water, for urea, and for chloride are functionally separated.     

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)