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.     

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.     

Studies with Composite Membranes: II. Measurement of Asymmetric Properties

Electrical potentials arising across composite membranes when they separate the same concentration of a (1:1) electrolyte or electrolytes have been measured. These potentials have been shown to arise from differences in the transport number of counterions contacting the two faces of the membrane which contained in its body a high concentration of electrolyte and polyelectrolyte. When the concentration of this trapped electrolyte or polyelectrolyte is low, the asymmetry potentials are small. Although measurements of current-voltage relations provided evidence for the existence of asymmetry between the two faces of the membrane, osmotic flow of water in either direction across the membrane and the salt flow in the two directions were symmetrical. These solvent and solute flux measurements lasted more than 30 hr. Short-term (about 4 hr) flux measurements, however, using tritiated water (THO), gave flows which were different in the two directions. Similarly, the salt flows measured using ²²Na isotope were different in the two directions. The usefulness of the present system as a model to use for studies concerned with carrier transport problems in biology has been pointed out.     

Plasmodesmata as a Modulator of Osmotic Water Fluxes in Plants

Solutions to some key problems in the relationships between the structure and functions of plasmodesmata, a component of the plant intercellular communication system, are proposed on the basis of the theory of osmotic flows through porous membranes. The theory accounts for structural characteristics of plasmodesmata, such as their dimension, shape, and length. It considers the steric and adsorption potentials of the solution–cell wall interaction and estimates water and solute (e.g., sucrose) flows under the sustained difference of osmotic pressures at the ends of plasmodesmata. The theory predicts that the water flow through plasmodesmata increases with the widening of the neck constriction and reaches its peak when its size is equal to the diameter of the solute molecule. The water-flow direction was found to depend on the opening of the annulus in neck constrictions at negative adsorption potentials of the plasmodesmata channel walls. Taking into account the presence of sphincters in the neck constrictions, our data suggest the role of plasmodesmata as a modulator of osmotic water fluxes in plants.     

Permeability of lipid membranes revised in relation to freeze-thaw processes.

Water and solute activity gradients created during freeze-thaw processes produce water and solute fluxes across the cell membrane resulting in volume changes. Under these conditions, osmotic and thermal stresses affect the curvature, the phase behavior, and the surface properties of the lipid bilayer. These structural changes are not considered by the classical formalisms describing permeability of lipid membranes to water and nonelectrolytes such as the Nernst-Planck equation, Eyring's absolute rate theory, and Kedem-Katchalsky's thermodynamic of irreversible processes approach. In this paper, the influence of such changes on the glycerol permeation kinetics are reported. The results indicate that osmotic and chemical effects of the cryoprotectant on the membrane properties affect the rate of volume swelling depending on whether the membrane is in the gel or in the liquid crystalline state.     

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.     

Osmotic Flow of Water across Permeable Cellulose Membranes

Direct measurements have been made of the net volume flow through cellulose membranes, due to a difference in concentration of solute across the membrane. The aqueous solutions used included solutes ranging in size from deuterated water to bovine serum albumin. For the semipermeable membrane (impermeable to the solute) the volume flow produced by the osmotic gradient is equal to the flow produced by the hydrostatic pressure RT ΔC, as given by the van't Hoff relationship. In the case in which the membrane is permeable to the solute, the net volume flow is reduced, as predicted by the theory of Staverman, based on the thermodynamics of the steady state. A means of establishing the amount of this reduction is given, depending on the size of the solute molecule and the effective pore radius of the membrane. With the help of these results, a hypothetical biological membrane moving water by osmotic and hydrostatic pressure gradients is discussed.     

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.     

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.     

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.     

Flow limits of Kedem-Katchalsky equations for fluid flux

The Kedem-Katchalsky equations for fluid flux across membranes may not be adequate for large solvent flows. In particular, for an example of two membranes in series, it is argued that they would predict physically unreasonable behavior. An alternate equation for solute flow is proposed for a simple sieving membrane. For the same example, this equation predicts more physically reasonable results.     

Volume regulation by flounder red blood cells in anisotonic media

The nucleated high K, low Na red blood cells of the winter flounder demonstrated a volume regulatory response subsequent to osmotic swelling or shrinkage. During volume regulation the net water flow was secondary to net inorganic cation flux. Volume regulation the net water flow was secondary to net inorganic cation flux. Volume regulation after osmotic swelling is referred to as regulatory volume decrease (RVD) and was characterized by net K and water loss. Since the electrochemical gradient for K is directed out of the cell there is no need to invoke active processes to explain RVD. When osmotically shrunken, the flounder erythrocyte demonstrated a regulatory volume increase (RVI) back toward control cell volume. The water movements characteristic of RVI were a consequence of net cellular NaCl and KCl uptake with Na accounting for 75 percent of the increase in intracellular cation content. Since the Na electrochemical gradient is directed into the cell, net Na uptake was the result of Na flux via dissipative pathways. The addition of 10(-4)M ouabain to suspensions of flounder erythrocytes was without effect upon net water movements during volume regulation. The presence of ouabain did however lead to a decreased ration of intracellular K:Na. Analysis of net Na and K fluxes in the presence and absence of ouabain led to the conclusion that Na and K fluxes via both conservative and dissipative pathways are increased in response to osmotic swelling or shrinkage. In addition, the Na and K flux rate through both pump and leak pathways decreased in a parallel fashion as cell volume was regulated. Taken as a whole, the Na and K movements through the flounder erythrocyte membrane demonstrated a functional dependence during volume regulation.     

Osmotic flow caused by polyelectrolytes

Osmotic flow of water caused by high concentrations of anionic polyelectrolytes across semipermeable membranes, permeable only to solvent and simple electrolyte, has been measured in a newly designed flow cell. The flow cell features small solution and solvent compartments and an efficient stirring mechanism. We have demonstrated that, while the osmotic pressure of the anionic polyelectrolytes is determined primarily by micro-counterions, the osmotic flow is determined by solution-dependent properties as embodied in the hydrodynamic frictional coefficient which is determined by the polymer backbone segment of the polyelectrolyte. The variation of the osmotic permeability coefficient, L(p)(o), with concentration and osmotic pressure closely correlated with the concentration dependence of this frictional coefficient. These studies confirm previous work that the kinetics of osmotic flow across a membrane impermeable to the osmotically active solute is primarily determined by the diffusive mobility of the solute.     

Local osmotic coupling to the active trans-endothelial bicarbonate flux in the rabbit cornea

The present experiments investigate HCO₃⁻, Cl⁻ and fluid fluxes across partially destromalised corneas. Although there is no net flux of Cl⁻, there is a net flux of HCO₃⁻ across the endothelium from stromal side to aqueous side which is accompanied by a flux of water in the same direction. Bulk phase osmosis cannot account for the initiation of the flux of fluid. Local osmotic coupling between ions and water is postulated to occur in the preparation. The exudate is hypertonic to the bathing Ringer solution.     

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.     

Transient transcapillary exchange of water driven by osmotic forces in the heart

Osmotic transient responses in organ weight after changes in perfusate osmolarity have implied steric hindrance to small-molecule transcapillary exchange, but tracer methods do not. We obtained osmotic weight transient data in isolated, Ringer-perfused rabbit hearts with NaCl, urea, glucose, sucrose, raffinose, inulin, and albumin and analyzed the data with a new anatomically and physicochemically based model accounting for 1) transendothelial water flux, 2) two sizes of porous passages across the capillary wall, 3) axial intracapillary concentration gradients, and 4) water fluxes between myocytes and interstitium. During steady-state conditions approximately 28% of the transcapillary water flux going to form lymph was through the endothelial cell membranes [capillary hydraulic conductivity (Lp) = 1.8 +/- 0.6 x 10-8 cm. s-1. mmHg-1], presumably mainly through aquaporin channels. The interendothelial clefts (with Lp = 4.4 +/- 1.3 x 10-8 cm. s-1. mmHg-1) account for 67% of the water flux; clefts are so wide (equivalent pore radius was 7 +/- 0.2 nm, covering approximately 0.02% of the capillary surface area) that there is no apparent hindrance for molecules as large as raffinose. Infrequent large pores account for the remaining 5% of the flux. During osmotic transients due to 30 mM increases in concentrations of small solutes, the transendothelial water flux was in the opposite direction and almost 800 times as large and was entirely transendothelial because no solute gradient forms across the pores. During albumin transients, gradients persisted for long times because albumin does not permeate small pores; the water fluxes per milliosmolar osmolarity change were 200 times larger than steady-state water flux. The analysis completely reconciles data from osmotic transient, tracer dilution, and lymph sampling techniques.     

Osmosis in Cortical Collecting Tubules : A Theoretical and Experimental Analysis of the Osmotic Transient Phenomenon

This paper reports a theoretical analysis of osmotic transients and an experimental evaluation both of rapid time resolution of lumen to bath osmosis and of bidirectional steady-state osmosis in isolated rabbit cortical collecting tubules exposed to antidiuretic hormone (ADH). For the case of a membrane in series with unstirred layers, there may be considerable differences between initial and steady-state osmotic flows (i.e., the osmotic transient phenomenon), because the solute concentrations at the interfaces between membrane and unstirred layers may vary with time. A numerical solution of the equation of continuity provided a means for computing these time-dependent values, and, accordingly, the variation of osmotic flow with time for a given set of parameters including: P_f (cm s^–1), the osmotic water permeability coefficient, the bulk phase solute concentrations, the unstirred layer thickness on either side of the membrane, and the fractional areas available for volume flow in the unstirred layers. The analyses provide a quantitative frame of reference for evaluating osmotic transients observed in epithelia in series with asymmetrical unstirred layers and indicate that, for such epithelia, P_f determinations from steady-state osmotic flows may result in gross underestimates of osmotic water permeability. In earlier studies, we suggested that the discrepancy between the ADH-dependent values of P_f and P_DDw (cm s^–1, diffusional water permeability coefficient) was the consequence of cellular constraints to diffusion. In the present experiments, no transients were detectable 20–30 s after initiating ADH-dependent lumen to bath osmosis; and steady-state ADH-dependent osmotic flows from bath to lumen and lumen to bath were linear and symmetrical. An evaluation of these data in terms of the analytical model indicates: First, cellular constraints to diffusion in cortical collecting tubules could be rationalized in terms of a 25-fold reduction in the area of the cell layer available for water transport, possibly due in part to transcellular shunting of osmotic flow; and second, such cellular constraints resulted in relatively small, approximately 15%, underestimates of P_f.     

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.