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.     

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.     

Further quantification of the role of internal unstirred layers during the measurement of transport coefficients in giant internodes of Chara by a new stop-flow technique

A new stop-flow technique was employed to quantify the impact of internal unstirred layers on the measurement of the solute permeability coefficient (P(s)) across the plasma membrane of internodes of the giant-celled alga Chara corallina using a cell pressure probe. During permeation experiments with rapidly permeating solutes (acetone, 2-propanol, and dimethylformamide), the solute concentration inside the cell was estimated and the external medium was adjusted to stop solute transport across the membrane, after which responses in turgor were measured. This allowed estimation of the solute concentration right at the membrane. Stop-flow experiments were also simulated with a computer. Both the stop-flow experiments and simulations provided quantitative data about internal concentration gradients and the contribution of unstirred layers to overall measured values of P(meas)(s) for the three solutes. The stop-flow experimental results agreed with stop-flow simulations assuming that solutes diffused into a completely stagnant cell interior. The effects of internal unstirred layers on the underestimation of membrane P(s) declined with decreasing P(s). They were no bigger than 37% in the presence of the most rapidly permeating solute, acetone (P(meas)(s) =4.2 x 10(-6) m s(-1)), and 14% for the less rapidly permeating dimethylformamide (P(meas)(s) =1.6x10(-6) m s(-1)). It is concluded that, even in the case of rapidly permeating solutes such as isotopic water and, even when making pessimistic assumptions about the internal mixing of solutes, an upper limit for the underestimation of P(s) due to internal unstirred layers was 37%. The data are discussed in terms of recent theoretical estimates of the effect of internal unstirred layers and in terms of some recent criticism of cell pressure probe measurements of water and solute transport coefficients. The current stop-flow data are in line with earlier estimations of the role of unstirred layers in the literature on cell water relations.     

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.     

Aquaporin Nt-TIPa can account for the high permeability of tobacco cell vacuolar membrane to small neutral solutes

Members of the major intrinsic protein (MIP) family, described in plants as water-selective channels (aquaporins), can also transport small neutral solutes in other organisms. In the present work, we characterize the permeability of plant vacuolar membrane (tonoplast; TP) and plasma membrane (PM) to non-electrolytes and evaluate the contribution of MIP homologues to such transport. PM and TP vesicles were purified from tobacco suspension cells by free-flow electrophoresis, and membrane permeabilities for a wide range of neutral solutes including urea, polyols of different molecular size, and amino acids were investigated by stopped-flow spectrofluorimetry. For all solutes tested, TP vesicles were found to be more permeable than their PM counterparts, with for instance urea permeabilities from influx experiments of 74.9 +/- 9.6 x 10(-6) and 1.0 +/- 0.3 x 10(-6) cm sec-1, respectively. Glycerol and urea transport in TP vesicles exhibited features of a facilitated diffusion process. This and the high channel-mediated permeability of the same TP vesicles to water suggested a common role for MIP proteins in water and solute transport. A cDNA encoding a novel tonoplast intrinsic protein (TIP) homologue named Nicotiana tabacum TIPa (Nt-TIPa) was isolated from tobacco cells. Immunodetection of Nt-TIPa in purified membrane fractions confirmed that the protein is localized in the TP. Functional expression of Nt-TIPa in Xenopus oocytes showed this protein to be permeable to water and solutes such as urea and glycerol. These features could account for the transport selectivity profile determined in purified TP vesicles. These results support the idea that plant aquaporins have a dual function in water and solute transport. Because Nt-TIPa diverges in sequence from solute permeable aquaporins characterized in other organisms, its identification also provides a novel tool for investigating the molecular determinants of aquaporin transport selectivity.     

A theory of cell hydration governed by adsorption of water on cell proteins rather than by osmotic pressure

It is postulated that cell hydration is governed by adsorption of water on cell proteins in accord with the Bradley adsorption isotherm, and that the action of a solute in the surrounding solution is to lower the vapor pressure of the solution so that cell water adsorption is decreased by moving down the Bradley isotherm. From these concepts, it is derived that cell volume (V) should be related to solute concentration (x) by the equationV=−E log₁₀ x+F whereE andF are constants which are independent of type of solute. For a non-adsorbed solute this agrees well with experimental data. For solutes which are adsorbed by cell proteins, a correction in the above equation may be necessary at higher solute concentrations, which is shown to be compatible with various experimental data. The types of experiments which are generally used to support the osmotic pressure theory of cell hydration agree equally well with the adsorption theory. The virtue of the adsorption theory is that, unlike the osmotic pressure theory of cell swelling, it is compatible with permeability of the cell membrane to solutes, which has been experimentally observed for various solutes. The opinions and conclusions contained in this report are those of the author. They are not to be construed as necessarily reflecting the views or the endorsement of the Navy Department.     

A re-examination of the minor role of unstirred layers during the measurement of transport coefficients of Chara corallina internodes with the cell pressure probe

The impact of unstirred layers (USLs) during cell pressure probe experiments with Chara corallina internodes has been quantified. The results show that the hydraulic conductivity (Lp) measured in hydrostatic relaxations was not significantly affected by USLs even in the presence of high water flow intensities ('sweep-away effect'). During pressure clamp, there was a reversible reduction in Lp by 20%, which was explained by the constriction of water to aquaporins (AQPs) in the C. corallina membrane and a rapid diffusional equilibration of solutes in arrays where water protruded across AQPs. In osmotic experiments, Lp, and permeability (Ps) and reflection (sigma s) coefficients increased as external flow rate of medium increased, indicating some effects of external USLs. However, the effect was levelling off at 'usual' flow rates of 0.20-0.30 m s(-1) and in the presence of vigorous stirring by air bubbles, suggesting a maximum thickness of external USLs of around 30 microm including the cell wall. Because the diameters of internodes were around 1 mm, internal USLs could have played a significant or even a dominating role, at least in the presence of the rapidly permeating solutes used [acetone, 2-propanol and dimethylformamide (DMF)]. A comparison of calculated (diffusion kinetics) and of measured permeabilities indicated an upper limit of the contribution of USLs for the rapidly moving solute acetone of 29%, and of 15% for the less rapidly permeating DME The results throw some doubt on recent claims that in C. corallina, USLs rather than the cell membrane dominate solute uptake, at least for the most rapidly moving solute acetone.     

Molecular modeling and simulation of Mycobacterium tuberculosis cell wall permeability

The low permeability of the mycobacterial cell wall is thought to contribute to the intrinsic drug resistance of mycobacteria. In this study, the permeability of the Mycobacterium tuberculosis cell wall is studied by computer simulation. Thirteen known drugs with diverse chemical structures were modeled as solutes undergoing transport across a model for the M. tuberculosis cell wall. The properties of the solute-membrane complexes were investigated by means of molecular dynamics simulation, especially the diffusion coefficients of the solute molecules inside the cell wall. The molecular shape of the solute was found to be an important factor for permeation through the M. tuberculosis cell wall. Predominant lateral diffusion within, as opposed to transverse diffusion across, the membrane/cell wall system was observed for some solutes. The extent of lateral diffusion relative to transverse diffusion of a solute within a biological cell membrane may be an important finding with respect to absorption distribution, metabolism, elimination, and toxicity properties of drug candidates. Molecular similarity measures among the solutes were computed, and the results suggest that compounds having high molecular similarity will display similar transport behavior in a common membrane/cell wall environment. In addition, the diffusion coefficients of the solute molecules across the M. tuberculosis cell wall model were compared to those across the monolayers of dipalmitoylphosphatidylethanolamine and dimyristoylphosphatidylcholine, are two common phospholipids in bacterial and animal membranes. The differences among these three groups of diffusion coefficients were observed and analyzed.     

The effect of tanning agents on the permeability of the toad bladder to water and solutes

Summary Previous studies with phloretin have shown that the movement of urea and other solutes across the toad bladder can be inhitited with no effect on osmotic water flow, active sodium transport, or the movement of ethanol and ethylene glycol. These findings have suggested that a vasopressin-sensitive carrier is involved in the transport of solutes such as urea across the luminal membrane of the epithelial cell. The present paper describes the effect of two agents other than phloretin: tannic acid and chromate, on water and solute movement across the bladder. The pattern of action of these two agents resembles that of phloretin, and supports our earlier findings of the independence of solute and water movement. The effect of chromate on urea movement is seen only in the presence of vasopressin, and only if chromate is added prior to vasopressin. Chromate also proves to be an irreversible inhibitor of urea movement. The implications of these findings are discussed. In view of the known interactions of both agents with proteins, it is suggested that carrier-mediated transport of urea proceeds across a protein component of the membrane.Presented in part at the 57th annual meeting, Federation of American Societies for Experimental Biology, Atlantic City, April 1973.     

Regulation of plant aquaporin activity

Accumulating evidence indicates that aquaporins play a key role in plant water relations. Plant aquaporins are part of a large and highly divergent protein family that can be divided into four subfamilies according to amino acid sequence similarity. As in other organisms, plant aquaporins facilitate the transcellular movement of water, but, in some cases, also the flux of small neutral solutes across a cellular membrane. Plant cell membranes are characterized by a large range of osmotic water permeabilities, and recent data indicate that plant aquaporin activity might be regulated by gating mechanisms. The factors affecting the gating behaviour possibly involve phosphorylation, heteromerization, pH, Ca2+, pressure, solute gradients and temperature. Regulation of aquaporin trafficking may also represent a way to modulate membrane water permeability. The aim of this review is to integrate recent molecular and biophysical data on the mechanisms regulating aquaporin activity in plant membranes and to relate them to putative changes in protein structure.     

Hydrostatic pressures developed by osmotically swelling vesicles bound to planar membranes

When phospholipid vesicles bound to a planar membrane are osmotically swollen, they develop a hydrostatic pressure (delta P) and fuse with the membrane. We have calculated the steady-state delta P, from the equations of irreversible thermodynamics governing water and solute flows, for two general methods of osmotic swelling. In the first method, vesicles are swollen by adding a solute to the vesicle-containing compartment to make it hyperosmotic. delta P is determined by the vesicle membrane's permeabilities to solute and water. If the vesicle membrane is devoid of open channels, then delta P is zero. When the vesicle membrane contains open channels, then delta P peaks at a channel density unique to the solute permeability properties of both the channel and the membrane. The solute enters the vesicle through the channels but leaks out through the region of vesicle-planar membrane contact. delta P is largest for channels having high permeabilities to the solute and for solutes with low membrane permeabilities in the contact region. The model predicts the following order of solutes producing pressures of decreasing magnitude: KCl greater than urea greater than formamide greater than or equal to ethylene glycol. Differences between osmoticants quantitatively depend on the solute permeability of the channel and the density of channels in the vesicle membrane. The order of effectiveness is the same as that experimentally observed for solutes promoting fusion. Therefore, delta P drives fusion. When channels with small permeabilities are used, coupling between solute and water flows within the channel has a significant effect on delta P. In the second method, an impermeant solute bathing the vesicles is isosmotically replaced by a solute which permeates the channels in the vesicle membrane. delta P resulting from this method is much less sensitive to the permeabilities of the channel and membrane to the solute. delta P approaches the theoretical limit set by the concentration of the impermeant solute.     

Peroxisomal membrane permeability and solute transfer

The review is dedicated to recent progress in the study of peroxisomal membrane permeability to solutes which has been a matter of debate for more than 40 years. Apparently, the mammalian peroxisomal membrane is freely permeable to small solute molecules owing to the presence of pore-forming channels. However, the membrane forms a permeability barrier for 'bulky' solutes including cofactors (NAD/H, NADP/H, CoA, and acetyl/acyl-CoA esters) and ATP. Therefore, peroxisomes need specific protein transporters to transfer these compounds across the membrane. Recent electrophysiological studies have revealed channel-forming activities in the mammalian peroxisomal membrane. The possible involvement of the channels in the transfer of small metabolites and in the formation of peroxisomal shuttle systems is described.     

Aqueous pathways dominate permeation of solutes across Pisum sativum seed coats and mediate solute transport via diffusion and bulk flow of water

The permeability of seed coats to solutes either of biological or anthropogenic origin plays a major role in germination, seedling growth and seed treatment by pesticides. An experimental set‐up was designed for investigating the mechanisms of seed coat permeation, which allows steady‐state experiments with isolated seed coats of Pisum sativum. Permeances were measured for a set of organic model compounds with different physicochemical properties and sizes. The results show that narrow aqueous pathways dominate the diffusion of solutes across pea seed coats, as indicated by a correlation of permeances with the molecular sizes of the compounds instead of their lipophilicity. Further indicators for an aqueous pathway are small size selectivity and a small effect of temperature on permeation. The application of an osmotic water potential gradient across isolated seed coats leads to an increase in solute transfer, indicating that the aqueous pathways form a water‐filled continuum across the seed coat allowing the bulk flow of water. Thus, the uptake of organic solutes across pea testae has two components: (1) by diffusion and (2) by bulk water inflow, which, however, is relevant only during imbibition.     

Determinants of epithelial cell volume

Epithelial cell volume is determined by the concentration of intracellular, osmotically active solutes. The high water permeability of the cell membrane of most epithelia prevents the establishment of large osmotic gradients between the cell and the bathing solutions. Steady-state cell volume is determined by the relative rates of solute entry and exit across the cell membranes. Inhibition of solute exit leads to cell swelling because solute entry continues; inhibition of solute entry leads to cell shrinkage because solute exit continues. Cell volume is then a measure of the rate and direction of net solute movements. Epithelial cells are also capable of regulation of the rate of solute entry and exit to maintain intracellular composition. Feedback control of NaCl entry into Necturus gallbladder epithelial cells is demonstrable after inhibition of the Na,K-ATPase or reduction in the NaCl concentration of the serosal bath. Necturus gallbladder cells respond to a change in the osmolality of the perfusion solution by rapidly regulating their volume to control values. This regulatory behavior depends on the transient activation of quiescent transport systems. These transport systems are responsible for the rapid readjustments of cell volume that follow osmotic perturbation. These powerful transporters may also play a role in steady-state volume regulation as well as in the control of cell pH.     

Solute transport process in intestinal epithelial cells

In rat small intestine, the active transport of organic solutes results in significant depolarization of the membrane potential measured in an epithelial cell with respect to a grounded mucosal solution and in an increase in the transepithelial potential difference. According to the analysis with an equivalent circuit model for the epithelium, the changes in emf's of mucosal and serosal membranes induced by active solute transport were calculated using the measured conductive parameters. The result indicates that the mucosal cell membrane depolarizes while the serosal cell membrane remarkably hyperpolarizes on the active solute transport. Corresponding results are derived from the calculations of emf's in a variety of intestines, using the data that have hitherto been reported. The hyperpolarization of serosal membrane induced by the active solute transport might be ascribed to activation of the serosal electrogenic sodium pump. In an attempt to determine the causative factors in mucosal membrane depolarization during active solute transport, cell water contents and ion concentrations were measured. The cell water content remarkably increased and, at the same time, intracellular monovalent ion concentrations significantly decreased with glucose transport. Net gain of glucose within the cell was estimated from the restraint of osmotic balance between intracellular and extracellular fluids. In contrast to the apparent decreases in intracellular Na+ and K+ concentrations, significant gains of Na+ and K+ occurred with glucose transport. The quantitative relationships among net gains of Na+, K+ and glucose during active glucose transport suggest that the coupling ratio between glucose and Na+ entry by the carrier mechanism on the mucosal membrane is approximately 1:1 and the coupling ratio between Na+-efflux and K+-influx of the serosal electrogenic sodium pump is approximately 4:3 in rat small intestine. In addition to the electrogenic ternary complex inflow across the mucosal cell membrane, the decreases in intracellular monovalent ion concentrations, the temporary formation of an osmotic pressure gradient across the cell membrane and the streaming potential induced by water inflow through negatively charged pores of the cell membrane in the course of an active solute transport in intestinal epithelial cells are apparently all possible causes of mucosal membrane depolarization.     

Hydrophilic solute transport across rat alveolar epithelium

Diffusional fluxes of a series of hydrophilic nonelectrolytes (molecular radii ranging from 0.15 to 0.57 nm) were measured across the alveolocapillary barrier in the isolated perfused fluid-filled rat lung. Radiolabeled solutes were lavaged into the distal air spaces of isolated Ringer-perfused lungs, and apparent permeability-surface area products were calculated from the rates of isotope appearance in the recirculating perfusate. These data were used to estimate theoretical equivalent pore radii in the alveolar epithelium, with the assumption of diffusive flow through water-filled cylindrical pores. The alveolar epithelium is best characterized by two pore populations, with small pores (radius 0.5 nm) occupying 98.7% of total pore area and larger pores (radius 3.4 nm) occupying 1.3% of total pore area. Net water flow out of the alveolar space was measured by including an impermeant solute (dextran) in the lavage fluid and measuring its concentration in the alveolar space as a function of time. Under control conditions, net water flow averaged 167 nl/s. When 24 microM terbutaline was added to the perfusate, net water flow increased significantly to 350 nl/s (P less than 0.001). Terbutaline had no effect on the fluxes of either glycerol (which traverses the small pore pathway) or sucrose (which traverses the large pore pathway). These findings indicate that the intact mammalian alveolar epithelium is complex and highly resistant to the flow of solutes and water.     

Application of fluorescent dextrans to the brain surface under constant pressure reveals AQP4-independent solute uptake

Extracellular solutes in the central nervous system are exchanged between the interstitial fluid, the perivascular compartment, and the cerebrospinal fluid (CSF). The “glymphatic” mechanism proposes that the astrocyte water channel aquaporin-4 (AQP4) is a major determinant of solute transport between the CSF and the interstitial space; however, this is controversial in part because of wide variance in experimental data on interstitial uptake of cisternally injected solutes. Here, we investigated the determinants of solute uptake in brain parenchyma following cisternal injection and reexamined the role of AQP4 using a novel constant-pressure method. In mice, increased cisternal injection rate, which modestly increased intracranial pressure, remarkably increased solute dispersion in the subarachnoid space and uptake in the cortical perivascular compartment. To investigate the role of AQP4 in the absence of confounding variations in pressure and CSF solute concentration over time and space, solutes were applied directly onto the brain surface after durotomy under constant external pressure. Pressure elevation increased solute penetration into the perivascular compartment but had little effect on parenchymal solute uptake. Solute penetration and uptake did not differ significantly between wild-type and AQP4 knockout mice. Our results offer an explanation for the variability in cisternal injection studies and indicate AQP4-independent solute transfer from the CSF to the interstitial space in mouse brain.     

A model for radial water transport across plant roots

Summary A model based on the canal theory (Katou andFurumoto 1986 a, b) is proposed for the absorption of solute and water at the root periphery. The present canal model in the periphery and the model which was previously proposed for the exudation in the stele (Katou et al. 1987), are organized into a model for radial transport across excised plant roots, in the light of anatomical and physiological knowledge of maize roots. The canal equations for both canals are numerically solved to give quite a good explanation for the observed exudation of maize roots. It is found that the regulation of solute transport has a primary importance in the regulation of water transport across excised roots. The internal cell pressure of the symplast adjusts the water absorption at the root periphery to the water secretion into the vessels. There seems no need for this explanation of the radial water transport across roots to assume cell membranes with low reflection coefficient or variable water permeability. It would seem that the apoplast wall layers play a crucial role in metabolic control of water transport in roots as well as in hypocotyls.Abbreviations J _s ^ex* the theoretically estimated rate of solute exudation per unit surface area of model maize roots - J that of volume exudation per unit surface area of model maize roots - the reflection coefficient of the cell membrane against solutes     

Anomalous properties of water in macromolecular gels.

Low molecular weight solutes often exhibit elution characteristics on gel filtration columns which deviate from ideal behaviour. In many previous studies this anomalous behaviour was attributed to the existence of extremely narrow pores in the gel, inaccessible even to very small solute molecules, to explain Kd values lower than unity. Kd values of small solutes higher than unity were usually ascribed to adsorption of the solute to the gel matrix. In the present paper several observations are presented that contradict these suggestions. Experimental evidence indicates that with small solute molecules Kd values differing from unity can be fully explained by the anomalous properties of vicinal water layers at the gel matrix-water interface.