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.     

A mechanical force contributes to the "osmotic swelling" of brush-border membrane vesicles

Brush-border membrane vesicles and an osmotic swelling assay have been used extensively to monitor the pore-forming activity of Bacillus thuringiensis toxins. After a hypertonic shock, Manduca sexta midgut brush-border membrane vesicles shrink rapidly and reswell partially to a volume that depends on membrane permeability and toxin concentration rather than regaining their original volume as expected from theoretical models. Because efflux of buffer from the vesicles, as they shrink, could contribute to this phenomenon, vesicles were mixed with a hypertonic solution of the buffer with which they were loaded. Under these conditions, they are not expected to reswell, since the same solute is present on both sides of the membrane. Nevertheless, with several buffers, vesicles reswelled readily, an observation that demonstrates the involvement of an additional restoration force. Reswelling also occurred when, in the absence of toxin, the buffers were replaced by glucose, a solute that diffuses readily across the membrane, but did not occur with rat liver microsomes, despite their permeability to glucose. Unexpected swelling was also observed with rabbit jejunum brush-border membrane vesicles, suggesting that the cytoskeleton, present in brush-border membrane vesicles but absent from microsomes, could be responsible for the restoration force.     

Modelling the swelling assay for aquaporin expression

The standard method of assaying the water transporting capability of a putative aquaporin-like entity is to express that entity in a cell of normally low water permeability and to measure the enhancement of swelling when the cell is subjected to hypo-osmotic shock. Because of the heterogeneous nature of cytoplasm, the interplay of advection and diffusion, and the coupling of internal and external media via a semipermeable elastic membrane, even simplified mathematical models can be difficult to resolve. This class of diffusion problem seems to have been but little studied. In this paper, the cell and its surround are at first modelled as perfectly-mixed phases separated by an ideal semipermeable membrane with vanishingly small elastic modulus; and the time course of swelling is evaluated analytically. This time course was found to be non-exponential, but such unexpected behavior should not seriously affect the traditional interpretation of experimental results because its short time limit is linear as in the traditional model; and normally only short time data are available. Next, the simplifications of diffusive equilibrium and of vanishing elastic modulus are examined. It is shown that diffusive equilibrium will be true only when diffusive movement of osmolyte is rather faster than the swelling and that this will probably not be the case for many assays. On the other hand, it should often be possible to neglect the elastic modulus. Finally, a more comprehensive model is formulated for a spherical cell in a hypotonic medium and the swelling behavior described in terms as a moving boundary problem (This type of moving boundary problem is often called a Stefan problem [ http://en.wikipedia.org/wiki/Stefan_problem ]) in which two phases containing diffusive osmolyte are separated by a weakly-elastic ideally-semipermeable membrane, the water flux across which is linear in the osmolality difference across it. This type of behavior was evaluated numerically by finite-difference time-domain techniques and found to be qualitatively similar to that of the perfect-mixing simplification.     

Elasticity of synthetic phospholipid vesicles and submitochondrial particles during osmotic swelling

A rapid and accurate method has been developed for measuring the elastic response of vesicle bilayer membranes to an applied osmotic pressure. The technique of dynamic light scattering is used to measure both the elastic constant and the elastic limit of dioleoylphosphatidic acid (DOPA) and DOPA-cholesterol vesicles and of submitochondrial particles derived from the inner membrane of bovine heart mitochondria. The vesicles prepared by the pH-adjustment method are unilamellar and of uniform size between 240 and 460 nm in diameter. The vesicles swell uniformly upon dilution. The observed change in size is not due to any change in the shape of the vesicles. The data also indicate that the vesicles are spherical and not flaccid. The total vesicle swelling in these studies resulted in a 3-4% increase in surface area for vesicles swollen in 0.15 M KCl and a 5-10% increase in surface area for vesicles swollen in 0.25 M sucrose. This maximum represents the elastic limit of the vesicles. Evidence is presented to show that the vesicles release contents after swelling to this maximum, reseal immediately, and reswell according to the osmotic pressure. For DOPA vesicles in a 0.15 M KCl-tris(hydroxymethyl)aminomethane hydrochloride (Tris-HCl) buffer (pH 7.55), the observed membrane modulus is found to be in the range of 10(8) dyn/cm2. The modulus was found to be in the order of 10(7) dyn/cm2 for DOPA vesicles in a 0.25 M sucrose-Tris-HCl buffer (pH 7.55). This is comparable to that of submitochondrial particles in the same sucrose-Tris-HCl buffer. The observed membrane modulus also decreases with vesicle size. Its magnitude and its variation with ionic strength indicate that the major component of bilayer elasticity is neither the inherent elasticity of the bilayer nor the bending modulus. The variation of the membrane modulus with respect to curvature suggests that its principal component may be related to surface tension effects including the negative charges on the vesicle surface. There is considerable variation between vesicles swollen in sucrose and those swollen in KCl in the membrane modulus, in the elastic limit at which the vesicles burst, and in the transbilayer pressure difference at bursting. The latter was found to be 4-6 mosM (10(5) dyn/cm2) in sucrose solution and 20-4 mosM (10(6) dyn/cm2) in KCl solution.     

Determination of membrane permeability to water from osmotically induced light-scattering changes of membrane vesicles: Analysis of the method

The kinetics of osmotically induced changes in vesicular volume and internal solute concentration were analyzed for membrane vesicles containing fixed quantity of impermeable osmoticum in the lumen. The kinetic curves of the concentration and volume changes were shown to be dissimilar. The average durations of these two processes may differ by several tens of percents, depending on the extent and polarity of the initially imposed osmotic gradient. For vesicles containing identical solutes in the internal and external solutions, the problem is analyzed of how the concentration and volume changes are manifested in changes of the effective scattering cross-section of the vesicle. The light scattering changes, directed oppositely to volume changes, were found to coincide roughly with the kinetics of volume changes. The analysis shows that calculations of water permeability coefficient should be based on average duration of volume changes rather than the duration of concentration changes. The replacement in calculations of the first parameter with the second one may result in overestimation of water permeability by a factor of 1.5. This might be relevant to the reported discrepancies in water permeability values determined by the osmotic and isotope methods. Although the allowance for 1.5-fold overestimation cannot fully account for the differences observed, it significantly lowers the discrepancy between these estimates in some cases. The opposite signs of light scattering and volume changes originate from the presence of two components in the optical path of the vesicle, i.e., the membrane and the lumenal solution.     

Osmotically reactive plasma membrane vesicles prepared from rabbit kidney tubules by mild hypotonic lysis

Plasma membrane vesicles were obtained by hypotonic lysis in an ice-cold medium containing EDTA and MgCl₂. The vesicles were isolated by differential centrifugation. Compared to a total kidney homogenate, a 10–12-fold enrichment of trehalase and alkaline phosphatase (marker enzymes for renal brush border), and a 6-fold enrichment of (Na⁺---:K⁺)-stimulated ATPase, (a marker enzyme for the basal and lateral plasma membrane of the tubule cell), was achieved. Contamination by other cell organelles was very low. The plasma membrane vesicles enclosed small amounts of the cytoplasmic enzymes lactate dehydrogenase and malate dehydrogenase, which exhibited full activity only after their release into the medium by sonication.Electron micrographs of this preparation showed microvilli with drumstick-like expansions, but also spherical vesicles. By measuring the distribution of radio-actively labelled compounds of different molecular weight in a packed sediment of the plasma membranes under isotonic conditions, an intravesicular volume of 82% or 9 μl/mg of membrane protein was estimated. The intravesicular volume decreased when the osmolality of the medium was augmented by raffinose. The scattering of light by the vesicular suspension could be used to monitor rapid volume changes. By this method, the following sequence of flux rates was established: glycerol>erythritol> adonitol>mannitol. The fluxes of LiCl, NaCl, and KCl were almost identical, but faster than those of adonitol and mannitol. The data indicate, that a large fraction of the plasma membrane isolated in this preparation have formed vesicles, and also that they have retained, as far as investigated, the permeability characteristics of the plasma membrane.     

Effects of solute concentration on the entrapment of solutes in phospholipid vesicles prepared by freeze-thaw extrusion.

Phospholipid vesicles prepared by the freeze-thaw extrusion method contain internal solute concentrations which are much higher than the external values (entrapment ratios much greater than 1). This concentrating effect is a complex function of the total impermeant solute concentration in the medium used to prepare vesicles, the presence or absence of permeant solutes in the medium and the apparent competitive binding interactions between solutes and phospholipid. Increases in water phase solute concentration during freezing are thought to underlie the concentrating phenomenon, while osmotic pressure driven lysis of vesicles during thawing appears to limit its magnitude. By judicious selection of solute concentration and physical properties, further increases in the entrapment ratio should be obtainable, improving the usefulness of these vesicles as drug delivery vesicles and experimental systems.     

Effect of salicylate on the elasticity, bending stiffness, and strength of SOPC membranes

Salicylate is a small amphiphilic molecule which has diverse effects on membranes and membrane-mediated processes. We have utilized micropipette aspiration of giant unilamellar vesicles to determine salicylate's effects on lecithin membrane elasticity, bending rigidity, and strength. Salicylate effectively reduces the apparent area compressibility modulus and bending modulus of membranes in a dose-dependent manner at concentrations above 1 mM, but does not greatly alter the actual elastic compressibility modulus at the maximal tested concentration of 10 mM. The effect of salicylate on membrane strength was investigated using dynamic tension spectroscopy, which revealed that salicylate increases the frequency of spontaneous defect formation and lowers the energy barrier for unstable hole formation. The mechanical and dynamic tension experiments are consistent and support a picture in which salicylate disrupts membrane stability by decreasing membrane stiffness and membrane thickness. The tension-dependent partitioning of salicylate was utilized to calculate the molecular volume of salicylate in the membrane. The free energy of transfer for salicylate insertion into the membrane and the corresponding partition coefficient were also estimated, and indicated favorable salicylate-membrane interactions. The mechanical changes induced by salicylate may affect several biological processes, especially those associated with membrane curvature and permeability.     

Swelling-activated pathways in human T-lymphocytes studied by cell volumetry and electrorotation

Small organic solutes, including sugar derivatives, amino acids, etc., contribute significantly to the osmoregulation of mammalian cells. The present study explores the mechanisms of swelling-activated membrane permeability for electrolytes and neutral carbohydrates in Jurkat cells. Electrorotation was used to analyze the relationship between the hypotonically induced changes in the electrically accessible surface area of the plasma membrane (probed by the capacitance) and its permeability to the monomeric sugar alcohol sorbitol, the disaccharide trehalose, and electrolyte. Time-resolved capacitance and volumetric measurements were performed in parallel using media of different osmolalities containing either sorbitol or trehalose as the major solute. Under mild hypotonic stress in 200 mOsm sorbitol or trehalose solutions, the cells accomplished regulatory volume decrease by releasing cytosolic electrolytes presumably through pathways activated by the swelling-mediated retraction of microvilli. This is suggested by a rapid decrease of the area-specific membrane capacitance C(m) (microF/cm2). The cell membrane was impermeable to both carbohydrates in 200 mOsm media. Whereas trehalose permeability remained also very poor in 100 mOsm medium, extreme swelling of cells in a strongly hypotonic solution (100 mOsm) led to a dramatic increase in sorbitol permeability as evidenced by regulatory volume decrease inhibition. The different osmotic thresholds for activation of electrolyte release and sorbitol influx suggest the involvement of separate swelling-activated pathways. Whereas the electrolyte efflux seemed to utilize pathways preexisting in the plasma membrane, putative sorbitol channels might be inserted into the membrane from cytosolic vesicles via swelling-mediated exocytosis, as indicated by a substantial increase in the whole-cell capacitance C(C) (pF) in strongly hypotonic solutions.     

Physicochemical Factors Controlling the Activity and Energy Coupling of an Ionic Strength-gated ATP-binding Cassette (ABC) Transporter

Cells control their volume through the accumulation of compatible solutes. The bacterial ATP-binding cassette transporter OpuA couples compatible solute uptake to ATP hydrolysis. Here, we study the gating mechanism and energy coupling of OpuA reconstituted in lipid nanodiscs. We show that anionic lipids are essential both for the gating and the energy coupling. The tight coupling between substrate binding on extracellular domains and ATP hydrolysis by cytoplasmic nucleotide-binding domains allows the study of transmembrane signaling in nanodiscs. From the tight coupling between processes at opposite sides of the membrane, we infer that the ATPase activity of OpuA in nanodiscs reflects solute translocation. Intriguingly, the substrate-dependent, ionic strength-gated ATPase activity of OpuA in nanodiscs is at least an order of magnitude higher than in lipid vesicles (i.e. with identical membrane lipid composition, ionic strength, and nucleotide and substrate concentrations). Even with the chemical components the same, the lateral pressure (profile) of the nanodiscs will differ from that of the vesicles. We thus propose that membrane tension limits translocation in vesicular systems. Increased macromolecular crowding does not activate OpuA but acts synergistically with ionic strength, presumably by favoring gating interactions of like-charged surfaces via excluded volume effects.     

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.     

Fusion of phospholipid vesicles with a planar membrane depends on the membrane permeability of the solute used to create the osmotic pressure

Phospholipid vesicles fuse with a planar membrane when they are osmotically swollen. Channels in the vesicle membrane are required for swelling to occur when the vesicle-containing compartment is made hyperosmotic by adding a solute (termed an osmoticant). We have studied fusion using two different channels, porin, a highly permeable channel, and nystatin, a much less permeable channel. We report that an osmoticant's ability to support fusion (defined as the magnitude of osmotic gradient necessary to obtain sustained fusion) depends on both its permeability through lipid bilayer as well as its permeability through the channel by which it enters the vesicle interior. With porin as the channel, formamide requires an osmotic gradient about ten times that required with urea, which is approximately 1/40th as permeant as formamide through bare lipid membrane. When nystatin is the channel, however, fusion rates sustained by osmotic gradients of formamide are within a factor of two of those obtained with urea. Vesicles containing a porin-impermeant solute can be induced to swell and fuse with a planar membrane when the impermeant bathing the vesicles is replaced by an isosmotic quantity of a porin-permeant solute. With this method of swelling, formamide is as effective as urea in obtaining fusion. In addition, we report that binding of vesicles to the planar membrane does not make the contact region more permeable to the osmoticant than is bare lipid bilayer. In the companion paper, we quantitatively account for the observation that the ability of a solute to promote fusion depends on its permeability properties and the method of swelling. We show that the intravesicular pressure developed drives fusion.     

Osmotic stress as a mechanism of freezing injury

When red cells are suspended in solutions of nonpenetrating solutes of osmolality in excess of 1300 mosm, changes in membrane permeability are seen: there is an influx of extracellular solute, cell volume increases, and the cells will hemolyze on return to isotonic suspension. Furthermore, if cells suspended in such a solution are exposed to a downward temperature change (thermal shock), many will hemolyze.     

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.     

Electrostatic forces control the penetration of membranes by charged solutes

Using fluorescent, anionic dyes such as carboxyfluorescein as model solutes, it is shown that the forces allowing such solutes to be retained within sealed lipid vesicles, against a large concentration gradient, can be primarily electrostatic in nature. At temperatures distant from that of the ordered-fluid lipid phase transition a small number of the anionic dye molecules trapped within lipid vesicles are capable of traversing the lipid bilayer and establishing an electrical diffusion potential across the membrane. Further solute movement can then only occur with the concomitant permeation of ions which restore electrical balance. A significant flux of dye can be triggered by (a) increasing the permeability of the membrane to ions (for example by the addition of ionophores such as gramicidin, or by allowing the lipid to approach a phase transition) or by (b) adding lipophilic counterions such as tetraphenylborate or dinitrophenol to the system.     

Electrostatic forces control the penetration of membranes by charged solutes

Using fluorescent, anionic dyes such as carboxyfluorescein as model solutes, it is shown that the forces allowing such solutes to be retained within sealed lipid vesicles, against a large concentration gradient, can be primarily electrostatic in nature. At temperatures distant from that of the ordered-fluid lipid phase transition a small number of the anionic dye molecules trapped within lipid vesicles are capable of traversing the lipid bilayer and establishing an electrical diffusion potential across the membrane. Further solute movement can then only occur with the concomitant permeation of ions which restore electrical balance. A significant flux of dye can be triggered by (a) increasing the permeability of the membrane to ions (for example by the addition of ionophores such as gramicidin, or by allowing the lipid to approach a phase transition) or by (b) adding lipophilic counterions such as tetraphenylborate or dinitrophenol to the system.     

Change in membrane elastic modulus on activation of glucose transport system of brush border membrane vesicles studied by osmotic swelling and dynamic light scattering.

The cell membrane having a transport system is inferred to be flexible when its function is being activated. For the brush border membrane vesicles prepared from rat small intestine, which have the co-transport system of Na+ and glucose, the membrane elasticity was measured as a function of the d-glucose concentration in the presence of Na+ ions. The elastic modulus of the vesicle membrane was obtained by an osmotic swelling method. Osmolality was changed by diluting the extravesicular d-mannitol concentration. The change in the diameter of the membrane vesicle in response to an osmolality change was measured by the dynamic light-scattering method. The elastic modulus of the vesicle membrane decreased from 150 dyn/cm to 80 (45) dyn/cm with the increase of d-glucose, from 0 mM to 10(30) mM in the presence of 10 mM Na+ ions. On the other hand, in the presence of 1 mM phlorizin, a glucose-transport inhibitor, the elastic modulus remained at a constant value of 160 dyn/cm in the same range of the d-glucose concentration. This indicates that the vesicle membrane becomes flexible when its transport function is activated. In a broad osmolality range, the brush border membrane vesicle showed cycles of "swell-burst-reseal". The vesicle membrane became flexible after every cycle, namely, the modulus was 150, 120, and 55 in units of dyn/cm in the presence of 1 mM d-glucose and 50 mM Na+ ions.     

Transport competence of plasma membrane vesicles from cultured human fibroblasts

We obtained plasma membranes from cultured human skin fibroblasts. The preparation was enriched 10-fold with about 40 percent yield. There was minimal contamination with other cell membranes. Various observations indicated vesicular conformation of a portion of the plasma membranes, notably by electron microscopy and from the effect of osmotic pressure on the distribution of solutes between mass and medium at equilibrium. Other studies indicated that these fibroblast plasma membrane vesicles retained mediated transport processes for a variety of substrates. The evidence included: stereospecific and temperature-dependent uptake of glucose; dependence of L-alanine uptake on sodium ion and an inward-directed transmembrane Na+ gradient; stimulation of L-alanine uptake, with overshoot, by enhancement of the interior-negative transmembrane potential; concentration dependent uptake of methotrexate with apparent competitive inhibition by folinic acid; stimulation of L-lysine uptake by trans-L-arginine. These findings indicate that human fibroblast plasma membrane vesicles could be used to study membrane transport processes and, perhaps, expression of mutant genes that cause inborn errors of transport.     

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.