The Mechanism of Isotonic Water Transport

The mechanism by which active solute transport causes water transport in isotonic proportions across epithelial membranes has been investigated. The principle of the experiments was to measure the osmolarity of the transported fluid when the osmolarity of the bathing solution was varied over an eightfold range by varying the NaCl concentration or by adding impermeant non-electrolytes. An in vitro preparation of rabbit gall bladder was suspended in moist oxygen without an outer bathing solution, and the pure transported fluid was collected as it dripped off the serosal surface. Under all conditions the transported fluid was found to approximate an NaCl solution isotonic to whatever bathing solution used. This finding means that the mechanism of isotonic water transport in the gall bladder is neither the double membrane effect nor co-diffusion but rather local osmosis. In other words, active NaCl transport maintains a locally high concentration of solute in some restricted space in the vicinity of the cell membrane, and water follows NaCl in response to this local osmotic gradient. An equation has been derived enabling one to calculate whether the passive water permeability of an organ is high enough to account for complete osmotic equilibration of actively transported solute. By application of this equation, water transport associated with active NaCl transport in the gall bladder cannot go through the channels for water flow under passive conditions, since these channels are grossly too impermeable. Furthermore, solute-linked water transport fails to produce the streaming potentials expected for water flow through these passive channels. Hence solute-linked water transport does not occur in the passive channels but instead involves special structures in the cell membrane, which remain to be identified.     

Epithelial water transport in a balanced gradient system.

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

Standing-gradient osmotic flow. A mechanism for coupling of water and solute transport in epithelia

At the ultrastructural level, epithelia performing solute-linked water transport possess long, narrow channels open at one end and closed at the other, which may constitute the fluid transport route (e.g., lateral intercellular spaces, basal infoldings, intracellular canaliculi, and brush-border microvilli). Active solute transport into such folded structures would establish standing osmotic gradients, causing a progressive approach to osmotic equilibrium along the channel's length. The behavior of a simple standing-gradient flow system has therefore been analyzed mathematically because of its potential physiological significance. The osmolarity of the fluid emerging from the channel's open end depends upon five parameters: channel length, radius, and water permeability, and solute transport rate and diffusion coefficient. For ranges of values of these parameters encountered experimentally in epithelia, the emergent osmolarity is found by calculation to range from isotonic to a few times isotonic; i.e., the range encountered in epithelial absorbates and secretions. The transported fluid becomes more isotonic as channel radius or solute diffusion coefficient is decreased, or as channel length or water permeability is increased. Given appropriate parameters, a standing-gradient system can yield hypertonic fluids whose osmolarities are virtually independent of transport rate over a wide range, as in distal tubule and avian salt gland. The results suggest that water-to-solute coupling in epithelia is due to the ultrastructural geometry of the transport route.     

The osmotic migration of cells in a solute gradient.

The effect of a nonuniform solute concentration on the osmotic transport of water through the boundaries of a simple model cell is investigated. A system of two ordinary differential equations is derived for the motion of a single cell in the limit of a fast solute diffusion, and an analytic solution is obtained for one special case. A two-dimensional finite element model has been developed to simulate the more general case (finite diffusion rates, solute gradient induced by a solidification front). It is shown that the cell moves to regions of lower solute concentration due to the uneven flux of water through the cell boundaries. This mechanism has apparently not been discussed previously. The magnitude of this effect is small for red blood cells, the case in which all of the relevant parameters are known. We show, however, that it increases with cell size and membrane permeability, so this effect could be important for larger cells. The finite element model presented should also have other applications in the study of the response of cells to an osmotic stress and for the interaction of cells and solidification fronts. Such investigations are of major relevance for the optimization of cryopreservation processes.     

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.     

Osmotic Transport across Cell Membranes in Nondilute Solutions: A New Nondilute Solute Transport Equation

The fundamental physical mechanisms of water and solute transport across cell membranes have long been studied in the field of cell membrane biophysics. Cryobiology is a discipline that requires an understanding of osmotic transport across cell membranes under nondilute solution conditions, yet many of the currently-used transport formalisms make limiting dilute solution assumptions. While dilute solution assumptions are often appropriate under physiological conditions, they are rarely appropriate in cryobiology. The first objective of this article is to review commonly-used transport equations, and the explicit and implicit assumptions made when using the two-parameter and the Kedem-Katchalsky formalisms. The second objective of this article is to describe a set of transport equations that do not make the previous dilute solution or near-equilibrium assumptions. Specifically, a new nondilute solute transport equation is presented. Such nondilute equations are applicable to many fields including cryobiology where dilute solution conditions are not often met. An illustrative example is provided. Utilizing suitable transport equations that fit for two permeability coefficients, fits were as good as with the previous three-parameter model (which includes the reflection coefficient, σ). There is less unexpected concentration dependence with the nondilute transport equations, suggesting that some of the unexpected concentration dependence of permeability is due to the use of inappropriate transport equations.     

Distribution of osmotic flow in stomach and gallbladder

Stomach and gallbladder actively transport fluids which are nearly isotonic to plasma. Consideration of the measured areas of the appropriate transporting surfaces gives a more realistic view of the osmotic gradient required to account for the observed net flow of water. Simple osmosis may be adequate if the transporting membrane has an osmotic permeability in the range observed for synthetic lecithin-cholesterol bilayer membranes.     

Analysis of time hierarchy in plant cell volume changes

A simple model of plant cell volume changes is presented. It is based on Kedem-Katchalsky equations for water and solute transport and on linear approximation of the dependence of intracellular hydrostatic pressure on the cell volume. Active transport of solute is also included. The time hierarchy within the system is analyzed by appropriate normalization of variables and by the assessment of the numerical values of model coefficients. The dynamics of the system comprises a slow process of solute exchange and a fast process of water transport. This explains the wellknown biphasic response of the cell volume to a sudden change in external conditions. An approximation of equations describing the system behaviour on the basis of the Tikhonov's theorem is proposed. The approximative solution is compared with the exact numerical solution of the original equations. The approximation is very good under physiological conditions, but it ceases to hold when the solute permeability of the cell membrane increases causing the breakdown of the entire time hierarchy within the system.     

Models for coupling of salt and water transport; Proximal tubular reabsorption in Necturus kidney

Models for coupling of salt and water transport are developed with two important assumptions appropriate for leaky epithelia. (a) The tight junction is permeable to both sale and water. (b) Active Na transport into the lateral speces is assumed to occur uniformly along the length of the channel. The proposed models deal specifically with the intraepithelial mechanism of proximal tubular resbsorption in the Necturus kidney although they have implications for epithelial transport in the gallbladder and small intestine as well. The first model (continuous version) is similar to the standing gradient model devised by Diamond and Bossert but used different boundary conditions. In contrast to Diamond and Bossert's model, the predicted concentration profiles are relatively flat with no sizable gradients along the interspace. The second model (compartment version) expands Curran's model of epithelial salt and water transport by including additional compartments and considering both electrical and chemical driving forces for individual Na and Cl ions as well as hydraulic and osmotic driving forces for water. In both models, ion and water fluxes are investigated as a function of the transport parameters. The behavior of the models is consistent with previously suggested mechanisms for the control of net transport, particularly during saline diuresis. Under all conditions the predicted ratio of net solute to solvent flux, or emergent concentration, deviates from exact isotonicity (except when the basement membrane has an appreciable salt reflection coefficient). However, the degree of hypertonicity may be small enough to be experimentally indistinguishable from isotonic transport.     

Transport of Salt and Water in Rabbit and Guinea Pig Gall Bladder

A simple and reproducible method has been developed for following fluid transport by an in vitro preparation of mammalian gall bladder, based upon weighing the organ at 5 minute intervals. Both guinea pig and rabbit gall bladders transport NaCl and water in isotonic proportions from lumen to serosa. In the rabbit bicarbonate stimulates transport, but there is no need for exogenous glucose. The transport rate is not affected by removal of potassium from the bathing solutions. Albumin causes a transient weight loss from the gall bladder wall, apparently by making the serosal smooth muscle fibers contract. Active NaCl transport can carry water against osmotic gradients of up to two atmospheres. Under passive conditions water may also move against its activity gradient in the presence of a permeating solute. The significance of water movement against osmotic gradients during active solute transport is discussed.     

Isotonic Water Transport in Secretory Epithelia ,

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

Roles of Aquaporin-3 Water Channels in Volume-Regulatory Water Flow in a Human Epithelial Cell Line

Membrane water transport is an essential event not only in the osmotic cell volume change but also in the subsequent cell volume regulation. Here we investigated the route of water transport involved in the regulatory volume decrease (RVD) that occurs after osmotic swelling in human epithelial Intestine 407 cells. The diffusion water permeability coefficient (Pd) measured by NMR under isotonic conditions was much smaller than the osmotic water permeability coefficient (Pf) measured under an osmotic gradient. Temperature dependence of Pf showed the Arrhenius activation energy (Ea) of a low value (1.6 kcal/mol). These results indicate an involvement of a facilitated diffusion mechanism in osmotic water transport. A mercurial water channel blocker (HgCl₂) diminished the Pf value. A non-mercurial sulfhydryl reagent (MMTS) was also effective. These blockers of water channels suppressed the RVD. RT-PCR and immunocytochemistry demonstrated predominant expression of AQP3 water channel in this cell line. Downregulation of AQP3 expression induced by treatment with antisense oligodeoxynucleotides was found to suppress the RVD response. Thus, it is concluded that AQP3 water channels serve as an essential pathway for volume-regulatory water transport in, human epithelial cells.     

A model of NaCl and water flow through paracellular pathways of renal proximal tubules.

To explain how hydrostatic pressure differences between tubule lumen and interstitium modulate isotonic reabsorption rates, we developed a model of NaCl and water flow through paracellular pathways of the proximal tubule. Structural elements of the model are a tight junction membrane, an intercellular channel whose walls transport NaCl actively at a constant rate, and a basement membrane. Equations of change were derived for the channel, boundary conditions were formulated from irreversible thermodynamics, and a pressure-area relationship typical of thin-walled tubing was assumed. The boundary value problem was solved numerically. The principal conclusions are: 1) channel NaCl concentration must remain within a few mOsm of isotonic values for reabsorption rates to be modulated by transtubular pressure differences known to affect this system: 2) basement membrane and channel wall parameters determine reabsorbate tonicity; tight junction parameters affect the sensitivity of reabsorption to transmural pressure; 3) channel NaCl concentration varies inversely with transmural pressure difference; this concentration variation controls NaCl diffusion through the tight junction; 4) modulation of NaCl diffusion through the tight junction controls the rate of isotonic reabsorption; modulation of water flow can increase sensitivity to transmural pressure; 5) no pressure-induced change in permeability of the tight junction or basement membrane is needed for pressure to modulate reabsorption; and 6) system performance is indifferent to the distribution of active transport sites, to the numerical value of the compliance function, and to the relationship between lumen and cell pressures.     

Permeability studies on red cell membranes of dog, cat, and beef

Water permeability coefficients of dog, cat, and beef red cell membranes have been measured under an osmotic pressure gradient. The measurements employed a rapid reaction stop flow apparatus with which cell shrinking was measured under a relative osmotic pressure gradient of 1.25 to 1.64 times the isosmolar concentration. For the dog red cell the osmotic permeability coefficient is 0.36 cm⁴/(sec, osmol). The water permeability coefficient for the dog red cell under a diffusion gradient was also measured (rate constant = 0.10/msec). The ratio between the two permeabilities was used to calculate an equivalent pore radius of 5.9 A. This value agrees welt with an equivalent pore radius of 6.2 A obtained from reflection coefficients of nonelectrolyte water-soluble molecules, and is consistent with data on the permeability of the dog red cell membrane to glucose. These data provide evidence supporting the existence of equivalent pores in single biological membranes.     

ULTRASTRUCTURAL STUDIES OF VASOPRESSIN EFFECT ON ISOLATED PERFUSED RENAL COLLECTING TUBULES OF THE RABBIT

Isolated cortical collecting tubules from rabbit kidney were studied during perfusion with solutions made either isotonic or hypotonic to the external bathing medium. Examination of living tubules revealed a reversible increase in thickness of the cellular layer, prominence of lateral cell membranes, and formation of intracellular vacuoles during periods of vasopressin-induced osmotic water transport. Examination in the electron microscope revealed that vasopressin induced no changes in cell structure in collecting tubules in the absence of an osmotic difference and significant bulk water flow across the tubule wall. In contrast, tubules fixed during vasopressin-induced periods of high osmotic water transport showed prominent dilatation of lateral intercellular spaces, bulging of apical cell membranes into the tubular lumen, and formation of intracellular vacuoles. It is concluded that the ultrastructural changes are secondary to transepithelial bulk water flow and not to a direct effect of vasopressin on the cells, and that vasopressin induces osmotic flow by increasing water permeability of the luminal cell membrane. The lateral intercellular spaces may be part of the pathway for osmotically induced transepithelial bulk water flow.     

Thermodynamic Model Equations for Heterogeneous Multicomponent Non-Ionic Solution Transport in a Multimembrane System

Non-equilibrium thermodynamic model equations for non-ionic and heterogeneous n-component solution transport in a m-membrane system are presented. This model is based on two equations. The first one describes the volume transport of the solution and the second the transport of the solute. Definitions of the hydraulic permeability, reflection and diffusive permeability coefficients of the m-membrane system and relations between the coefficients of the m-membrane system and the respective membranes of the system are also given. The validity of this model for binary and ternary solutions was verified, using a double-membrane cell with a horizontally mounted membrane. In the cell, volume and solute fluxes were measured as a function of concentration and gravitational configuration.     

Responding phospholipid membranes--interplay between hydration and permeability.

Osmotic forces are important in regulating a number of physiological membrane processes. The effect of osmotic pressure on lipid phase behavior is of utmost importance for the extracellular lipids in stratum corneum (the outer part of human skin), due to the large gradient in water chemical potential between the water-rich tissue on the inside, and the relative dry environment on the outside of the body. We present a theoretical model for molecular diffusional transport over an oriented stack of two-component lipid bilayers in the presence of a gradient in osmotic pressure. This gradient serves as the driving force for diffusional motion of water. It also causes a gradient in swelling and phase transformations, which profoundly affect the molecular environment and thus the local diffusion properties. This feedback mechanism generates a nonlinear transport behavior, which we illustrate by calculations of the flux of water and solute (nicotine) through the bilayer stack. The calculated water flux shows qualitative agreement with experimental findings for water flux through stratum corneum. We also present a physical basis for the occlusion effect. Phase behavior of binary phospholipid mixtures at varying osmotic pressures is modeled from the known interlamellar forces and the regular solution theory. A first-order phase transformation from a gel to a liquid--crystalline phase can be induced by an increase in the osmotic pressure. In the bilayer stack, a transition can be induced along the gradient. The boundary conditions in water chemical potential can thus act as a switch for the membrane permeability.     

Routes of epithelial water flow: aquaporins versus cotransporters

The routes water takes through membrane barriers is still a matter of debate. Although aquaporins only allow transmembrane water movement along an osmotic gradient, cotransporters are believed to be capable of water transport against the osmotic gradient. Here we show that the renal potassium-chloride-cotransporter (KCC1) does not pump a fixed amount of water molecules per movement of one K⁺ and one Cl⁻, as was reported for the analogous transporter in the choroid plexus. We monitored water and potassium fluxes through monolayers of primary cultured renal epithelial cells by detecting tiny solute concentration changes in the immediate vicinity of the monolayer. KCC1 extruded K⁺ ions in the presence of a transepithelial K⁺ gradient, but did not transport water. KCC1 inhibition reduced epithelial osmotic water permeability P_f by roughly one-third, i.e., the effect of inhibitors was small in resting cells and substantial in hormonal stimulated cells that contained high concentrations of aquaporin-2 in their apical membranes. The furosemide or DIOA (dihydroindenyl-oxy-alkanoic acid)-sensitive water flux was much larger than expected when water passively followed the KCC1-mediated ion flow. The inhibitory effect of these drugs on water flux was reversed by the K⁺-H⁺ exchanger nigericin, indicating that KCC1 affects water transport solely by K⁺ extrusion. Intracellular K⁺ retention conceivably leads to cell swelling, followed by an increased rate of endocytic AQP2 retrieval from the apical membrane.     

Analysis of proximal tubule salt and water transport in standing droplets.

A mathematical model has been developed describing solute and water movement in the renal proximal tubule standing droplet experiment. The model explicitly incorporates the constraint of isosmotic reabsorption. Solute asymmetry due to the unequal distribution of protein, bicarbonate and other solutes between plasma and the standing droplet is shown to be one of the major reabsorptive forces; however, the introduction of an additional reabsorptive mechanism into the system equations is required in order to obtain a quantitative fit with experimental observations. The model demonstrates that limiting concentration gradients can be obtained in the absence of active transport and that their magnitudes will vary inversely with the permeability of the poorly permeant solute. Conversely, situations can occur where active transport will not elicit a limiting gradient. Consequently, previous interpretations of the meaning of limiting gradients and their magnitudes need to be reconsidered. The model further predicts that the technique for measuring non-electrolyte permeability using standing droplet experiments is likely to underestimate the true permeability. Finally, it is shown that a previous theoretical model of standing droplets, which does not explicitly include the constraint of isomotic reabsorption, cannot fit experimental data from proximal tubules.     

Studies on the Movement of Water through the Isolated Toad Bladder and Its Modification by Vasopressin

Measurements of diffusion permeability and of net transfer of water have been made across the isolated urinary bladder of the toad, Bufo marinus, and the effects thereon of mammalian neurohypophyseal hormone have been examined. In the absence of a transmembrane osmotic gradient, vasopressin increases the unidirectional flux of water from a mean of 340 to a mean of 570 µl per cm² per hour but the net water movement remains essentially zero. In the presence of an osmotic gradient but without hormone net transfer of water remains very small. On addition of hormone large net fluxes of water occur; the magnitude of which is linearly proportional to the osmotic gradient. The action of the hormone on movement of water is not dependent on the presence of sodium or on active transport of sodium. Comparison of the net transport of water and of unidirectional diffusion permeability of the membrane to water indicates that non-diffusional transport must predominate as the means by which net movement occurs in the presence of an osmotic gradient. An action of the hormone on the mucosal surface of the bladder wall is demonstrated. The effects of the hormone on water movement are most simply explained as an action to increase the permeability and porosity of the mucosal surface of the membrane.