Functional consequences of ultrastructural geometry in "backwards" fluid-transporting epithelia

Many fluid-transporting epithelia possess dead-end, long, and narrow channels opening in the direction to which fluid is being transported (basal infoldings, lateral intercellular spaces, etc.). These channels have been thought to possess geometrical significance as standing-gradient flow systems, in which active solute transport into the channel makes the channel contents hypertonic and permits water-to-solute coupling. However, some secretory epithelia (choroid plexus, Malpighian tubule, rectal gland, etc.) have "backwards" channels opening in the direction from which fluid is being transported. It is shown that these backwards channels can function as standing-gradient flow systems in which solute transport out of the channel makes the channel contents hypotonic and results in coupled water flow into the channel mouth. The dependence of the transported osmolarity (isotonic or hypertonic) on channel radius, length, and other parameters is calculated for backwards channels for values of these parameters in the physiological range. In addition to backwards channels' being hypotonic rather than hypertonic, they are predicted to differ from "forwards" channels in that some restrictions are imposed by the problem of solute exhaustion, and in the presence of a sweeping-in effect on other solutes which limits the solutes that may be transported.     

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.     

Coupled water transport in standing gradient models of the lateral intercellular space.

A standing gradient model of the lateral intercellular space is presented which includes a basement membrane of finite solute permeability. The solution to the model equations is estimated analytically using the "isotonic convection approximation" of Segel. In the case of solute pumps uniformly distributed along the length of the channel, the achievement of isotonic transport depends only on the water permeability of the cell membranes. The ability of the model to transport water against an adverse osmotic gradient is the sum of two terms: The first term is simply that for a well-stirred compartment model and reflects basement membrane solute permeability. The second term measures the added strength due to diffusion limitation within the interspace. It is observed, however, that the ability for uphill water transport due to diffusion limitation is diminished by high cell membrane water permeability. For physiologically relevant parameters, it appears that the high water permeability required for isotonic transport renders the contribution of the standing gradient relatively ineffective in transport against an osmotic gradient. Finally, when the model transports both isotonically and against a gradient, it is shown that substantial intraepithelial solute polarization effects are unavoidable. Thus, the measured epithelial water permeability will grossly underestimate the water permeability of the cell membranes. The accuracy of the analytic approximation is demonstrated by numerical solution of the complete model equations.     

Standing-gradient osmotic flow Examination of its validity using an analytical method

The solutions to the non-linear differential equations governing solute-solvent coupling in the intercellular spaces of epithelial layers have been obtained by using an analytical method, rather than the usual numerical ones. When the present series solution includes second-order correction terms, the concentration and velocity profiles obtained by the analytical method agree very well with those coming from numerical solutions. This method has further allowed us to examine the standing-gradient hypothesis when applied to the backwards fluid transport system of the corneal endothelium. With the information presently available for the relevant parameters (osmotic permeability, rate of transport, radius and length of the spaces, and location of the pumping sites), near-isotonicity of the transported fluid would not be explained by the standing-gradient model.     

A New Approach to Epithelial Isotonic Fluid Transport: An Osmosensor Feedback Model

A model for control of the transport rate and osmolarity of epithelial fluid (isotonic transport) is presented by using an analogy with the control of temperature and flow rate in a shower. The model brings recent findings and theory concerning the role of aquaporins in epithelia together with measurements of epithelial paracellular flow into a single scheme. It is not based upon osmotic equilibration across the epithelium but rather on the function of aquaporins as osmotic sensors that control the tonicity of the transported fluid by mixing cellular and paracellular flows, which may be regarded individually as hyper- and hypo-tonic fluids, to achieve near-isotonicity. The system is built on a simple feedback loop and the quasi-isotonic behavior is robust to the precise values of most parameters. Although the two flows are separate, the overall fluid transport rate is governed by the rate of salt pumping through the cell. The model explains many things: how cell pumping and paracellular flow can be coupled via control of the tight junctions; how osmolarity is controlled without depending upon the precise magnitude of membrane osmotic permeability; and why many epithelia have different aquaporins at the two membranes.The model reproduces all the salient features of epithelial fluid transport seen over many years but also indicates novel behavior that may provide a subject for future research and serve to distinguish it from other schemes such as simple osmotic equilibration. Isotonic transport is freed from constraints due to limited permeability of the membranes and the precise geometry of the system. It achieves near-isotonicity in epithelia in which partial water transport by co-transporters may be present, and shows apparent electro-osmotic effects. The model has been developed with a minimum of parameters, some of which require measurement, but the model is flexible enough for the basic idea to be extended both to complex systems of water and salt transport that still await a clear explanation, such as intestine and airway, and to systems that may lack aquaporins or use other sensors.     

Osmotic water flow in leaky epithelia

I review three currently unsolved and controversial problems in understanding solute-linked water transport in epithelia. 1. Values of osmotic water permeability (Posm) calculated from steady-state osmotic flow in response to a gradient of a probe molecule tend to be underestimates, because of three unstirred-layer (USL) effects. These are: dissipation of the probe's gradient by diffusion in USL's; reduction of the probe's gradient, due to the sweeping-away effect of water flow generated by the probe itself; and solute polarization (creation of an opposing gradient of an initially symmetrically distributed solute by the sweeping-away effect). These errors increase with probe permeability, USL thickness, Posm, and concentration ratio of symmetrically distributed solute to probe, and vary inversely as the fractional area available for water flow (e.g., lateral intercellular space width). The form of an osmotic transient, and the possibility of extracting a true Posm value from the transient, depend on the relative values of three time constants: those for solute diffusion in USL's, for solute polarization by water flow in USL's and for measuring water flow. Sweeping-away effects cause major underestimates (by one or more orders of magnitude) in epithelial Posm determinations, as shown by apparent streaming potentials during osmotic flow and by transiently reversed flows after removal of the proble. True Posm values for leaky epithelia probably exceed 10(-3) or 10(-2) cm/sec.osm. The necessary conditions for resolving osmotic transients are set out. 2. I illustrate the difficulties in deciding what fraction of transepithelial water flow is via the cells, and what fraction via the junctions. There is no existing method for answering this question. 3. Controversies about the validity, or need for modification, of the standing-gradient theory are discussed. Progress in this field requires new methods: to resolve osmotic transients; to separate transcellular and transjunctional water flows; and to measure solute concentrations in lateral intercellular spaces directly.     

Salt-water coupling in leaky epithelia

Summary The theory of quasi-isotonic transport by cellular osmosis (the standing-gradient theory) has been challenged on the grounds that the osmotic permeabilities of the mucosal and interspace membranes are too low; if they were as high as the theory requires then the osmotic permeability of the whole epithelium would be 2–3 orders of magnitude higher than observed. This objection has basically been accepted for it is now claimed that these enormous permeabilities do exist, but are masked by unstirred-layer effects; I show that this is incorrect because unstirredlayer corrections are small and that the situation has not changed since 1975.The view that the route of fluid transport is junctional is replacing the cellular theory, and trans-junctional water flows seem to account for major fractions of the flow in various epithelia. I argue on grounds of general theory that these are unlikely to be osmotic flows because the junctional pores cannot satisfy both the osmotic and diffusive properties required of them, but the basic osmotic theory is also rather vague here.Non-osmotic theories, if junctional flow is accepted, must be either electro-kinetic or peristaltic.     

On the influence of a leaky tight junction on water and solute transport in epithelia

The role of a leaky tight junction in epithelia is examined by considering the flow of water and solute through a channel consisting of two sections representing the intercellular space and tight junction. Two cases are considered, flow through a channel with a circular cross-section and flow between parallel planes. Analytical solutions are obtained using the isotonic convection approximation. The flow is driven by active transport of solute and imposed concentration and pressure differences. Particular attention is paid to the flux of solute through the tight junction. It is shown that the shape of the channel cross-section is important.The theory is applied to the rat proximal tube epithelium. It is deduced that the emergent osmolarity is close to that predicted for a closed tight junction, but that transepithelial hydrostatic pressure differences are potentially important. The influence of transepithelial concentration differences appears to be unimportant in this model.     

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.     

The Ultrastructural Route of Fluid Transport in Rabbit Gall Bladder

The route of fluid transport across the wall of the rabbit gall bladder has been examined by combined physiological and morphological techniques. Fluid transport was either made maximal or was inhibited by one of six physiological methods (metabolic inhibition with cyanide-iodoacetate, addition of ouabain, application of adverse osmotic gradients, low temperature, replacement of Cl by SO₄, or replacement of NaCl by sucrose). Then the organ was rapidly fixed and subsequently embedded, sectioned, and examined by light and electron microscopy. The structure of the gall bladder is presented with the aid of electron micrographs, and changes in structure are described and quantitated. The most significant morphological feature seems to be long, narrow, complex channels between adjacent epithelial cells; these spaces are closed by tight junctions at the luminal surface of the epithelium but are open at the basal surface. They are dilated when maximal fluid transport occurs, but are collapsed under all the conditions which inhibit transport. Additional observations and experiments make it possible to conclude that this dilation is the result of fluid transport through the spaces. Evidently NaCl is constantly pumped from the epithelial cells into the spaces, making them hypertonic, so that water follows osmotically. It is suggested that these spaces may represent a "standing-gradient flow system," in which osmotic equilibration takes place progressively along the length of a long channel.     

A central role for cell osmolarity in isotonic fluid transport across epithelia

Previous theoretical models for solute-solvent coupling in epithelia that dealt only with the intercellular channel did not predict isotonic transport except when very high cell membrane permeabilities were assumed. To study this issue, we have developed the formalisms for osmotic equilibration at an alternative location, the apical cell membrane (including its adjacent unstirred layer), which are somewhat simpler than those for the channel. Much as in other models, we confirm that only rather unrealistically high values of the cell membrane permeability lead to isotonic transport. We have also found, however, that isotonic transport can occur at much lower values of the cell membrane permeability if the concentration within the cell differs slightly from that in the ambient medium. This emphasizes the importance of incorporating the intracellular concentration as an integral part to any transport model, such as in the present apical membrane version of local osmosis.     

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.     

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.     

Isosmotic volume reabsorption in rat proximal tubule

A theoretical model incorporation both active and passive forces has been developed for fluid reabsorption from split oil droplets in rat intermediate and late proximal tubule. Of necessity, simplifying assumptions have been introduced; we have assumed that the epithelium can be treated as a single membrane and that the membrane "effective" HCO3 permeability is near zero. Based on this model with its underlying assumptions, the following conclusions are drawn. Regardless of the presence or absence of active NaCl transport, fluid reabsorption from the split oil droplet is isosmotic. The reabsorbate osmolarity can be affected by changes in tubular permeability parameters and applied forces but is not readily altered from an osmolarity essentially equal to that of plasma. In a split droplet, isosmotic flow need not be a special consequence of active Na transport, is not the result of a particular set of permeability properties, and is not merely a trivial consequence of a very high hydraulic conductivity; isosmotic flow can be obtained with hydraulic conductivity nearly an order of magnitude lower than that previously measured in the rat proximal convoluted tubule. Isosmotic reabsorption is, in part, the result of the interdependence of salt and water flows, their changing in parallel, and thus their ratio, the reabsorbate concentration being relatively invariant. Active NaCl transport can cause osmotic water flow by reducing the luminal fluid osmolarity. In the presence of passive forces the luminal fluid can be hypertonic to plasma, and active NaCl transport can still exert its osmotic effect on volume flow. There are two passive forces for volume flow: the Cl gradient and the difference in effective osmotic pressure; they have an approximately equivalent effect on volume flow. Experimentally, we have measured volume changes in a droplet made hyperosmotic by the addition of 50 mM NaCl; the experimental results are predicted reasonably well by our theoretical model.     

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.     

On the mechanism of fluid transport across corneal endothelium and epithelia in general

The mechanism by which fluid is transported across epithelial layers is still unclear. The prevalent idea is that fluid traverses these layers transcellularly, driven by local osmotic gradients secondary to electrolyte transport and utilizing the high osmotic permeability of aquaporins. However, recent findings that some aquaporin knockout mice epithelia transport fluid sow doubts on local osmosis. This review discusses recent evidence in corneal endothelium that points instead to electro-osmosis as the mechanism underlying fluid transport. In this concept, a local recirculating electrical current would result in electro-osmotic coupling at the level of the intercellular junctions, dragging fluid via the paracellular route. The text also mentions possible mechanisms for apical bicarbonate exit from endothelial cells, and discusses whether electro-osmosis could be a general mechanism.     

The osmotic behavior of corn mitochondria

The volume changes undergone by corn (Zea mays L.) mitochondria suspended in solutions of constant or varying osmolarity were studied. Within the range of osmotic pressure from 1.8 to 8.4 atmospheres, corn mitochondria behave as osmometers, if allowance is made for an osmotic “dead space” of about 6.9 μl/mg protein. The final equilibrium volume of mitochondria swollen in solutions containing both ribose and sucrose were shown to depend upon the concentration of impermeable solute (sucrose) present and not upon the concentration of ribose present. Osmotic reversibility was found for mitochondria swollen in isotonic solutions of KCI or ribose. The passive swelling of corn mitochondria may be due to the osmotic flow of water coupled to the diffusion of a permeable solute.     

Local Osmosis and Isotonic Transport

Osmotically driven water flow, u (cm/s), between two solutions of identical osmolarity, c_o (300 mM in mammals), has a theoretical isotonic maximum given by u = j/c_o, where j (moles/cm²/s) is the rate of salt transport. In many experimental studies, transport was found to be indistinguishable from isotonic. The purpose of this work is to investigate the conditions for u to approach isotonic. A necessary condition is that the membrane salt/water permeability ratio, ε, must be small: typical physiological values are ε = 10⁻³ to 10⁻⁵, so ε is generally small but this is not sufficient to guarantee near-isotonic transport. If we consider the simplest model of two series membranes, which secrete a tear or drop of sweat (i.e., there are no externally-imposed boundary conditions on the secretion), diffusion is negligible and the predicted osmolarities are: basal = c_o, intracellular ≈ (1 + ε)c_o, secretion ≈ (1 + 2ε)c_o, and u ≈ (1 − 2ε)j/c_o. Note that this model is also appropriate when the transported solution is experimentally collected. Thus, in the absence of external boundary conditions, transport is experimentally indistinguishable from isotonic. However, if external boundary conditions set salt concentrations to c_o on both sides of the epithelium, then fluid transport depends on distributed osmotic gradients in lateral spaces. If lateral spaces are too short and wide, diffusion dominates convection, reduces osmotic gradients and fluid flow is significantly less than isotonic. Moreover, because apical and basolateral membrane water fluxes are linked by the intracellular osmolarity, water flow is maximum when the total water permeability of basolateral membranes equals that of apical membranes. In the context of the renal proximal tubule, data suggest it is transporting at near optimal conditions. Nevertheless, typical physiological values suggest the newly filtered fluid is reabsorbed at a rate u ≈ 0.86 j/c_o, so a hypertonic solution is being reabsorbed. The osmolarity of the filtrate c_F (M) will therefore diminish with distance from the site of filtration (the glomerulus) until the solution being transported is isotonic with the filtrate, u = j/c_F.With this steady-state condition, the distributed model becomes approximately equivalent to two membranes in series. The osmolarities are now: c_F ≈ (1 − 2ε)j/c_o, intracellular ≈ (1 − ε)c_o, lateral spaces ≈ c_o, and u ≈(1 + 2ε)j/c_o. The change in c_F is predicted to occur with a length constant of about 0.3 cm. Thus, membrane transport tends to adjust transmembrane osmotic gradients toward εc_o, which induces water flow that is isotonic to within order ε. These findings provide a plausible hypothesis on how the proximal tubule or other epithelia appear to transport an isotonic solution.     

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.     

Contribution of solvent drag through intercellular junctions to absorption of nutrients by the small intestine of the rat

The lumen of the small intestine in anesthetized rats was recirculated with 50 ml perfusion fluid containing normal salts, 25 mM glucose and low concentrations of hydrophilic solutes ranging in size from creatinine (mol wt 113) to Inulin (mol wt 5500). Ferrocyanide, a nontoxic, quadrupally charged anion was not absorbed; it could therefore be used as an osmotically active solute with reflection coefficient of 1.0 to adjust rates of fluid absorption, Jv, and to measure the coefficient of osmotic flow, Lp. The clearances from the perfusion fluid of all other test solutes were approximately proportional to Jv. From Lp and rates of clearances as a function of Jv and molecular size we estimate (a) the fraction of fluid absorption which passes paracellularly (approx. 50%), (b) coefficients of solvent drag of various solutes within intercellular junctions, (c) the equivalent pore radius of intercellular junctions (50 A) and their cross sectional area per unit path length (4.3 cm per cm length of intestine). Glucose absorption also varied as a function of Jv. From this relationship and the clearances of inert markers we calculate the rate of active transport of glucose, the amount of glucose carried paracellularly by solvent drag or back-diffusion at any given Jv and luminal glucose concentration and the concentration of glucose in the absorbate. The results indicate that solvent drag through paracellular channels is the principal route for intestinal transport of glucose or amino acids at physiological rates of fluid absorption and concentration. In the absence of luminal glucose the rate of fluid absorption and the clearances of all inert hydrophilic solutes were greatly reduced. It is proposed that Na-coupled transport of organic solutes from lumen to intercellular spaces provides the principal osmotic force for fluid absorption and triggers widening of intercellular junctions, thus promoting bulk absorption of nutrients by solvent drag. Further evidence for regulation of channel width is provided in accompanying papers on changes in electrical impedance and ultrastructure of junctions during Na-coupled solute transport.