A two-barrier compartment model for volume flow across amphibian skin

The amphibian skin has long been used as a model tissue for the study of ion transport and osmotic water movement across tight epithelia. To understand the mechanism of water uptake across amphibian skin, we model the skin as a well-stirred compartment bounded by an apical barrier and a tissue barrier. The compartment represents the lateral intercellular space between cells in the stratum granulosum. The apical barrier represents the stratum corneum, the principal/mitochondria-rich cells, and the junctional area between cells. This barrier is hypothesized to have the ability to actively transport solutes through Na+-K+-ATPase. The actively transported solute flux is assumed to satisfy the Michaelis-Menten relationship. The tissue barrier represents a composite barrier comprising the stratum spinosum, the stratum germinativum, the basal lamina, and the dermis. Our model shows that 1) the predicted rehydration rates from apical bathing solutions are in good agreement with the experiment results in Hillyard and Larsen (J Comp Physiol 171: 283-292, 2001); 2) under their experimental conditions, there is a substantial volume flux coupled to the active solute flux and this coupled volume flux is nearly constant when the osmolality of the apical bathing solution is >100 mosmol/kgH2O; 3) the molar ratio of the actively transported solute flux to the coupled water flux is about 1:160, which is the same as that reported in Nielsen (J Membr Biol 159: 61-69, 1997).     

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.     

Pseudo-streaming potentials in Necturus gallbladder epithelium. II. The mechanism is a junctional diffusion potential

The mechanisms of apparent streaming potentials elicited across Necturus gallbladder epithelium by addition or removal of sucrose from the apical bathing solution were studied by assessing the time courses of: (a) the change in transepithelial voltage (Vms). (b) the change in osmolality at the cell surface (estimated with a tetrabutylammonium [TBA+]-selective microelectrode, using TBA+ as a tracer for sucrose), and (c) the change in cell impermeant solute concentration ([TMA+]i, measured with an intracellular double-barrel TMA(+)-selective microelectrode after loading the cells with TMA+ by transient permeabilization with nystatin). For both sucrose addition and removal, the time courses of Vms were the same as the time courses of the voltage signals produced by [TMA+]i, while the time courses of the voltage signals produced by [TBA+]o were much faster. These results suggest that the apparent streaming potentials are caused by changes of [NaCl] in the lateral intercellular spaces, whose time course reflects the changes in cell water volume (and osmolality) elicited by the alterations in apical solution osmolality. Changes in cell osmolality are slow relative to those of the apical solution osmolality, whereas lateral space osmolality follows cell osmolality rapidly, due to the large surface area of lateral membranes and the small volume of the spaces. Analysis of a simple mathematical model of the epithelium yields an apical membrane Lp in good agreement with previous measurements and suggests that elevations of the apical solution osmolality elicit rapid reductions in junctional ionic selectivity, also in good agreement with experimental determinations. Elevations in apical solution [NaCl] cause biphasic transepithelial voltage changes: a rapid negative Vms change of similar time course to that of a Na+/TBA+ bi-ionic potential and a slow positive Vms change of similar time course to that of the sucrose-induced apparent streaming potential. We conclude that the Vms changes elicited by addition of impermeant solute to the apical bathing solution are pseudo-streaming potentials, i.e., junctional diffusion potentials caused by salt concentration changes in the lateral intercellular spaces secondary to osmotic water flow from the cells to the apical bathing solution and from the lateral intercellular spaces to the cells. Our results do not support the notion of junctional solute-solvent coupling during transepithelial osmotic water flow.     

Osmotic water permeability of Necturus gallbladder epithelium

An electrophysiological technique that is sensitive to small changes in cell water content and has good temporal resolution was used to determine the hydraulic permeability (Lp) of Necturus gallbladder epithelium. The epithelial cells were loaded with the impermeant cation tetramethylammonium (TMA+) by transient exposure to the pore-forming ionophore nystatin in the presence of bathing solution TMA+. Upon removal of the nystatin a small amount of TMA+ is trapped within the cell. Changes in cell water content result in changes in intracellular TMA+ activity which are measured with intracellular ion-sensitive microelectrodes. We describe a method that allows us to determine the time course for the increase or decrease in the concentration of osmotic solute at the membrane surface, which allows for continuous monitoring of the difference in osmolality across the apical membrane. We also describe a new method for the determination of transepithelial hydraulic permeability (Ltp). Apical and basolateral membrane Lp's were assessed from the initial rates of change in cell water volume in response to anisosmotic mucosal or serosal bathing solutions, respectively. The corresponding values for apical and basolateral membrane Lp's were 0.66 x 10(-3) and 0.38 x 10(-3) cm/s.osmol/kg, respectively. This method underestimates the true Lp values because the nominal osmotic differences (delta II) cannot be imposed instantaneously, and because it is not possible to measure the true initial rate of volume change. A model was developed that allows for the simultaneous determination of both apical and basal membrane Lp's from a unilateral exposure to an anisosmotic bathing solution (mucosal). The estimates of apical and basal Lp with this method were 1.16 x 10(-3) and 0.84 x 10(-3) cm/s.osmol/kg, respectively. The values of Lp for the apical and basal cell membranes are sufficiently large that only a small (less than 3 mosmol/kg) transepithelial difference in osmolality is required to drive the observed rate of spontaneous fluid absorption by the gallbladder. Furthermore, comparison of membrane and transepithelial Lp's suggests that a large fraction of the transepithelial water flow is across the cells rather than across the tight junctions.     

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.     

Cellular volume homeostasis

All cells face constant challenges to their volume either through changes in intracellular solute content or extracellular osmolality. Cells respond to volume perturbations by activating membrane transport and/or metabolic processes that result in net solute loss or gain and return of cell volume to its normal resting state. This paper provides a brief overview of fundamental concepts of osmotic water flow across cell membranes, mechanisms of cell volume perturbation, the role of inorganic ions and organic osmolytes in cell volume regulation and the signaling mechanisms that regulate the activity of cell volume-sensitive transport and metabolic pathways.     

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.     

Influence of cellular and paracellular conductance patterns on epithelial transport and metabolism

Theoretical analysis of transepithelial active Na transport is often based on equivalent electrical circuits comprising discrete parallel active and passive pathways. Recent findings show, however, that Na+ pumps are distributed over the entire basal lateral surface of epithelial cells. This suggests that Na+ that has been actively transported into paracellular channels may to some extent return to the apical (mucosal) bathing solution, depending on the relative conductances of the pathways via the tight junctions and the lateral intercellular spaces. Such circulation, as well as the relative conductance of cellular and paracellular pathways, may have an important influence on the relationships between parameters of transcellular and transepithelial active transport and metabolism. These relationships were examined by equivalent circuit analysis of active Na transport, Na conductance, the electromotive force of Na transport, the "stoichiometry" of transport, and the degree of coupling of transport to metabolism. Although the model is too crude to permit precise quantification, important qualitative differences are predicted between "loose" and "tight" epithelia in the absence and presence of circulation. In contrast, there is no effect on the free energy of metabolic reaction estimated from a linear thermodynamic formalism. Also of interest are implications concerning the experimental evaluation of passive paracellular conductance following abolition of active transport, and the use of the cellular voltage-divider ratio to estimate the relative conductances of apical and basal lateral plasma membranes.     

Nonequilibrium thermodynamic model of the rat proximal tubule epithelium.

The rat proximal tubule epithelium is represented as well-stirred, compliant cellular and paracellular compartments bounded by mucosal and serosal bathing solutions. With a uniform pCO2 throughout the epithelium, the model variables include the concentrations of Na, K, Cl, HCO3, H2PO4, HPO4, and H, as well as hydrostatic pressure and electrical potential. Except for a metabolically driven Na-K exchanger at the basolateral cell membrane, all membrane transport within the epithelium is passive and is represented by the linear equations of nonequilibrium thermodynamics. In particular, this includes the cotransport of Na-Cl and Na-H2PO4 and countertransport of Na-H at the apical cell membrane. Experimental constraints on the choice of ionic conductivities are satisfied by allowing K-Cl cotransport at the basolateral membrane. The model equations include those for mass balance of the nonreacting species, as well as chemical equilibrium for the acidification reactions. Time-dependent terms are retained to permit the study of transient phenomena. In the steady state the energy dissipation is computed and verified equal to the sum of input from the Na-K exchanger plus the Gibbs free energy of mass addition to the system. The parameter dependence of coupled water transport is studied and shown to be consistent with the predictions of previous analytical models of the lateral intercellular space. Water transport in the presence of an end-proximal (HCO3-depleted) luminal solution is investigated. Here the lower permeability and higher reflection coefficient of HCO3 enhance net sodium and water transport. Due to enhanced flux across the tight junction, this process may permit proximal tubule Na transport to proceed with diminished energy dissipation.     

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.     

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.     

Regulation of single sodium channels in renal tissue: a role in sodium homeostasis

The kidney is responsible for the maintenance of an organism's body solute and water balance (i.e., Na+ homeostasis). The distal nephron and the cortical collecting duct (CCD) (an example of a tight epithelium) are important sites of regulatory control over the rate of Na+ reabsorption. The Na+ channel, a specialized protein located in the apical membrane of CCD cells, is the specific site of transepithelial Na+ movement. Na+ entry into the cell across the apical membrane occurs by passive diffusion of Na+ down an electrochemical gradient. We have used the patch-voltage clamp method to examine single-channel conductance events of the amiloride-sensitive apical Na+ channel in A6 cells, a model of CCD. Two types of Na+ channel were identified. One type was characterized by low selectivity (Na+ to K+) and high conductance, the other by high selectivity and low conductance. The type and frequency of channel observed depended on the transporting state of the epithelium. In a tissue with poor transport rates, the low-selectivity type of channel was prevalent (the other type of channel was present, but in a very low density). Therefore, the poorly transporting tissue had an overall low apical Na+ conductance. In a tissue with high transport rates, the highly selective channel appeared to be predominant. In this case the net result was a highly Na+ conductive apical membrane.     

Interaction between the basolateral K+ and apical Na+ conductances in Necturus urinary bladder

Experimental modulation of the apical membrane Na+ conductance or basolateral membrane Na+-K+ pump activity has been shown to result in parallel changes in the basolateral K+ conductance in a number of epithelia. To determine whether modulation of the basolateral K+ conductance would result in parallel changes in apical Na+ conductance and basolateral pump activity, Necturus urinary bladders stripped of serosal muscle and connective tissue were impaled through their basolateral membranes with microelectrodes in experiments that allowed rapid serosal solution changes. Exposure of the basolateral membrane to the K+ channel blockers Ba2+ (0.5 mM/liter), Cs+ (10 mM/liter), or Rb+ (10 mM/liter) increased the basolateral resistance (Rb) by greater than 75% in each case. The increases in Rb were accompanied simultaneously by significant increases in apical resistance (Ra) of greater than 20% and decreases in transepithelial Na+ transport. The increases in Ra, measured as slope resistances, cannot be attributed to nonlinearity of the I-V relationship of the apical membrane, since the measured cell membrane potentials with the K+ channel blockers present were not significantly different from those resulting from increasing serosal K+, a maneuver that did not affect Ra. Thus, blocking the K+ conductance causes a reduction in net Na+ transport by reducing K+ exit from the cell and simultaneously reducing Na+ entry into the cell. Close correlations between the calculated short-circuit current and the apical and basolateral conductances were preserved after the basolateral K+ conductance pathways had been blocked. Thus, the interaction between the basolateral and apical conductances revealed by blocking the basolateral K+ channels is part of a network of feedback relationships that normally serves to maintain cellular homeostasis during changes in the rate of transepithelial Na+ transport.     

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.     

The effect of ethanol on ion transport in frog skin.

Frog skin has been used as a model epithelial sodium-transporting system to study the effect of ethanol on ion transport. Treatment of the outside of frog skin with ethanol decreased the net sodium transport due to inhibition of 22Na+ influx. Ethanol did not alter sodium outflux when bathin the outside of the skin. The inhibition was in proportion to the concentration of ethanol, 0.25 M resulting in 50% inhibition. The chloride permeability of the skin was increased several-fold when the skin was exposed to ethanol in either bathing solution. With 0.4 M ethanol in the inner bathing solution, all the unidirectional fluxes of Na+ and C1- were increased. The movement of C1- was evaluated by comparison of C1- flux with urea flux, since urea is thought to move passively across frog skin via an extracellular (shunt) pathway. Chloride flux was increased to a greater extent than urea flux. These experiments indicate that ethanol affects chloride permeability beyond an increase in extracellular ion flow and independent of its effect of Na+ transport.     

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.     

Potassium transport across the frog retinal pigment epithelium

Previous experiments indicate that the apical membrane of the frog retinal pigment epithelium contains electrogenic Na:K pumps. In the present experiments net potassium and rubidium transport across the epithelium was measured as a function of extracellular potassium (rubidium) concentration, [K]0 ( [Rb]0). The net rate of retina-to-choroid 42K(86Rb) transport increased monotonically as [K]0 ( [Rb]0) increased from approximately 0.2 to 5 mM on both sides of the tissue or on the apical (neural retinal) side of the tissue. No further increase was observed when [K]0 ( [Rb]0) was elevated to 10 mM. Net sodium transport was also stimulated by elevating [K]0. The net K transport was completely inhibited by 10-4 M ouabain in the solution bathing the apical membrane. Ouabain inhibited the unidirectional K flux in the direction of net flux but had no effect on the back-flux in the choroid-to-retina direction. The magnitude of the ouabain-inhibitable 42K(86Rb) flux increased with [K]0 ( [Rb]0). These results show that the apical membrane Na:K pumps play an important role in the net active transport of potassium (rubidium) across the epithelium. The [K]0 changes that modulate potassium transport coincide with the light-induced [K]0 changes that occur in the extracellular space separating the photoreceptors and the apical membrane of the pigment epithelium.     

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.     

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.