A Mathematical Model of Electrolyte and Fluid Transport across Corneal Endothelium

To predict the behavior of a transporting epithelium by intuitive means can be complex and frustrating. As the number of parameters to be considered increases beyond a few, the task can be termed impossible. The alternative is to model epithelial behavior by mathematical means. For that to be feasible, it has been presumed that a large amount of experimental information is required, so as to be able to use known values for the majority of kinetic parameters. However, in the present case, we are modeling corneal endothelial behavior beginning with experimental values for only five of eleven parameters. The remaining parameter values are calculated assuming cellular steady state and using algebraic software. With that as base, as in preceding treatments but with a distribution of channels/transporters suited to the endothelium, temporal cell and tissue behavior are computed by a program written in Basic that monitors changes in chemical and electrical driving forces across cell membranes and the paracellular pathway. We find that the program reproduces quite well the behaviors experimentally observed for the translayer electrical potential difference and rate of fluid transport, (a) in the steady state, (b) after perturbations by changes in ambient conditions HCO₃^–, Na⁺, and Cl^– concentrations), and (c) after challenge by inhibitors (ouabain, DIDS, Na^+- and Cl^–-channel inhibitors). In addition, we have used the program to compare predictions of translayer fluid transport by two competing theories, electro-osmosis and local osmosis. Only predictions using electro-osmosis fit all the experimental data.     

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.     

Corneal endothelium transports fluid in the absence of net solute transport

The corneal endothelium transports fluid from the corneal stroma to the aqueous humor, thus maintaining stromal transparency by keeping it relatively dehydrated. This fluid transport mechanism is thought to be driven by the transcellular transports of HCO(3)(-) and Cl(-) in the same direction, from stroma to aqueous. In parallel to these anion movements, for electroneutrality, there are paracellular Na(+) and transcellular K(+) transports in the same direction. The resulting net flow of solute might generate local osmotic gradients that drive fluid transport. However, there are reports that some 50% residual fluid transport remains in nominally HCO(3)(-) free solutions. We have examined the driving force for this residual fluid transport. We confirm that in nominally HCO(3)(-) free solutions, 48% of control fluid transport remains. When in addition Cl(-) channels are inhibited, 30% of control fluid movement still remains. Addition of a carbonic anhydrase inhibitor has no further effect. These manipulations combined inhibit the transcellular transport of all anions, without which there cannot be any net transport of solute and consequently no local osmotic gradients, yet there is residual fluid movement. Only the further addition of benzamil, an inhibitor of epithelial Na(+) channels, abolishes fluid transport completely. Our data are inconsistent with transcellular local osmosis and instead support the paradigm of paracellular fluid transport driven by electro-osmotic coupling.     

The Role of the Tight Junction in Paracellular Fluid Transport across Corneal Endothelium. Electro-osmosis as a Driving Force

The mechanism of epithelial fluid transport is controversial and remains unsolved. Experimental difficulties pose obstacles for work on a complex phenomenon in delicate tissues. However, the corneal endothelium is a relatively simple system to which powerful experimental tools can be applied. In recent years our laboratory has developed experimental evidence and theoretical insights that illuminate the mechanism of fluid transport across this leaky epithelium. Our evidence points to fluid being transported via the paracellular route by a mechanism requiring junctional integrity, which we attribute to electro-osmotic coupling at the junctions. Fluid movements can be produced by electrical currents. The direction of the movement can be reversed by current reversal or by changing junctional electrical charges by polylysine. Aquaporin 1 (AQP1) is the only AQP present in these cells, and its deletion in AQP1 null mice significantly affects cell osmotic permeability but not fluid transport, which militates against the presence of sizable water movements across the cell. By contrast, AQP1 null mice cells have reduced regulatory volume decrease (only 60% of control), which suggests a possible involvement of AQP1 in either the function or the expression of volume-sensitive membrane channels/transporters. A mathematical model of corneal endothelium predicts experimental results only when based on paracellular electro-osmosis, and not when transcellular local osmosis is assumed instead. Our experimental findings in corneal endothelium have allowed us to develop a novel paradigm for this preparation that includes: (1) paracellular fluid flow; (2) a crucial role for the junctions; (3) hypotonicity of the primary secretion; (4) an AQP role in regulation and not as a significant water pathway. These elements are remarkably similar to those proposed by the Hill laboratory for leaky epithelia.     

Evidence for a central role for electro-osmosis in fluid transport by corneal endothelium

The mechanism of transepithelial fluid transport remains unclear. The prevailing explanation is that transport of electrolytes across cell membranes results in local concentration gradients and transcellular osmosis. However, when transporting fluid, the corneal endothelium spontaneously generates a locally circulating current of approximately 25 microA cm(-2), and we report here that electrical currents (0 to +/-15 microA cm(-2)) imposed across this layer induce fluid movements linear with the currents. As the imposed currents must be approximately 98% paracellular, the direction of induced fluid movements and the rapidity with which they follow current imposition (rise time < or =3 sec) is consistent with electro-osmosis driven by sodium movement across the paracellular pathway. The value of the coupling coefficient between current and fluid movements found here (2.37 +/- 0.11 microm cm(2) hr(-1) microA (-1), suggests that: 1) the local endothelial current accounts for spontaneous transendothelial fluid transport; 2) the fluid transported becomes isotonically equilibrated. Ca(++)-free solutions or endothelial damage eliminate the coupling, pointing to the cells and particularly their intercellular junctions as a main site of electro-osmosis. The polycation polylysine, which is expected to affect surface charges, reverses the direction of current-induced fluid movements. Fluid transport is proportional to the electrical resistance of the ambient medium. Taken together, the results suggest that electro-osmosis through the intercellular junctions is the primary process in a sequence of events that results in fluid transport across this preparation.     

Corneal endothelium transports fluid in the absence of net solute transport

The corneal endothelium transports fluid from the corneal stroma to the aqueous humor, thus maintaining stromal transparency by keeping it relatively dehydrated. This fluid transport mechanism is thought to be driven by the transcellular transports of HCO₃⁻ and Cl⁻ in the same direction, from stroma to aqueous. In parallel to these anion movements, for electroneutrality, there are paracellular Na⁺ and transcellular K⁺ transports in the same direction. The resulting net flow of solute might generate local osmotic gradients that drive fluid transport. However, there are reports that some 50% residual fluid transport remains in nominally HCO₃⁻ free solutions. We have examined the driving force for this residual fluid transport. We confirm that in nominally HCO₃⁻ free solutions, 48% of control fluid transport remains. When in addition Cl⁻ channels are inhibited, 30% of control fluid movement still remains. Addition of a carbonic anhydrase inhibitor has no further effect. These manipulations combined inhibit the transcellular transport of all anions, without which there cannot be any net transport of solute and consequently no local osmotic gradients, yet there is residual fluid movement. Only the further addition of benzamil, an inhibitor of epithelial Na⁺ channels, abolishes fluid transport completely. Our data are inconsistent with transcellular local osmosis and instead support the paradigm of paracellular fluid transport driven by electro-osmotic coupling.     

Lack of correlation between transepithelial transport capacity and paracellular pathway ultrastructure in Alcian blue-treated rabbit gallbladders

The effects of mucosal application of 1 mg% Alcian blue (a trivalent cationic phthalocyanine dye) on functional and ultrastructural parameters of the isolated rabbit gallbladder have been studied. Apart from minor changes in the shape of the group of central microvilli observed in thin-section electron microscopy and scanning electron microscopy, the major ultrastructural change induced by Alcian blue was an almost complete collapse of intercellular spaces in the region above the tight junctions up to the bases of the marginal microvilli as revealed by thin-section electron microscopy. Freeze-fracture electron microscopy demonstrated a complete disappearance of intramembrane particles of neighboring cell membranes corresponding to the region of interspace collapse. Transepithelial electrical resistance (RT) increased from 44.5 to 58.7 ohm . cm2 upon treatment with Alcian blue. This increase could be well accounted for by the observed structural changes in the paracellular pathway if this pathway determines the low resistance of the rabbit gallbladder epithelium. Despite the increase in RT, net mucosa-to-serosa fluid transport and the spontaneous mucosa- positive potential difference of 3 mV were unaltered by Alcian blue treatment, supporting the hypothesis that the transepithelial transport mechanism per se is electroneutral. A calculation of the maximal paracellular mucosa-to-serosa waterflow in response to a lateral intercellular space hypertonicity of 20 mosM demonstrates that in the Alcian blue-treated gallbladder the resulting figure is about three orders of magnitude too low to keep up with the unaltered spontaneous transepithelial net fluid transport. It is therefore concluded that the tight junction pathway in rabbit gallbladders does not serve as a route for net fluid transport.     

Water channels and their roles in some ocular tissues

Water is a major component of the eye, and water channels (aquaporins) are ubiquitous in ocular tissues, and quite abundant at their different locations. AQP1 is expressed in corneal endothelium, lens epithelium, ciliary epithelium, and retinal pigment epithelium. AQP3 is expressed in corneal epithelium, and in conjunctival epithelium. AQP4 is expressed in ciliary epithelium and retinal Muller cells. AQP5 is expressed in corneal epithelium, and conjunctival epithelium. AQP0 is expressed in lens fiber cells. It is known that five ocular tissues transport fluid, namely: (1) Corneal endothelium; (2) Conjunctival epithelium; (3) Lens epithelium; (4) Ciliary epithelium; (5) Retinal pigment epithelium. For the corneal endothelium, aquaporins are not the main route for trans-tissue water movement, which is paracellular. Instead, we propose that aquaporins allow fast osmotic equilibration of the cell, which is necessary to maintain optimal rates of fluid movement since the cyclic paracellular water transfer mechanism operates separately and tends to create periodic osmotic imbalances (τ～5s).     

Absorptive activity of calcium in the isolated cecal epithelium adaptively increased by 2 week's feeding of difructose anhydride III in rats

We compared net Ca absorption and Lucifer Yellow (LY), a paracellular passage dye, permeability in the epithelium isolated from the rat small intestine, cecum, and colon after feeding with control and difructose anhydride (DFA) III diets for 14 days using the Ussing chamber system. Feeding of DFA III increased net Ca transport and LY passage in the cecal but not in small intestinal or colonic epithelium. Ability of paracellular Ca passage via Tight-junction (TJ) in the cecum was changed adaptively by feeding of DFA III. Changes in microbial fermentation may affect the functional changes of Ca transport in cecal epithelium itself.     

Effects of ouabain on fluid transport and electrical properties of Necturus gallbladder. Evidence in favor of a neutral basolateral sodium transport mechanism

Net fluid transport (Jv) and electrical properties of the cell membranes and paracellular pathway of Necturus gallbladder epithelium were studied before and after the addition of ouabain (10(-4) M) to the serosal bathing medium. The glycoside inhibited Jv by 70% in 15 min and by 100% in 30 min. In contrast, the potentials across both cell membranes did not decrease significantly until 20 min of exposure to ouabain. At 30 min, the basolateral membrane potential (Vcs) fell only by ca 7 mV. If basolateral Na transport were electrogenic, with a coupling ratio (Na:K) of 3:2, the reductions of Vcs at 15 and 30 min should be 12--15 and 17--21 mV, respectively. Thus, we conclude that the mechanism of Na transport from the cells to the serosal bathing solution is not electrogenic under normal transport conditions. The slow depolarization observed in ouabain is caused by a fall of intracellular K concentration, and by a decrease in basolateral cell membrane K permeability. Prolonged exposure to ouabain results also in an increase in paracellular K selectivity, with no change of P Na/P Cl.     

Septate junctions mediate the barrier to paracellular permeability in sea urchin embryos

In sea urchin embryos, blastula formation occurs between the seventh and tenth cleavage and is associated with changes in the permeability properties of the epithelium although the structures responsible for mediating these changes are not known. Tight junctions regulate the barrier to paracellular permeability in chordate epithelia; however, the sea urchin blastula epithelium lacks tight junctions and instead possesses septate junctions. Septate junctions are unique to non-chordate invertebrate cell layers and have a characteristic ladder-like appearance whereby adjacent cells are connected by septa. To determine the function of septate junctions in sea urchin embryos, the permeability characteristics of the embryonic sea urchin epithelia were assessed. First, the developmental stage at which a barrier to paracellular permeability arises was examined and found to be in place after the eighth cleavage division. The mature blastula epithelium is impermeable to macromolecules; however, brief depletion of divalent cations renders the epithelium permeable. The ability of the blastula epithelium to recover from depletion of divalent cations and re-establish a barrier to paracellular permeability using fluorescently labelled lectins was also examined. Finally, septate junction structure was examined in embryos in which the permeability status of the epithelium was known. The results provide evidence that septate junctions mediate the barrier to paracellular permeability in sea urchin embryos.     

Microtubule Integrity Is Necessary for the Epithelial Barrier Function of Cultured Thyroid Cell Monolayers

Vectorial transport in the thyroid epithelium requires an efficient barrier against passive paracellular flux, a role which is principally performed by the tight junction (zonula occludens). There is increasing evidence that tight junction integrity is determined by integral and peripheral membrane proteins which interact with the cell cytoskeleton. Although the contribution of the actin cytoskeleton to tight junction physiology has been intensively studied, less is known about possible interactions with microtubules. In the present study we used electrophysiological and immunohistochemical approaches to investigate the contribution of microtubules to the paracellular barrier in cultured thyroid cell monolayers which displayed a high transepithelial electrical resistance (6000-9000 ohm · cm²). Colchicine (1 μM) caused a progressive fall in electrical resistance to <10% of baseline after 6 h and depolarization of the transepithelial electrical potential difference consistent with a significant increase in paracellular permeability. The effect of colchicine on TER was not affected by agents which inhibit the major apical conductances of thyroid cells but was reversed upon removal of the drug. Immunofluorescent staining for tubulin combined with confocal laser scanning microscopy demonstrated that thyroid cells possessed a dense microtubule network extending throughout the cytoplasm which was destroyed by colchicine. Colchicine also produced changes in the localization of the tight junction-associated protein, ZO-1: its normally continuous junctional distribution was disrupted by striking discontinuities and the appearance of many fine strands which extended into the cytoplasm. A similar disruption in E-cadherin staining was also observed, but colchicine did not affect the distribution of vinculin associated with adherens junctions nor the integrity of the perijunctional actin ring. We conclude that microtubules are necessary for the functional and structural integrity of tight junctions in this electrically tight, transporting epithelium.     

The tight junctional protein occludin is found in the uterine epithelium of squamate reptiles

Occludin, an integral protein associated with the mammalian tight junction, has for the first time been identified in the uterus of squamate reptiles. The tight junction is made up of anastamosing strands and forms a selective barrier that regulates paracellular diffusion of solutes across uterine epithelium. Occludin exclusively labels tight junctional strands and is an excellent marker for tight junction permeability. Using western blotting and immunohistochemistry, occludin expression was examined in the uterine epithelium of five species of Australian skinks at different stages of gestation. More occludin was detected during late stage pregnancy/gravidity compared to the lower levels of occludin detected in vitellogenic and post-parturient females in three of the five species. We conclude that the paracellular permeability of the squamate uterine epithelium decreases as gestation progresses. As placental transport of ions and solutes to the embryo is highest during the last third of pregnancy in viviparous squamates, it is likely that a decrease in paracellular permeability is compensated by an upregulation of other transporting mechanisms such as histotrophy.     

Mechanisms of alveolar protein clearance in the intact lung

Transport of protein across the alveolar epithelial barrier is a critical process in recovery from pulmonary edema and is also important in maintaining the alveolar milieu in the normal healthy lung. Various mechanisms have been proposed for clearing alveolar protein, including transport by the mucociliary escalator, intra-alveolar degradation, or phagocytosis by macrophages. However, the most likely processes are endocytosis across the alveolar epithelium, known as transcytosis, or paracellular diffusion through the epithelial barrier. This article focuses on protein transport studies that evaluate these two potential mechanisms in whole lung or animal preparations. When protein concentrations in the air spaces are low, e.g., albumin concentrations <0.5 g/100 ml, protein transport demonstrates saturation kinetics, temperature dependence indicating high energy requirements, and sensitivity to pharmacological agents that affect endocytosis. At higher concentrations, the protein clearance rate is proportional to protein concentration without signs of saturation, inversely related to protein size, and insensitive to endocytosis inhibition. Temperature dependence suggests a passive process. Based on these findings, alveolar albumin clearance occurs by receptor-mediated transcytosis at low protein concentrations but proceeds by passive paracellular mechanisms at higher concentrations. Because protein concentrations in pulmonary edema fluid are high, albumin concentrations of 5 g/100 ml or more, clearance of alveolar protein occurs by paracellular pathways in the setting of pulmonary edema. Transcytosis may be important in regulating the alveolar milieu under nonpathological circumstances. Alveolar degradation may become important in long-term protein clearance, clearance of insoluble proteins, or under pathological conditions such as immune reactions or acute lung injury. acute respiratory distress syndrome; endocytosis; diffusion; protein transport pulmonary edema     

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.     

The Integrin β1 Subunit Regulates Paracellular Permeability of Kidney Proximal Tubule Cells

Epithelial cells lining the gastrointestinal tract and kidney have different abilities to facilitate paracellular and transcellular transport of water and solutes. In the kidney, the proximal tubule allows both transcellular and paracellular transport, while the collecting duct primarily facilitates transcellular transport. The claudins and E-cadherin are major structural and functional components regulating paracellular transport. In this study we present the novel finding that the transmembrane matrix receptors, integrins, play a role in regulating paracellular transport of renal proximal tubule cells. Deleting the integrin β1 subunit in these cells converts them from a “loose” epithelium, characterized by low expression of E-cadherin and claudin-7 and high expression of claudin-2, to a “tight” epithelium with increased E-cadherin and claudin-7 expression and decreased claudin-2 expression. This effect is mediated by the integrin β1 cytoplasmic tail and does not entail β1 heterodimerization with an α-subunit or its localization to the cell surface. In addition, we demonstrate that deleting the β1 subunit in the proximal tubule of the kidney results in a major urine-concentrating defect. Thus, the integrin β1 tail plays a key role in regulating the composition and function of tight and adherens junctions that define paracellular transport properties of terminally differentiated renal proximal tubule epithelial cells.     

Impairment of blood-cerebrospinal fluid barrier properties by retrovirus-activated T lymphocytes: reduction in cerebrospinal fluid-to-blood efflux of prostaglandin E2

The choroid plexus epithelium forms the interface between the blood and the CSF. In conjunction with the tight junctions restricting the paracellular pathway, polarized specific transport systems in the choroidal epithelium allow a fine regulation of CSF-borne biologically active mediators. The highly vascularized stroma delimited by the choroidal epithelium can be a reservoir for retrovirus-infected or activated immune cells. In this work, new insight in the implication of the blood-CSF barrier in neuroinfectious and inflammatory diseases is provided by using a differentiated cellular model of the choroidal epithelium, exposed to infected T lymphocytes. We demonstrate that T cells activated by a retroviral infection, but not non-infected cells, reduce the transporter-mediated CSF-to-blood efflux of organic anions, in particular that of the potent pro-inflammatory prostaglandin PGE2, via the release of soluble factors. A moderate alteration of the paracellular permeability also occurs. We identified the viral protein Tax, oxygenated free radicals, matrix-metalloproteinases and pro-inflammatory cytokines as active molecules released during the exposure of the epithelium to infected T cells. Among them, tumour necrosis factor and interleukin 1 are directly involved in the mechanism underlying the decrease in some choroidal organic anion efflux. Given the strong involvement of CSF-borne PGE2 in sickness behaviour syndrome, these data suggest that the blood-CSF barrier plays an important role in the pathophysiology of neuroinflammation and neuroinfection, via changes in the transport processes controlling the CSF biodisposition of PGE2.     

Electroosmosis in Membranes: Effects of Unstirred Layers and Transport Numbers: I. Theory

When a current is passed through a membrane system, differences in transport numbers between the membrane and the adjacent solutions will, in general, result in depletion and enhancement of concentrations at the membrane-solution interfaces. This will be balanced by diffusion back into the bulk solution, diffusion of solute back across the membrane itself, and osmosis resulting from these local concentration gradients. The two main results of such a phenomenon are (1) that there is a current-induced volume flow, which may be mistaken for electroosmosis, and (2) that there will generally develop transient changes in potential difference (PD) across membranes during and after the passage of current through them.     

Dynamic changes to claudins in the uterine epithelial cells of the marsupial Sminthopsis crassicaudata (Dasyuridae) during pregnancy

The fluid that surrounds the embryo in the uterus contains important nourishing factors and secretions. To maintain the distinct microenvironment in the uterine lumen, the tight junctions between uterine epithelial cells are remodeled to decrease paracellular movement of molecules and solutes. Modifications to tight junctions between uterine epithelial cells is a common feature of pregnancy in eutherian mammals, regardless of placental type. Here we used immunofluorescence microscopy and western blot analysis to describe distributional changes to tight junctional proteins, claudin‐1, ‐3, ‐4, and ‐5, in the uterine epithelial cells of a marsupial species, Sminthopsis crassicaudata. Immunofluorescence microscopy revealed claudin‐1, ‐3, and ‐5 in the tight junctions of the uterine epithelium of S. crassicaudata during pregnancy. These specific claudins are associated with restricting passive movement of fluid between epithelial cells in eutherians. Hence, their function during pregnancy in S. crassicaudata may be to maintain the uterine luminal content surrounding developing embryos. Claudin‐4 disappears from all uterine regions of S. crassicaudata at the time of implantation, in contrast with the distribution of this claudin in some eutherian mammals. We conclude that like eutherian mammals, distributional changes to claudins in the uterine epithelial cells of S. crassicaudata are necessary to support pregnancy. However, the combination of individual claudin isoforms in the tight junctions of the uterine epithelium of S. crassicaudata differs from that of eutherian mammals. Our findings suggest that the precise permeability of the paracellular pathway of the uterine epithelium is species‐specific.