Local osmosis and isotonic transport

Modulation of Membrane Trafficking of AQP5 in the Lens in Response to Changes in Zonular Tension Is Mediated by the Mechanosensitive Channel TRPV1

In mice, the contraction of the ciliary muscle via the administration of pilocarpine reduces the zonular tension applied to the lens and activates the TRPV1-mediated arm of a dual feedback system that regulates the lens' hydrostatic pressure gradient. In the rat lens, this pilocarpine-induced reduction in zonular tension also causes the water channel AQP5 to be removed from the membranes of fiber cells located in the anterior influx and equatorial efflux zones. Here, we determined whether this pilocarpine-induced membrane trafficking of AQP5 is also regulated by the activation of TRPV1. Using microelectrode-based methods to measure surface pressure, we found that pilocarpine also increased pressure in the rat lenses via the activation of TRPV1, while pilocarpine-induced removal of AQP5 from the membrane observed using immunolabelling was abolished by pre-incubation of the lenses with a TRPV1 inhibitor. In contrast, mimicking the actions of pilocarpine by blocking TRPV4 and then activating TRPV1 resulted in sustained increase in pressure and the removal of AQP5 from the anterior influx and equatorial efflux zones. These results show that the removal of AQP5 in response to a decrease in zonular tension is mediated by TRPV1 and suggest that regional changes to PH2O contribute to lens hydrostatic pressure gradient regulation.

The Effect of the Osmotically Active Compound Concentration Difference on the Passive Water and Proton Fluxes across a Lipid Bilayer

The molecular details of the passive water flux across the hydrophobic membrane interior are still a matter of debate. One of the postulated mechanisms is the spontaneous, water-filled pore opening, which facilitates the hydrophilic connection between aqueous phases separated by the membrane. In the paper, we provide experimental evidence showing that the spontaneous lipid pore formation correlates with the membrane mechanics; hence, it depends on the composition of the lipid bilayer and the concentration of the osmotically active compound. Using liposomes as an experimental membrane model, osmotically induced water efflux was measured with the stopped-flow technique. Shapes of kinetic curves obtained at low osmotic pressure differences are interpreted in terms of two events: the lipid pore opening and water flow across the aqueous channel. The biological significance of the dependence of the lipid pore formation on the concentration difference of an osmotically active compound was illustrated by the demonstration that osmotically driven water flow can be accompanied by the dissipation of the pH gradient. The application of the Helfrich model to describe the probability of lipid pore opening was validated by demonstrating that the probability of pore opening correlates with the membrane bending rigidity. The correlation was determined by experimentally derived bending rigidity coefficients and probabilities of lipid pores opening.

Calcium Dynamics and Water Transport in Salivary Acinar Cells

Saliva is secreted from the acinar cells of the salivary glands, using mechanisms that are similar to other types of water-transporting epithelial cells. Using a combination of theoretical and experimental techniques, over the past 20 years we have continually developed and modified a quantitative model of saliva secretion, and how it is controlled by the dynamics of intracellular calcium. However, over approximately the past 5 years there have been significant developments both in our understanding of the underlying mechanisms and in the way these mechanisms should best be modelled. Here, we review the traditional understanding of how saliva is secreted, and describe how our work has suggested important modifications to this traditional view. We end with a brief description of the most recent data from living animals and discuss how this is now contributing to yet another iteration of model construction and experimental investigation.

Fluid and solute transport across the retinal pigment epithelium: a theoretical model

The retina is composed of two main layers-the neuroretina and the retinal pigment epithelium (RPE)-that are separated by a potential gap termed the sub-retinal space (SRS). Accumulation of fluid in the SRS may result in a retinal detachment. A key function of the RPE is to prevent fluid accumulation in the SRS by actively pumping fluid from this space to the choroid. We have developed a mathematical model of this process that incorporates the transport of seven chemical species: Na⁺, K⁺, Cl^-, HCO3-, H⁺, CO₂ and H₂CO₃. This allows us to estimate solute and water fluxes and to understand the role of the different membrane ion channels. We have performed a global sensitivity analysis using the extended Fourier amplitude sensitivity test to investigate the relative importance of parameters in generating the model outputs. The model predicts that flow across the RPE is driven by an osmotic gradient in the cleft gap between adjacent cells. Moreover, the model estimates how water flux is modified in response to inhibition of membrane ion channels and carbonic anhydrase (CA). It provides a possible explanation for how CA inhibitors, which are used clinically to prevent fluid accumulation in the SRS, may be acting.

A Bidomain Model for Lens Microcirculation

There exists a large body of research on the lens of the mammalian eye over the past several decades. The objective of this work is to provide a link between the most recent computational models and some of the pioneering work in the 1970s and 80s. We introduce a general nonelectroneutral model to study the microcirculation in the lens of the eye. It describes the steady-state relationships among ion fluxes, between water flow and electric field inside cells, and in the narrow extracellular spaces between cells in the lens. Using asymptotic analysis, we derive a simplified model based on physiological data and compare our results with those in the literature. We show that our simplified model can be reduced further to the first-generation models, whereas our full model is consistent with the most recent computational models. In addition, our simplified model captures in its equations the main features of the full computational models. Our results serve as a useful link intermediate between the computational models and the first-generation analytical models. Simplified models of this sort may be particularly helpful as the roles of similar osmotic pumps of microcirculation are examined in other tissues with narrow extracellular spaces, such as cardiac and skeletal muscle, liver, kidney, epithelia in general, and the narrow extracellular spaces of the central nervous system, the "brain." Simplified models may reveal the general functional plan of these systems before full computational models become feasible and specific.

Aquaporins in the lung

The lung is the interface between air and blood where the exchange of oxygen and carbon dioxide occurs. The surface liquid that is directly exposed to the gaseous compartment covers both conducting airways and respiratory zone and forms the air-liquid interface. The barrier that separates this lining fluid of the airways and alveoli from the extracellular compartment is the pulmonary epithelium. The volume of the lining fluid must be kept in a range that guarantees an appropriate gas exchange and other functions, such as mucociliary clearance. It is generally accepted that this is maintained by balancing resorptive and secretory fluid transport across the pulmonary epithelium. Whereas osmosis is considered as the exclusive principle of fluid transport in the airways, filtration may contribute to alveolar fluid accumulation under pathologic conditions. Aquaporins (AQP) facilitate water flux across cell membranes, and as such, they provide a transcellular route for water transport across epithelia. However, their contribution to near-isosmolar fluid conditions in the lung still remains elusive. Herein, we discuss the role of AQPs in the lung with regard to fluid homeostasis across the respiratory epithelium.

Feedback Regulation of Intracellular Hydrostatic Pressure in Surface Cells of the Lens

In wild-type lenses from various species, an intracellular hydrostatic pressure gradient goes from ∼340 mmHg in central fiber cells to 0 mmHg in surface cells. This gradient drives a center-to-surface flow of intracellular fluid. In lenses in which gap-junction coupling is increased, the central pressure is lower, whereas if gap-junction coupling is reduced, the central pressure is higher but surface pressure is always zero. Recently, we found that surface cell pressure was elevated in PTEN null lenses. This suggested disruption of a feedback control system that normally maintained zero surface cell pressure. Our purpose in this study was to investigate and characterize this feedback control system. We measured intracellular hydrostatic pressures in mouse lenses using a microelectrode/manometer-based system. We found that all feedback went through transport by the Na/K ATPase, which adjusted surface cell osmolarity such that pressure was maintained at zero. We traced the regulation of Na/K ATPase activity back to either TRPV4, which sensed positive pressure and stimulated activity, or TRPV1, which sensed negative pressure and inhibited activity. The inhibitory effect of TRPV1 on Na/K pumps was shown to signal through activation of the PI3K/AKT axis. The stimulatory effect of TRPV4 was shown in previous studies to go through a different signal transduction path. Thus, there is a local two-legged feedback control system for pressure in lens surface cells. The surface pressure provides a pedestal on which the pressure gradient sits, so surface pressure determines the absolute value of pressure at each radial location. We speculate that the absolute value of intracellular pressure may set the radial gradient in the refractive index, which is essential for visual acuity.

Net Fluorescein Flux Across Corneal Endothelium Strongly Suggests Fluid Transport is due to Electro-osmosis

We have presented prior evidence suggesting that fluid transport results from electro-osmosis at the intercellular junctions of the corneal endothelium. Such phenomenon ought to drag other extracellular solutes. We have investigated this using fluorescein-Na₂ as an extracellular marker. We measured unidirectional fluxes across layers of cultured human corneal endothelial (HCE) cells. SV-40-transformed HCE layers were grown to confluence on permeable membrane inserts. The medium was DMEM with high glucose and no phenol red. Fluorescein-labeled medium was placed either on the basolateral or the apical side of the inserts; the other side carried unlabeled medium. The inserts were held in a CO₂ incubator for 1 h (at 37 °C), after which the entire volume of the unlabeled side was collected. After that, label was placed on the opposite side, and the corresponding paired sample was collected after another hour. Fluorescein counts were determined with a (Photon Technology) DeltaScan fluorometer (excitation 380 nm; emission 550 nm; 2 nm bwth). Samples were read for 60 s. The cells utilized are known to transport fluid from the basolateral to the apical side, just as they do in vivo in several species. We used 4 inserts for influx and efflux (total: 20 1-h periods). We found a net flux of fluorescein from the basolateral to the apical side. The flux ratio was 1.104 ± 0.056. That difference was statistically significant (p = 0.00006, t test, paired samples). The endothelium has a definite restriction at the junctions. Hence, an asymmetry in unidirectional fluxes cannot arise from osmosis, and can only point instead to paracellular solvent drag. We suggest, once more, that such drag is due to electro-osmotic coupling at the paracellular junctions.

Multiscale modelling of saliva secretion

We review a multiscale model of saliva secretion, describing in brief how the model is constructed and what we have so far learned from it. The model begins at the level of inositol trisphosphate receptors (IPR), and proceeds through the cellular level (with a model of acinar cell calcium dynamics) to the multicellular level (with a model of the acinus), finally to a model of a saliva production unit that includes an acinus and associated duct. The model at the level of the entire salivary gland is not yet completed. Particular results from the model so far include (i) the importance of modal behaviour of IPR, (ii) the relative unimportance of Ca(2+) oscillation frequency as a controller of saliva secretion, (iii) the need for the periodic Ca(2+) waves to be as fast as possible in order to maximise water transport, (iv) the presence of functional K(+) channels in the apical membrane increases saliva secretion, (v) the relative unimportance of acinar spatial structure for isotonic water transport, (vi) the prediction that duct cells are highly depolarised, (vii) the prediction that the secondary saliva takes at least 1mm (from the acinus) to reach ionic equilibrium. We end with a brief discussion of future directions for the model, both in construction and in the study of scientific questions.

The effects of age on lens transport

PURPOSE

Age-related nuclear cataracts involve denaturation and aggregation of intracellular proteins. We have documented age-dependent changes in membrane transport in the mouse lens to see what might initiate changes in the intracellular milieu.

METHODS

Microelectrode-based intracellular impedance studies of intact lenses were used to determine gap junction coupling conductance, fiber and surface cell membrane conductances, effective extracellular resistivity, and intracellular voltage. Fiber cell connexin expression was detected by Western blotting. Intracellular hydrostatic pressure was measured with a microelectrode/manometer system. Concentrations of intracellular sodium and calcium were measured by intracellular injection of sodium-binding benzofuran isophthalate and Fura2, respectively.

RESULTS

In adult lenses, as age increased: fiber cell gap junction coupling conductance declined significantly, correlating with decreases in Cx46 and Cx50 labeling in Western blots; fiber and surface cell membrane conductances did not change systematically; effective extracellular resistivity increased monotonically; center to surface gradients for intracellular pressure, sodium, calcium, and voltage all increased, but in an interdependent manner that moderated changes. In newborn pup lenses, there were changes that did not simply fit with the above paradigm.

CONCLUSIONS

In newborn pup lenses, the observed changes may relate to growth factors that are not related to age-dependent changes seen in adult lenses. The major change in adult lenses was an age-dependent decrease in gap junction coupling, probably due to oxidative damage leading to degradation of connexin proteins. These changes clearly lead to compromise of intracellular homeostasis and may be a causal factor in age-related nuclear cataracts.

A computer model of lens structure and function predicts experimental changes to steady state properties and circulating currents

BACKGROUND

In a previous study (Vaghefi et al. 2012) we described a 3D computer model that used finite element modeling to capture the structure and function of the ocular lens. This model accurately predicted the steady state properties of the lens including the circulating ionic and fluid fluxes that are believed to underpin the lens internal microcirculation system. In the absence of a blood supply, this system brings nutrients to the core of the lens and removes waste products faster than would be achieved by passive diffusion alone. Here we test the predictive properties of our model by investigating whether it can accurately mimic the experimentally measured changes to lens steady-state properties induced by either depolarising the lens potential or reducing Na+ pump rate.

METHODS

To mimic experimental manipulations reported in the literature, the boundary conditions of the model were progressively altered and the model resolved for each new set of conditions. Depolarisation of lens potential was implemented by increasing the extracellular [K+], while inhibition of the Na+ pump was stimulated by utilising the inherent temperature sensitivity of the pump and changing the temperature at which the model was solved.

RESULTS

Our model correctly predicted that increasing extracellular [K+] depolarizes the lens potential, reducing and then reversing the magnitude of net current densities around the lens. While lowering the temperature reduced Na+ pump activity and caused a reduction in circulating current, it had a minimal effect on the lens potential, a result consistent with published experimental data.

CONCLUSION

We have shown that our model is capable of accurately simulating the effects of two known experimental manipulations on lens steady-state properties. Our results suggest that the model will be a valuable predictive tool to support ongoing studies of lens structure and function.

What do aquaporin knockout studies tell us about fluid transport in epithelia?

The investigation of near-isosmotic water transport in epithelia goes back over 100 years; however, debates over mechanism and pathway remain. Aquaporin (AQP) knockouts have been used by various research groups to test the hypothesis of an osmotic mechanism as well as to explore the paracellular versus transcellular pathway debate. Nonproportional reductions in the water permeability of a water-transporting epithelial cell (e.g., a reduction of around 80-90 %) compared to the reduction in overall water transport rate in the knockout animal (e.g., a reduction of 50-60 %) are commonly found. This nonproportionality has led to controversy over whether AQP knockout studies support or contradict the osmotic mechanism. Arguments raised for and against an interpretation supporting the osmotic mechanism typically have partially specified, implicit, or incorrect assumptions. We present a simple mathematical model of the osmotic mechanism with clear assumptions and, for models based on this mechanism, establish a baseline prediction of AQP knockout studies. We allow for deviations from isotonic/isosmotic conditions and utilize dimensional analysis to reduce the number of parameters that must be considered independently. This enables a single prediction curve to be used for multiple epithelial systems. We find that a simple, transcellular-only osmotic mechanism sufficiently predicts the results of knockout studies and find criticisms of this mechanism to be overstated. We note, however, that AQP knockout studies do not give sufficient information to definitively rule out an additional paracellular pathway.

The effect of size and species on lens intracellular hydrostatic pressure

PURPOSE

Previous experiments showed that mouse lenses have an intracellular hydrostatic pressure that varied from 335 mm Hg in central fibers to 0 mm Hg in surface cells. Model calculations predicted that in larger lenses, all else equal, pressure should increase as the lens radius squared. To test this prediction, lenses of different radii from different species were studied.

METHODS

All studies were done in intact lenses. Intracellular hydrostatic pressures were measured with a microelectrode-manometer-based system. Membrane conductances were measured by frequency domain impedance analysis. Intracellular Na(+) concentrations were measured by injecting the Na(+)-sensitive dye sodium-binding benzofuran isophthalate.

RESULTS

Intracellular hydrostatic pressures were measured in lenses from mice, rats, rabbits, and dogs with radii (cm) 0.11, 0.22, 0.49, and 0.57, respectively. In each species, pressure varied from 335 ± 6 mm Hg in central fiber cells to 0 mm Hg in surface cells. Further characterization of transport in lenses from mice and rats showed that the density of fiber cell gap junction channels was approximately the same, intracellular Na(+) concentrations varied from 17 mM in central fiber cells to 7 mM in surface cells, and intracellular voltages varied from -45 mV in central fiber cells to -60 mV in surface cells. Fiber cell membrane conductance was a factor of 2.7 times larger in mouse than in rat lenses.

CONCLUSIONS

Intracellular hydrostatic pressure is an important physiological parameter that is regulated in lenses from these different species. The most likely mechanism of regulation is to reduce the density of open Na(+)-leak channels in fiber cells of larger lenses.

Development of a 3D finite element model of lens microcirculation

BACKGROUND

It has been proposed that in the absence of a blood supply, the ocular lens operates an internal microcirculation system. This system delivers nutrients, removes waste products and maintains ionic homeostasis in the lens. The microcirculation is generated by spatial differences in membrane transport properties; and previously has been modelled by an equivalent electrical circuit and solved analytically. While effective, this approach did not fully account for all the anatomical and functional complexities of the lens. To encapsulate these complexities we have created a 3D finite element computer model of the lens.

METHODS

Initially, we created an anatomically-correct representative mesh of the lens. We then implemented the Stokes and advective Nernst-Plank equations, in order to model the water and ion fluxes respectively. Next we complemented the model with experimentally-measured surface ionic concentrations as boundary conditions and solved it.

RESULTS

Our model calculated the standing ionic concentrations and electrical potential gradients in the lens. Furthermore, it generated vector maps of intra- and extracellular space ion and water fluxes that are proposed to circulate throughout the lens. These fields have only been measured on the surface of the lens and our calculations are the first 3D representation of their direction and magnitude in the lens.

CONCLUSION

Values for steady state standing fields for concentration and electrical potential plus ionic and fluid fluxes calculated by our model exhibited broad agreement with observed experimental values. Our model of lens function represents a platform to integrate new experimental data as they emerge and assist us to understand how the integrated structure and function of the lens contributes to the maintenance of its transparency.

Efficiency of primary saliva secretion: an analysis of parameter dependence in dynamic single-cell and acinus models, with application to aquaporin knockout studies

Secretion from the salivary glands is driven by osmosis following the establishment of osmotic gradients between the lumen, the cell and the interstitium by active ion transport. We consider a dynamic model of osmotically driven primary saliva secretion and use singular perturbation approaches and scaling assumptions to reduce the model. Our analysis shows that isosmotic secretion is the most efficient secretion regime and that this holds for single isolated cells and for multiple cells assembled into an acinus. For typical parameter variations, we rule out any significant synergistic effect on total water secretion of an acinar arrangement of cells about a single shared lumen. Conditions for the attainment of isosmotic secretion are considered, and we derive an expression for how the concentration gradient between the interstitium and the lumen scales with water- and chloride-transport parameters. Aquaporin knockout studies are interpreted in the context of our analysis and further investigated using simulations of transport efficiency with different membrane water permeabilities. We conclude that recent claims that aquaporin knockout studies can be interpreted as evidence against a simple osmotic mechanism are not supported by our work. Many of the results that we obtain are independent of specific transporter details, and our analysis can be easily extended to apply to models that use other proposed ionic mechanisms of saliva secretion.

Lens intracellular hydrostatic pressure is generated by the circulation of sodium and modulated by gap junction coupling

We recently modeled fluid flow through gap junction channels coupling the pigmented and nonpigmented layers of the ciliary body. The model suggested the channels could transport the secretion of aqueous humor, but flow would be driven by hydrostatic pressure rather than osmosis. The pressure required to drive fluid through a single layer of gap junctions might be just a few mmHg and difficult to measure. In the lens, however, there is a circulation of Na(+) that may be coupled to intracellular fluid flow. Based on this hypothesis, the fluid would cross hundreds of layers of gap junctions, and this might require a large hydrostatic gradient. Therefore, we measured hydrostatic pressure as a function of distance from the center of the lens using an intracellular microelectrode-based pressure-sensing system. In wild-type mouse lenses, intracellular pressure varied from ∼330 mmHg at the center to zero at the surface. We have several knockout/knock-in mouse models with differing levels of expression of gap junction channels coupling lens fiber cells. Intracellular hydrostatic pressure in lenses from these mouse models varied inversely with the number of channels. When the lens' circulation of Na(+) was either blocked or reduced, intracellular hydrostatic pressure in central fiber cells was either eliminated or reduced proportionally. These data are consistent with our hypotheses: fluid circulates through the lens; the intracellular leg of fluid circulation is through gap junction channels and is driven by hydrostatic pressure; and the fluid flow is generated by membrane transport of sodium.

Fluid Transport Across Leaky Epithelia: Central Role of the Tight Junction and Supporting Role of Aquaporins

The mechanism of epithelial fluid transport remains unsolved, which is partly due to inherent experimental difficulties. However, a preparation with which our laboratory works, the corneal endothelium, is a simple leaky secretory epithelium in which we have made some experimental and theoretical headway. As we have reported, transendothelial fluid movements can be generated by electrical currents as long as there is tight junction integrity. The direction of the fluid movement can be reversed by current reversal or by changing junctional electrical charges by polylysine. Residual endothelial fluid transport persists even when no anions (hence no salt) are being transported by the tissue and is only eliminated when all local recirculating electrical currents are. Aquaporin (AQP) 1 is the only AQP present in these cells, and its deletion in AQP1 null mice significantly affects cell osmotic permeability (by ∼40%) but fluid transport much less (∼20%), which militates against the presence of sizable water movements across the cell. In 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 we have developed correctly predicts experimental results only when paracellular electro-osmosis is assumed rather than transcellular local osmosis. Our evidence therefore suggests that the fluid is transported across this layer via the paracellular route by a mechanism that we attribute to electro-osmotic coupling at the junctions. From our findings we have developed 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; and 4) an AQP role in regulation rather than as a significant water pathway. These elements are remarkably similar to those proposed by the laboratory of Adrian Hill for fluid transport across other leaky epithelia.

Lens gap junctions in growth, differentiation, and homeostasis

The cells of most mammalian organs are connected by groups of cell-to-cell channels called gap junctions. Gap junction channels are made from the connexin (Cx) family of proteins. There are at least 20 isoforms of connexins, and most tissues express more than 1 isoform. The lens is no exception, as it expresses three isoforms: Cx43, Cx46, and Cx50. A common role for all gap junctions, regardless of their Cx composition, is to provide a conduit for ion flow between cells, thus creating a syncytial tissue with regard to intracellular voltage and ion concentrations. Given this rather simple role of gap junctions, a persistent question has been: Why are there so many Cx isoforms and why do tissues express more than one isoform? Recent studies of lens Cx knockout (KO) and knock in (KI) lenses have begun to answer these questions. To understand these roles, one must first understand the physiological requirements of the lens. We therefore first review the development and structure of the lens, its numerous transport systems, how these systems are integrated to generate the lens circulation, the roles of the circulation in lens homeostasis, and finally the roles of lens connexins in growth, development, and the lens circulation.

Frequency spectrum of transepithelial potential difference reveals transport-related oscillations

How epithelia transport fluid is a fundamental issue that is unresolved. Explanations offered include molecular engines, local transcellular osmosis, local paracellular osmosis, and paracellular fluid transport. On the basis of experimental and theoretical work done on corneal endothelium, a fluid transporting epithelium, we suggest electroosmotic coupling at the level of the intercellular junctions driven by the transendothelial electrical potential difference as an explanation of paracellular fluid transport. We collect frequency spectra of that potential difference in real-time. For what we believe is the first time for any epithelium, we report that, unexpectedly, the potential difference displays oscillations at many characteristic frequencies. We also show that on both stimulating cell activity and inhibiting ion transport mechanisms, there are corresponding changes in the oscillations amplitudes that mirror changes known previously in rates of fluid transport. We believe these findings provide a novel tool to study the kinetics of electrogenic elements such as channels and transporters, which from this evidence would give rise to current oscillations with characteristic periods going from 150 ms to 8 s.

Fluid transport phenomena in ocular epithelia

This article discusses three largely unrecognized aspects related to fluid movement in ocular tissues; namely, (a) the dynamic changes in water permeability observed in corneal and conjunctival epithelia under anisotonic conditions, (b) the indications that the fluid transport rate exhibited by the ciliary epithelium is insufficient to explain aqueous humor production, and (c) the evidence for fluid movement into and out of the lens during accommodation. We have studied each of these subjects in recent years and present an evaluation of our data within the context of the results of others who have also worked on electrolyte and fluid transport in ocular tissues. We propose that (1) the corneal and conjunctival epithelia, with apical aspects naturally exposed to variable tonicities, are capable of regulating their water permeabilities as part of the cell-volume regulatory process, (2) fluid may directly enter the anterior chamber of the eye across the anterior surface of the iris, thereby representing an additional entry pathway for aqueous humor production, and (3) changes in lens volume occur during accommodation, and such changes are best explained by a net influx and efflux of fluid.

Application of the Na+ recirculation theory to ion coupled water transport in low- and high resistance osmoregulatory epithelia

The theory of Na+ recirculation for isosmotic fluid absorption follows logically from Hertz's convection-diffusion equation applied to the exit of water and solutes from the lateral intercellular space. Experimental evidence is discussed indicating Na+ recirculation based upon the following approaches: (i) An isotope tracer method in small intestine. Simultaneous measurement of water flow and ion transport in toad skin epithelium demonstrating, (ii) occasional hyposmotic absorbates, and (iii) reduced fluid absorption in the presence of serosal bumetanide. (iv) Studies of the metabolic cost of net Na+ absorption demonstrating an efficiency that is lower than the 18 Na+ per O2 consumed given by the stoichiometry of the Na+/K+-pump. Mathematical modeling predicts a significant range of observations such as isosmotic transport, hyposmotic transport, solvent drag, anomalous solvent drag, the residual hydraulic permeability in proximal tubule of AQP1(-/-) mice, the adverse relationship between hydraulic permeability and the concentration difference needed to reverse transepithelial water flow, and in a non-contradictory way the wide range of metabolic efficiencies from above to below 18 Na+/O2. Certain types of observations are poorly or not at all reproduced by the model. It is discussed that such lack of agreement between model and experiment is due to cellular regulations of ion permeabilities that are not incorporated in the modeling. Clarification of these problems requires further experimental studies.

The Lens Circulation

The lens is the largest organ in the body that lacks a vasculature. The reason is simple: blood vessels scatter and absorb light while the physiological role of the lens is to be transparent so it can assist the cornea in focusing light on the retina. We hypothesize this lack of blood supply has led the lens to evolve an internal circulation of ions that is coupled to fluid movement, thus creating an internal micro-circulatory system, which makes up for the lack of vasculature. This review covers the membrane transport systems that are believed to generate and direct this internal circulatory system.

Na+ Recirculation and Isosmotic Transport

The Na(+) recirculation theory for solute-coupled fluid absorption is an expansion of the local osmosis concept introduced by Curran and analyzed by Diamond & Bossert. Based on studies on small intestine the theory assumes that the observed recirculation of Na(+) serves regulation of the osmolarity of the absorbate. Mathematical modeling reproducing bioelectric and hydrosmotic properties of small intestine and proximal tubule, respectively, predicts a significant range of observations such as isosmotic transport, hyposmotic transport, solvent drag, anomalous solvent drag, the residual hydraulic permeability in proximal tubule of AQP1 (-/-) mice, and the inverse relationship between hydraulic permeability and the concentration difference needed to reverse transepithelial water flow. The model reproduces the volume responses of cells and lateral intercellular space (lis) following replacement of luminal NaCl by sucrose as well as the linear dependence of volume absorption on luminal NaCl concentration. Analysis of solvent drag on Na(+) in tight junctions provides explanation for the surprisingly high metabolic efficiency of Na(+) reabsorption. The model predicts and explains low metabolic efficiency in diluted external baths. Hyperosmolarity of lis is governed by the hydraulic permeability of the apical plasma membrane and tight junction with 6-7 mOsm in small intestine and < or = 1 mOsm in proximal tubule. Truly isosmotic transport demands a Na(+) recirculation of 50-70% in small intestine but might be barely measurable in proximal tubule. The model fails to reproduce a certain type of observations: The reduced volume absorption at transepithelial osmotic equilibrium in AQP1 knockout mice, and the stimulated water absorption by gallbladder in diluted external solutions. Thus, it indicates cellular regulation of apical Na(+) uptake, which is not included in the mathematical treatment.