Solvent drag of sucrose during absorption indicates paracellular water flow in the rat kidney proximal tubule

Stationary and Nonstationary Ion and Water Flux Interactions in Kidney Proximal Tubule: Mathematical Analysis of Isosmotic Transport by a Minimalistic Model

Our mathematical model of epithelial transport (Larsen et al. Acta Physiol. 195:171–186, 2009) is extended by equations for currents and conductance of apical SGLT2. With independent variables of the physiological parameter space, the model reproduces intracellular solute concentrations, ion and water fluxes, and electrophysiology of proximal convoluted tubule. The following were shown:

Modeling oxygen consumption in the proximal tubule: effects of NHE and SGLT2 inhibition

The objective of this study was to investigate how physiological, pharmacological, and pathological conditions that alter sodium reabsorption (TNa) in the proximal tubule affect oxygen consumption (QO2 ) and Na(+) transport efficiency (TNa/QO2 ). To do so, we expanded a mathematical model of solute transport in the proximal tubule of the rat kidney. The model represents compliant S1, S2, and S3 segments and accounts for their specific apical and basolateral transporters. Sodium is reabsorbed transcellularly, via apical Na(+)/H(+) exchangers (NHE) and Na(+)-glucose (SGLT) cotransporters, and paracellularly. Our results suggest that TNa/QO2 is 80% higher in S3 than in S1-S2 segments, due to the greater contribution of the passive paracellular pathway to TNa in the former segment. Inhibition of NHE or Na-K-ATPase reduced TNa and QO2 , as well as Na(+) transport efficiency. SGLT2 inhibition also reduced proximal tubular TNa but increased QO2 ; these effects were relatively more pronounced in the S3 vs. the S1-S2 segments. Diabetes increased TNa and QO2 and reduced TNa/QO2 , owing mostly to hyperfiltration. Since SGLT2 inhibition lowers diabetic hyperfiltration, the net effect on TNa, QO2 , and Na(+) transport efficiency in the proximal tubule will largely depend on the individual extent to which glomerular filtration rate is lowered.

Claudins and the kidney

Claudins are tight-junction membrane proteins that function as both pores and barriers in the paracellular pathway in epithelial cells. In the kidney, claudins determine the permeability and selectivity of different nephron segments along the renal tubule. In the proximal tubule, claudins have a role in the bulk reabsorption of salt and water. In the thick ascending limb, claudins are important for the reabsorption of calcium and magnesium and are tightly regulated by the calcium-sensing receptor. In the distal nephron, claudins need to form cation barriers and chloride pores to facilitate electrogenic sodium reabsorption and potassium and acid secretion. Aldosterone and the with-no-lysine (WNK) proteins likely regulate claudins to fine-tune distal nephron salt transport. Genetic mutations in claudin-16 and -19 cause familial hypomagnesemic hypercalciuria with nephrocalcinosis, whereas polymorphisms in claudin-14 are associated with kidney stone risk. It is likely that additional roles for claudins in the pathogenesis of other types of kidney diseases have yet to be uncovered.

Fluid reabsorption in proximal convoluted tubules of mice with gene deletions of claudin-2 and/or aquaporin1

Deletions of claudin-2 (Cldn2) and aquaporin1 (AQP1) reduce proximal fluid reabsorption (PFR) by about 30% and 50%, respectively. Experiments were done to replicate these observations and to determine in AQP1/claudin-2 double knockout mice (DKO) if the effects of deletions of these established water pores are additive. PFR was determined in inactin/ketamine-anesthetized mice by free-flow micropuncture using single-nephron I(125)-iothalamate (io) clearance. Animal means of PFR [% of glomerular filtration rate (GFR)] derived from TF/Piothalamate ratios in 12 mice in each of four groups [wild type (WT), Cldn2(-/-), AQP1(-/-), and DKO) were 45.8 ± 0.85 (51 tubules), 35.4 ± 1 (54 tubules; P < 0.01 vs. WT), 36.8 ± 1 (63 tubules; P < 0.05 vs. WT), and 33.9 ± 1.4 (69 tubules; P < 0.01 vs. WT). Kidney and single-nephron GFRs (SNGFR) were significantly reduced in all mutant strains. The direct relationship between PFR and SNGFR was maintained in mutant mice, but the slope of this relationship was reduced in the absence of Cldn2 and/or AQP1. Transtubular osmotic pressure differences were not different between WT and Cldn2(-/-) mice, but markedly increased in DKO. In conclusion, the deletion of Cldn2, AQP1, or of both Cldn2 and AQP1 reduces PFR by 22.7%, 19.6%, and 26%, respectively. Our data are consistent with an up to 25% paracellular contribution to PFR. The reduced osmotic water permeability caused by absence of AQP1 augments luminal hypotonicity. Aided by a fall in filtered load, the capacity of non-AQP1-dependent transcellular reabsorption is sufficient to maintain PFR without AQP1 and claudin-2 at 75% of control.

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.

Beta-adrenergic activation of solute coupled water uptake by toad skin epithelium results in near-isosmotic transport

Transepithelial potential (V(T)), conductance (G(T)), and water flow (J(V)) were measured simultaneously with good time resolution (min) in isolated toad (Bufo bufo) skin epithelium with Ringer on both sides. Inside application of 5 microM isoproterenol resulted in the fast increase in G(T) from 1.2+/-0.3 to 2.4+/-0.4 mS x cm(-2) and slower increases in equivalent short circuit current, I(SC)(Eqv) = -G(T) x V(T), from 12.7+/-3.2 to 33.1+/-6.8 microA cm(-2), and J(V) from 0.72+/-0.17 to 3.01+/-0.49 nL cm(-2) s(-1). Amiloride in the outside solution abolished I(SC)(Eqv) (-1.6+/-0.1 microA cm(-2)) while J(V) decreased to 0.50+/-0.15 nL cm(-2) x s(-1), which is significantly different from zero. Isoproterenol decreased the osmotic concentration of the transported fluid, C(osm) approximately 2 x I(SC)(Eqv)/J(V), from 351+/-72 to 227+/-28 mOsm (Ringer's solution: 252.8 mOsm). J(V) depicted a saturating function of [Na+]out in agreement with Na+ self-inhibition of ENaC. Ouabain on the inside decreased I(SC)(Eqv) from 60+/-10 to 6.1+/-1.7 microA cm(-2), and J(V) from 3.34+/-0.47 to 1.40+/-0.24 nL cm(-2) x s(-1). Short-circuited preparations exhibited a linear relationship between short-circuit current and J(V) with a [Na+] of the transported fluid of 130+/-24 mM ([Na+]Ringer's solution = 117.4 mM). Addition of bumetanide to the inside solution reduced J(V). Water was transported uphill and J(V) reversed at an excess outside osmotic concentration, deltaC(S,rev) = 28.9+/-3.9 mOsm, amiloride decreased deltaC(S,rev) to 7.5+/-1.5 mOsm. It is concluded that water uptake is accomplished by osmotic coupling in the lateral intercellular space (lis), and hypothesized that a small fraction of the Na+ flux pumped into lis is recirculated via basolateral NKCC transporters.

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.

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.

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.

Mathematical models of renal fluid and electrolyte transport: acknowledging our uncertainty

Mathematical models of renal tubular function, with detail at the cellular level, have been developed for most nephron segments, and these have generally been successful at capturing the overall bookkeeping of solute and water transport. Nevertheless, considerable uncertainty remains about important transport events along the nephron. The examples presented include the role of proximal tubule tight junctions in water transport and in regulation of Na(+) transport, the mechanism by which axial flow in proximal tubule modulates solute reabsorption, the effect of formate on proximal Cl(-) transport, the assessment of potassium transport along collecting duct segments inaccessible to micropuncture, the assignment of pathways for peritubular Cl(-) exit in outer medullary collecting duct, and the interaction of carbonic anhydrase-sensitive and -insensitive pathways for base exit from inner medullary collecting duct. Some of these uncertainties have had intense experimental interest well before they were cast as modeling problems. Indeed, many of the renal tubular models have been developed based on data acquired over two or three decades. Nevertheless, some uncertainties have been delineated as the result of model exploration and represent communications from the modelers back to the experimental community that certain issues should not be considered closed. With respect to model refinement, incorporating more biophysical detail about individual transporters will certainly enhance model reliability, but ultimate confidence in tubular models will still be contingent on experimental development of critical information at the tubular level.

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.

The paracellular permeability of opossum kidney cells, a proximal tubule cell line

The paracellular permeability of opossum kidney cells, a proximal tubule cell line.

BACKGROUND

The regulation of the unusually leaky paracellular pathway of the proximal tubule is poorly understood partially because of the lack of an appropriate in vitro cell model. In this study, we determined whether the paracellular permeability of opossum kidney (OK) cells would resemble that of the in vivo proximal tubule epithelium.

METHODS

The parental and subclonal OK cells and, for comparison, LLC-PK1 cells were cultured on permeable Transwell supports. The apparent paracellular permeability coefficient (Papp) for the extracellular marker 3H-mannitol was determined.

RESULTS

The Papp of OK cell sheets (12.17 x10-6 cm/sec) was remarkably close to the previously reported Papp of rat proximal tubules. The Papp of LLC-PK1 cells, another proximal tubule cell line, however, was approximately 20-fold lower than that of both OK cells and the in vivo proximal tubule. Phorbol 12-myristate 13-acetate, a protein kinase C activator, enhanced the Papp of OK cell sheets. The characteristic response of paracellular permeability to Ca2+ switch was demonstrated in OK cell sheets. Slight variations of Papp among several OK subclones were observed. Basal to apical Papp was uniformly higher than apical to basal Papp, independent of cell subtype. This rectification was attenuated by inhibition of active transport.

CONCLUSIONS

OK cell sheets cultured on Transwell supports possess a leaky paracellular pathway resembling that of the proximal tubule epithelium in vivo.

Water does not flow across the tight junctions of MDCK cell epithelium

Although it has been known for decades that the tight junctions of fluid-transporting epithelia are leaky to ions, it has not been possible to determine directly whether significant transjunctional water movement also occurs. An optical microscopic technique was developed for the direct visualization of the flow velocity profiles within the lateral intercellular spaces of a fluid-absorptive, cultured renal epithelium (MDCK) and used to determine the velocity of the fluid flow across the tight junction. The flow velocity within the lateral intercellular spaces fell to near zero adjacent to the tight junction, showing that significant transjunctional flow did not occur, even when transepithelial fluid movement was augmented by imposition of osmotic gradients.

Routes and mechanism of fluid transport by epithelia

The mechanism of fluid transport by leaky epithelia and the route taken by the transported fluid are in dispute. A consideration of current mathematical models for coupling of solutes and water, as well as the methodologies for the study of fluid transport, shows that local osmosis best accounts for water movement. Although it seems virtually certain that the tight junctions are water permeable, the fraction of absorbed fluid that crosses the tight junction cannot yet be determined with confidence.

Influence of trifluoperazine and verapamil on the isolated perfused rat kidney

1. Isolated rat filtering kidneys were perfused with Ringer bicarbonate solutions containing either trifluoperazine (TFP, 50 microM) or verapamil (VER, 100 microM) to prevent tissue dysfunctions observed during perfusion. 2. Water, sodium and chloride kidney contents diminished under both treatments as compared with control preparations, and potassium content increased. 3. When albumin concentration was increased (10 g%) in the perfusion medium (nonfiltering kidney preparation) these effects of TFP or VER were not observed. 4. Lipid peroxidation and LDH release diminished significantly under 50 microM TFP but only slightly under 100 microM VER.

Cyclic AMP in the Malpighian tubule fluid and in the urine of Rhodnius prolixus

We demonstrate the presence of cyclic adenosine monophosphate (cAMP) in the fluid secreted by isolated Malpighian tubules of Rhodnius prolixus. In addition, we show that fifth-instar R. prolixus excrete cAMP in the urine after a meal of human blood. Nonstimulated isolated Malpighian tubules secrete small amounts of cAMP that increase about 10-fold after the addition of 5-hydroxytryptamine (5-HT). 5-HT is known to mimic R. prolixus diuretic hormone. The present findings demonstrate that 5-HT also acts via cAMP. The presence of cAMP in the rectal sac of the insect could be of importance in the differentiation of Trypanosoma cruzi and in the cycle of Chagas disease.