A simple network thermodynamic method for series-parallel coupled flows: II. The non-linear theory, with applications to coupled solute and volume flow in a series membrane

Building on the linear network thermodynamic model presented in the first paper in this series (Mikulecky, Wiegand &; Shiner, 1977), a method of non-linear analysis is developed based mainly on the methods of Chua (1969). Using coupled salt and volume flow through membranes as an example, it is shown that the Kedem &; Katchalsky (1963a,b,c) linear model of series combinations of membranes behaves in a physically unrealistic manner (negative and infinite concentrations occur in the compartment between the membranes). Using the model introduced by Patlak, Goldstein &; Hoffman (1963) to obtain characteristics for a non-linear 2-port, the series network is well behaved and self-regulated. In the coordinate system of the linear reciprocal 2-port, the non-linear 2-port is shown to be a non-reciprocal element. Another co-ordinate system, which utilizes unidirectional fluxes (as measured by isotope fluxes, for example) and their conjugate driving forces, shows the non-linear 2-port to be separable in the sense of Li (1962) and Rosen (1968). A set of three pseudo-independent force-flow pairs completely characterizes the system and is compatible with a very simple non-linear network analysis which utilizes experimentally accessible and practical parameters such as the unidirectional solute fluxes, concentrations in the baths, volume flow and the hydrostatic minus effective osmotic pressure. As constitutive relations, the forward and backward permeabilities, which are dependent on volume flow and the filtration coefficient are all that are needed. A reflection coefficient appears in the driving force conjugate to volume flow in that the effective osmotic pressure is δΔπ and thus four independent coefficients, two of which depend on volume flow, are needed to determine the system. From the network analysis, the global properties of the series and/or parallel combinations of non-linear 2-ports are readily obtained. Although applied to a particular example, these non-linear methods are perfectly general. They are essentially the graphical form of the algebraic analysis in the linear theory, and are essentially based on the generalized version of Kirchhoff's laws used in graph and network theory. In the particular case of coupled solute and volume flow through membranes the non-linear element has a natural piecewise linearization which allows the linear theory to be applied using different values for the elements in each region.In an initial analysis, a linear network is drawn using the I-equivalent network of 1-port elements to model the linear 2-port in a series system. From this over-simplication a great deal of the qualitative behavior of the system can be visualized. For example, it is an easy way to see that solute will be accumulated or depleted in the central compartment between the membranes in an asymmetric series system. After this the non-linear analysis is used to further quantitatively describe the system's behavior and such phenomena as rectification of volume flow in the series membrane system. An appendix introduces a general theory for a class of non-linear transport phenomena.     

The static head method for determining the charge stoichiometry of coupled transport systems. Applications to the sodium-coupled D-glucose transporters of the renal proximal tubule

The static head method for determining the charge stoichiometry (the number of moles of charge translocated per mole of substrate) of a coupled transport system is presented. The method involves establishing experimental conditions under which a membrane potential exactly balances the thermodynamic driving force of a known substrate gradient. The charge stoichiometry can then be calculated from thermodynamic principles. In contrast to the usual steady-state method for determining charge stoichiometry in cell suspensions and vesicle preparations, the static head method is applicable to systems which are not capable of maintaining a constant membrane potential over time. The charge stoichiometries of two renal sodium coupled D-glucose transporters previously identified in brush-border membrane vesicle preparations from the outer cortex (early proximal tubule) and outer medulla (late proximal tubule) are determined. The charge stoichiometries of these transporters are in good agreement with their sodium/glucose coupling ratios arguing against the possibility that glucose transport is coupled to ions other than sodium in these membranes.     

Avian renal proximal tubule epithelium urate secretion is mediated by Mrp4

Birds are uricotelic and, like humans, maintain high plasma urate concentrations (approximately 300 microM). The majority of their urate waste, as in humans, is eliminated by renal proximal tubular secretion; however, the mechanism of urate transport across the brush-border membrane of the intact proximal tubule epithelium during secretion is uncertain. The dominance of secretory urate transport in the bird provides a convenient model for examining this process. The present study shows that short hairpin RNA interference (shRNAi) effectively knocked down gene expression of multidrug resistance protein 4 (Mrp4; 25% of control) in primary monolayer cultures of isolated chicken proximal tubule epithelial cells (cPTCs). Control and Mrp4-shRNAi-treated cPTCs were mounted in Ussing chambers and unidirectional transepithelial fluxes of urate were measured. To detect nonspecific effects, transepithelial electrical resistance (TER) and sodium-dependent glucose transport (Iglu) were monitored throughout experiments. Knocking down Mrp4 expression resulted in a reduction of transepithelial urate secretion to 35% of control with no effects on TER or Iglu. Although electrical gradient-driven urate transport in isolated brush-border membrane vesicles was confirmed, potassium-induced depolarization of the plasma membrane in intact cPTCs failed to inhibit active transepithelial urate secretion. However, electrical gradient-dependent vesicular urate transport was inhibited by the MRP4 inhibitor MK-571 also known to inhibit active transepithelial urate transport by cPTCs. Based on these data, direct measure of active transepithelial urate secretion in functional avian proximal tubule epithelium indicates that Mrp4 is the dominant apical membrane exit pathway from cell to lumen.     

Transepithelial transport of vinblastine by kidney-derived cell lines. Application of a new kinetic model to estimate in situ Km of the pump

We present a new transport model that may be useful for many kinds of transepithelial transport experiments. The model permits estimation of a pump Km and pump activity solely on the basis of transepithelial tracer fluxes. We apply the model to studies of a multidrug efflux pump, P-glycoprotein, which is normally located in the apical plasma membrane of certain transporting epithelia such as kidney proximal tubule cells. To determine the functional properties of this multidrug transporter in an epithelium, we studied the transepithelial transport of the chemotherapeutic drug, vinblastine, in epithelia formed by the kidney cell lines MDCK, LLC-PK1, and OK. We have previously shown that basal to apical flux of 100 nM vinblastine was about five times higher than apical to basal flux in MDCK epithelia, indicating that there is a net transepithelial transport of vinblastine across MDCK epithelia. Addition of unlabeled vinblastine reduced basal to apical flux of tracer and increased apical to basal flux of tracer in a concentration-dependent manner, a pattern expected if there is a saturable pump that extrudes vinblastine at the apical plasma membrane. The model permits estimation of a pump Km and pump activity solely on the basis of transepithelial tracer fluxes. According to the transport model the apical membrane pump has Michaelis-Menten kinetics with an apparent Km = 1.1 microM. Net basal to apical transport of vinblastine was also observed in LLC-PK1 cells and OK cells which are other kidney-derived cell lines. The order of potency of the transport is LLC-PK1 greater than MDCK greater than OK cells. The organic cation transporter is not involved in this vinblastine transport because vinblastine transport in MDCK cells was not affected by 3 mM tetramethyl- or tetraethylammonium. Inhibitors of vinblastine transport in MDCK cells was not affected by potency, were verapamil greater than vincristine greater than actinomycin D greater than daunomycin. The transport pattern we observed is that predicted to result from the function of the multidrug transporter in the apical plasma membrane.     

The static head method for determining the charge stoichiometry of coupled transport systems Applications to the sodium-coupled d-glucose transporters of the renal proximal tubule

The static head method for determining the charge stoichiometry (the number of moles of charge translocated per mole of substrate) of a coupled transport system is presented. The method involves establishing experimental conditions under which a membrane potential exactly balances the thermodynamic driving force of a known substrate gradient. The charge stoichiometry can then be calculated from thermodynamic principles. In contrast to the usual steady-state method for determining charge stoichiometry in cell suspensions and vesicle preparations, the static head method is applicable to systems which are not capable of maintaining a constant membrane potential over time. The charge stoichiometries of two renal sodium coupled d-glucose transporters previously identified in brush-border membrane vesicle preparations from the outer cortex (early proximal tubule) and outer medulla (late proximal tubule) are determined. The charge stoichiometries of these transporters are in good agreement with their sodium/glucose coupling ratios arguing against the possibility that glucose transport is coupled to ions other than sodium in these membranes.     

Time course of pump inhibition by ouabain in amphibian epithelia

Inhibition by ouabain of rheogenic Na⁺ transport across the basolateral membranes of frog skin is found to be manifest within 3–4 min. This rate of pump inhibition is not different from the rate of diffusion through extracellular tissue layers between the serosal bath and the actual site of action, i.e., the epithelial cell layers. It is concluded that the well-known slow time course of decrease in transepithelial current flow is due ionic redistribution and conductance changes of the epithelial membranes secondary to pump inhibition.     

Transport of chlorine in the proximal tubule. Its effects on water-electrolyte absorption

Several studies in rat kidney have established that an appreciable fraction of proximal absorption is passive in nature and occurs across the highly conductive paracellular pathway. Passive absorption is generally ascribed to the transepithelial Cl- distribution, luminal Cl- activity (alpha lCl) being higher than plasma Cl- activity (alpha pCl). The inequality alpha lCl greater than alpha pCl generates a transepithelial diffusion potential, lumen positive, which taken together with the chemical potential differences of Cl- and Na+ across the epithelium gives rise to transepithelial electrochemical potential differences for Cl- and Na+ favoring their absorption. The alpha lCl greater than alpha pCl distribution is traditionally ascribed to preferential bicarbonate absorption. We argue that HCO3- absorption alone cannot generate a non equilibrium transepithelial Cl- distribution. Other mechanisms are necessary. Our measurements in amphibian proximal tubule demonstrate that the intracellular Cl- activity, alpha cCl, is higher than the theoretical value predicted for equilibrium. This distribution is the result of two basolateral coupled transport processes (Cl-/HCO3- exchange and Cl-/Na+ cotransport). It contributes to the exit of Cl- from cell to lumen (by passive diffusion and K+/Cl- cotransport), yielding alpha lCl values higher than the theoretical value for equilibrium with regard to plasma. Thus, a small transcellular flux of Cl- (without solvent) proceeds from interstitium to lumen. It compensates the dissipative tendency of a much higher paracellular Cl- absorptive flux (in association with water) on the transepithelial Cl- gradient. The result is a steady-state luminal Cl- distribution above equilibrium, along the major part of the proximal tubule.     

Conductive properties of the proximal tubule in Necturus kidney

The electrical properties of the proximal tubule of the in vivo Necturus kidney were investigated by injecting current (as rectangular waves) into the lumen or into the epithelium of single tubules and by studying the resulting changes of transepithelial (VL) and/or cell membrane potential (VC) at various distances from the source. In some experiments paired measurements of VL and VC were performed at two abscissas x and x'. The luminal length constant of about 1,030 micrometer was shown to provide a good estimate of the transepithelial resistance, specific resistance (RTE = 420 omega.cm2) and/or per unit length (rTE = 1.3 x 10(4) omega.cm). The apparent intraepithelial length constant was subject to distortions arising from concomitant current spread in the lumen. The resistances of luminal membrane (rL), basolateral membrane (rB), and shunt pathway (rS) were estimated by two independent methods at 3.5 x 10(4), 1.2 x 10(4), and 1.7 x 10(4) omega.cm, respectively. The corresponding specific resistances were close to 1,200, 600, and 600 omega.cm2. There are two main conclusions of this study. (a) The resistances of cell membranes and shunt pathway are of the same order of magnitude. The figure of the shunt resistance is at variance with the notion that the proximal tubule of Necturus is a leaky epithelium. (b) A rigorous assessment of the conductive properties of concentric cylindrical double cables (such as renal tubules) requires that electrical interactions arising from one cable to another be taken into account. Appropriate equations were developed to deal with this problem.     

Transepithelial transport of drugs by the multidrug transporter in cultured Madin-Darby canine kidney cell epithelia

We studied transepithelial transport of 3H-labeled hydrophobic cationic drugs in epithelia formed by wild-type and by drug-resistant Madin-Darby canine kidney (MDCk) cells that had been infected with a retrovirus carrying the multidrug-resistance (MDR1) cDNA which encodes the P-glycoprotein. P-glycoprotein is an ATP consuming plasma membrane multidrug transporter responsible for the efflux of cytotoxic chemotherapeutic drugs from resistant cancer cells. Wild-type MDCK cells have small amounts of P-glycoprotein detected by immunoprecipitation. Net transepithelial transport across wild-type MDCK epithelia was demonstrated. Basal to apical flux of 100 nM vinblastine was about six times higher than apical to basal flux. Addition of unlabeled vinblastine reduced basal to apical flux of tracer and increased apical to basal flux of tracer, a pattern expected if there is a saturable pump that extrudes vinblastine at the apical plasma membrane. Daunomycin, vincristine, and actinomycin D were also actively transported and at 20 microM these agents inhibited transport of vinblastine, suggesting that wild-type MDCK cells have a common transporter for all these drugs. Vinblastine transport was also inhibited by 20 microM verapamil, which inhibits the multidrug transporter and reverses multidrug-resistance in non-polarized cells. Net transepithelial transport of all these cytotoxic drugs and of verapamil was much higher in epithelia formed by MDCK cells infected with a human MDR1 virus (MDR-MDCK) which is expressed on the apical surface of MDR-MDCK monolayers. Because the transport of these cytotoxic drugs and verapamil is increased in MDR-MDCK epithelia compared to wild-type MDCK epithelia, transport in both these cell populations can be attributed to P-glycoprotein. These results are consistent with a role for P-glycoprotein in multidrug secretory transport across the epithelium of the proximal tubule since P-glycoprotein is normally expressed on the apical membrane of proximal tubule cells.     

A mathematical model of calcium-induced fluid secretion in airway epithelium

Regulation of periciliary liquid (PCL) depth is of central importance to mucociliary clearance by the airway epithelium. Without adequate hydration mucociliary transport would cease, leading to build up of mucus in the airways, and impairing the clearance of any trapped inhaled particulates. Airway epithelial cells are known to release ATP under a number of stress conditions. Cell surface receptors bind ATP and trigger an intracellular calcium response which regulates the gating of specific ion channels on the apical and basolateral cell membranes. This shifts the electrochemical balance, resulting in the accumulation of Na⁺ and Cl^- in the periciliary liquid, and providing an osmotic driving force for water flux.In this study, we present a mathematical model of a single airway epithelial cell which describes the fluid secretion elicited after a rise in intracellular calcium. The model provides a basis to quantitatively analyse the influence of intracellular calcium signalling on fluid movement. The model demonstrates behaviour consistent with a number of experimental data on manipulating periciliary liquid volume and tonicity, and provides a quantitative basis for analysing the role of the different membrane ion channels in determining water flux following different physiological stimuli.     

Selective Assembly of V-ATPase Subunit Isoforms in Mouse Kidney

The kidney plays vital roles in acid–base homeostasis, and the reabsorption of water, ions, and proteins. These processes are achieved through acidification of urine and endosomes of proximal tubule epithelial cells. Multisubunit vacuolar-type proton ATPase (V-ATPase) is one of the major acidification-machinery proteins that localizes to the apical or basolateral plasma membranes of intercalated cells in collecting ducts and the endosomal region at the base of brush border microvilli in proximal tubules. Multiple subunit isoforms of V-ATPase, which are expressed in kidney, have been identified. One obvious question is whether the pumps at different locations in the kidney have their own unique subunit identities. We have used a combination of methods to study this enzyme in kidney including immunocytochemical staining and immunoprecipitation analyses. The subunit isoforms of V-ATPase exhibited selective association/assembly in kidney: kidney-specific isoforms predominantly formed the intercalated cell proton pump, whereas the pump located in the brush border comprised ubiquitously expressed counterparts.     

Role of the Paracellular Pathway in Isotonic Fluid Movement Across the Renal Tubule

Evidence for a highly permeable paracellular shunt in the proximal tubule is reviewed. The paracellular pathway is described as a crucial site for the regulation of net absorption and for solute-solvent interaction. Available models for the coupling of salt and water transport are assessed with respect to the problem of isotonic water movement. Two new models are proposed taking into account that the tight junctions are permeable to salt and water and that active transport sites for sodium are distributed uniformly along the lateral cell membrane. The first model (continuous model) is a modification of Diamond and Bossert''s proposal using different assumptions and boundary conditions. No appreciable standing gradients are predicted by this model. The second model (compartmental model) is an expansion of Curran''s double membrane model by including additional compartments and driving forces. Both models predict a reabsorbate which is not isosmotic. For the particular case of the proximal tubule it is shown that in the presence of a leaky epithelium these deviations from isotonicity might have escaped experimental observation.     

Cortisol alters carbonic anhydrase-mediated renal sulfate secretion

Active transepithelial sulfate secretion rate by winter flounder renal proximal tubule epithelium in primary culture (fPTC) is dependent on intracellular carbonic anhydrase (CA) and enhanced by cortisol. To further evaluate this relationship, a partial cDNA clone (327 bp) of carbonic anhydrase II (CAII) with high sequence similarity to CAII from numerous species including fish, chicken, and human was obtained from fPTCs. The majority of CA activity and CAII protein was present in the cytosol of fPTCs; however, significant amounts of both (in addition to SDS-resistant CA activity, i.e., CAIV-like isoform) were present in concentrated plasma membranes. CAII from concentrated membranes migrated differently than purified CAII on nondenaturing PAGE gels, suggesting that CAII associates with another membrane component. Treatment of fPTCs with the cell-soluble CA inhibitor methazolamide (100 microM) caused a 58% reduction in active transepithelial SO4(2-) secretion. fPTCs that were previously cultured under high-cortisol concentrations, when subjected to 5 days of low physiological levels of cortisol, had decreased CA activity (28%), CAII protein abundance (65%), and net active SO4(2-) secretion (28%), with no effect on epithelial differentiation. Methazolamide and low-cortisol treatment in combination inhibited net active SO4(2-) secretion 56%, which was not different than the effect of methazolamide treatment alone. These data indicate that cortisol directly increases renal CA activity, CAII protein abundance, and CA-dependent SO4(2-) secretion in the marine teleost renal proximal tubule.     

Comparison of the effects of dDAVP and AVP on the sodium transport in the frog skin

The effect of 1-deamino-8-D-arginine-vasopressin, dDAVP, the synthetic analogue of vasopressin, upon the active sodium transport across the frog skin was studied using standard microelectrode technique and compared with the effect of synthetic arginine-vasopressin, AVP. dDAVP applied to the basolateral side of the epithelium stimulated the active sodium transport as reflected by the increase of short-circuit current, Isc, and transepithelial electrical potential difference, Voc. Potential difference across both the apical, Vo, and the basolateral, Vi, cell membranes decreased. The driving force of transepithelial sodium transport, ENa, did not change. The transepithelial electrical resistance, Rt, ohmic resistance of the active sodium transport, RNa, and apical cell membrane resistance, Ro, rapidly decreased, while the resistance of the basolateral cell membrane, Ri, and the resistance of the shunt pathway, Rs, remained unchanged. It is concluded that dDAVP primarily increases sodium permeability of the apical cell membrane which subsequently stimulates sodium pump activity. This action is similar to that of AVP.     

The effect of osmotically induced water flows on the permeability and ultrastructure of the rabbit gallbladder

Summary The purpose of these experiments was to determine the effect of osmotic gradients on the permeability of the rabbit gallbladder. Increasing the tonicity of the mucosal solution reduced the permeability of the gallbladder to both ions and nonelectrolytes, whereas there was no significant effect when the serosal solution was made hypertonic. These results cannot be explained by solvent/solute interactions in either the epithelial membranes or the unstirred layers. Associated with the changes in permeability was the appearance of the transport number effect and current induced resistance changes. Morphological studies of the gallbladder under these conditions showed that the extracellular spaces of the epithelium and the rest of the wall dilate in the presence of osmotic flow to the serosa, but that the spaces collapse when the flow is in the opposite direction. Reconstruction of the permeability changes from the dimensions of the tissue show that all the physiological phenomena are accounted for by the changes in morphology, the dominant effect being in the lateral intercellular spaces. These results suggest that the lateral spaces are a common pathway shared by all solutes crossing the epithelium, and that diffusion along these spaces becomes rate limiting as the spaces collapse.     

Spontaneous tubular (cuboidal) metaplasia of the parietal layer of Bowman's capsule in Cynomolgus monkeys (Macaca fascicularis)

Tubular (cuboidal) metaplasia of the parietal epithelium of Bowman's capsule was observed in 19 (10 males, 9 females) of 56 adult control Cynomolgus monkeys. Cuboidal epithelium replaced the normally present flattened epithelium to various degrees in animals affected. Cuboidal cells revealed an eosinophilic cytoplasm and vesicular nuclei, thus resembling proximal convoluted epithelial cells in all respects. Continuity of the cuboidal glomerular epithelium with that of the proximal tubule was occasionally observed.     

Modifications of the genital kidney proximal and distal tubules for sperm transport in Notophthalmus viridescens (Amphibia,Urodela, Salamandridae)

Male salamanders use nephrons from the genital kidney to transport sperm from the testicular lobules to the Wolffian duct. The microstructure of the epithelia of the genital kidney proximal tubule and distal tubule was studied over 1 year in a population of Notophthalmus viridescens from Crawford and Pike counties in central Missouri. Through ultrastructural analysis, we were able to support the hypothesis that the genital kidney nephrons are modified to aid in the transportation of sperm. A lack of folding of the basal plasma membrane, in both the genital kidney proximal and distal tubules when compared to the pelvic kidney proximal and distal tubules, reduces the surface area and thus likely decreases the efficiency of reabsorption in these nephron regions of the genital kidney. Ciliated epithelial cells are also present along the entire length of the genital kidney proximal tubule, but are lacking in the epithelium of the pelvic kidney proximal tubule. The exact function of these cilia remains unknown, but they may aid in mixing of seminal fluids or the transportation of immature sperm through the genital kidney nephrons. Ultrastructural analysis of proximal and distal tubules of the genital kidney revealed no seasonal variation in cellular activity and no mass production of seminal fluids throughout the reproductive cycle. Thus, we failed to support the hypothesis that the cellular activity of the epithelia lining the genital kidney nephrons is correlated to specific events in the reproductive cycle. The cytoplasmic contents and overall structure of the genital and pelvic kidney epithelial cells were similar to recent observations in Ambystoma maculatum, with the absence of abundant dense bodies apically in the epithelial cells lining the genital kidney distal tubule. J. Morphol. 275:914–922, 2014. © 2014 Wiley Periodicals, Inc.     

Electrolyte transport across a simple epithelium. Steady-state and transient analysis.

A simple transporting epithelium is represented as a cellular compartment, compliant in all dimensions, and a paracellular channel, of arbitrary shape, between well-stirred mucosal ans serosal baths. The equations for mass balance, Poiseuille flow, and the Nernst-Planck equation are used to describe the continuous behavior of the system along cell and channel, whereas passive transport across membranes is given by the relations of Kedem and Katchalsky. Time-dependent terms are retained to permit study of transient phenomena. Boundary conditions at the baths demand only mass conservation and specify no a priori estimates of the system variables. A numerical model containing Na+,K+,Cl-, and impermeant cellular anions is formulated with membrane parameters taken from the literature on Necturus gallbladder. The differential equations are represented as a finite difference scheme and solved using Newton's method. It appears that apical cellular NaCl cotransport is necessary to obtain a reasonable cell chloride concentration. Investigation of the osmolality of the transepithelial flow shows that at steady state a leaky epithelium cannot separate baths of substantially different tonicity, although this does not guarantee isotonic transport between equiosmolar media. Changes in bath pressure, application of transepithelial electrical potential, and simulation of ion-substitution experiments are performed to understand the role of membrane permeabilities in determining the dynamic behavior of the epithelium.