Filled pore approximation: a theoretical framework for solute-solvent coupling in narrow water channels.

A phenomenological model is presented of water and solute transport that is applicable to water pores with radii less than approximately 2 A. This includes such examples as gramicidin A, the proximal tubule basolateral membrane, and the aquaporin 1 (CHIP28) water channel. The model differs from the conventional single-file model by allowing for a variation of unoccupied volume within the pores. It is shown that the accessible or free portion of the unoccupied volume can be related to the mechanical frictional coefficients and thereby to the filtration and diffusive permeabilities by the filled pore approximation. In general, the smallness of the unoccupied volume represents the compactness of the molecules within the pore and is indicative of the single-file character of the motion of water and solute moving together. When that volume is equal to a single water volume, the results are identical to the conventional single-file model. An important result is that, despite very low diffusive permeabilities, the reflection coefficient of a solute can remain at approximately 0.5 if its frictional interaction with the channel walls is comparable with its frictional interaction with neighboring water molecules. This is consistent with values previously reported for NaCl in cell membranes of proximal tubule. The model predicts a minimum effective pore radius for a water channel of 1.78 A and corresponds to a maximum filtration-to-diffusion permeability ratio that is proportional to the length of the effective pore or channel. This limiting condition corresponds to a water channel completely filled by water and may be applicable to the aquaporin 1 water channel.

Measurement of albumin reflection coefficient with isolated rat glomeruli.

Macromolecular permeability of the glomerular capillary has been inferred from the clearance of endogenous protein or infused macromolecules. Permeability is increased after treatment with polycations as well as after renal injury. It has previously been shown that the capillaries of glomeruli isolated from normal mammals expand or collapse in response to transcapillary albumin gradients and that the magnitude of the changes in capillary volume and in total glomerular volume are directly proportional to the applied oncotic gradients. In the experiments presented here, the volume responses of control glomeruli and of glomeruli treated with protamine (100 to 600 micrograms/mL for up to 60 min) were used to calculate the albumin reflection coefficient, sigma albumin, and the convectional permeability, P convectional albumin = (1 - sigma albumin), of the capillary wall. Sigma albumin for normal glomeruli was about 1 (P convectional albumin = 0); sigma albumin fell to a minimum of 0.2 +/- 0.1 (P convectional albumin = 0.8 +/- 0.1) after incubation with protamine sulfate (600 micrograms/mL) for 30 min. Retraction and fusion of podocyte foot processes and denudation of the underlying matrix was seen on scanning electron micrographs of protamine-treated glomeruli. These results confirm that it is possible to study macromolecular permeability of the glomerular capillary in vitro and to calculate sigma albumin independent of hemodynamic and systemic humoral influences. This method will permit the assessment of the effects of individual mediators of glomerular injury and the study of glomeruli from kidneys affected by experimentally induced or naturally occurring renal diseases.

Relative osmotic effects of raffinose, KCl, and NaCl across basolateral cell membrane.

Lumen-collapsed segments of rabbit S2 proximal tubule were bathed in isotonic medium and then exposed acutely to a medium made hypertonic by the addition of raffinose, NaCl, KCl, Na gluconate, K gluconate, or choline Cl. The result was a rapid efflux of water and a shrinking of the tubule, which could be measured by video techniques within the first 0.1 s. After reequilibration in isotonic medium, each tubule was then exposed to a second hypertonic medium to provide a direct comparison between two different solutes, either NaCl vs. KCl or raffinose vs. any one of the other solutes. Because raffinose is impermeant across the basolateral cell membrane, the ratio of its effect to that of another solute is a measure of the reflection coefficient (sigma) of that other solute. The following results were obtained: sigma KCl = 0.70 +/- 0.02, sigma K gluconate = 0.97 +/- 0.07, sigma Na gluconate = 0.84 +/- 0.06, and sigma choline Cl = 0.75 +/- 0.06. We previously have reported sigma NaCl = 0.56 +/- 0.07. If sigma of each salt is considered to be the arithmetic average of its component parts, and if gluconate and choline are considered to be impermeant, we also obtain sigma Na+ = 0.68, sigma K+ = 0.94, and sigma Cl- = 0.50.

Renal tubular differentiation in mouse and mouse metanephric culture. II. Na-K-ATPase activity.

Sodium-potassium adenosine triphosphatase (Na-K-ATPase) activity was measured by microassay, and the surface density of basolateral membranes was measured morphometrically in postglomerular segments of single tubules isolated from normally developing, intact mouse kidneys and from transfilter metanephric cultures. Proximal tubule Na-K-ATPase activity was 1092 +/- 480 pmol/mm per hour in newborn mice, increasing to 2462 +/- 258 in 1-week-old and 3470 +/- 578 pmol/mm per hour in adult mice. The Na-K-ATPase activity in newborn mice was approximately one-third of the activity in adult mice. Tubular Na-K-ATPase in transfilter metanephric culture was 972 +/- 536 pmol/mm per hour, a mean value almost identical to that in newborn mice. The surface density of basolateral cell membranes was 1.36 +/- 0.60 microns2/microns3 in newborn mice and 1.34 +/- 0.45 microns2/microns3 in 1-week-old mice, increasing to 2.70 +/- 0.98 microns2/microns3 in 4-week-old mice and 2.89 +/- 0.51 microns2/microns3 in adult mice. The surface density of tubular basolateral cell membranes in transfilter metanephric culture was 1.13 +/- 0.51 microns2/microns3, not significantly different from the surface density in newborn mice. The calculated mean surface area of basolateral membranes per unit tubular length was greater in cultures than in newborns, however, because total epithelial volume per unit length was significantly larger in the cultured tubules. Membrane surface area in intact mice increased with age, the surface area per unit length of tubule in adults being 4.6 times the area in newborn animals.(ABSTRACT TRUNCATED AT 250 WORDS)

Renal tubular differentiation in mouse and mouse metanephric culture. I. Ultrastructural studies.

We studied the morphologic features of renal tubular differentiation in transfilter metanephric culture. Differentiation of portions of the S-shaped loop into proximal convoluted tubule was detected shortly after 72 h of culture by the appearance of microvilli, coated membrane invaginations, and an apical vacuolar-microtubular network. These features developed synchronously, and the microvilli became progressively more numerous and more compact to form a brush border. Computer-assisted morphometric analysis showed only minor differences between proximal tubular cells from 18-day embryos and tubular cells from 7-day cultures of blastema taken from 11-day embryos. Segments of tubule corresponding to distal convoluted tubules were lined with relatively simple cells that contained few differentiating characteristics. Morphometric modeling of the tubular cells indicated a simple shape consistent with an inherent transport function.

Model of renal cell volume regulation without active transport: role of a heteroporous membrane.

Isolated proximal renal tubules of rabbit reach a passive steady-state volume in isotonic medium after active transport is inhibited by ouabain or by inhibition of cellular metabolism or lack of metabolic substrates. If the tubules are then placed in a hypotonic NaCl medium they swell rapidly and then exhibit a volume regulatory decrease (VRD) similar to that seen when active transport is present. We have mathematically modeled these transient events by assuming that the basolateral cell membrane is permeated by pores having at least two distinct reflection coefficients with respect to sodium, potassium, and chloride. VRD depends on the difference of the values of the reflection coefficients of the pore types. As hydrostatic pressure is exerted by the stretching basement membrane, water and ions can be expelled from the cells across the lower reflection coefficient pores and cause VRD. When the hydrostatic pressure compliance is removed, the cells fail to volume decrease unless sufficient extracellular impermeant solute is present to provide an osmotic force for water and ion exit. We conclude that a heteroporous membrane may be an essential feature for cell volume regulation and maintenance.

Theoretical models of cyst formation and growth.

Although the formation of fluid-filled, epithelial-lined cysts is a common event in a variety of tissues, the mechanisms involved are not well understood. Discussed here are means by which those mechanisms might be elucidated. In general, there are too few data available for complete analysis of in vivo disease processes. It can be suggested only that epithelial proliferation and basement membrane growth are probably absolute requirements. Whether the forces for fluid accumulation precede or follow the stimuli for cell growth cannot be stated with certainty. On the other hand, in certain in vitro model systems the forces required to keep cyst cavities filled with fluid may be so small that cell growth, rather than fluid accumulation, seems the more likely primary event.

Relationship between structure and function in renal proximal tubule.

Epithelia which support large transepithelial fluid movements are generally found to have histologic specializations which increase the surface areas of the cell membranes across which flows occur. A relationship between structure and function seems obvious in those cases. On the other hand, the area increasing specializations may also result in complicated shapes for the cells and their adjacent intercellular channels. In this paper we review the means for examining cell shape by quantitative stereologic techniques and the results obtained for the epithelium of the proximal renal tubule. We conclude that cell shape not only is a critical ingredient in any structure-function correlation for that tissue but also a "fingerprint" and a powerful tool with which one can predict and study epithelial absorptive flows and their driving forces.

Video measurement of basolateral NaCl reflection coefficient in proximal tubule.

Isolated, lumen-collapsed, proximal and distally occluded segments of rabbit S1 and S2 proximal tubule were equilibrated in isotonic NaCl or isosmotic raffinose medium and then exposed acutely to hypotonic or hypertonic raffinose or NaCl solution. The result was a water flux per millimeter tubule length, JVo, across the basolateral cell membranes and a consequent cell swelling or shrinkage that could be measured by a video technique in the initial 0.1 s or less after a change from steady state. The cell volume change was proportional to the applied osmolality difference, delta pi, and differed consistently with the solute employed. From the equation JVo/delta pi = sigma LpA, where sigma is the basolateral membrane reflection coefficient for the osmotic solute used and LpA is the membrane hydraulic conductivity per millimeter tubule length, and from the assumption that sigma raffinose = 1, sigma NaCl was obtained by dividing the JVo/delta pi values from the NaCl studies by those from the raffinose studies. For both S1 and S2 segments, sigma NaCl was found to be approximately 0.5. A similar value was obtained from the rate of cell shrinkage immediately after isosmolar exchange of raffinose for NaCl medium.

Morphometric analysis of distinct microanatomy near the base of proximal tubule cells.

Models of cell shape in the rabbit S2 proximal renal tubule were derived from transmission electron micrographs and compared with scanning micrographs. Standard morphometric procedures were used to measure basolateral cell membrane surface density (SVt) relative to total epithelial volume in numerous zones of cell height. In the basal 20% region we also measured the volume fraction (F) of intercellular spaces and calculated new surface densities in reference only to the intercellular volume, SVi = SVt/F, or to the cellular volume, SVc = SVt/(1-F). Combined use of these surface densities then enabled us to calculate the diameter, length, and separation of effectively cylindrical microvilli at the cell base. Assuming that lateral cell membranes are radially oriented in the apical region but disposed on microvillus like structures of arbitrary orientation at the cell base, an improved cell model was developed that agreed with the scanning picture throughout the entire cell height. Basal microvillar elements contain approximately 60% of the total basolateral cell membrane surface area and possibly constitute a hydrostatic resistive region for absorbate flow. These features have interesting physiological implications.

Morphological changes with Na+-free fluid absorption in isolated perfused snake tubules.

Snake (Thamnophis spp.) proximal renal tubules were perfused and bathed in vitro either with medium containing sodium or with medium in which the sodium was replaced with choline. Net fluid absorption was measured by changes in volume marker concentration, and cell volumes and cell membrane surface areas were measured by ultrastructural morphometric methods. Net fluid absorption did not differ significantly in the presence or absence of sodium. However, during the 20-25-min perfusion in the absence of sodium, significant morphological changes took place. The volume of the cells, doubled and the volume of the intercellular spaces nearly quintupled. The areas of the lateral and apical cell membranes approximately doubled, but their surface densities remained essentially constant. Therefore the larger cells in the absence of sodium had proportionally enlarged surface areas, so that the volume-to-surface area ratio remained constant. These morphological changes occurred concomitantly with the maintenance of net fluid absorption and might play a permissive role in such maintenance in the absence of sodium.

Localization of tissue potassium pools in the amphibian kidney.

Techniques were developed to determine the location of exchangeable K pools that had been identified previously in kinetic studies of the intact perfused bullfrog kidney. Following perfusion of the kidneys with 42K, a washout of the isotope was begun and interrupted at various times; the kidneys were removed, frozen, dried at low pressure and temperature, and then microdissected. Glomerular capillary tufts, small segments of tissue containing early distal tubules (diluting segment), and other segments containing proximal tubular convolutions were removed and analyzed for total content of K and 42K. In the intact kidney 77% of tissue K exchanged in 60 min. The exchangeable K concentration was 95 mu eq/ml cell water. Correction for the K activity coefficient in Ringer solution yielded an activity of 72 mu eq/ml. Thirty-two percent of glomerular capillary K exchanged in 60 min; 7% exchanged with a half time of 3.5 min; and the remainder exchanged at a rate too slow to measure. The data from tissue containing proximal tubular segments were too scattered to permit analysis. In segments containing early distal tubules, 67% of tissue K was contained in two exchangeable pools: one pool exchanged at a rate 10-fold greater than did the other. The data for these two distal pools were analyzed in terms of a parallel model (two cell types?) and a nested model (cytoplasm and subcellular organelles?). Pool size and exchange rates were calculated for both models. Electron microscopic analysis revealed that early distal tubular segments contain only one cell type which has a large population of mitochondria. This suggests that the nested model is more plausible. The fast distal pool exchanged at the same rate as the fast-exchanging pool identified in kinetic studies of the intact functioning kidney and is considered to be the K secretory pool.

Video measurement of basolateral membrane hydraulic conductivity in the proximal tubule.

Isolated, lumen-collapsed S1, S2, and S3 proximal tubule segments from the rabbit were exposed acutely to media made hypotonic or hypertonic by adjusting the concentration of the impermeant solute raffinose. The result was a water flux into or out of the cells across their basolateral cell membranes and a consequent swelling or shrinking of the cells. From tubule volume changes measured at 1/60-s intervals during the first 0.03-0.2 s of video recordings, the earliest water fluxes were found to be 0.76 +/- 0.04 nl X min-1 X mm-1 X mosM-1 in S1, 0.53 +/- 0.03 in S2, and 0.35 +/- 0.04 in S3. When normalized to outer tubule surface areas, these fluxes yield statistically different hydraulic conductivities of about 5,500, 4,000, and 3,000 microns X s-1 in the three segments. However, when normalized to the basolateral membrane surface areas, the basolateral membrane hydraulic conductivities are all approximately 300 microns X s-1 and not statistically different. If one assumes that the hydraulic conductivities of the basolateral and apical cell membranes are equal, the latter value agrees with reported transtubular measurements and is sufficient to allow nearly isotonic transcellular absorption to occur with driving forces of 2-3 mosM.

Morphometric comparison of rabbit cortical connecting tubules and collecting ducts.

Connecting tubule (CNT) segments of the rabbit distal nephron were examined by scanning electron microscopy and computer-assisted morphometric analysis of transmission electron micrographs. CNT were very similar to the cortical collecting ducts (CCD) described previously. The epithelium of both segments contains two cell types, both of which can be modeled as simple cuboidal cells, and two distinct systems of extracellular channels. The lateral intercellular channels are comparable to the spaces between simple cuboidal cells but are modified by short projecting microvilli which produce a modest increase in lateral cell surface area. The basal infolded channels are best developed in the connecting tubule cells of CNT and contribute 63% of all channel-associated membranes in CNT. Total membrane areas are similar in CNT and CCD. The two segments differ only in the degree of extracellular channel dilation and the distribution of infolded membrane relative to cell height in the connecting tubule and principal cells. The relatively minor morphometric differences between CNT and CCD do not correlate well with the marked difference in transtubular volume flow induced in the two segments by ADH and an osmotic gradient.

Shape of cells and extracellular channels in rabbit cortical collecting ducts.

Superficial cortical collecting ducts of rabbits were examined by scanning electron microscopy and by computer-assisted morphometric analysis of transmission electron micrographs. The epithelium contains two cell types, principal and intercalated, which have similar surface concentrations for apical and basal cell membranes and which can be modeled as simple cuboidal cells. The epithelium also contains two distinct and markedly different systems of extracellular channels. One system, the lateral intercellular channels, is comparable to the spaces between simple cuboidal cells but is modified by laterally projecting microvilli and ridges that produce a 1.8-fold magnification of the lateral cell surfaces. Those surfaces are nearly identical in the two cell types and constitute 38% of all cell membranes facing extracellular channels. The other channel system, the basal infolded channels, is well developed only in the basal 40% of principal cells and constitutes 62% of all channel-associated membrane. Its unique feature is an exponential increase in surface area, which is reminiscent of all channel-associated membranes in proximal nephron segments and which can be modeled as the interdigitation of cellular leaflets entirely within the boundaries of single cells.

Effects of sodium and chloride on potassium transport by the bullfrog kidney.

We have studied the effect on K transport of reductions in the Na and Cl concentrations of solutions perfusing the isolated bullfrog kidney. We used recently developed techniques for estimating the unidirectional reabsorptive and secretory K fluxes. Reduction of Na and Cl concentrations in the arterial perfusate from 112 and 100 mM to 22 and 10 mM, respectively, inhibited K secretion 82% and K reabsorption 97%. Reduction of only the Na concentration inhibited K secretion 42% but did not affect K reabsorption. Arterial and portal perfusion with 37 mM Na, 23 mM Cl reduced urine Na concentration to 6 mM and Na reabsorption by 59%. However, K secretion rose 88% and reabsorption fell 76%. Arterial and portal perfusates with 37 mM Na, 100 mM Cl reduced urine Na concentration to 2 mM and Na reabsorption by 46%. Still, K secretion was elevated 57% by an increase in urine flow rate. K reabsorption was not reduced. Arterial and portal perfusates with 112 mM Na, 23 mM Cl, and containing SO4 also stimulated K secretion 26% and inhibited K reabsorption 91%. Thus, reduction of perfusate Na concentration to 22 mM inhibited secretion but 37 mM was sufficient to permit stimulation of secretion by low Cl concentrations and by increased tubular fluid flow rate. Reduction of the perfusate Cl concentration stimulated secretion and inhibited reabsorption. We conclude that a minimum level of Na reabsorption is required to maintain K secretion, but above that minimum level changes in the rate of Na reabsorption do not affect the rate of K secretion. The tubular fluid Cl concentration or the rate of Cl reabsorption affects both reabsorption and secretion of K and, therefore, may be an important regulator of the rate of K excretion.

Computer-assisted morphometric analysis for three-dimensional cell shape.

Quantitative, morphometric analysis of 3-dimensional cell shape may prove to be a valuable adjunct to scanning electron microscopy and to the evaluation of epithelial transport phenomena. Therefore, to facilitate the wider use of cell shape analysis, a computer-assisted technique has been developed to supplement or replace the usually tedious and otherwise limited manual techniques previously available. The computer programs described here have been designed to run in a small laboratory computer, do not require a large amount of operator time, and are shown to provide an accuracy and efficiency not practical with manual procedures.

Prediction of total body water from the early arterial disappearance curve of isotopic water.

With the use of tritiated water, total body water was measured by isotope dilution in 17 normal dogs. Analysis of the plasma arterial disappearance curve up to 20 minutes by a computer program using a weighted least-squares technique makes it possible to predict the final volume of dilution, with acceptable precision from the early curve.

Effects of ouabain on potassium transport in the perfused bullfrog kidney.

We studied the effect of ouabain on transepithelial and cellular potassium transport in the isolated perfused bullfrog kidney. We used recently developed techniques for estimating the unidirectional reabsorptive and secretory K fluxes (Jr and Js) and measuring the kinetics of cellular K transport. Two hours of perfusion with 1 X 10(-6) M ouabain did not affect GFR, reduced fractional Na reabsorption 57%, increased K excretion 41%, and inhibited Jr 34%. Js rose 68% at 60 min and then returned to the control level. Ninety minutes of perfusion with 5 X 10(-6) M ouabain reduced GFR 28% and fractional Na reabsorption 76%. K excretion rapidly increased 71% within 30 min and then fell to 60% of the control level, while Jr fell 64%. Js rose 42% in 30 min and then fell to 23% of the control level. Both doses reduced K uptake into cellular pools from the circulation and increased the rate coefficients for efflux into tubular fluid. The data indicate that ouabain inhibited reabsorption and transiently accelerated the rate of loss of K from the cells into the tubular fluid. This initially masked the ultimate inhibition of K secretion from the circulation into the tubular fluid.

Cell shape as an indicator of volume reabsorption in proximal nephron.

If the complex shape of cells and intercellular channels in the renal proximal tubule is determined in part by the forces of large transepithelial water flow, the cell and channel shapes might serve as indicators of the type and magnitude of the forces required for water flow and the routes of that flow. We review here the known morphologic and functional data from the convoluted and straight portions of the rabbit proximal tubule and test the hypothesis of structure-function correlation in that tissue by means of a mass balance equation. If the lateral cell walls are sufficiently deformable to communicate small transmembrane differences in hydrostatic pressure, the resulting phenomenological model suggests an important new role for peritubular serum proteins and can be used to compute reasonable values for cell wall hydraulic conductivity, intercellular protein diffusion constant, and a channel fluid osmolality not more than 1% greater than that of luminal fluid. We conclude that quantitative morphologic studies may serve as a powerful means for evaluating and understanding transport phenomenons in the nephron.