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.

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.

Physical properties of isolated perfused basement membranes from rabbit loop of Henle.

Isolated, perfused segments of late proximal straight tubule, descending thin limb of Henle, and ascending thick limb of Henle from the rabbit were studied before and after removal of the epithelium with sodium deoxycholate. The relationship between transmural hydrostatic pressure and outer tubule diameter was similar in paired intact tubules and basement membranes, indicating that basement membrane is the principal determinent of tubule distensibility. As calculated from teh measured perfusate flow at several different transmembrane hydrostatic pressures, the hydraulic conductivity of the basement membranes was 6-8 X 10(-3) cm3/cm2.min.cmH2O. With use of these LP values and the calculated oncotic pressure required experimentally to reduce transmembrane hydrostatic pressure transiently to zero, the apparent reflection coefficient of the basement membranes for serum albumin was estimated to be 0.05-0.16. It is concluded that basement membranes of the loop and of other previously studied segments of rabbit nephron provide very strong and elastic mechanical support to the epithelium while having minimal resistance to flow of water and of solutes as large as serum albumin.

Surface areas of brush border and lateral cell walls in the rabbit proximal nephron.

A morphometric technique is used to estimate the absolute and relative surface areas of the brush border microvilli and cell walls bordering lateral intercellular spaces. In isolated, perfused proximal tubule from rabbit, the luminal and lateral surfaces are equal in area. For proximal convoluted tubules (PCT) each surface is 4.1 +/- 0.3 mu2/mu3 of epithelial cell volume or approximately 2.9 X 10(6) mu2/mm of tubule length. In proximal straight tubules (PST) the areas are 2.6 +/- 0.2 mu2/mu3 or 1.2 X 10(6) mu2/mm. Brush border enlarges the apical cell surface 36-fold in PCT and 15-fold in PST. The luminal and lateral cell surfaces each are approximately 20-fold (in PCT) and 10-fold (in PST) greater than the areas of the basal cell surface and tubule basement membrane. These data may be important in the context of an intercellular transport model.

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.

Shape of epithelial cells and intercellular channels in the rabbit proximal nephron.

In electron micrographs of proximal convoluted (PCT) and proximal straight tubules (PST), epithelial height was divided into five zones of equal thickness. Morphometric techniques were used to calculate surface area of cell wall bordering intercellular channels in each zone. Surface concentration of total lateral cell surface is 3.85 mu2/mu3 of PCT and 2.90 mu2/mu3 of PST. For tubules normalized to outer diameter = 40mu and inner diameter = 25mu, total lateral area is 29 X 10(5) mu2/mm of PCT and 22 X 10(5) mu2/mm of PST. Zone 5 adjacent to basement membrane has similar area (congruent to 17 X 10(5) mu2/mm) and fine structure in PCT and PST. However, the luminal four-fifths of the two cells differ markedly. Lateral area in PCT zones 1 through 4 increases approximately exponentially (from 1.1 X 10(5) to 6.4 X 10(5) mu2/mm) and constitutes 44% of total area. Respective areas in PST increase at a rate greater than exponential (from 0.7 X 10(5) to 2.6 X 10(5) mu2/mm) but constitute only 23% of total. From these data and the estimated number of cells per millimeter of tubule (825), circumferences of individual cells were estimated and quantitative three-dimensional cell models were constructed. The shape of intercellular channels is similar to that of the space between concentric, truncated and pleated horns.

Pressure-flow-diameter relationships in isolated perfused thin limb of Henle.

To measure directly the relationships between flow rate, tubule diameter, and flow resistance in thin descending limbs of Henle, isolated tubule segments from the rabbit were studied by in vitro microperfusion. Small increases in pressure and flow cause rapid enlargement of the tubule. Flow resistance is inversely related to tubule diameter and, by its effect on transmural pressure, indirectly limits the extent of tubule dilation. In a range of transmural pressures comparable to that in vivo, the tubule is capable of radial dilations as great as 35% and does not reach its structural limit of distensibility. Flow resistance may be approximately by a Poiseuille equation for cylindrical tubules. The effective luminal diameter is approximately a constant fraction of outer tubule diameter and is defined approximately by the innermost projection of semirigid epithelial nuclei.

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.

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.

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.

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.

Shape of cells and intercellular channels in rabbit thick ascending limb of Henle.

Electron micrographs of cortical thick ascending limb of Henle (TALH) were studied using morphometric techniques. The apical cell surface and the tubule basement membrane have identical areas of 0.8 x 10(5) mu2/mm of tubule length in a typical tubule (I.D. = 15 mu, O.D. = 25 mu). The total area of lateral cell walls bordering intercellular channels in 7.9 x 10(5) mu2/mm of typical tubule, and the ratio of apical cell surface to lateral surface in 0.10 +/- 0.01. When the photographed tubule mass was divided into five concentric zones of equal thickness, the lateral wall areas per zone were found to increase more rapidly than exponential, from 0.63 x 10(5) mu2/mm in that zone nearest the lumen to 3.6 c 10(5) mu2/mm in that zone adjacent to basement membrane. From these data and the estimated number of cells per mm of tubule length (764 cells), the circumferences of individual cells could be calculated for each zone, and quantative three-dimensional cell model could be constructed. The shape of intercellular channels is similar to that of the space between concentric, truncated, and plated horns. TALH cells are compared to previously described cells of rabbit proximal convoluted and straight tubules.

Phenomenological model relating cell shape to water reabsorption in proximal nephron.

If the complex pattern of intercellular channels in proximal tubule is determined in part by the forces of large transepithelial water flow, the shape of the cells is an indicator of the type and magnitude of the forces required for water movement and the routes of that flow. To test this thesis, morphologic data and volume flow parameters for rabbit proximal tubule are related generally by a mass balance equation. If the intercellular boundaries are assumed to be highly deformable and to respond to changes in hydrostatic pressure, the solution to that equation is a simple relationship between cell shape and the forces required for water movement. 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. It is concluded that quantitative morphologic studies may serve as a powerful means for evaluating and understanding transport phenomena in the nephron.

Potassium reabsorption and secretion in the perfused bullfrog kidney.

Techniques have been developed for obtaining comparative estimates of the rates of K secretion and reabsorption in the artificially perfused bullfrog kidney and the use of 42K infused into the portal circulation. In control experiments in which Kexc/Kfilt averaged 0.65, approximately 30% of filtered K escaped reabsorption and excreted K was composed of roughly equal parts of filtered K and secreted K. Fractional reabsorption of K was constant at 70% over a wide range of filtration rates. The rate of K secretion correlated significantly with the rate of Na reabsorption and with the urine flow rate. Acetazolamide stimulated secretion and inhibited reabsorption.

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.

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.

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.

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.

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)