Abstract
ABSTRACT. This is the first functional study of glomerular size and charge selectivity in mice. The aim was to investigate the controversial issue of glomerular permselectivity in animals exposed to glucosaminoglycan-degrading enzymes, hyaluronidase, and heparinase. Fractional clearances (θ) for FITC-Ficoll and albumin were estimated in isoflurane anesthetized mice in vivo and in cooled isolated perfused kidneys (cIPK). In cIPK, a significant increase of θalbumin from 0.0023 (95% confidence interval, 0.0014 to 0.0033) in controls to 0.0130 (95% confidence interval, 0.0055 to 0.0206) was seen after hyaluronidase treatment. The θ for neutral Ficoll of similar size as albumin was 0.063 to 0.093 in all groups. According to a heterogeneous charged fiber model, the fiber volume fraction of negatively charged fibers decreased by 10% after enzyme treatments. It is concluded that glomerular size and charge selectivity in mice is similar to that previously shown for rats. Moreover, hyaluronic acid, chondroitin sulfate, and heparan sulfate are of importance for charge selectivity. E-mail: marie.jeansson@kidney.med.gu.se
Received October 25, 2002. Accepted March 31, 2003.
The ability of the normal glomerular capillary wall to restrict the passage of macromolecules and albumin in particular plays a pivotal role for the electrolyte and fluid balance in the body. However, the filtration barrier is not yet fully understood, and even less is known about the disturbances leading to proteinuria. It has been demonstrated both in vivo and in vitro that the glomerular filtration barrier restricts the passage of anionic macromolecules relative to uncharged ones of similar size and configuration (1–6⇓⇓⇓⇓⇓). Some investigators also suggest that the effects of solute charge are negligible (7).
The specific location for such a charge barrier remains controversial. Electron microscopy using different cationic probes such as cationized ferritin (1,8,9⇓⇓) and lysozyme (10) has demonstrated the presence of anionic sites in the glomerular basement membrane (GBM). When anionic probes tended to be excluded from the GBM, this was suggested as the location of charge selectivity (1). However, anionic sites have also been demonstrated on endothelial (1,11⇓) and epithelial cells (12), whereas functional studies on filtration across isolated GBM have shown much less charge selectivity than that observed in vivo (13–15⇓⇓). This suggests that charge selectivity resides mainly at endothelial or epithelial cells or that charged structures are lost in the process of isolating the GBM.
Different enzymatic tools have been used to investigate the anionic charges found in GBM and in the glycocalyx of endothelial and epithelial cells. Studies using enzymes against different glucosaminoglycans (GAG) in isolated GBM indicate that heparan sulfate is the major GAG component (9,16–18⇓⇓⇓) but the nonsulfated hyaluronic acid is present as well (18). Glomerular endothelial and epithelial cell glycocalyx is mostly composed of negatively charged molecules such as sialoproteins (19,20⇓) and proteoglycan GAG (19,21⇓). Most of the GAG found are heparan sulfate, but hyaluronic acid is abundant in the endothelial cell glycocalyx as well (19,22,23⇓⇓). In this context, the glycocalyx includes a stagnant endothelial cell surface layer of loosely attached components.
The endothelial glycocalyx has also been implicated in the regulation of blood flow and microvascular permeability. Thus, heparinase, which cleaves heparan sulfate proteoglycans, has been shown to increase blood flow in cerebral (24) and mesenteric capillaries (25). Furthermore, hyaluronidase, cleaving hyaluronic acid, chondroitin, and chondroitin sulfate, seems to increase permeation of dextrans in hamster cremaster capillaries (22). In the latter study, the authors found that the enzyme reduced the endothelial “exclusion zone” representing a removal of GAG from the glycocalyx. Digestion of sialoproteins with neuraminidase decreased blood flow resistance in rat capillaries (25) and the binding of cationic ferritin to rat glomerular endothelium (19).
In this study, we hypothesize that the GAG in the endothelial cell glycocalyx, i.e., hyaluronan, chondroitin, chondroitin sulfate, and/or heparan sulfate, are of importance for charge selectivity. Hyaluronidase and heparinase were used to test this hypothesis. Albumin and a broad fraction of Ficolls allowed charged fiber analysis, thus giving a detailed description of size and charge selectivity of the glomerular filtration barrier. The experiments were performed both in vivo and in isolated perfused mice kidneys at low temperature to reduce tubular cell and protease activity.
Materials and Methods
Experiments were performed in female mice of the c57bl/6jbom strain (M&B, Stensved, Denmark) that weighed 18 to 25 g. The mice were kept on standard diet and had free access to water before the experiments. The experiments were approved by the Local Ethics Review Committee in Göteborg.
Anesthesia was induced and continued by inhalation of isoflurane (2 to 3% vol/vol; Pharmacia & Upjohn, Stockholm, Sweden) mixed with air (approximately 1 L/min) in an isoflurane vaporizer (Ohmeda Isotec 5; Simtec Engineering, Askim, Sweden). The body temperature of the mouse was kept at 37°C during the preparations by means of a thermostatically controlled heating pad and a temperature-sensitive lamp connected to a rectal probe. The carotid artery was cannulated with a PE-10 cannula for recordings of arterial pressure with a T-tube connected to a pressure transducer (PVB Medizintechnik, Kirchenseeon, Germany). The catheter also served as a route for subsequent administration of drugs and collection of blood. A cannula (PE-25) was put in the bladder for collection of urine.
Arterial pressure (PA) and urine weight changes were monitored by computer (PC 586) using Labview (National Instruments, Austin, TX) computer software. The experiments were performed both in vivo and in isolated perfused kidneys at 8°C (cIPK) using a control group and three enzyme-treatment protocols.
Enzyme Treatments and Controls
Each protocol was used both in vivo and in cIPK. Enzyme dissolved in saline or saline alone (controls) was given as a bolus dose via the carotid artery.
Bovine testis hyaluronidase (H3506; Sigma-Aldrich, Stockholm, Sweden) at a dose of 15 × 103 U/kg was given 60 min before first sample collection. Flavobacterium heparinum, heparinase III (H8891; Sigma-Aldrich), was given at a dose of 8.2 U/kg or 82 U/kg 60 and 15 min before the first urine sample collections, respectively.
Perfusate and Tracers
Perfusate was prepared using a modified Tyrode solution with human albumin (18 g/L; Immuno, Vienna, Austria) to which the tracers were added. The solution had the following composition: 113 mM NaCl, 4.3 mM KCl, 2.5 mM CaCl2, 0.8 mM MgCl2, 25.5 mM NaHCO3, 0.5 mM NaH2PO4, 5.6 mM glucose, 0.9 mM nitroprusside (Merck, Darmstadt, Germany), 10 mg/L furosemide, 300 mg/L FITC-labeled Ficoll (Bioflor HB, Uppsala, Sweden), and 0.16 MBq/L 51Cr-EDTA (Amersham Pharmacia Biotech, Buckinghamshire, UK). All solutions were made with fresh distilled water (Millipore, Bedford, MA) with a resistivity of 18.2 MΩ/cm. The perfusate (pH 7.4) was protected from light and gassed with 5% CO2 in O2.
Experimental Protocols
In Vivo.
The jugular vein was cannulated (PE-25) to serve as a route for infusion of tracer solution at a rate of 0.7 ml/h by a syringe pump (Razel Scientific Instruments, Stamford, CT). The tracer solution was composed as follows: 3 MBq/L 51Cr-EDTA, 1.5 MBq/L 125I-labeled human serum albumin (HSA IT.20S; Isopharma AS, Kjeller, Norway), 3 g/L FITC-Ficoll, 83 mM glucose, 30 mM bicarbonate, and 205 mM saline. 125I-HSA was filtered through an equilibrated desalting column (Sephadex G-25 PD-10; Amersham Pharmacia Biotech, Uppsala, Sweden) to remove the free iodide content before it was added to the tracer solution. Infusion of tracer solution was started 30 min before sample collections.
An injection of furosemide (2 mg/kg; Benzon Pharma A/S, Kobenhavn, Denmark) was given 5 min before the first urine collection. Blood samples were aspirated from the carotid artery at 10-min intervals, and urine was collected between each sequential two of the three blood samples, allowing estimations of GFR and fractional clearances (θ) for Ficolls and albumin.
Cooled Isolated Perfused Mouse Kidneys.
The mouse was eviscerated, and the intestines were removed. The aorta and caval vein was freed from surrounding tissues and clamped distal to the renal arteries. The aorta was cannulated with a T-tube (PE-25), connected to a pressure transducer, a few millimeters distal to the clamp in a retrograde direction. The clamp was removed, thus allowing perfusion of the kidneys by means of a pulsatile pump (Ismatec IPC; Zurich, Switzerland). The aorta was then ligated proximal to the renal arteries and the caval vein, distal to the renal arteries, was opened for venous outflow. After a short period of equilibration, two to eight urine samples were collected and weighed as above. Great care was taken not to touch the kidneys and to provide adequate perfusion with either blood or perfusate during the preparation procedure. The temperature of the perfusate was kept at 8°C to inhibit tubular function as well as energy consumption and myogenic tone (26,27⇓) without altering capillary permeability (6,28⇓).
Data Analysis
Perfusate, plasma, and urine samples were analyzed for 51Cr-EDTA, and plasma and urine samples also were analyzed for 125I-HSA count using a gamma-counter (Cobra AutoGamma Counting systems; Packard Instrument Co., Meridan, CT). Data was used for later calculations of GFR and θ for albumin. Corrections were made for background activity and 51Cr-EDTA spillover. In addition, the albumin concentration of all urine samples from the cIPK was determined by RIA (Pharmacia and Upjohn Diagnostics Sverige AB, Uppsala, Sweden).
Analysis of Ficoll
The θ for different radii of FITC-Ficoll were calculated by subjecting perfusate, plasma, and urine samples to gel filtration (BioSep-SEC-S3000; Phenomenex, Torrance, CA) and detection of fluorescence (Dionex fluorimeter RF-2000; Dionex Softron, Gynkotek, Germering, Germany) using Chromeleon (Gynkotek) software. A 0.05 M phosphate buffer with 0.15 M NaCl (pH 7.0) was used as eluent. A volume of 5 μl from each sample was analyzed at an emission wavelength of 520 nm and an excitation wavelength of 492 nm. The flow rate (1 ml/min) and the sampling frequency (1 per second) were maintained constant during the analysis and so were pressure (approximately 4 MPa) and temperature (8°C). The error in the CU/CP ratios for Ficoll were estimated to be <1% for most molecular sizes.
Electron Microscopy
To ensure that the enzymes did not destroy the ultra-structure of the glomerular filtration barrier, i.e., endothelial cells, glomerular basement membrane, and podocytes, we used electron microscopy. Under anesthesia, controls and mice that were treated with hyaluronidase (15 × 103 U/kg for 60 min) or heparinase (82 U/kg for 15 min) were perfused at 100 mmHg intracardially with Tyrode buffer containing 1 mg/ml Xylocaine followed by fixative containing 2.5% glutaraldehyde in 0.05 M Na-cacodylate (pH 7.2). The kidneys were removed, cut into 1-mm slices, and put in fixative. Cubes of 1 mm were excised from renal cortex and further fixed. They were then washed in 0.1 M Na-cacodylate buffer (pH 7.4) and postfixed in 1% OsO4 + 1% K ferricyanide for 2 h at 4°C followed by staining en bloc with 0.5% uranylacetate. After dehydration, the specimens were embedded in epoxy resin (Agar 100) and cured by heat. Ultrathin tissue sections, 50 to 60 nm, were obtained with an ultramicrotome (Ultracut E, Reichert, Austria) fitted with a diamond knife. Sections were contrasted with lead citrate and uranyl acetate and examined in a Zeiss 902 electron microscope.
Calculations
Glomerular Filtration Rate.
GFR was calculated from the urine over plasma concentration ratios (CU/CP), determined by 51Cr-EDTA times urine flow (QU) according to the following equation 
Fractional Clearance.
The renal clearance (Cl) of a solute X can be calculated from the amount excreted in the urine (CU) over the plasma concentration (CP) during a certain period of time according to the following equation: Cl = (CU/CP)X· QU. The θ of a solute is given by its Cl over GFR. Thus, combining Eq. 1 with the Cl equation above gives the following: equation 
Selectivity of the Glomerular Barrier
In this study, we used a heterogeneous charged fiber model analysis that combines size and charge selectivity. For comparison, the gel-membrane model, with two-pore analysis and calculation of charge densities, and the lognormal distribution + shunt analysis were calculated in controls.
Heterogeneous Charged Fiber Model.
There have been few attempts to combine size and charge selectivity in one model, because of the complex equations involved. However, Johnson and Deen (29) extended the partitioning theory of Ogston, predicting the concentration ratio of a solute at equilibrium in and outside a gel by a Boltzmann factor, thus obtaining partition coefficients for neutral and charged solutes in charged fiber gels. The endothelial surface layer (glycocalyx) could be considered as such a charged fiber gel, where fibrous chains of membrane glycoproteins form an aqueous fiber matrix or gel structure. The GBM is another charged gel. We previously used the analysis in a quantitative analysis of charge selectivity (5), but the present analysis differs in one important aspect, namely the introduction of heterogeneous fiber densities, i.e., a shunt pathway or large pores.
The prediction of the concentration ratio at equilibrium in a fiber matrix, the partition coefficient (Φ), is as follows equation 
where g(h) is the probability of finding the closest fiber at a distance, h, from a spherical solute in a dilute solution equation 
where φ is the volume fraction of fibers, rs is the solute radius, and rf is the fiber radius. By integrating Eq. 3, Ogston (30) reached the following expression for Φ: equation 
Johnson and Deen (29) introduced a Boltzmann factor to describe the relative probability at different energy states, e.g., in charged gels. Multiplying g(h) by this factor gives the following: equation 
where E(h) is the electrostatic free energy of the interactions between the solute and the nearest fiber divided with kT, where k is Boltzmann’s constant and T is absolute temperature. One important aspect is that E in this case only is dependent of one position variable, h, i.e., the interaction of the solute and the nearest fiber. In a true system, the solute would interact with multiple fibers and E would depend on multiple position variables, not only h. Johnson and Deen (29) solved Eq. 6 using a linearized Poisson-Boltzmann equation. In the equation, the parameters were made dimensionless scaled by the electrical potential RT/F, where R is the gas constant, T is temperature in Kelvin, and F is Faraday’s constant.
Moreover, the interaction between solute and fiber will give a change in the free electrochemical energy: equation 
where the subscripts s, f, and sf refer to the isolated solute, isolated fiber, and combined solute-fiber system, respectively. Note that to obtain ΔG, nested polynomial equations are required, making the calculations more complex (29).
Finally, the energy needed in Eq. 6 can be obtained by multiplying ΔG with the ratio of the electrostatic and thermal energy: equation 
where R, T, and F are explained above, and ε is the dielectric permittivity for the solvent. The dielectric permittivity is the relative dielectric constant multiplied by ε0, the constant for vacuum (ε0 = 8.8542 · 10−12 C · V−1·m−1). In the case of uncharged solute or fiber, the low dielectric constant will change the potential field of the charged solute or fiber surrounding, thus increasing the electrostatic free energy. For further details of the equations, please consult Johnson and Deen (29).
To apply the partition coefficients to experimental data, one must calculate θ. In the concept of “fiber matrix,” Curry and Michel (31) used the expression of Anderson and Malone (32) to calculate the reflection coefficient (ς) from the partition coefficient (Φ): equation 
It should be noted that the estimates of the reflection coefficients do not quite match experimental observations in agarose gels (33). There are, however, limited experimental studies of reflection coefficients in biologic gels, and to our knowledge, this is the best equation available.
Finally, the diffusion capacity (PS) is given by the following: equation 
where A0/Δx is the unrestricted exchange area over diffusion distance, and D is the free diffusion constant. The equations of Philips (34) for hindered diffusion of probes in gels were not used in the present analysis. Such a correction will reduce the fiber density substantially and probably improve the analysis further, but it will not affect any conclusions of the study. The θ is obtained using nonlinear flux equations (35): equation 
Basically, the important parameters in the model are the fiber radius (rf), the relative concentration of fibers in the gel (φ), the surface charge densities of solute (qs) and fiber (qf), the unrestricted exchange area overdiffusion distance (A0/Δx), and the large pore radius (rL). By using nonlinear regression analysis, the model parameters are fitted to the experimental θ of albumin and the neutral Ficolls of different radii (150 data points).
We assumed the rf to be 5 Å and the rs to be 35.5 Å and the surface charge densities (q) of fiber, albumin, and Ficoll to be −0.2, −0.022, and 0 C/m2, respectively.
Gel-Membrane Model.
According to the gel-membrane model (36), the glomerular barrier is composed of two separate compartments in series: one charge selective (gel) and one size selective (membrane). The gel is in contact with plasma and contains fixed negative charges, reducing the concentration of anionic solutes, such as albumin. The second compartment of the barrier behaves as a membrane exerting size discrimination but no charge selectivity. The concentration of solutes in the primary urine will depend on the effects of these two barrier components as outlined below. For calculations of charge selectivity, the θ for albumin and its neutral counterpart of same size, Ficoll35.5Å, are compared, giving an estimation of the charge density. Size-selective properties can be described using a two-pore model with experimental θ data for Ficolls, of molecular radii ranging from 30 to 70 Å. In brief, the exchange can be described using the following parameters: the functional small pore radius (rS), the rL, the large pore fraction of the glomerular filtrate (fL), and the A0/Δx (37). By using a nonlinear regression analysis and a previously defined set of physiologic equations (36), model parameters are fitted to the experimental θ of spherical neutral Ficoll of different radii (150 data points). Nonlinear flux equations are used to calculate the net fluxes of fluid and solutes for each pore pathway, individually (37). For further details regarding calculations, please consult Ohlson et al. (36).
Lognormal Distribution + Shunt Model.
Experimental θ data for Ficolls, of molecular radii ranging from 30 to 70 Å, can also be described using a lognormal distribution + shunt model (38,39⇓). In this model, the glomerular barrier is consider to have many pores with a radius that obey a lognormal probability distribution together with a few nonselective shunts. The parameters to determine in the model are mean pore radius, the width of the lognormal distribution (s), the large pore fraction of the fL, and the A0/Δx. The shunt was set at 150 Å, because a nonselective or higher shunt radius gives a poor fit for large solutes.
Fit between Experimental and Modeled Data in Nonlinear Regression Analysis
Powell’s χ2 was used to calculate the fit between experimental data and the modeled data received from nonlinear regression analysis in all models equation 
where θi(experimental) and θi(modeled) are the experimentally obtained and computer modeled θ for the size (i) of Ficoll and (n) the number of sizes.
Statistical Analyses
Results are presented as means with their 95% confidence intervals. Statistical comparisons were made using one-way ANOVA, with post hoc Games-Howell to test for significant differences. In the case of uneven distribution, the statistical analysis was based on their logarithmic values. Powell’s χ2 was used to estimate the fit between modeled and experimental data during nonlinear regression analysis. P < 0.05 was considered statistically significant. For a detailed description regarding equations and calculations in the heterogenous charged fiber model, please consult http://kidney.med.gu.se/9
Results
General
The mean wet weight of the kidneys (immediately after finished experiment) was 335 mg. General data regarding mean PA and GFR for in vivo and cIPK experiments are presented in Tables 1 and 2⇓. There were no significant differences in recorded PA between groups.
Table 1. PA and GFR in vivo
Table 2. PA and GFR in clPK
As expected, GFR was lower in the cIPK than in vivo (P < 0.001) for all experimental groups. Treatment with low-dose heparinase (LD60) increased GFR, in vivo with approximately 80% (P < 0.05) and in cIPK with 100% (P < 0.01). A fourfold (P < 0.05) increase in GFR was seen after high-dose heparinase (HD15) treatment in cIPK experiments but not in vivo. After hyaluronidase treatment, the 60% increase of GFR did not reach statistical significance.
The average urine to perfusate ratio of 51Cr-EDTA in cIPK was 1.19, reflecting a nearly complete inhibition of fluid reabsorption. In vivo, the average urine to perfusate ratio was 18.8.
θ for Albumin and Ficoll
Data regarding θ for albumin, Ficoll35.5Å, and Ficoll55Å for in vivo and cIPK experiments are summarized in Tables 3 and 4⇓. The θalbumin values were underestimated by one order of magnitude in vivo as a result of significant tubular reabsorption and degradation of albumin. In cIPK, hyaluronidase caused a fourfold increase of θalbumin (P < 0.05). After treatment with heparinase, no increase in θalbumin could be seen. The θ for Ficoll35.5Å was 0.06 to 0.10 in all groups, with no significant difference. Thus, the θ for albumin was almost 30 times lower than that for neutral Ficoll of similar size (35.5Å) in cIPK controls.
Table 3. Summary of θ for albumin, Ficoll35.5 A and Ficoll55 A, in vivo
Table 4. Summary of θ for albumin, Ficoll35.5A and Ficoll55A, in cIPK
Comparing in vivo and cIPK controls, a threefold higher θ could be seen in the cIPK for molecules larger than 55 Å (P < 0.001). Statistically, the low-dose heparinase-treated animals in vivo showed a decrease in θ compared with controls for molecules >55 Å (Tables 3 and 4⇑).
Permselectivity of the Glomerular Barrier
The properties of the glomerular barrier were modeled using a heterogeneous charged fiber analysis based on θ for Ficoll (30 to 70 Å) and albumin. The important parameters of this model are the fiber volume fraction, the large pore fraction of the glomerular filtrate (fL), the unrestricted exchange area overdiffusion distance (A0/Δx), and the large pore radius (rL). In the analysis, the fiber radius (rf) was constant at 5 Å and the fiber charge was −0.200 C/m2. The net charge for albumin and Ficoll was −0.022 C/m2 and 0 C/m2, respectively. The θ for a broad fraction of Ficoll, 30 to 70 Å, in eight representative cIPK control experiments can be seen in Figure 1. Note the almost perfect match between experimentally determined and modeled values. In vivo, a significant reduction of the fiber volume fraction could be seen, from 7.3% in controls to 6.8% in heparinase high dose (HD15)-treated animals (P > 0.05). In cIPK, significant (P > 0.01) reductions from 7.4% in controls to 6.7% and 6.4% could be seen in hyaluronidase and high-dose heparinase (HD15)-treated animals, respectively. The fiber charge volumes are summarized in Figure 2.
Figure 1. The fit between experimentally determined (•) and modeled (__) fractional clearances (θ) for Ficoll 30 to 70 Å in eight representative control experiments. Each curve has a representative scale on the x axis. Every second value was cut out to obtain a better resolution.
Figure 2. The estimated fiber volume fraction from charged fiber analysis. Circles represent mean, and bars represent the 95% confidence interval (CI) for controls and animals treated with hyaluronidase (Hya), heparinase low dose for 60 min (Hep LD60), or heparinase high dose for 15 min (Hep HD15) in vivo (•) and in cIPK (○).
The large pore fractions of the glomerular filtrate (fL) were significantly higher in controls in cIPK compared with in vivo (P < 0.05). In vivo, no differences were seen between groups, but in cIPK, a sevenfold increase was seen after hyaluronidase treatment (P < 0.05; Figure 3). The A0/Δx, shown in Figure 4, was 1 order of magnitude higher in vivo than in cIPK controls (P < 0.001), being 1 to 3 × 106 cm in vivo. In cIPK, however, an increase of >200% was seen after hyaluronidase treatment (P < 0.01). The rL was the same in all groups, 142 to 190Å, with no significant difference between the groups.
Figure 3. The estimated large pore fraction of the glomerular filtrate (fL) from charged fiber analysis. Circles represent mean, and bars represent the 95% CI for controls and animals treated with hyaluronidase (Hya), heparinase low dose for 60 min (Hep LD60), or heparinase high dose for 15 min (Hep HD15) in vivo (•) and in cIPK (○). Note the logarithmic scale.
Figure 4. The estimated unrestricted exchange area over diffusion distance (A0/Δx) from charged fiber analysis. Circles represent mean, and bars represent the 95% CI for controls and animals treated with hyaluronidase (Hya), heparinase low dose for 60 min (Hep LD60), or heparinase high dose for 15 min (Hep HD15) in vivo (•) and in cIPK (○). Note the logarithmic scale.
The fit between experimentally obtained θ and the computer-calculated data for Ficolls can be described using Powell’s χ2 test. In the charged fiber analysis, Powell’s χ2 test was calculated for every analysis giving an average of 0.024. In Figure 1, representative θ for Ficoll in controls are shown together with the values obtained using the charged fiber analysis.
Because no data have been presented previously using the heterogeneously charged fiber model, we used the gel-membrane model (36) and the lognormal distribution + shunt to analyze the control groups. Hereby, it is possible to compare our data with other studies. According to the gel-membrane model, the estimated charge density was 52 mEq/L (95% confidence interval, 44 to 60 mEq/L), the rS was 46Å, the rL was 96Å, the large pore fraction of the fL was 0.32%, and the A0/Δx was 30,000 cm. Results from two models are summarized in Table 5.
Table 5. Results in controls using lognormal distribution + shunt analysis and gel-membrane model
Electron Microscopy
Electron microscopic examination of glomerular capillaries from kidneys treated with hyaluronidase or heparinase showed no signs of ultrastructural changes of the filtration barrier, i.e., endothelial cells, GBM, and podocytes. As an example, Figure 5 shows electron micrographs from a hyaluronidase-treated animal.
Figure 5. Electron micrographs of a glomerular capillary (A) and the filtration barrier (B) from a hyaluronidase-treated animal. CL, capillary lumen; EC, endothelial cell; BM, basement membrane; P, podocyte; US, urinary space; SL, slit diaphragms; RBC, red blood cell. Magnification ×14,200 in A and ×113,700 in B. Bar = 0.6 μm in A and 1.7 μm in B.
Discussion
This is, to our knowledge, the most extensive analysis of glomerular size and charge selectivity performed in mice, with measurements being done in vivo and in isolated kidneys perfused at 8°C (cIPK). Our main findings are as follows: (1) the normal glomerular wall is indeed highly size and charge permselective, in agreement with the classical concept; this is reflected by the 30 times lower θ for albumin than its neutral counterpart Ficoll35.5Å; (2) glomerular permselectivity is similar in vivo and in the isolated perfused kidneys at 8°C except for an increased number of large pores in the cIPK; (3) mice seem to have similar glomerular properties as the extensively studied rats; (4) a heterogeneous charged fiber model was found to be remarkably accurate in predicting the glomerular sieving of neutral Ficolls and albumin; (5) treatment with hyaluronidase increased the θ for albumin (fourfold) in cIPK without altering θ for the size-matched Ficoll; (6) hyaluronidase increased the number of large pores estimated by charged fiber analysis as reflected by higher θ for larger Ficolls (<55Å); and (7) hyaluronidase and high-dose heparinase (HD15) decreased the volume fraction of negatively charged fibers.
In Vivo versus cIPK
In this study, the θ for albumin in controls were higher in cIPK than in vivo, 0.0023 and 0.00038, respectively. In vivo, the clearance for albumin is underestimated as a result of tubular reabsorption and degradation of proteins that occurs in vivo. This is in accordance with micropuncture data obtained both in vivo and in isolated perfused rat kidneys (40). Also, the uptake of filtered proteins along the nephron was demonstrated using fractional micropuncture technique by Tojo and Endou (41). The results are well in accordance with other studies in vivo (40,42⇓) and cIPK (5,6,42⇓⇓). The θ for Ficoll35.5Å was the same in all groups independent of in vivo or cIPK experiment in accordance with observations in rats (39,42,43⇓⇓) and humans (44).
Low GFR and filtration fractions in cIPK, compared with in vivo experiments, can be explained by the low temperature and the erythrocyte-free perfusate. At 37°C, the viscosity of the perfusate is one half to one third of that in blood. For maintaining a given PA, the flow rate must be increased, thus reducing the filtration fraction by a factor of 2 to 3. However, low temperature (8°C) will increase the viscosity and thus partly compensate for the loss of erythrocytes. Conversely, low temperature will reduce hydraulic conductivity by a factor of 2, according to Poiseuille’s law, and increase tubular fluid viscosity. The increased tubular fluid viscosity elevates the intratubular pressure causing a reduced GFR. The increased tubular fluid volume, caused by inhibited tubular reabsorption, raises tubular hydrostatic pressure and reduces the filtration gradient across the glomerular capillary wall (45). Furthermore, there are fewer functionally active nephrons in the isolated perfused kidney with marked heterogeneity (46). All of these effects reduce the magnitude of GFR and the absolute values of renal clearance, but the function of individual glomeruli and hence the θ will not be affected. Indeed, no difference has been found in fractional albumin clearance between homogeneously and heterogeneously perfused kidneys (46). The A0/Δx is approximately 1 order of magnitude less in cIPK than in vivo, reflecting fewer active nephrons in cIPK, again without altering of the glomerular permselectivity or θalbumin.
Glomerular Barrier
The finding that θ for albumin is much lower than that of Ficoll of equivalent size supports the classical notion of a charge barrier. In cIPK, hyaluronidase treatment increased θ for albumin fourfold. The tendency of increased θ for albumin also occurred in vivo but for reasons discussed above were not that pronounced. Although a high dose of hyaluronidase was used, twice the one that Charmaine et al. (22) used in hamster cremaster capillaries, a total loss of charge selectivity was not seen, which may indicate that other components contribute to glomerular charge selectivity as well.
Analyzing our data with the heterogeneous charged fiber model, we found a decrease in fiber volume fraction after hyaluronidase treatment in cIPK and after high-dose heparinase treatment for 15 min in vivo and cIPK. The analysis thus supports the hypothesis that hyaluronic acid and/or chondroitin sulfate is of importance for charge selectivity. Low-dose heparinase treatment for 60 min had no effect on charge selectivity. However, high-dose heparinase treatment for 15 min is somewhat ambiguous. Thus, using the θ for albumin per se, the effects on charge selectivity were not apparent. Whereas, the heterogeneous charged fiber analysis revealed an effect on the fiber volume fraction of charged fibers. Because the analysis is based on all clearance data, we consider it to be more accurate than comparing individual data pairs of θ for albumin and Ficoll35.5Å.
The surface charge of the fibers was set to −0.2 C/m2, and a reduced fiber volume fraction could reflect a loss of charged fibers in the gel. However, theoretically, there may also be a partial loss of surface charge of each fiber by the enzyme. We decided to set the fiber charge as a constant and compare the fiber volume fraction of the charged fibers because separation of the two factors would require additional information using solutes of different molecular charge.
In our hands, the heterogeneous charged fiber model gives an accurate prediction of glomerular permeability (Figure 1), although it is highly complex. Nevertheless, the model represents an oversimplification of the reality, for example, the assumption of interaction between a solute and one fiber. In reality, the solute will interact with multiple fibers because the glomerular barrier is highly complex and contains plasma proteins as well (47). In the present study, we introduced heterogeneity into the charged fiber model. Hereby, the adaption to the experimentally determined Ficoll data improved dramatically, and it is probably the most accurate theory for analysis of glomerular permeability.
Charge Density, Two-Pore, and Lognormal Distribution + Shunt Analysis
The estimated charge density of approximately 50 mEq/L in controls is similar to that previously estimated in rat (5,6,42⇓⇓). Two-pore model analysis in cIPK controls gave a functional rS close to 46 Å and 96 Å for the less frequent large pore. The results concerning pore sizes are well in accordance with previous studies by us in rats (5,6,42⇓⇓). The results from lognormal distribution gave a mean pore radius for controls in vivo of 44Å and 36Å in cIPK, which are similar radii as reported previously (43,44⇓). However, when comparing in vivo and cIPK, there are significant differences in mean pore radius and in the width of the distribution. When performing a regression analysis, it was evident that the wider the distribution, the smaller the mean pore radius. Considering this, no conclusions from lognormal distribution + shunt analysis were made.
So where is the charge-selective barrier located? In the late 1970s, investigators found that the GBM contained anionic charges (3,8,10,17⇓⇓⇓), which led to the widespread agreement that GBM was the main filtration barrier. More recently, Daniels and co-workers (13,15⇓) showed that the anionic charges in isolated GBM are much lower than those found in vivo or in isolated glomeruli, a finding also supported by others (14). Using isolated intact glomeruli and isolated GBM, Daniels et al. (15) showed that permeability in intact glomeruli was increased by heparinase or protamine but not in isolated GBM. In 1976, Ryan and Karnovsky (48) showed that the distribution of albumin in the rat glomeruli, during normal blood flow, was largely confined to the glomerular capillary lumen and the endothelial fenestrae. Later, in 1988, Avasthi and Koshy (19) suggested a role for glomerular endothelial glycocalyx in charge selectivity. They showed that digestion of sialoproteins erased the cationic ferritin binding on endothelial cells and that digestion with hyaluronidase and heparinase induced a small decrease in cationic ferritin binding, preferentially in the endothelial fenestrae. Charmaine et al. (22) used FITC-labeled dextrans in hamster cremaster capillaries and illustrated the functional lumen of the vessel. Hyaluronidase treatment increased the penetration of 70- and 145-kD dextrans into the glycocalyx, suggesting a role for hyaluronic acid and/or chondroitin sulfate in the glycocalyx. It is also interesting that the glycocalyx could be reconstituted after infusion of hyaluronic acid and chondroitin sulfate together. Placing the charge barrier at the endothelial cell glycocalyx could explain the reversible alteration in charge density when changing perfusate ionic strength (4,5⇓), an effect not seen altering osmolality (46). It has also been shown that glomerular permeability is affected by plasma composition (49,50⇓), supporting the idea of an intimate relationship between charge selectivity and plasma, probably exerted by endothelial cell glycocalyx. The delicate structure of the glycocalyx, sensitive to hypoxia and/or reperfusion (51), may explain why some investigators have failed in demonstrating charge selectivity.
We found no ultrastructural changes of endothelial cells, GBM, or podocytes after enzyme treatment (see Figure 5). Also, the enzymes used are large molecules, the size of albumin (hyaluronidase 56 kD, heparinase III 71 kD), thus the concentration of enzymes must have been highest intravascularly. Therefore, it is most likely that the endothelial glycocalyx has been exposed to the highest enzyme concentrations. It is not possible, however, to exclude that other components of the glomerular barrier, besides the glycocalyx, may have been affected by the enzymes.
In summary, our hypothesis that hyaluronic acid and/or chondroitin sulfate is of importance for charge selectivity is supported by this study. Heparan sulfate is probably important as well. Also, digestion of hyaluronic acid and/or chondroitin sulfate elevated the number of large pores. In future perspectives, our cIPK in mice and the heterogeneous charged fiber model opens interesting possibilities for studies of glomerular permselectivity in genetically engineered mice.
Acknowledgments
This study was supported by the Swedish Medical Research Council Grant 9898, the Knut and Alice Wallenberg Research Foundation, the IngaBritt and Arne Lundbergs Research Foundation, the Göteborg Medical Society, the National Association for Kidney Diseases, and Sahlgrenska University Hospital Grant LUA-S11733.
We are grateful to Prof. B.R. Johansson for help with electron microscopy and the interpretation of micrographs.
- © 2003 American Society of Nephrology
References
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