INTRODUCTION

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THE ABILITY OF THE NORMAL glomerular capillary wall to restrict the passage of anionic macromolecules, relative to uncharged tracers of similar size and configuration, has been demonstrated in vivo, using a variety of test molecules (15, 21). The fractional clearances (or sieving coefficients) of polyanions are normally much lower than those of neutral macromolecules, but these differences are reduced or eliminated in various proteinuric disorders. This suggests that the glomerular capillary wall normally possesses fixed negative charges that provide an electrostatic barrier to the filtration of serum albumin and other polyanions and that the fixed charge content is greatly reduced in the nephrotic syndrome. The specific location of the charge barrier remains controversial. Various electron-dense cationic tracers have been found to be localized in the glomerular basement membrane (GBM), whereas anionic tracers tend to be excluded, suggesting that the charge barrier may reside in the GBM (19, 25). However, studies of the ultrafiltration of anionic macromolecules across isolated GBM have demonstrated much less charge selectivity than that observed in vivo (3, 5, 7, 27), which is more consistent with the view that the charge barrier is provided by the endothelial or epithelial cells.

The information that can be gained from measurements of sieving coefficients, either in vivo or in vitro, is very dependent on the properties of the test molecules employed. With proteins, it is not possible to vary molecular size and/or charge while maintaining the same molecular structure. Moreover, the reabsorption of proteins by the renal tubules complicates the interpretation of their urinary clearances. To avoid tubular reabsorption and to allow isolation of charge and size effects, many studies have used dextran and dextran sulfate. However, dextran and its derivatives do not resemble ideal, rigid spheres, and the interpretation of data obtained using dextran sulfate is complicated by its binding to plasma proteins (15). Ficoll, a cross-linked copolymer of sucrose and epichlorohydrin, has the biological inertness of dextran and, in addition, is rigid and spherical. It has been used recently in fractional clearance studies in both laboratory animals and humans (4, 23, 24). This suggests that Ficoll sulfate, which has not been used previously in physiological studies, might be an excellent probe for examining glomerular charge selectivity. In the present study, Ficoll sulfate was synthesized, and its permeation across isolated GBM was compared with that of neutral Ficoll to examine the size and charge selectivity of this part of the glomerular capillary wall.

	METHODS

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Synthesis and labeling of Ficoll sulfate. Ficoll sulfate was synthesized by reacting Ficoll 70 (Pharmacia, Piscataway, NJ) with chlorosulfonic acid in the presence of pyridine, as described by Ricketts (26) for the preparation of dextran sulfate. The extent of sulfation was controlled by varying the amount of Ficoll added to the chlorosulfonic acid-pyridine complex. Two Ficoll sulfate preparations were employed, one with 9% sulfur by weight and the other with 16-17% sulfur. The sulfur assays were performed by Galbraith Laboratories (Knoxville, TN). Gel chromatography revealed that the molecular size distribution of the Ficoll sulfate was of similar breadth to that of Ficoll 70 but that sulfation resulted in a modest increase in the average molecular radius.

Ficoll sulfate was labeled using 6-[(4,6-dichlorotriazin-2-yl)-amino]fluorescein (DTAF) (Sigma, St. Louis, MO), following De Belder and Granath (9). Unreacted DTAF was removed by elution through 10-ml disposable desalting columns (Econ-Pac 10DG; Bio-Rad, Hercules, CA) with 1.0 M NaCl. The labeled Ficoll sulfate was concentrated in a 200-ml ultrafiltration cell (model 8200; Amicon, Danvers, MA) with a 5-kDa-molecular-mass cutoff membrane (PLCC, Amicon) prior to freeze drying. The degree of fluorescein substitution was estimated by comparing the Ficoll sulfate fluorescence with a fluorescein standard curve, as determined with a fluorimeter (model RF-551; Shimadzu, Columbia, MD). The preparation with 9% sulfur had one fluorescein group per 18 ± 4 Ficoll sulfate molecules. Ficoll sulfate with 16% sulfur had ~400 times less fluorescence and was more difficult to detect. In this case, it appears that almost all of the hydroxyl groups that are normally substituted by DTAF were occupied by sulfate.

Ion exchange chromatography showed that the Ficoll sulfate was uniformly anionic. When labeled Ficoll sulfate was injected into a 5-ml disposable gel column containing cationic tertiary amines (high trap Q, Pharmacia), none of the sample eluted in 0.02 M Tris buffer at pH 7.4, whereas it eluted promptly when 1.0 M NaCl was added to the buffer. In contrast, almost all fluorescein Ficoll eluted at the low ionic strength. The fact that some "neutral" Ficoll eluted at the high ionic strength (15% of that recovered) may be attributed to the small amount of negative charge conferred by the label (~1 charge/fluorescein).

It is worth noting that Ficoll sulfate tends to be more highly charged than bovine serum albumin (BSA). For a Stokes-Einstein radius (r_s) of 36 Å (similar to BSA) and a sulfur content of 9%, the molecular weight of Ficoll sulfate is ~38,000, indicating that there are ~100 sulfate groups. Thus the Ficoll sulfate charge is 100, compared with a BSA charge under physiological conditions of about 20.

Ficoll sulfate-BSA binding. Prior to the studies with isolated GBM, the binding of Ficoll sulfate and other test molecules to BSA was assessed using two methods. The first approach involved interactions with immobilized BSA. Beads of 4% agarose with 15 mg of BSA insolubilized per milliliter of gel (Sigma) were packed in a column (16/20 C, Pharmacia). Five fluorescently labeled polymers were tested: Ficoll, Ficoll sulfate with 9% sulfur, Ficoll sulfate with 17% sulfur, dextran sulfate with 7% sulfur, and dextran sulfate with 15% sulfur. The synthesis of the dextran sulfates (from dextran 40, Sigma) was similar to that for the Ficoll sulfates, and the labeling procedure was the same for all of the polymers. The tracers were injected and eluted first with phosphate-buffered saline (PBS) at pH 7.4. After the peak was detected, the ionic strength of the buffer was increased (PBS with 1.0 M NaCl instead of 0.12 M). It was anticipated that the high ionic strength would suppress the electrostatic interactions and cause any macromolecules bound to the immobilized BSA to desorb. The percentage of the injected macromolecule that was bound was estimated by comparing the peak areas at the physiological and high ionic strengths. To determine whether the gel or the linker arm used to immobilize BSA contributed to the binding, control experiments were performed using a column packed with agarose-glycine (Sigma).

The results are shown in Fig. 1. For both Ficoll sulfate and dextran sulfate, the amount of binding to immobilized BSA increased greatly as the sulfur content was increased. The structure of the sulfated polysaccharide (linear coil for dextran sulfate, cross-linked sphere for Ficoll sulfate) was of only secondary importance. There was little evidence for binding of neutral Ficoll to BSA or for binding of the sulfated polymers to the control (glycine) beads. These results suggest that electrostatic forces are responsible for the binding of the sulfated polymers to BSA and that the charge density of the test molecule is more important than its shape or rigidity.

View larger version (15K): [in this window] [in a new window]   Fig. 1.   Binding of Ficoll, Ficoll sulfate, and dextran sulfate to gel columns containing immobilized BSA or glycine as a function of sulfur content of test molecule. Percent bound was calculated as percent of sample that eluted initially when physiological ionic-strength buffer was used, compared with percent that eluted when high-ionic-strength buffer was used.

The second method used to evaluate binding to BSA was to compare sieving curves measured with cellulose ester ultrafiltration membranes, with or without BSA present in the retentate. Approximately 1 mg/ml of polydisperse Ficoll, Ficoll sulfate with 9% sulfur, or dextran sulfate with 18% sulfur (similar to commercial dextran sulfates) was added to PBS or to PBS containing 0.4 g/dl BSA, and the pH was adjusted to 7.4. (A subphysiological concentration of BSA was used to minimize osmotic effects and yield filtration rates similar to those for protein-free solutions.) The solutions were ultrafiltered across a 30-kDa-molecular-mass cutoff cellulose ester membrane (PLCC, Amicon) in a 3-ml stirred cell (model 3, Amicon). The cell was pressurized to 100 mmHg, using nitrogen, and the filtrate was collected for 15 min. Samples of the filtrate, retentate, and initial solutions were chromatographed on a 10/20 C column packed with Superdex 200 (Pharmacia). The void volume was determined from the elution of fluorescently labeled 2,000-kDa dextran (FITC-dextran, Sigma). The eluent was 0.05 M ammonium acetate with 0.15 M KCl at pH 7. The column was calibrated with fluorescently labeled Ficoll standards with Stokes-Einstein radii of 29.7, 37.7, 46.4, and 58.7 Å (16). Sieving curves were constructed by plotting the ratio of filtrate to retentate concentration () as a function of molecular radius.

It was found that the sieving curves for Ficoll were not affected by BSA. Those for Ficoll sulfate showed a slight reduction of  for the largest molecules when BSA was present, possibly due to BSA binding. In contrast, the sieving curves for dextran sulfate were depressed significantly by BSA for all molecular radii, consistent with the formation of dextran sulfate-BSA complexes in the ultrafiltration cell. More revealing was the effect of BSA on the chromatographic elution profiles. As shown in Fig. 2, the dextran sulfate samples with BSA yielded a new peak that eluted early, which is evidence for large complexes. No such secondary peak was observed with Ficoll or Ficoll sulfate. It was concluded that BSA binds extensively to highly sulfated dextran sulfate, does not bind to Ficoll, and binds minimally to moderately sulfated Ficoll sulfate. Ficoll sulfate with 9% sulfur was used in the remainder of this study because of its minimal binding to BSA and its ease of detection.

View larger version (16K): [in this window] [in a new window]   View larger version (15K): [in this window] [in a new window]   Fig. 2.   Elution profiles for dextran sulfate (A) and Ficoll sulfate (B) from gel chromatographic columns, with or without BSA present. Samples are final retentates in ultrafiltration experiments performed with Amicon 30-kDa-molecular-weight cutoff membranes; rs, Stokes-Einstein radius.

Ultrafiltration across isolated GBM. Glomeruli were isolated from male Sprague-Dawley rats, and the cells were removed by detergent lysis, as described previously (8). The resulting glomerular skeletons maintained the general shape of the glomerulus and were composed predominantly of GBM, with occasional areas of residual mesangial matrix. Immunofluorescence microscopy of GBM obtained in this manner shows the presence of type IV collagen, laminin, and heparan sulfate proteoglycan (8). To form filters, 150 µg of GBM suspended in pH 7.4 Krebs-bicarbonate buffer were added to a 3 ml ultrafiltration cell (model 3, Amicon). Stirring was initiated, and the cell was pressurized to 1,500 mmHg with compressed air for 1 h to consolidate the GBM into a homogeneous layer on a piece of filter paper. The buffer was then replaced with a test solution containing 0.5 mg/ml of polydisperse Ficoll or Ficoll sulfate. Filtration studies were carried out at 27°C with an applied pressure of 60 mmHg and a stirring rate of 220 rpm. After an equilibration period of 10-20 min, the filtrate was collected for 30-60 min. Samples of the filtrate, the retentate at the beginning of the collection period, and retentate at the end of the collection period were chromatographed for determination of sieving coefficients as a function of molecular radius. The samples were chromatographed on a 1.6-cm ID column (XK 16/70, Pharmacia) packed with Superdex 200. The eluent was 0.05 M ammonium acetate with 0.15 M KCl at pH 7, and the flow rate was maintained at 1.5 ml/min using a dual-piston pump (P500, Pharmacia). The Ficoll calibration standards and the marker used to determine the void volume were as described above.

The apparent sieving coefficient for a given molecule was defined as ' = C_F/C_R, where C_F is the filtrate concentration and C_R is the concentration in the bulk retentate. C_R was obtained from the arithmetic average of the initial and final values. The true sieving coefficient is given by  = C_F/C_M, where C_M is the solute concentration at the upstream membrane surface. Because of concentration polarization, C_M > C_R and  < '. The true sieving coefficient was calculated from the apparent one using

(1)

where v is the superficial velocity of the filtrate (i.e., the volume flux) and k_c is the mass transfer coefficient in the retentate. The mass transfer coefficient for this particular ultrafiltration cell was evaluated as

(2)

where k_c is in cm/s, µ is the viscosity of water in centipoise, and D is the solute diffusivity in cm²/s (12). For the results reported here with isolated GBM, the true sieving coefficients were calculated to be ~30% lower than the apparent values.

The hydraulic permeability (L_p) of the GBM layer was calculated as

(3)

where P is the applied pressure and _BSA and _BSA are the reflection coefficient and osmotic pressure difference, respectively, for BSA. The reflection coefficient was estimated as _BSA = 1  _BSA and _BSA was calculated from the concentrations of BSA at the upstream surface and in the filtrate, using the correlation of Vilker et al. (29).

In the first series of experiments with GBM, the Ficoll or Ficoll sulfate was added to Krebs buffer, with or without 4 g/dl BSA. A single collection period was employed with each membrane. These data were analyzed in an unpaired manner to determine the effects of tracer charge and BSA. In a second series of experiments, there were two collection periods, allowing a paired comparison of Ficoll and Ficoll sulfate in each membrane at a given ionic strength. The order of exposure to Ficoll or Ficoll sulfate was varied randomly. These studies were performed with a low-ionic-strength buffer, 0.01 M phosphate at pH 7.4, or with a physiological buffer. In this series, BSA was absent. The reason for using a low ionic strength in some of the experiments was to reduce the electrostatic screening due to the dissolved salts, thereby making it possible to detect relatively weak charge interactions between the membrane and the test macromolecules.

Ultrafiltration across synthetic membranes. In addition to the preliminary experiments used to examine the binding of the test molecules with BSA, sieving measurements with synthetic membranes were performed under conditions similar to those employed with GBM. In this case, the membranes were track-etched polycarbonate with a nominal pore diameter of 0.015 µm (Corning Costar, Cambridge, MA). Such membranes have been shown to have fixed negative charges (11). The initial solution consisted of 10 mg/dl of fluoresceinated Ficoll or Ficoll sulfate in 0.01 M phosphate buffer at pH 7.0 or in that buffer with 1 M KCl added. The 3-ml ultrafiltration cell was pressurized to 60 psi, using nitrogen. The cell was equilibrated for 15 min, and the filtrate was collected for 30 min, after which the ionic strength was changed. The experiments were performed in varying order three times for each tracer at each ionic strength. The filtrate and the initial and final retentates were chromatographed, and the sieving coefficients were determined as described above.

	RESULTS

Top Abstract Introduction Methods Results Discussion References

Ultrafiltration across GBM at physiological ionic strength. The mean sieving curves for Ficoll and Ficoll sulfate in isolated GBM, with or without BSA, are compared in Fig. 3. The sieving coefficient () is plotted as a function of the Stokes-Einstein radius (r_s). Whether BSA was present or absent, there was no significant difference between the sieving curves for the uncharged and anionic forms of Ficoll. However, the sieving coefficients for both forms of Ficoll were elevated when BSA was present. An analysis of variance for the unpaired data indicates that the effects of BSA on  were statistically significant for a wide range of molecular sizes (P < 0.05 for both Ficoll sulfate and Ficoll with 20  r_s  46 Å). A physical explanation for these effects of BSA is provided later.

View larger version (17K): [in this window] [in a new window]   Fig. 3.   Sieving curves for Ficoll and Ficoll sulfate in isolated glomerular basement membrane (GBM) at physiological strength, with or without BSA present; , ratio of filtrate to retentate concentration. Values are shown as means ± SE with n = 7 for Ficoll without BSA, n = 6 for Ficoll with BSA, n = 7 for Ficoll sulfate without BSA, and n = 8 for Ficoll sulfate with BSA.

As shown in Table 1, the filtration velocity was lowered by BSA in a manner consistent with its osmotic pressure. That is, there was no detectable effect of BSA on the hydraulic permeability of the GBM. The sieving coefficient for BSA was lower than that for Ficoll sulfate or Ficoll of a similar r_s (36 Å); _BSA = 0.085 ± 0.007 vs. _FS = 0.21 ± 0.02 and _F = 0.21 ± 0.01. 

Ultrafiltration across synthetic membranes. One possible interpretation of the results with isolated GBM is that the difference in charge between Ficoll and Ficoll sulfate was insufficient to yield a difference in sieving coefficients. Accordingly, ultrafiltration across anionic track-etched membranes was used to test whether the tracers could be distinguished. As shown in Fig. 4, at a high ionic strength, the Ficoll and Ficoll sulfate sieving curves were essentially identical, but, at a low ionic strength, the sieving coefficients for Ficoll sulfate were significantly lower than those for Ficoll. The results at low ionic strength confirm that, when electrostatic interactions are not screened by a high salt concentration, the filtration of Ficoll sulfate is affected by the membrane charge. The results at the high ionic strength reinforce the assertion that the two tracers differ only in their charge characteristics.

View larger version (14K): [in this window] [in a new window]   View larger version (13K): [in this window] [in a new window]   Fig. 4.   Sieving curves for Ficoll and Ficoll sulfate in track-etched membranes at low (A) or high (B) ionic strength. Values are shown as means ± SE, with n = 3 for each case.

Ultrafiltration across GBM at low ionic strength. The absence of any difference between the sieving coefficients of Ficoll and Ficoll sulfate in GBM at physiological ionic strength could mean that there was little or no fixed membrane charge or it could indicate that the electrostatic interactions were completely screened under these conditions. To test for functional membrane charges, paired comparisons of Ficoll and Ficoll sulfate sieving were made at low ionic strength. As shown by a representative experiment in Fig. 5A, at low ionic strength, the sieving coefficients for Ficoll sulfate were well below those for Ficoll. This is the behavior expected for a negatively charged membrane. However, as shown by another representative experiment in Fig. 5B, there was little or no difference between Ficoll sulfate and Ficoll at physiological ionic strength. An analysis of seven paired experiments at the low ionic strength indicated that the differences in the sieving coefficients of Ficoll sulfate and Ficoll were statistically significant (P < 0.05) for 20  r_s  48 Å. The three paired experiments at physiological ionic strength merely reinforced the findings shown in Fig. 4, namely, that there was no significant charge discrimination under these conditions. These experiments confirm that GBM has fixed negative charges, although not at high enough concentration for them to be functionally effective at physiological ionic strength.

View larger version (12K): [in this window] [in a new window]   View larger version (10K): [in this window] [in a new window]   Fig. 5.   Representative sieving curves for Ficoll and Ficoll sulfate in GBM at low (A) and high (B) ionic strength. Each plot shows results of paired experiments using same membrane.

The filtration data in Table 1 show a slight tendency for L_p to be reduced at low ionic strength, although the difference was not statistically significant.

	DISCUSSION

Top Abstract Introduction Methods Results Discussion References

The main finding of this study is that there were no significant differences between the sieving curves of Ficoll sulfate and Ficoll in isolated GBM at physiological ionic strength (Fig. 3). This absence of charge selectivity is generally consistent with previous results obtained with various GBM preparations. Bray and Robinson (5) found only a slight reduction in the sieving of dextran sulfate relative to neutral dextran. Likewise, Bertolatus and Klinzman (3) found only a small difference in the filtration rates of native (anionic) or cationized BSA. Moreover, they showed that neutralization of carboxyl groups by methylation, which should have abolished much of the GBM charge, had only a slight effect on the sieving of BSA. Daniels (7) found that treating the GBM with heparatinase to remove heparan sulfate proteoglycan, adding protamine to neutralize GBM polyanions, or reducing the experimental pH to the isoelectric point of the GBM or BSA had little or no effect on the sieving coefficient of BSA. Robinson and Walton (27) also found that the sieving of BSA across isolated GBM was the same at pH 7.4 as at pH 5.7, the isoelectric point of GBM. Taken together, these results suggest that it is unlikely that the GBM makes an important contribution to the charge selectivity exhibited by the glomerular capillary wall in vivo.

The conclusion that the GBM makes little or no contribution to normal glomerular charge selectivity is based, of course, on the assumption that isolated GBM is not functionally different from that in vivo. The possibility that GBM is altered during the isolation process has been examined previously using a variety of methods. Immunofluorescent microscopy of consolidated GBM filters prepared as in the present study demonstrated the presence of laminin, type IV collagen, and the core protein of heparan sulfate proteoglycan (8), the main components of GBM. The sulfated side chains of GBM proteoglycans are also present in GBM isolated using the present methodology (7). The permeability of the GBM filters was not changed when a milder detergent, Triton X-100, which has been shown to preserve heparan sulfate proteoglycan, was used to lyse glomerular cells (7). That isolated GBM is relatively intact is suggested also by electron microscopy studies; the spatial distribution of cationic ferritin has been found to be similar to that in vivo (18).

Functional confirmation of the presence of negatively charged groups in isolated GBM was provided by the present results at low ionic strength, in which the sieving coefficients for Ficoll sulfate were found to be substantially lower than those for Ficoll (Fig. 5). Reductions in ionic strength amplify electrostatic interactions by increasing the distance in an electrolyte solution over which fixed charges are "felt"; the relevant length scale is termed the Debye length. A comparison of the results at the two ionic strengths indicates that fixed negative charges are indeed present in the GBM but at too low a concentration to confer appreciable charge selectivity under physiological conditions. This conclusion was reached previously by Zamparo and Comper (30) on the basis of studies using model anionic polysaccharide matrices. Experimental estimates of GBM charge density have been reported using titration (5) and an isotopic ion exchange technique (6).

The conclusion that the GBM is unlikely to contribute significantly to normal glomerular charge selectivity contradicts inferences made from numerous histological studies employing electron-dense tracers (19). Such studies have advanced the understanding of structure-function correlations, but they are qualitative and reflect transient phenomena rather than steady-state conditions. Distinguishing between tracer particles that are strongly bound to GBM and those that are freely mobile is one of several difficulties in using electron micrographs to reach quantitative conclusions about the sieving characteristics of molecules at steady state. As emphasized above, the present results do not dispute the existence of fixed negative charges in the GBM, as inferred using electron microscopy and other methods; they suggest only that the charge density is insufficient to be functionally important.

The sieving coefficient of BSA in isolated GBM was found to be roughly half that of comparably sized Ficoll or Ficoll sulfate. Of interest is that such differences in  between BSA and uncharged test molecules of similar size are sometimes taken as evidence of charge selectivity. The fact that the sieving coefficients of Ficoll and Ficoll sulfate did not differ (at physiological ionic strength) indicates that some other factor was responsible for the relatively low sieving coefficient of BSA, such as its nonspherical shape.

If the GBM makes little or no contribution, then glomerular charge selectivity must be conferred by the endothelial or epithelial cell layers. In support of a role for the cells, Daniels (7) found that removal of heparan sulfate proteoglycans increased the permeability of intact glomeruli (studied in a filtration cell) to BSA but not the permeability of GBM. Likewise, protamine increased the permeability of layers of whole glomeruli but not those of GBM. It has been hypothesized that the negative charges on the epithelial cells and slit diaphragms help maintain spaces between foot processes for the passage of filtrate, because neutralization of these charges with protamine or cationic ferritin causes foot processes to broaden and occlude filtration channels (17, 20). Negative charges on the slit diaphragms could also be responsible for the charge selectivity observed in vivo, in that these fibrous structures are in close proximity to molecules passing between the foot processes. An alternative hypothesis is that the passage of anionic tracers across the glomerular capillary wall is selectively reduced by cellular uptake (28). Whether cellular uptake is physiologically important seems uncertain, in that electron microscopy studies have not shown cationic or anionic ferritin (18, 25) bound to or within glomerular epithelial cells.

The sieving curves of both Ficoll sulfate and Ficoll were significantly higher when BSA was present than when it was not (Fig. 3). This can be explained as the combined result of two physical factors: the reduced filtration rate of water with BSA and the effect of BSA on the partitioning of other molecules within the membrane. Neither factor is specific to BSA or GBM, rather, these phenomena occur generally for macromolecular solutes in any porous or fibrous membrane. The theory for the second (partitioning) effect has been developed only for macromolecules of uniform size. Accordingly, the calculations described below focus on the sieving behavior of a Ficoll with r_s = 36 Å, the same Stokes-Einstein radius as BSA. The sieving coefficient of this size of Ficoll was 73% higher, on average, when BSA was present.

The effect of the filtration rate on the sieving coefficient, which is due to the increased importance of diffusion at lower filtration velocities, is a well-known phenomenon in ultrafiltration. Decreasing the filtration rate enhances the tendency of diffusion to equilibrate the filtrate and retentate and thereby increases the sieving coefficient. The inverse relationship predicted between  and filtration rate for a membrane of thickness  is described by

(4)

(5)

where Pe is the membrane Peclet number,  is the partition coefficient, K_c is the convective hindrance factor, and K_d is the diffusive hindrance factor (12). The osmotic pressure of BSA caused a reduction in v (Table 1). To calculate the corresponding change in Pe, it was necessary to estimate the values of K_c and K_d. Both of these products are expected to decrease rapidly with increasing molecular radius, although too little is known about the structure of the GBM to predict their values from first principles. Accordingly, we assumed that

(6)

(7)

where A and B are empirical constants. With the sieving data for neutral Ficoll with 20  r_s  50 Å, without BSA, the best-fit values obtained using Powell's method were A = 0.126 and B = 0.0670.¹ The value of the membrane thickness was assumed to be 6.02 µm, as determined by Edwards et al. (12) for the same experimental conditions. With these values in Eq. 4, the predicted increase in  for r_s = 36 Å was 24%. Thus the effect of filtrate velocity accounts for only about one-third of the observed 73% increase in the sieving coefficient with BSA.

When macromolecule solutions are not infinitely dilute, solute-solute interactions can have a significant effect on the membrane-to-external-solution concentration ratio at equilibrium or . The available theories for cylindrical pores (2, 14) and random fiber matrices (13) predict that repulsive interactions (either hard-sphere or electrostatic) will cause  to increase with increasing concentration. These predictions are supported by sieving data obtained using track-etch membranes (22). Although, in the present study, the concentration of Ficoll was low, it is likely that  for Ficoll was increased by its repulsive interactions with BSA, which was present at a significant concentration (4.0 g/dl in the bulk retentate and 6.2 g/dl at the upstream surface of the membrane). To estimate the magnitude of this effect, BSA and 36-Å Ficoll were regarded as indistinguishable, neutral spheres. The neglect of electrostatic interactions is justified by our finding that the effects of BSA on Ficoll and Ficoll sulfate were indistinguishable, at least at physiological ionic strength. Because the theory for fiber matrices has not been implemented for parameter values likely to be representative of GBM, we employed the qualitatively similar theory for cylindrical pores. An effective pore radius of 52 Å was obtained by fitting the sieving data for Ficoll with 20  r_s  50 Å, using the standard dilute-solution theory (10). With the use of the theoretical results of Anderson and Adamski (2) for hard-sphere, solute-solute interactions, it was calculated that  for a 36-Å Ficoll should be increased by 74% in the presence of 6.2 g/dl BSA. The corresponding increase in  was 70%²

Considering both effects of BSA simultaneously (reduced filtration velocity and enhanced solute-solute interactions), the sieving coefficient for a 36-Å Ficoll was predicted to increase by 106%. Given the uncertainties in applying the idealized theory to the GBM, this prediction is in remarkably good agreement with the observed increase of 73%. Thus it appears that there is no need to postulate an effect of BSA on the GBM itself. It seems unlikely that this conclusion would be altered if a more structurally realistic theory were available to describe solute-solute interactions in the GBM. Supporting the view that BSA does not affect the intrinsic properties of the GBM is the observation that there was no change in the hydraulic permeability (Table 1).³ We conclude that, although BSA binds to GBM (1), any structural changes in the membrane that might result are too small to affect its permeability properties.

In filters prepared by consolidating many glomerular skeletons, as done here, a small amount of the filtrate may pass around the GBM rather than through it. This was suggested by the tendency of the Ficoll sulfate and Ficoll sieving coefficients to asymptotically approach a small but nonzero value at large molecular radii and was evidenced in a previous study by the passage of small amounts of 2,000-kDa dextran (7). Such a shunt would lead to overestimates of the true sieving coefficients for the GBM, with the percentage error increasing with molecular size. To minimize the effects of such artifacts, the calculations described above used Ficoll sieving data only for r_s  50 Å. To examine this source of error, the calculations were performed also by first subtracting the sieving coefficient of the 80-Å Ficoll (an upper bound for the magnitude of the shunt) from the entire curve. When the calculations were done in this manner, the predicted increase in the Ficoll sieving coefficient due to the presence of BSA was again in excellent agreement with that measured.

In conclusion, we found that there was no significant difference between the sieving coefficients of Ficoll sulfate and Ficoll in isolated GBM, suggesting that GBM is unlikely to contribute significantly to glomerular charge selectivity in vivo. This supports the hypothesis that the glomerular cells and not the GBM are responsible for glomerular charge selectivity. The sieving coefficients of Ficoll sulfate and Ficoll were elevated similarly in the presence of BSA, which could be explained as the combined effect of nonspecific physical factors. The more novel of these, which seems not to have been recognized previously in physiology, is the ability of finite concentrations of one macromolecule (e.g., BSA) to augment the transmembrane passage of a second, tracer macromolecule (e.g., Ficoll), via intermolecular repulsions. The theory for this effect needs further development, in that it is presently restricted to molecules of the same size. A more complete theory, as well as additional data, is needed to determine whether this phenomenon is important for the interpretaton of sieving data in vivo. Finally, this study represents the first use of Ficoll sulfate to probe the charge selectivity of a biological tissue. The minimal binding of this tracer to serum albumin, together with its more rigid and spherical shape, make it an attractive alternative to dextran sulfate for use in future physiological studies.