Effects of filtration rate on the glomerular barrier and clearance of four differently shaped molecules

Maria Ohlson1, Jenny Sörensson1, Karin Lindström1, Anna M. Blom3, Erik Fries3, and Börje Haraldsson1,2

Departments of 1 Physiology and 2 Nephrology, Göteborg University, Göteborg SE-504 30; and 3 Department of Medical Biochemistry and Microbiology, Uppsala University, Uppsala SE-75123, Sweden


    ABSTRACT
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

The effect of shape on the transglomerular passage of solutes has not been hitherto systematically studied. We perfused isolated rat kidneys to determine the fractional clearances (theta ) at various filtration rates for four molecules of different shapes but with similar Stokes-Einstein radii (aSE = 34-36 Å). The theta  for hyaluronan, bikunin, and Ficoll36 Å were 66, 16, and 11%, respectively, at a glomerular filtration rate (GFR) of 0.07 ml · min-1 · g wet wt-1 and decreased to 46, 14, and 7%, respectively, on a fivefold increase in GFR. Under the same conditions, theta  for albumin increased from 0.15 to 0.74%, and similar behavior was observed for larger Ficolls (aSE >45 Å). Pore analysis showed that the "apparent neutral" solute radii of Ficoll, albumin, bikunin, and hyaluronan were 35, 64, 33, and 24 Å, respectively, despite similar aSE. In addition, the properties of the glomerular filter changed with increasing GFR and hydrostatic pressure. We conclude that elongated shape, irrespective of size and charge, drastically increases the transglomerular passage of a solute, an effect that is related to its frictional ratio.

glomerular filter; macromolecular transport; solute shape


    INTRODUCTION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

SEVERAL STUDIES WITH NEUTRAL and charge-modified dextran polymers have shown that the glomerular barrier is both size and charge selective (2-6, 9, 10, 31). The glomerular membrane seems to be heteroporous, with numerous small and a few large pores (11, 20). However, the validity of the dextran data has been seriously questioned in the last decade. Thus sulfated dextran has been found to bind to glomerular vascular cells (42) and basement membrane components (41). Certain charged dextran fractions may even bind to plasma proteins (15). These effects all tend to reduce the concentration of sulfated dextran in the urine and hence lead to an overestimation of the charge density in the glomerular barrier. Indeed, some investigators consider the effects of solute shape and charge to be negligible (33).

Little is known about the transport of native macromolecules across the glomerular wall as the content of the primary urine is markedly and variably modified during tubular passage (8). These problems can be overcome by inhibiting the tubular activity using toxins (33) or reduced temperature (28, 34). The low temperature does not affect glomerular permeability per se (30) but rather seems to protect the glomerular charge barrier from ischemic damage in kidneys perfused with erythrocyte-free solutions. Experiments in the cooled isolated perfused kidney, cIPK, have confirmed the glomerular size selectivity with functional small and large pores (30). Moreover, both pore pathways seem to be charge discriminating (25).

In a previous study, we found that the plasma protein bikunin had 80 times higher fractional clearance (theta ) than albumin despite similar size and charge. We suggested that this difference might be due to the more elongated shape of bikunin, which would cause the molecule to become oriented in the flow direction when it passes through the glomerular pores. This idea was based on results obtained with studies on the sieving of flexible molecules through artificial membranes (26, 27). Similar studies have not been systematically performed for capillary membranes such as the glomerular barrier. We wanted to evaluate why elongated molecules have higher theta  values and whether the glomerular barrier can be affected by hydrostatic pressure and/or glomerular filtration rate (GFR).

In this study we investigated the influence of filtration rate on theta  of four molecules with similar Stokes-Einstein radii (aSE; 36 Å) but with different shapes and charges. Two proteins and a polysaccharide with similar net charges were used, namely, albumin, bikunin (elongated), and hyaluronan (linear), together with a neutral solute, Ficoll (spherical). The clearances of these solutes were estimated over a wide GFR interval in isolated rat kidneys perfused with albumin solutions at 8°C.


    METHODS
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ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Kidney Perfusion Technique

Experiments were performed in 15 male rats (Wistar strain; Møllegaard, Stensved, Denmark), weighing 310 ± 9 g, and 7 female rats, weighing 260 ± 6 g (Sprague-Dawley; Møllegaard). The rats were kept on standard chow and had free access to water before the experiments. The local ethics committee approved the experiments.

Anesthesia was induced with pentobarbitone (60 mg/kg ip), and a thermostatically controlled heating pad maintained the body temperature at 37°C. The tail artery was cannulated for recording of the arterial pressure (PA) and subsequent administration of drugs. One kidney was prepared and perfused as described in detail previously (17, 39). The rat was eviscerated. Cannulation of the left ureter (PE-25 cannulas) was facilitated by enhanced diuresis after injection of furosemide (2 mg/kg; Benzon Pharma, Copenhagen, Denmark). The rat was heparinized (2,000 IU/kg), and the aorta was clamped distal to the renal arteries and cannulated in a retrograde direction. The aorta was thereafter ligated proximal to the left renal artery, and the caval vein was cut open, establishing a perfusion line for the left kidney. The perfusate was administered by use of a peristaltic pump (Ismatech IPC-04 V1.32; Zurich, Switzerland). Thus the kidney was fully perfused with either blood or perfusate during the entire preparation. The perfusate was kept in a water bath at 8°C and passed through a bubble trap and a thermoequilibrator placed close to the kidney. The low temperature was used to inhibit tubular function, energy consumption, and myogenic tone (7, 13), as well as protease activity.

PA was measured with a T tube placed near the aortic inlet and connected to a pressure transducer (PVB Medizintechnik, Kirchenseeon, Germany). The urine was collected in a vial, which was continuously weighed for assessment of urine flow. A computer (PC 586), using Labview computer software, monitored PA and urine weight changes as well as urine flow and pump speed.

Perfusate

A modified Tyrode solution containing human albumin (18 g/l; Immuno, Vienna, Austria) with the following composition was used (in mM): 113 NaCl, 4.3 KCl, 0.8 MgCl2, 25.5 NaHCO3, 0.5 NaH2PO4, 2.5 CaCl2, 5.6 glucose, and 0.9 nitroprusside (Merck, Darmstadt, Germany) as well as furosemide (10 mg/l; Benzon Pharma). The solution was made with freshly distilled water (Millipore) with a resistivity of 18 MOmega /cm. The perfusate was bubbled with 5% CO2-95% O2. The pH was 7.4 and remained stable during the experiments. The colloid osmotic pressure of the perfusate was 6 mmHg.

Tracers

Cr-EDTA. For determinations of GFR, 51Cr-EDTA (0.34 MBq/l; Amersham Pharmacia Biotech, Buckinghamshire, UK) was added to the perfusate.

Bikunin. Bikunin was isolated from rat urine and labeled with 125I as previously described (37, 38). Bikunin is a plasma protein with a total mass of 25 kDa containing an 8-kDa chondroitin sulfate chain with a low degree of sulfation. Its aSE is 34-36 Å (24), and its frictional ratio, which is a measure of the asymmetry (and/or hydration) of a molecule, is 1.8. On the basis of its electrophoretic mobility, bikunin has a charge similar to that for albumin at physiological pH, i.e., -23 net surface charges.

Hyaluronan. Hyaluronan has a mass of >1,000 kDa in lymph (22). However, it is bound and processed by the liver (21), and the remaining circulating hyaluronan has a mass of 10-200 kDa (40). Bacterial hyaluronan dissolved in water (5 mg in 0.5 ml) was fragmented by being autoclaved for 4 h at 110°C. The sample was applied on a Sephacryl S-300 column (16 × 500 mm) with 0.15 M NH4HCO3, and the fractions corresponding to the elution volume of albumin and 12-kDa hyaluronan were pooled and freeze-dried. The obtained material (2 mg) was dissolved in water and labeled with [125I]tyrosine as described (16). Part of the labeled material was applied on the gel column and was found to have the same elution volume as albumin. The frictional ratio of a 12-kDa hyaluronan is 2.3. The structure and charge density of hyaluronan are similar to those of low-sulfated chondroitin sulfate. We therefore assume that the net charge of the 12-kDa hyaluronan molecule is similar to that of bikunin (and albumin). Gel filtration on a Sepharose 6 PC 3.2/3.0 column (SMART HPLC) after the experiments confirmed the aSE of hyaluronan (34 Å).

Albumin. The protein has a total mass of 67 kDa, an aSE of 36 Å, and a frictional ratio of 1.3. The net surface charge for albumin is -23 (14).

Thus the tracer proteins bikunin, hyaluronan, and albumin had similar hydrodynamic radii and net surface charges. However, because the molecular masses for bikunin and hyaluronan are lower (25 and 12 kDa, respectively) than that of albumin (67 kDa), the former two molecules must be more elongated.

Ficoll. FITC-labeled Ficoll (Ficoll70; Bioflor, Uppsala, Sweden) in the molecular radius range of 12-72 Å was used. Ficoll is considered to be almost spherical, having a frictional ratio close to 1.0. Labeling with FITC would be expected to add one negative charge to Ficoll, but we could not detect any electrophoretic mobility of FITC-Ficoll (30).

Experimental Protocol

In 15 of the experiments, the isolated kidneys were first perfused with albumin solutions containing 51Cr-EDTA for 15 min, yielding control values of GFR and albumin clearance. Radiolabeled rat bikunin was added to the perfusate, and additional urine samples were collected over the entire biological range of GFR in this experimental model (0-0.5 ml/min).

In an additional seven rats, the perfusate contained 125I-labeled hyaluronan, 51Cr-EDTA, and albumin (18 g/l). 125I-hyaluronan was eluted on an equilibrated desalting column (Sephadex G-25 PD-10; Amersham Pharmacia Biotech) to reduce the free iodide content and then added to the perfusate. The perfusate in these experiments also contained 0.5 g/l of FITC-Ficoll. The isolated kidneys were first perfused for 15 min for steady state. The perfusate flow rates were then changed to yield urine flows between 0.025 and 0.4 ml/min, and urine samples were collected.

Radioactivity was measured in a gamma counter (Cobra Auto-Gamma Counting systems, Packard Instrument, Meriden, CT), and due corrections were made for background activity and 51Cr spillover. The albumin concentration was measured by RIA (Pharmacia and Upjohn Diagnostics, Uppsala, Sweden).

Biochemical Analysis of Bikunin and Hyaluronan

Shortly after each experiment, urine samples were subjected to gel chromatography on a Sephadex G2-25 Superfine column (SMART HPLC) and a Sepharose 6 PC 3.2/3.0 column (SMART HPLC) for bikunin and hyaluronan, respectively, and the amount of tracer-bound radioactivity was determined. Analysis of perfusate and urine samples showed that the tracer-bound fraction was mainly intact bikunin or hyaluronan, which was in accordance with a previous paper (24). Thus the clearance data for bikunin and hyaluronan were based on the amount of intact proteins in urine and plasma and were not affected by contamination of unbound 125I.

Analysis of Ficoll Concentrations

For the calculation of the sieving coefficients for FITC-Ficoll, both perfusates and urine samples were subjected to gel filtration (BioSep-SEC-S3000; Phenomenex, Torrance, CA) and detection of fluorescence (RF 1002 Fluorescense HPLC Monitor; Gynkotek, Germering, Germany) using Chromeleon (Gynkotek) software. A 0.05 M phosphate buffer with 0.15 M NaCl, pH 7.0, was used as an eluent. A 10-µl sample was analyzed at an excitation wavelength of 492 nm, an emission wavelength of 520 nm, and at a flow rate of 1 ml/min by using a fixed sampling frequency of 1 sample/s. The pressure was ~4 MPa, and the temperature was kept at 8°C during the analysis. We estimated the error in the urine-to-plasma Ficoll concentration ratio (CU/CP) to be <1% for most molecular sizes. However, the wavelength noise increased for the largest Ficolls, resulting in less precise estimations of large-pore radii.

Six monodisperse samples of FITC-Ficoll with known molecular radii were used to obtain a calibration curve on the BioSep-SEC-S3000, as previously described in detail (30).

Control Experiments

Perfusion of isolated kidneys has previously been shown to be heterogenous (23). A hyperosmolar solution, obtained by adding 52 g/l of mannitol to the normal perfusate, makes the glomeruli more uniformly perfused (23). To test the influence of heterogeneity, theta  values for 125I-labeled bikunin were determined at various GFRs with a normal solution followed by perfusion with a hyperosmolar solution.

Calculations

GFR. GFR was calculated as CU/CP of 51Cr-EDTA times urine flow (QU), i.e.
GFR<IT>=</IT><FENCE><FR><NU>C<SUB>U</SUB></NU><DE>C<SUB>P</SUB></DE></FR></FENCE><SUB>Cr-EDTA</SUB><IT>·</IT>Q<SUB>U</SUB> (1)

theta for Ficoll, albumin, bikunin, and hyaluronan. The renal clearance (Cl) for a solute, X, can be calculated from its CU/CP, i.e.
Cl<IT>=</IT><FENCE><FR><NU>C<SUB>U</SUB></NU><DE>C<SUB>P</SUB></DE></FR></FENCE><SUB><IT>X</IT></SUB><IT>·</IT>Q<SUB>U</SUB> (2)
Cl over GFR gives the theta  value of a solute. Hence theta  for a solute, X, equals
&thgr;=<FR><NU>(C<SUB>U</SUB><IT>/</IT>C<SUB>P</SUB>)<SUB><IT>X</IT></SUB></NU><DE>(C<SUB>U</SUB><IT>/</IT>C<SUB>P</SUB>)<SUB>Cr-EDTA</SUB></DE></FR> (3)

The two-pore model. The exchange can be described by using the following parameters: small-pore radius, rs; large-pore radius, rL; the large-pore fraction of the hydraulic conductance, fL; and, finally, the unrestricted pore area over diffusion distance, A0/Delta x. The net fluxes of fluid and solutes are calculated for each pore pathway separately by using nonlinear flux equations (35). The free diffusion constant, unique for every molecular radius, was included in the model. The temperature will affect viscosity and diffusion, effects that were taken into account. It will also slightly influence the charge interactions, as evident from the equations for Debye length (see Ref. 39), but the effect on Debye length is small (5%) and was not included in the analysis.

The Cl of a solute can be estimated by using the following nonlinear flux equation (35), where sigma  is the reflection coefficient of a solute
Cl<IT>=</IT><FR><NU><IT>J</IT><SUB>V</SUB><IT>·</IT>(<IT>1−&sfgr;</IT>)</NU><DE><IT>1−&sfgr;·e</IT><SUP><IT>−</IT>Pe</SUP></DE></FR> (4)
and JV equals the flux through each pore pathway in heteroporous models.

The Peclet number, Pe, describes the relative contribution of diffusion and convection
Pe<IT>=</IT><FR><NU><IT>J</IT><SUB>V</SUB><IT>·</IT>(<IT>1−&sfgr;</IT>)</NU><DE><IT>PS</IT></DE></FR> (5)
where PS is the permeability surface area product
PS=<FR><NU>A<SUB>P</SUB></NU><DE><IT>A<SUB>0</SUB></IT></DE></FR><IT>·D</IT><SUB><IT>a</IT><SUB>SE</SUB></SUB><IT>·</IT><FR><NU><IT>A<SUB>0</SUB></IT></NU><DE><IT>&Dgr;x</IT></DE></FR> (6)
AP/A0 is the diffusional pore restriction factor, and D is the free diffusion constant for a solute.

The fluid flux, JV, can thus be estimated for each pore pathway, e.g., for the small-pore pathway, as
Jv<SUB>s</SUB><IT>=</IT>(<IT>1−</IT>f<SUB>L</SUB>)<IT>·L</IT>p<IT>S·⌊&Dgr;</IT>P<IT>−<A><AC>&sfgr;</AC><AC>&cjs1171;</AC></A></IT><SUB>s</SUB><IT>·&pgr;</IT><SUB>p</SUB><IT>⌋</IT> (7)
where LpS is the hydraulic conductance, Delta P is the hydrostatic pressure gradient across the glomerular barrier, pi p is the colloid osmotic pressure of the plasma proteins, and <A><AC>&sfgr;</AC><AC>&cjs1171;</AC></A> is the average reflection coefficient for proteins. The LpS equals GFR over the filtration pressure (for details, see Ref. 29). From fL it is also possible to calculate the individual pore A0/Delta x and hence PS and Cl. Finally, the sieving coefficient is obtained by dividing the sum of clearances through the two pore pathways (Cls + ClL) by GFR.

Statistics

Results are presented as means ± SE, and differences were tested by using Student's t-test. Certain analysis was done by using ANOVA, and in such cases this is stated in the text.


    RESULTS
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ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

General (Control Period)

The isolated kidneys in the two experimental groups were initially perfused at a flow rate of 6 ml/min, giving PA values of ~70 mmHg. With the assumption that the venous pressure is small, the vascular resistance (PRU100) can be estimated as 0.15 ± 0.01 mmHg · min · 100 g wet wt-1 · ml-1. The GFR values were 0.18 ± 0.01 (n = 15) and 0.17 ± 0.01 ml · min-1 · g wet wt-1, respectively (n = 7). The two groups were studied on two different occasions, so no attempts were made to analyze the effect of gender (15 males, 7 females). GFR with corresponding perfusion pressures as well as pump flows are presented in Table 1.

                              
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Table 1.   Glomerular filtration rates, arterial pressures, and pump flows

Hyaluronan

The theta  for hyaluronan, theta hyaluronan, was 66 ± 2% when the GFR was 0.067 ml · min-1 · g wet wt-1 and fell to 48 ± 2% when the GFR was 0.37 ml · min-1 · g wet wt-1 (P < 0.001, n = 7), a 28% reduction (see Fig. 1). The following expression describes theta hyaluronan vs. GFR: theta hyaluronan = 227 · GFR3 - 70.6 · GFR2 - 74.4 · GFR + 72.2, where GFR is given in milliliters per minute and theta  as a percentage.


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Fig. 1.   Fractional clearance (theta ) for hyaluronan (open circle ) at various glomerular filtration rates (GFR). The theta  for hyaluronan fell when the GFR increased. Solid line, equations that best described these changes with reference to the GFR. See RESULTS.

Bikunin

The theta  for bikunin, theta bikunin, decreased with increasing GFR: from 22 ± 2 to 14 ± 0.5% (P < 0.001, n = 15) when GFR was raised from 0.025 to 0.39 ml · min-1 · g wet wt-1, i.e., theta  fell by 34% (see Fig. 2). The equation theta bikunin = -136 · GFR3 + 149 · GFR2 - 57.0 · GFR + 20.8 best describes these changes, with GFR and theta  expressed as milliliters per minute and a percentage, respectively, as above.


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Fig. 2.   theta for bikunin () and Ficoll36 Å (triangle ) fell when the GFR increased. Solid lines, equations that best described these changes with reference to the GFR. See RESULTS.

Ficoll36 Å

Ficoll with a aSE of 36 Å showed a similar pattern, and theta  (theta Ficoll36 Å) fell from 11 ± 1 to 6.8 ± 0.9% (P < 0.01, n = 7) when the GFR increased from 0.067 to 0.36 ml · min-1 · g wet wt-1; i.e., theta  fell by 36% (see Fig. 2). The equation was theta Ficoll36 Å -134 · GFR3 + 140 · GFR2 - 52.8 · GFR + 13.7, with units as above.

Albumin

In contrast, the low theta  value for albumin, theta albumin, increased from 0.15 ± 0.02 to 0.74 ± 0.01% (P < 0.001, n = 15) when GFR was increased from 0.025 to 0.37 ml · min-1 · g ww-1 (see Fig. 3). The marked increase is evident from the following polynomial expression: 17.7 · GFR3 - 4.53 · GFR2 + 0.91 · GFR + 0.14, where GFR is given in milliliters per minute and theta  as a percentage. Similar theta  data for albumin were found in the second group but were not included in the analysis.


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Fig. 3.   theta for albumin and larger Ficolls (>45 Å) showed a different pattern from those for hyaluronan, bikunin, and Ficoll36 Å, and theta  increased when GFR was increased. Graphs for albumin () and Ficoll with Stokes-Einstein radius (aSE) = 55 Å () are shown. Solid lines, equations that best described these changes with reference to the GFR. See RESULTS.

Ficoll55 Å

Larger Ficoll molecules (aSE >45 Å) showed a pattern similar to that for albumin, and the theta  value increased with increasing GFR. However, the increase was less pronounced. Thus for Ficoll55 Å there was a twofold increase in the theta , theta Ficoll55 Å, vs. GFR, albeit in the same range as for albumin; i.e., theta Ficoll55 Å increased from 0.34 ± 0.09 to 0.75 ± 0.18% (P < 0.05, n = 7) when GFR was increased from 0.067 to 0.45 ml · min-1 · g wet wt-1 (see Fig. 3). The polynomial equation was theta Ficoll55 Å = 3.91 · GFR2 -0.92 · GFR + 0.388, with units as above.

Heterogeneity

The theta bikunin during perfusion with mannitol-containing solutions fell from 21 ± 0.4 to 11 ± 0.4% when the GFR was increased from 0.08 to 0.42 ml · min-1 · g wet wt-1. This was slightly lower than during perfusion with normal osmolality, where the theta bikunin fell from 24 ± 1 to 12 ± 0.3% when the GFR was increased from 0.06 to 0.45 ml · min-1 · g wet wt-1. Thus the same pattern was observed in both groups where an increased GFR decreased the theta bikunin.

Two-Pore Analysis

A neutral two-pore analysis was performed on the sieving coefficients of Ficolls with aSE of 12-72 Å. The mean values of the experimentally obtained CU/CP ratios for each molecular Ficoll radius at GFRs of 0.1, 0.2, and 0.4 ml · min-1 · g wet wt-1 (60 data pairs) were used in the calculations (for more details, see Table 2). The experimentally obtained and the calculated sieving coefficients from the two-pore analysis at GFRs of 0.1, 0.2, and 0.4 ml · min-1 · g wet wt-1 are shown in Fig. 4. The analysis revealed that the small-pore radius decreased from 47.0 to 45.7 Å when the GFR increased from 0.1 to 0.4 ml · min-1 · g wet wt-1 (P < 0.001, n = 7) (see Fig. 5). The large-pore radius was much more variable, and the changes did not reach statistical significance (see Fig. 5). Also, the large-pore fraction of the hydraulic conductance (fL) increased from 0.39 to 1.1% when GFR was increased from 0.1 to 0.4 ml · min-1 · g wet wt-1 (P < 0.001, n = 7) (see Fig. 6). Increasing GFR from 0.1 to 0.4 ml · min-1 · g wet wt-1 increased A0/Delta x from 120,000 to 380,000 cm (P < 0.001, n = 7) (see Fig. 6). Similar results were obtained when the two-pore analysis was applied to each individual experiment instead of the mean values.

                              
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Table 2.   The two-pore analysis



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Fig. 4.   Best fit between the experimentally obtained (circles) and the calculated (lines) urinary-to-plasma (U/P) ratios for FITC-Ficoll at GFRs of 0.1 (shaded circles), 0.2 (open circle ), and 0.4 () ml · min-1 · g ww-1, where ww is wet weight.



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Fig. 5.   Small (rs)- and large-pore radii (rL) for GFRs of 0.1, 0.2, and 0.4 ml · min-1 · g ww-1.



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Fig. 6.   Large-pore fraction of the hydraulic conductance (fL) and the pore area over diffusion distance (A0/Delta x) for GFRs of 0.1, 0.2, and 0.4 ml · min-1 · g ww-1.

The two-pore analysis was also performed with the assumption of various glomerular capillary pressure values (Delta PGC; see Figs. 7 and 8). The Delta PGC in the cooled isolated perfused kidneys have previously been determined (18) and are shown in Figs. 7 and 8. The pore parameters were rather stable over the entire capillary pressure interval, except for fL. This means that possible variations in Delta PGC do not affect the results of the two-pore analysis.


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Fig. 7.   rs and rL against various glomerular capillary pressures (Delta PGC) for GFRs of 0.1 (diamond ), 0.2 (), and 0.4 (open circle ) ml · min-1 · g ww-1. Filled symbols, previously estimated glomerular capillary pressures (18).



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Fig. 8.   fL and A0/Delta x against various Delta PGC for GFRs of 0.1 (diamond ), 0.2 (), and 0.4 (open circle ) ml · min-1 · g ww-1. Filled symbols, previously estimated Delta PGC (18).

The Peclet numbers were calculated for the small- and large-pore pathways at GFRs of 0.1, 0.2, and 0.4 ml · min-1 · g ww-1. We performed a full two-pore analysis of the Ficoll CU/CP ratios (aSE 12-72 Å) for each of the GFR intervals, which generated different small- and large-pore radii for each A0/Delta x. In each group, the small- and large-pore fluid fluxes were estimated and the individual Peclet numbers were computed. The result of such analysis showed that not only fluid flux increased with GFR but also PS. Therefore, the Peclet numbers were found to be largely unaffected by GFR (see Fig. 9).


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Fig. 9.   Estimated Peclet numbers for large- and small-pore pathways, respectively, for GFRs of 0.1, 0.2, and 0.4 ml · min-1 · g ww-1. cIPK, cold isolated perfused kidney.

On the basis of data from the literature, the Peclet numbers were also calculated for humans (1) and for intact rats (32) (see Fig. 10). Please note that kidneys from humans and intact rats and isolated perfused kidneys all have rather similar Peclet values in the small-pore pathway. Diffusion is the dominating transport mechanism for solutes with molecular radii <30 Å (see Fig. 10).


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Fig. 10.   Estimated Peclet numbers for small-pore pathways in kidney from humans (1) and intact rats (32) and in cIPK (0.4 ml · min-1 · g ww-1).

The Apparent Neutral Molecular Radius

The transglomerular passage of a neutral spherical solute of any size is readily estimated by using the parameters obtained in the two-pore analysis based on the Ficoll data (Table 2). The fluid fluxes through the small- and large-pore pathways are also given by the analysis. The data in Table 2 can be used to calculate theta  for a neutral solute of known molecular radius. Thus the reflection coefficient and the diffusional pore restriction factor are calculated from the solute over pore radii. The values are then used to estimate the clearances through the small- and large-pore pathways and hence theta . Accordingly, theta albumin, theta bikunin, and theta hyaluronan can be converted to an apparent molecular radius for a neutral solute (see Table 3). The diffusion constant for these solutes is the same as for Ficoll35 Å, because the aSE is 35-36 Å. Because of its negative net charge, albumin behaves as a much larger neutral molecule, having an apparent molecular radius of 63.7 ± 3.9 Å, calculated as the mean molecular radius for GFRs of 0.1-0.4 ml · min-1 · g wet wt-1 (see Fig. 11). However, the apparent molecular radii of bikunin and hyaluronan, 32.9 ± 0.1 and 24.4 ± 0.3 Å, respectively, were much lower, despite charges and hydrodynamic sizes similar to those of albumin. Figure 11 illustrates the apparent molecular radii for the four different solutes with aSE of 35-36 Å. Indeed, the apparent molecular radius is related to the frictional ratio of the solute (see Fig. 12). The frictional ratio, which is unity for a spherical solute like Ficoll, is 1.3 for albumin, 1.8 for bikunin, and 2.3 for hyaluronan. Thus increasing the frictional ratio by 38% from 1.3 will reduce the apparent molecular radius by ~50%.

                              
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Table 3.   The apparent neutral molecular radius for Ficoll, albumin, bikunin, and hyaluronan through small pores at a GFR of 0.1 ml · min-1 · g wet wt-1



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Fig. 11.   Apparent neutral molecular radii for Ficoll, albumin, bikunin, and hyaluronan for GFRs of 0.1, 0.2, and 0.4 ml · min-1 · g ww-1.



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Fig. 12.   Apparent neutral molecular radii for the 3 anionic tracers, albumin, bikunin, and hyaluronan, as a function of their frictional ratio, i.e., 1.3, 1.8, and 2.3, respectively. Spheres have frictional ratios of 1.0, and higher values indicate more extended molecules. Data are plotted for 3 different GFR levels. Curve is given by the empirical relationship y = 44.5x2 - 199x + 248.

Charge Interactions

The theta albumin is far less than that predicted for a neutral Ficoll of the same size (36 Å), indicating considerable charge selectivity. The data are compatible with a gel having a charge density of 45 meq/l, as calculated using the theories of ion-ion interaction as previously described in detail (39). The fact that theta albumin increased almost five times with increasing GFR whereas there was only a twofold increase of theta Ficoll55 Å suggests a reduced charge density in addition to an increased number of large pores. This increase in theta albumin was partly a time-dependent effect (see Results of ANOVA). The elongated solutes bikunin and hyaluronan have theta  values that exceed that of the neutral Ficoll of similar size. An elongated solute shape therefore seems to overcome the effects of charge.

Results of ANOVA

ANOVA was performed using time, GFR, and animal as independent variables. The theta hyaluronan, theta bikunin, theta albumin, theta Ficoll36 Å (P < 0.001 for all 4 solutes), and theta Ficoll55 Å (P < 0.05) were strongly dependent on GFR. There was also a strong link to time per se for albumin (P < 0.001, n = 15) as previously reported (30) but not for the other solutes. Indeed, the time-dependent effect could explain half of the increase in theta albumin with GFR.


    DISCUSSION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

In the present paper we used isolated perfused rat kidneys to study the effect of filtration rate on the transglomerular passage of albumin and three other molecules of similar hydrodynamic radius. The two elongated and negatively charged molecules, hyaluronan and bikunin, had >100 times higher theta  values than albumin despite similar sizes and charges. The same was true for Ficoll, a branched, spherical, and neutral polysaccharide (aSE = 36 Å). For hyaluronan, bikunin, and Ficoll36 Å, the theta  values decreased with increasing GFRs. In contrast, theta albumin and theta  values for large Ficoll molecules (aSE > 45 Å) increased with increasing GFRs.

There are two main conclusions that can be drawn from this study regarding the effects of filtration rate. First, the glomerular barrier is a dynamic structure and does not have the static properties of an artificial membrane. This is obvious from the fall in theta  for the spherical molecule Ficoll36 Å with GFR. Thus the reduced contribution of diffusion that occurs with increasing GFR (see Eq. 5) could only partly explain the data. In addition, the small-pore radius fell, the number of large pores increased, and A0/Delta x increased (see Table 2). Second, the elongated solutes bikunin and hyaluronan had high theta  values in the entire GFR range studied. This is reflected in the apparent molecular radius, which was ~33 Å for bikunin and 24 Å for hyaluronan compared with 64 Å for albumin, despite similar net charges and hydrodynamic sizes (Fig. 11).

In a previous study we reported that the elongated plasma protein bikunin had a much higher glomerular sieving than albumin despite similarities in size and charge. We now present the data of yet another solute, hyaluronan, with a aSE similar to that of albumin and bikunin according to gel filtration. Hyaluronan is even more elongated than bikunin, with a frictional ratio of 2.3 compared with 1.8 for bikunin and 1.3 for albumin. Indeed, the highly negatively charged polysaccharide with the size of albumin had a theta  of 0.66, almost four times higher than theta  for bikunin and 400 times that of albumin. Thus both the two negatively charged molecules, hyaluronan and bikunin, had higher theta  values than the neutral Ficoll of similar size. Indeed, the theta  values increased with the frictional ratio, which supports the notion that molecular shape may actually outweigh the effects of charge. It must be mentioned that the nominal values of the GFR are low in the cIPK. This has been evaluated in a previous study from our group (23). With the use of hyperosmolar mannitol solutions, the glomerular capillaries were uniformly perfused. It was suggested that the low GFR in the cIPK is due to intrarenal heterogeneity of flow with a reduced number of functional nephrons. However, there was no difference in theta albumin between the homogeneously and the heterogeneously perfused kidneys; i.e., the heterogeneity did not affect the glomerular permeability. Similar results were found in the present study, where theta bikunin values were similar in the heterogeneously and in the homogenously perfused kidneys and the theta  decreased with increasing GFR in both cases. The low GFRs are therefore not directly comparable to those in vivo, but the convective flow rate in the individual pore is most likely in the biologically significant range. This is further supported by the results presented in Fig. 10, where the Peclet numbers for the small-pore pathway in cIPK and two different in vivo situations are shown. Thus for the small pores the Peclet numbers are rather similar for humans (1), intact rats (32) and the cIPK.

The transglomerular passage of albumin and Ficoll36 Å was estimated under identical conditions. The theta  for the neutral Ficoll was one to two orders of magnitude higher than theta albumin, indicating a glomerular fixed charge density of 45 meq/l for the lowest GFRs. This value is in agreement with recent estimates using myoglobin (43), horseradish peroxidase (39), and lactate dehydrogenase (25) but is considerably less than the 120-170 meq/l predicted from dextran data (12).

One may ask why the theta  value can increase with GFR for some molecules and decrease for others. The solution to this apparent paradox can be found in the magnitudes of the theta  values and in the two-pore model. Small solutes with theta  values approaching unity will mainly pass through the functional small pores because they have the larger total pore area. Thus the fall in theta bikunin, theta hyaluronan, and theta Ficoll36 Å reflects a reduction in the small-pore radius from 47.0 to 45.7 Å and a reduced diffusional component. Larger molecules, on the other hand, must pass through the far less frequent large pores, resulting in lower theta  values. Indeed, the present two-pore analysis revealed that the number of large pores increased twofold, which explains the increase in theta Ficoll55 Å (Fig. 3). It is evident that theta Ficoll36 Å, theta bikunin, or theta hyaluronan will not be affected by an increased number of large pores because the theta  values are almost two orders of magnitude higher, i.e., 0.10, 0.22, and 0.66, respectively, compared with 0.0015 and 0.0034 for theta albumin and FicollFicoll55 Å. An increase in the number of large pores (shunts) caused by the elevated hydrostatic pressure, a "stretched-pore phenomenon," has previously been demonstrated in other organs (36) and has been suggested for the kidney as well (19). At a high filtration rate, there was an additional 2.5-fold increase in theta albumin compared with theta Ficoll55 Å, which most likely represents a time-dependent effect (see Results of ANOVA).

To summarize, we present the first data on the effects of filtration rate on the glomerular barrier and the glomerular clearance of differently shaped solutes. The results show that the properties of the glomerular filter are affected by hydrostatic pressure and/or filtration rate, as might be expected for a dynamic biological membrane. This conclusion is evident because the sieving of spherically neutral Ficoll molecules changed with GFR more than expected from the reduced contribution of diffusion. A two-pore analysis revealed that the changes were due to a reduction of the small-pore radius and an increased number of large pores. Second, the clearances of bikunin and hyaluronan were high over the entire GFR interval. Third, there was a significant charge selectivity of the glomerular barrier because albumin had a much lower theta  value than neutral Ficoll molecules of similar size. Fourth, the apparent neutral solute radii for the four solutes with similar Stokes-Einstein radii, i.e., Ficoll36 Å, albumin, bikunin, and hyaluronan, were 35, 64, 33, and 24 Å, respectively. Finally, we conclude that the glomerular clearance of an elongated molecule can be predicted from its frictional ratio, size, and charge.


    ACKNOWLEDGEMENTS

This study was supported by Swedish Medical Research Council Grants 9898, 2855, and 12567, the Swedish Natural Science Research Council, the Göteborg Medical Society, the Swedish Society for Medical Research, the Knut and Alice Wallenberg Foundation, the IngaBritt and Arne Lundbergs Foundation, and the National Association of Kidney Diseases. Part of this work was presented at the 32nd Annual Meeting of the American Society of Nephrology, November 5-8, 1999, Miami, FL.


    FOOTNOTES

Address for reprint requests and other correspondence: B. Haraldsson, Dept. of Nephrology, Sahlgrenska University Hospital, SE-41345 Gothenburg, Sweden (E-mail: borje.haraldsson{at}kidney.med.gu.se).

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

Received 18 June 2000; accepted in final form 26 February 2001.


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DISCUSSION
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