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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
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ABSTRACT |
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 TOP
 ABSTRACT
 INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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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 (
) at various filtration rates for four molecules of
different shapes but with similar Stokes-Einstein radii
(aSE = 34-36 Å). The 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 wt1 and
decreased to 46, 14, and 7%, respectively, on a fivefold increase in
GFR. Under the same conditions, 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
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INTRODUCTION |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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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 () 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 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 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.
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METHODS |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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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 M
/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).
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, 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.
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(1) |
for Ficoll, albumin, bikunin, and hyaluronan.
The renal clearance (Cl) for a solute, X, can be calculated
from its CU/CP, i.e.
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(2) |
value of a solute. Hence for a
solute, X, equals
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(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/
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.
is the reflection
coefficient of a solute
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(4) |
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(5) |
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(6) |
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(7) |
P is the hydrostatic pressure gradient across the glomerular
barrier, 
p is the colloid osmotic pressure of the plasma
proteins, and 
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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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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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 wt1 · ml1. The GFR values were
0.18 ± 0.01 (n = 15) and 0.17 ± 0.01 ml · min1 · g wet wt1,
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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Hyaluronan
The for hyaluronan, hyaluronan, was
66 ± 2% when the GFR was 0.067 ml · min1 · g wet wt1 and
fell to 48 ± 2% when the GFR was 0.37 ml · min1 · g wet wt1
(P < 0.001, n = 7), a 28%
reduction (see Fig. 1). The following expression describes hyaluronan vs. GFR:
hyaluronan = 227 · GFR3 70.6 · GFR2 74.4 · GFR + 72.2, where GFR is given in milliliters per minute and as a
percentage.
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Bikunin
The for bikunin, 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 · min1 · g
wet wt1, i.e., fell by 34% (see Fig.
2). The equation
bikunin = 136 · GFR3 + 149 · GFR2 57.0 · GFR + 20.8 best describes these changes, with GFR and expressed as milliliters
per minute and a percentage, respectively, as above.
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Ficoll36 Å
Ficoll with a aSE of 36 Å showed a similar pattern, and (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 · min1 · g wet wt1;
i.e., fell by 36% (see Fig. 2). The equation was
Ficoll36 Å = 134 · GFR3 + 140 · GFR2 52.8 · GFR + 13.7, with units as above.
Albumin
In contrast, the low value for albumin,
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 · min1 · g ww1 (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 as a percentage.
Similar data for albumin were found in the second group but were
not included in the analysis.
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Ficoll55 Å
Larger Ficoll molecules (aSE >45 Å) showed a pattern similar to that for albumin, and the value
increased with increasing GFR. However, the increase was less
pronounced. Thus for Ficoll55 Å there was a twofold
increase in the , Ficoll55 Å, vs. GFR, albeit in the same range as for albumin; i.e.,
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 · min1 · g wet wt1 (see
Fig. 3). The polynomial equation was
Ficoll55 Å = 3.91 · GFR2 0.92 · GFR + 0.388, with
units as above.
Heterogeneity
Thebikunin 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 · min1 · g wet wt1. This
was slightly lower than during perfusion with normal osmolality, where
the bikunin fell from 24 ± 1 to 12 ± 0.3%
when the GFR was increased from 0.06 to 0.45 ml · min1 · g wet wt1. Thus
the same pattern was observed in both groups where an increased GFR
decreased the 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 · min1 · g wet wt1 (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 · min1 · g wet
wt1 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 · min1 · g wet wt1
(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 · min1 · g wet
wt1 (P < 0.001, n = 7)
(see Fig. 6). Increasing GFR from 0.1 to
0.4 ml · min1 · g wet wt1
increased A0/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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The two-pore analysis was also performed with the assumption of various
glomerular capillary pressure values (PGC; see Figs. 7 and 8).
The 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 PGC do not affect the results of the
two-pore analysis.
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The Peclet numbers were calculated for the small- and large-pore
pathways at GFRs of 0.1, 0.2, and 0.4 ml · min1 · g ww1. 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/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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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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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 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
. Accordingly, albumin, bikunin, and
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 · min1 · g wet wt1 (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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Charge Interactions
Thealbumin 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
albumin increased almost five times with
increasing GFR whereas there was only a twofold increase of
Ficoll55 Å suggests a reduced
charge density in addition to an increased number of large pores. This
increase in albumin was partly a time-dependent effect
(see Results of ANOVA). The elongated solutes bikunin and
hyaluronan have 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. Thehyaluronan,
bikunin, albumin,
Ficoll36 Å (P < 0.001 for all 4 solutes), and 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 albumin with GFR.
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DISCUSSION |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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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 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 values
decreased with increasing GFRs. In contrast,
albumin and 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 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/x increased (see Table 2).
Second, the elongated solutes bikunin and hyaluronan had high 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 of 0.66, almost four times higher than for bikunin and 400 times that of
albumin. Thus both the two negatively charged molecules, hyaluronan and
bikunin, had higher values than the neutral Ficoll of similar size.
Indeed, the 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 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 bikunin
values were similar in the heterogeneously and in the homogenously
perfused kidneys and the 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 for the neutral Ficoll
was one to two orders of magnitude higher than 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 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 values and in the two-pore model.
Small solutes with values approaching unity will mainly pass
through the functional small pores because they have the larger total
pore area. Thus the fall in bikunin,
hyaluronan, and
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 values. Indeed, the present two-pore analysis revealed that the number of large pores
increased twofold, which explains the increase in
Ficoll55 Å (Fig. 3). It is evident that
Ficoll36 Å,
bikunin, or hyaluronan will not be
affected by an increased number of large pores because the 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
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
albumin compared with
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 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.
| |
REFERENCES |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
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) at various glomerular filtration rates (GFR). The
) and
Ficoll36 Å (
) fell when the GFR
increased. Solid lines, equations that best described these changes
with reference to the GFR. See RESULTS.
) 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.
), 0.2 (
