Glomerular filtration rate dependence of sieving of albumin and some neutral proteins in rat kidneys

Ulla Lund1, Anna Rippe1, Daniele Venturoli1, Olav Tenstad2, Anders Grubb3, and Bengt Rippe1

Departments of 1 Nephrology and 3 Clinical Chemistry, University Hospital, S-221 85 Lund, Sweden; and 2 Department of Physiology, University of Bergen, N-5509 Bergen, Norway


    ABSTRACT
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX A
REFERENCES

The size and charge-selective properties of the glomerular barrier are partly controversial. Glomerular sieving coefficients (theta ) for proteins have rarely been determined noninvasively before in vivo. Therefore, theta  was assessed vs. glomerular filtration rate (GFR; 51Cr-EDTA clearance) in intact rats for radiolabeled myoglobin, kappa -dimer, neutral horseradish peroxidase (nHRP), neutral human serum albumin (nHSA), and native albumin (HSA). To obtain theta , glomerular tracer clearance, assessed from the 7- to 8-min kidney uptake of protein, was divided by the GFR. The data were fitted with a two-pore model of glomerular permeability, where the small-pore radius was 37.35 ± 1.11 (SE) Å, and the "unrestricted pore area over diffusion path length" (A0/Delta X) 1.84 ± 0.43 · 106 cm. Although seemingly horizontal for nHRP and nHSA, the log theta  vs. GFR curves showed slightly negative slopes for the proteins investigated in the GFR interval of 2-4.5 ml/min. Strong negative (linear) correlations between (log) theta  and GFR were obtained for myoglobin (P = 0.002) and HSA (P = 0.006), whereas they were relatively weak for nHRP and nHSA and nonsignificant for kappa -dimer. theta  for nHSA was markedly higher than that for HSA. In conclusion, there were no indications of increases in theta  vs. GFR, as indicative of concentration polarization, for the proteins investigated at high GFRs. Furthermore, the glomerular small-pore radius assessed from endogenous (neutral) protein sieving data was found to be smaller than previously determined using dextran or Ficoll as test molecules.

glomerular permeability; macromolecules; reflection coefficient; transport


    INTRODUCTION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX A
REFERENCES

THE GLOMERULAR BARRIER SELECTS molecules based on their size, shape, and charge, and it almost completely prevents large macromolecules from reaching Bowman's space (8). The fenestrated endothelium with its glycocalyx, the glomerular basement membrane (GBM), and the epithelial filtration slits are arranged in series to produce this highly selective sieving filter. There is little agreement as to where the major barrier function is located (8). It has been suggested that the most size-selective portion of the glomerular barrier be represented by the podocyte slit membrane (PSM), especially by a zipper-like arrangement of structures in this membrane (24), conceivably made up (partly) of nephrin molecules (38). Some authors have brought attention to the fact that the most charge-selective barrier may be located close to the plasma compartment, possibly in the endothelial glycocalyx (25), whereas the most size-selective barrier may be more distally located (18). That the charge selectivity may be located in the endothelial glycocalyx has become even more evident after measurements of the charge-barrier properties of isolated GBMs, which were similar for neutral and negatively charged Ficoll molecules (2) or for native (anionic) and cationized albumin (1).

If the PSM were the major sieving barrier of the glomerular filter, this arrangement would result in concentration polarization of proteins in the GBM at high glomerular filtration rates (GFRs) (9). According to the fact that the relative contribution of diffusional transport decreases with increasing GFRs, high filtration rates will normally lead to reductions in the glomerular sieving coefficients (theta ) for (small) macromolecules (4, 20, 21, 23, 33). By contrast, if concentration polarization occurs, then increases in theta  may instead be expected for the highest filtration rates (9). However, only very few studies have been performed, particularly in vivo, in which the GFR dependence of theta  for macromolecules has been systematically investigated.

In view of the paucity of data on fractional clearances of macromolecules, especially of proteins, as a function of GFR, we assessed the glomerular theta  for a number of neutral proteins and albumin at normal and high GFRs using a noninvasive technique in intact rats (35, 36). Measured theta  values were consistent with a two-pore model of glomerular permselectivity (23, 33), in which the small-pore radius was ~37.4 Å, when the (negatively charged) large-pore radius was set at 110 Å. Whereas the small-pore radius was smaller than that usually obtained using Ficoll or dextran as test molecules, measured diffusional small-solute capacities, i.e., the effective area for diffusion over unit path length (A0/Delta X), were largely consistent with the calculated glomerular filtration coefficient (LpS). Furthermore, A0/Delta X (and LpS) remained stable as a function of GFR. In addition, there were no indications of concentration polarization (increases in theta ) occurring at the highest filtration rates.


    METHODS
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ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX A
REFERENCES

Experiments were performed in 85 male Wistar rats (Møllegaard, Stensved, Denmark) weighing 270 ± 8 (SE) g. The rats were kept on standard chow and had free access to water before the start of the experiments. Experiments were approved by the Animal Ethics Committee at Lund University.

Anesthesia was induced using pentobarbital sodium (50 mg/kg ip), and a thermostatically controlled heating pad maintained the body temperature at 37°C. A tracheotomy was performed to ensure free airways. The tail artery was cannulated for recording the arterial pressure (PA) and for subsequent administration of drugs. The right jugular artery and the left jugular vein were cannulated for infusion and sampling purposes. Via an abdominal incision, a catheter was placed in the urinary bladder for continuous urine sampling, the abdominal insertion being sealed with Histoacryl (Melsungen, Germany).

Tissue uptake technique. The technique has been described in detail and validated by Tenstad et al. (35, 36). When a tracer protein is added to the plasma compartment, it will mix with the plasma, dissipate within the extracellular space, and filter across the glomerular barrier. After appearing in Bowman's space, it will be reabsorbed, more or less completely, by the renal proximal tubules to be processed by the tubular cells. During the first 7-9 min of protein reabsorption, the breakdown of the protein and the subsequent reabsorption to the plasma of split products will be negligible, whereas a tiny fraction of the tracer will appear in the urine. This is the principle utilized in the present experiments. Glomerular protein clearance was assessed as the timed total (cortical) kidney uptake plus the (precipitable) urine excretion of protein tracer divided by the average plasma tracer protein concentration. theta  Was calculated from the protein clearance divided by GFR, determined by the simultaneous assessment of the plasma-to-urine clearance of 51Cr-EDTA.

For GFR measurements, 51Cr-EDTA (Amersham, Biosciences, Buckinghamshire, UK) was given in a priming dose (0.09 MBq in 0.2 ml iv), followed by a constant infusion (0.005 MBq/min) for repeated measurements of the plasma-to-urine 51Cr-EDTA clearance during 20-min intervals throughout the study. During the infusion, blood sampling (20 µl at a time) was performed approximately every 10 min using microcapillaries. Urine was also sampled approximately every 10 min. After at least one measurement of 51Cr-EDTA clearance, a constant infusion of tracer protein was performed for 7-8 min, concomitant with repeated sampling of plasma (20 µl every 2 min) and urine for the entire infusion period (7-8 min), after which the animals were killed using saturated KCl (iv). Both kidneys were then removed, blotted, weighed, and assessed for radioactivity. TCA (10%)-precipitable urine radioactivity was assessed and included in the clearance measurements. All radioactivity measurements were performed in a gamma scintillation counter (Wizard 1480, LKP Wallac, Turku, Finland). Appropriate corrections for radioactive decay and spillover from the 51Cr to the 125I channel were performed.

A modified protocol was used for native and neutralized albumin. After 8 min of tracer infusion, a whole body vascular washout was started by rapidly infusing an equal mixture of 0.9% saline and heparinized horse serum (SVA, Uppsala, Sweden) containing 1 mg/l papaverine (vasodilator, P 3510, Sigma, St. Louis, MO) via the jugular vein (or sometimes via the carotid artery) at a rate of 20 ml/min, after the inferior vena cava was opened via a laparotomy. This usually occurred at ~10 min after the start of the tracer infusion, because the laparotomy usually lasted 2-3 min. During the subsequent 8 min of washout, the animals usually expired within the first 2 min. In the albumin experiments, the inner renal medulla (rich in interstitial tissue) was dissected away from the rest of the kidney and not included in the radioactivity measurements. TCA-precipitable urine radioactivity, however, was included.

Experiments were performed at either the prevailing GFR or at elevated GFRs. Increases in GFR were induced by volume loading the animals via an infusion (iv) of horse serum and by infusing glucagon (iv) . Five milliliters of horse serum were given for ~1 min, starting 5 min before the protein tracer infusion period, and 2 ml were given, starting 2 min before the test period. Furthermore, to further increase renal blood flow, glucagon (1 mg/ml iv, Novo Nordisk, Copenhagen, Denmark) was infused at 3 µg/min, starting 2 min before and continuing throughout the test period.

Tracers and labeling procedures. The protein probes were labeled with 125I by using 1,3,4,6-tetrachloro-3alpha ,6alpha -diphenylglycouril (Iodo-Gen) (10). Briefly, 0.1 mg Iodo-Gen (T0656, Sigma) dissolved in 0.1 ml chloroform was dispersed in a 1.8-ml Nunc vial (Nunc-Kamstrup, Roskilde, Denmark). A film of the virtually water-insoluble Iodo-Gen was formed in the Nunc vial by allowing the chloroform to evaporate to dryness under nitrogen. Then, 1 ml 0.05 M PBS solution, pH 7.5, containing 1-2 mg protein to be labeled, 5 MBq 125I (Institute for Energy Technique, Kjeller, Norway), and 15 µl 0.01 M NaI were added, and the iodinating tube was gently agitated for 10 min before the reaction was terminated by removing the solution from the Iodo-Gen tube. Unincorporated iodine isotope accounting for <10% of the total radioactivity, as estimated by TCA precipitation, was removed by dialyzing the tracer against 1,000 ml 0.9% saline containing 0.02% azide. The stock solution was stored in the dark at 4°C and dialyzed for at least 24 h before use.

The following proteins were tested: myoglobin (M 0630, Sigma), horseradish peroxidase (HRP; type XII; P8415, Sigma), a human myeloma dimeric kappa -chain (a gift from Prof. Anders Grubb, Dept. of Clinical Chemistry, University Hospital, Lund, Sweden), neutral human serum albumin (nHSA; prepared by Olav Tenstad according to the technique described below), and prelabeled native albumin (125I-HSA) purchased from Kjeller, Norway (Institute for Energy Technique, Horten, Norway). Tracer characteristics (molecular weight, Stokes-Einstein radius, and isoelectric point), as determined using HPLC (Superdex 75HP and Superose 12 HR columns) and isoelectric focusing, respectively (see below), are shown in Table 1. Calibration standard curves used for the Superdex 75HP gel filtration determinations were based on BSA, egg albumin, chymotrypsinogen, and RNase. The level of free (unbound) 125I was always checked before use by TCA precipitation and was kept below 1.5% (usually <0.5%).

                              
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Table 1.   Physical characteristics of the molecules investigated

Neutralization of HSA. nHSA was obtained by a graded modification of the COOH groups using a procedure modified from that described by Hoare and Koshland (11) as follows. HSA (1.5 g) was dissolved in 15 ml 0.133 M glycine methyl ester at pH 4.75 (at room temperature). A solution of 5 ml of 0.04 M N-ethyl-N'-(3-dimethylaminopropyl) carbodiimide hydrochloride (EDC) was then added to the mixture to initiate the reaction. The pH was continuously recorded and kept at 4.75 by addition of 0.1 M NaOH. Aliquots (1 ml) were removed every 5 min for 60 min and immediately added to 1 ml of 4.0 M acetate buffer at pH 4.75 to quench the reaction. After being kept for a few minutes at room temperature, these solutions were dialyzed overnight against two changes of 10 liters of distilled water, and the dialysate was freeze-dried and stored at -20°C. The effect of the reaction was evaluated by isoelectric focusing using a vertical minigel system (CBS Scientific) and Novex (Novel Experimental Technology, San Diego, CA) precast gels. It turned out that a 45-min reaction time produced albumin with an average isoelectric point close to 7.4 without any significant change in hydrodynamic radius, as measured by HPLC (Superdex 75 HR and Superose 12 HR).

Calculations. Renal tracer protein clearance was calculated from the amount of tracer radioactivity accumulated in both kidneys plus the TCA-precipitable urine tracer activity (collected during the tracer infusion period) divided by the average venous plasma tracer concentration and by the tracer infusion time until death. In washout experiments, clearance was assessed by the amount of tracer in kidneys plus urine divided by the area under the curve of the plasma tracer concentration vs. time function. Protein theta  values were calculated by dividing the measured protein clearance by the simultaneously assessed GFR.

Values of theta  calculated as described above, or corrected for the fact that plasma proteins are upconcentrated in the glomeruli due to the filtration process, will be presented in this study. When corrections were used, we employed the formula (cf. Ref. 21)
&thgr;<IT>=&thgr;</IT><SUB>m</SUB><IT> · </IT><FR><NU>2[1<IT>−</IT>FF(1<IT>−&thgr;</IT><SUB>m</SUB>)]</NU><DE>2<IT>−</IT>FF(1<IT>−&thgr;</IT><SUB>m</SUB>)</DE></FR> (1)
where theta m represents the measured protein sieving coefficient and theta  the corrected sieving coefficient. FF is the filtration fraction, which was determined under identical conditions measuring 125I-hippuran clearance simultaneously with 51Cr-EDTA clearance at normal and elevated (and reduced) GFRs in a parallel study yielding the following relationship between FF and GFR
FF<IT>=</IT>0.47<IT> · e</IT><SUP>−0.225<IT> · </IT>GFR</SUP> (2)
GFR was calculated from
GFR<IT>=</IT><FR><NU>C<SUB>u, E</SUB><IT> · </IT>V<SUB>u</SUB></NU><DE>C<SUB>pw</SUB></DE></FR> (3)
where Cu, E represents the urinary concentration of Cr-EDTA and Vu represents the urine flow (per min), respectively, and Cpw is the plasma water concentration of Cr-EDTA. Cpw was obtained from (41)
C<SUB>pw</SUB> = <FR><NU>C<SUB>P, E</SUB></NU><DE>0.984 − 0.000718 · C<SUB>prot</SUB></DE></FR> (4)
where CP, E represents the plasma concentration of Cr-EDTA, and Cprot represents the plasma concentration of total protein.

Data for theta  were fitted to a two-pore model of membrane permeability (23, 34) using nonlinear least squares regression analysis. A number of highly sophisticated glomerular sieving models have been published recently (for a review, see Ref. 8). We chose a pore model, because such models have been widely applied over the past few decades. Furthermore, a pore model is perhaps the simplest model that may adequately describe glomerular transport data. The following parameters were estimated: the small-pore radius (rs), the unrestricted pore area over unit diffusion path length [A0/Delta X; from which the hydraulic conductance (LpS) could be calculated], and the fractional LpS accounted for by the large pores (alpha L). The large-pore radius (rL) was set at 110 Å based on results from a previous study from our laboratory (34). Based on that estimate, the large-pore volume flow (Jv, L) was determined from the sieving coefficient of native albumin. Because native albumin is negatively charged, it should be completely excluded (see below) from the small-pore pathway in the glomerular filter. It can thus be predicted to be entirely dependent on convective transport across the large pores (according to Refs. 23 and 34)
&thgr;<SUB>alb</SUB> = <FR><NU><IT>J</IT><SUB>v, L</SUB> · (1 − &sfgr;<SUB>L</SUB>)</NU><DE>GFR</DE></FR> (5)
where sigma L is the large-pore albumin reflection coefficient, as calculated taking the negative charge of albumin and the large pores into account (see below), and theta alb is the sieving coefficient for albumin. theta alb Was found to be 0.00066 ± 0.000054 (theta alb, when corrected according to Eq. 1, was determined to be 0.00057 ± 0.000038). Knowing Jv, L, the small-pore volume flow (Jv, s) could be calculated for any given GFR. Furthermore, alpha L could also be assessed (from Eq. 4 in Ref. 34), assuming rL to be 110 Å and Delta pi (the transglomerular oncotic pressure gradient) to be 26 mmHg, setting LpS at 0.36 ml · min-1 · mmHg-1 (from corrected data), as calculated from the value of A0/Delta X obtained (23, 34).

The degree of restricted diffusion and the magnitude of sigma  were modeled as a function of solute radius according to the equations given by Mason et al. (16). With respect to the glomerular transport of native albumin (HSA), the negative solute and pore charge were approximately accounted for by applying the Debye-Hückel theory of ion-ion interaction by adding 8 Å to the molecular radius and subtracting 8 Å from the pore radius (17). Although somewhat crude, the Debye-Hückel theory, compared with a more exact description given by Smith and Deen (28) of the rejection of charged solutes from pores with charged walls, proved to agree excellently with the exact theory for solutes with radii ranging from 10 to 70 Å and pores with radii of ~100 Å for equal solute and membrane charge (-20 mM) (6).

All calculations were performed using nonlinear flux analysis (20), as described in detail previously (34), and Microsoft Excel and an incorporated analysis tool, Solver, according to a modification of the method described in Ref. 39.

Statistics. Values are given as means ± SE. Differences among groups were detected using ANOVA. Calculating the variance-covariance matrix (see APPENDIX A) assessed the SE of the fitted parameters.


    RESULTS
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ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX A
REFERENCES

In Fig. 1, fractional clearances (uncorrected theta  values or "theta raw") for the neutral proteins investigated and for native albumin are plotted vs. GFR in a semilogarithmic diagram. In the GFR interval of 2.0-4.5 ml/min, theta  correlated negatively with GFR for all proteins investigated, except for the kappa -dimer (see below). Values for theta  corrected according to Eq. 1 are plotted vs. GFR in Fig. 2, and, furthermore, the best fitting two-pore parameters were here fitted to the data. According to the two-pore model, rs was calculated to be 37.35 ± 1.11 (SE) Å (for uncorrected data we obtained 37.55 ± 0.75 Å) when rL was fixed at 110 Å. Furthermore, A0/Delta X was 1.84 · 106 ± 4.29 · 105 cm (2.40 · 106 ± 5.19 · 105 cm for uncorrected data), and alpha l was 4.86 · 10-4 ± 2.34 · 10-4 (4.61 · 10-4 ± 6.25 · 10-5 for uncorrected data). Average data, corrected and uncorrected (or raw), for theta  (at an average GFR of ~3 ml/min) and sigma  for myoglobin, kappa -dimer, neutral HRP, and neutral and negative albumin are shown in Table 2. LpS calculated from A0/Delta X (corrected data) was 0.36 ml · min-1 · mmHg-1 (both kidneys). For a GFR of 3 ml/min, with the assumption of a net transglomerular pressure gradient on the order of 10 mmHg in our experimental animals, LpS can be estimated to be 0.3 ml · min-1 · mmHg-1. Thus the A0/Delta X calculated from sieving data for small and intermediate size solutes was largely consistent with the filtration coefficient of the glomerular filtration barrier. Furthermore, these two entities could be set constant (and independent of GFR) in all simulations.


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Fig. 1.   Fractional clearances (theta ) for the neutral proteins myoglobin (triangle ), kappa -dimer (diamond ), neutral horseradish peroxidase (nHRP; ), and neutral human serum albumin (nHSA; open circle ), together with those for native albumin (HSA; ) plotted as a function of glomerular filtration rate (GFR) in a semilog diagram. Data were not corrected according to Eq. 1.



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Fig. 2.   Values for theta  for the proteins investigated, corrected according to Eq. 1, plotted as a function of GFR in a semilog diagram. Symbols are as defined in Fig 1. Computer simulated theta  vs. GFR curves are shown for the best fitting 2-pore parameters, i.e., for small-pore radius (rs) = 37.35 Å, unrestricted pore area over diffusion path length (A0/Delta X) = 1.84 · 106 cm, and fractional hydraulic conductance (alpha L) = 0.00049, when large-pore radius (rL) was preset at 110 Å. The prominent diffusive protein transport at low GFRs resulted in a negative dependence of theta  on GFR, particularly evident for myoglobin. For native (negative) HSA, passing only through large pores, there is also a dependence of theta  on GFR because the fractional large-pore volume flow asymptotically falls (to approach alpha L) with increases in GFR. There is no obvious indication of concentration polarization for any of the proteins investigated.


                              
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Table 2.   Sieving coefficients of the test molecules investigated

Figures 1 and 2 indicate the presence of a negative dependence of theta  on GFR. By applying a simple linear regression analysis of log theta  vs. GFR, we obtained a highly significant negative correlation for myoglobin (P = 0.002 for corrected theta ), HSA (P = 0.006), and nHSA (P = 0.01), but a barely significant one for nHRP (P = 0.04), whereas it was nonsignificant for the kappa -dimer. The regression coefficients with their 95% confidence intervals (for corrected and raw data) are listed in Table 3. The theta -GFR relationships are largely consistent with models in which diffusion and convection occur simultaneously across a size (and/or charge)-selective barrier. Thus for small proteins, the reduction in the diffusional component of transport with increasing filtration rates will cause reductions in theta . However, for large proteins, and at high filtration rates, the impact of diffusion is small. This results in an essentially flat theta  vs. GFR curve, where theta  approximates (1 - sigma ) at high GFRs. Note that for solutes with radii larger than the small-pore radius (37.35 Å), one would, according to the two-pore model, also expect a dependency of theta  on GFR. In a heteroporous model, this phenomenon results from the fact that the fractional large-pore volume flow (Jv, L/GFR) will asymptotically fall with increases in GFR to approach alpha L at high GFRs. This behavior is expected for HSA, because the presence of charge interactions may completely prevent HSA from entering the small pores, whereas nHSA may filter through both small and large pores. Note also that nHSA transport was one order of magnitude higher than that of native (negatively charged) albumin. Finally, for all proteins, including the two largest investigated (nHSA and HSA), there were no indications of concentration polarization occurring at any filtration rates.

                              
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Table 3.   Statistical analysis of the measured sieving coefficients

Figure 3 illustrates (log) theta  vs. both GFR and solute radius in a three-dimensional diagram simulated using the present two-pore parameters (for corrected data). Here, it is again evident that, for solutes with radii <15 Å , theta  is unity and completely independent of GFR, whereas theta  for solutes with radii ranging between 15 and 30 Å theta  is dependent on GFR. In the GFR interval of 2-5 ml/min, however, solutes with radii of 30-37 Å exhibit rather stable theta  values, which are close to their (1 - sigma ) values. For solutes with radii larger than the small-pore radius, there is again a dependency of theta  on GFR, determined by the JV, L/GFR ratio, as mentioned above.


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Fig. 3.   Values for simulated theta  vs. both GFR and solute radius in a 3-dimensional diagram of the 2-pore model parameters obtained in the present study. Note the semilogarithmic scale. Solutes with radii <15 Å have a theta  of 1 (or close to 1) throughout the GFR interval. Solutes with radii of 15-30 Å show marked GFR dependence of their theta , being most pronounced for solutes with radii of 18-28 Å. For solutes with radii >30 Å, but smaller than the pore radius, the GFR dependence in the GFR interval 2-5 ml/min is moderate. For solutes with radii larger than small-pore radii, or for negatively charged macromolecules, which are confined to the large-pore pathway for their passage across the glomerular membrane, there is a marked dependence of theta  on GFR, attributable to the fact that the ratio of the large-pore volume flow over GFR (Jv, L/GFR) is higher than alpha L, but asymptotically approaches alpha L when GFR is high.


    DISCUSSION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX A
REFERENCES

The essential result of this study is that the fractional clearances (theta ) of small endogenous neutral proteins and of albumin in rats, assessed as a function of GFR in vivo, slightly declined with increases in GFR in the GFR interval of 2.0-4.5 ml/min. This was particularly evident for myoglobin. The results essentially agree with dextran sieving data obtained during isoncotic volume expansion, performed to increase GFR, in Munich-Wistar rats (4). With increases in GFR, dextrans with radii of 20-38 Å clearly decreased their theta  values. In the present study, there was no evidence for concentration polarization (increasing theta  values) occurring at high GFRs, either for the small proteins investigated or for neutral or native albumin. Furthermore, the theta  values for small proteins and albumin were lower than previously obtained using Ficoll or dextran of equal hydrodynamic radii as probes for testing glomerular permselectivity. Also, there was a marked charge dependency of glomerular transport, as evidenced by the large difference in theta  for neutralized vs. negatively charged albumin.

There have been very few previous analyses of the dependence of protein theta  values on GFR, at least in vivo. In the isolated perfused rat kidney (IPK) at 8°C, however, there is one recent set of theta  measurements of this kind for "asymmetrical" proteins (19). Although in the IPK the GFR (per kidney) was only 20% of those obtained at 37°C in the intact rat in vivo, the observed theta  for the most permeable proteins investigated (hyaluronan and bikunin) showed a similar asymptotic reduction as a function of GFR, as found in the present study. This is indeed the expected behavior of theta  when the diffusional component of transport is high, because this component will theoretically decrease asymptotically with increases in GFR according to nonlinear transport formalism (20). Only at high GFRs, the impact of the diffusional component will become negligible, so that the protein theta  will equal (1 - sigma ) (7, 8, 20, 21, 23, 33). Contrary to results from the IPK (19), there were no indications of increases in microvascular permeability occurring for albumin at high intraglomerular hydrostatic pressures in the present study. A tentative explanation could be that the IPK, although partly protected from inflammatory mediators or ischemia-reperfusion injury by the temperature reduction, might be more vulnerable to high intraluminal pressures than is the intact kidney under in vivo conditions.

One important consequence of the presence of a large diffusional component of small protein transport across the glomerular filter, i.e., a large A0/Delta X for the renal microcirculation, is that assessments of theta  for small proteins must be standardized to rather narrow GFR ranges to be compared between different experimental conditions. For example, if an ischemia-reperfusion insult per se results in a fall in GFR, then by necessity theta  for a small protein, such as myoglobin or beta 2-microglobulin, must increase, even if the glomerular permeability is unaffected. On the other hand, if GFR is increased but the permeability is unchanged, then theta  for a protein will fall. For the largest neutral molecules investigated in the present study (kappa -dimer, nHRP, and nHSA), however, the diffusional contribution to theta  was expected to be low in the whole GFR range investigated. Indeed, theta  was independent of GFR changes for the kappa -dimer and nearly so for nHRP. Unexpectedly, there was, however, a slight decline of the log theta  vs. GFR relationship for nHSA.

Theoretically, theta  of a magnitude measured for HRP and nHSA would remain stable as a function of GFR even at high filtration rates, if the major barrier to solute sieving were close to the blood side of the membrane. However, if the major barrier function were instead located close to Bowman's space, e.g., at the PSM, then one would expect at least some degree of concentration polarization to occur at high filtration rates. According to a recent modeling study of the sieving behavior of the glomerular capillary wall (9), it was assumed that the glomerular barrier exhibited three transport resistances arranged in series, with a major portion of the overall transport resistance to macromolecules present at the level of the PSM. Furthermore, it was assumed that the resistance of the transport of large solutes was low (negligible) at the fenestrae. Under such assumptions, a rise in single-nephron GFR from 40-45 to ~80 nl/min, corresponding to a rise in whole rat (300 g) GFR from ~2.5 to 5 ml/min, caused a significant rise in theta  for (neutral) solutes having a theta  similar to that of albumin (nHSA and HSA) in the present study. However, because we were not able to detect any signs of concentration polarization occurring in the GFR interval of 2-4.5 ml/min, we are inclined to conclude that the case for a major sieving barrier located at the PSM is rather weak. In case the slit membrane would still be the major filtration barrier, the present data indicate that serial barriers proximal to the PSM must be very highly permeable to macromolecules to prevent the buildup of concentration polarization layers at the PSM.

The present study essentially confirms and extends previous measurements of theta  using micropuncture techniques. Micropuncture techniques have been criticized, because they imply exposure of and mechanical interactions with an intact kidney. Furthermore, proteins sampled from the tubules may bind to the glass pipette, and interstitial proteins may leak into the tubules during the micropuncture. Moreover, because the tubular micropuncture procedure has to be performed at sites distally to Bowman's capsule, primary urine cannot be directly assessed (15). Indeed, tubular protein concentration falls along the distance of the proximal tubule, because protein reabsorption is usually more avid than that of water. In an attempt to avoid all these sources of error, Tojo and Endou (37) used a double-barrel pipette technique, which made it possible to seal the punctured (rat) proximal tubule from the interstitium. Furthermore, they assessed the tubular concentration of protein together with that of a filtration marker (inulin) at various distances from Bowman's capsule (37). With this technique, they were able to quite precisely estimate the urinary albumin protein concentration of Bowman's capsule by an extrapolation procedure. Using this careful technique, they estimated the theta  value for native albumin to be 6.2 · 10-4, which is almost identical to that assessed by the present technique in vivo (6.6 · 10-4). Also, our assessments of theta  values for myoglobin, dimeric kappa -chain (Bence Jones proteins), and nHRP are remarkably close to estimates previously obtained using micropuncture techniques (14).

All measured values of theta  for neutral proteins in the present study are much lower than the corresponding theta  values previously obtained for neutral Ficoll, which, in turn, are much lower than theta  values for dextran (15). The marked discrepancy between glomerular protein sieving data and glomerular dextran sieving data was discussed at some length in the classic review by Renkin and Gilmore (21). It may be due to the fact that dextrans are flexible molecules, and thereby hyperpermeable in vivo, so that they may actually transmigrate through pores, which are even smaller than their Stokes-Einstein radii, sometimes denoted "reptation" (17). Moreover, recent data indicate that the more ideal Ficoll molecule, a copolymer of epichlorhydrine and sucrose, may not behave in all aspects as an ideal ridgid sphere (12, 27), but we will return to this issue in a forthcoming publication. At any rate, the permselectivity of the glomerular barrier, in terms of the small-pore radius, for example, seems to be dependent on the physical properties of the probe used for testing permeability. Using neutral dextran as a probe, the average glomerular rs has been determined to be on the order of 50-55 Å (15). Using Ficoll at normal ionic strength, rs has been determined to be on the order of 45 Å (18, 19), whereas at low ionic strengths rs was only 41 Å (30). This value is similar to the rather low rs estimate of the present study and to earlier estimates using proteins for probing glomerular permeability (21).

It has been well established since the 1970s and 1980s that the glomerular filter discriminates among macromolecules based on both their net charge as well as their size (15). Much of the evidence in favor of charge selectivity of the glomerular filter has been based on comparisons between sieving data for uncharged and anionic dextran (dextran sulfate) (3). Although vivid arguments against glomerular charge selectivity have been raised during the last decade (5, 26, 32, 42), strong evidence supporting the classic view was recently given by comparing neutral and anionic lactate dehydrogenase or neutral and anionic HRP in the IPK (13, 31). These studies largely confirm the classic studies by Rennke et al. (22) for differently charged HRP (22). The present data are entirely consistent with the glomerular filter as a charge-selective barrier, producing a near 10-fold difference in theta  for neutralized vs. negatively charged (native) albumin.

The present tissue uptake technique has been validated for small proteins in previous publications (35, 36). For proteins with very low renal clearances, such as albumin, it is crucial that the kidneys are completely washed free of intravascular tracer and that the bulk of interstitially accumulated tracer (and free iodine) is to a large extent cleared by back-diffusion to the rinse fluid. The washout procedure is thus crucial to the success of the technique. Even though we consider the washout to have been more or less complete, we cannot completely rule out that some tracer remained either intravascularly or extracellularly after tracer washout. From that point of view, the present theta  for native albumin of 6.6 · 10-4 may represent an overestimate. Still, the value obtained is in agreement with the recent careful micropuncture study by Tojo and Endou (37) referred to above. Therefore, we feel confident that the degree of overestimation of theta  for native albumin was, after all, rather moderate.

In conclusion, there was a dependence of glomerular small-protein theta  on GFR for neutral molecules with molecular radii ranging between 15 and 30 Å and also for native albumin. The data were readily fitted to a two-pore model of glomerular permeability where rs was found to be ~37-38 Å. Neither for small proteins nor for albumin was there any evidence for concentration polarization present at high GFRs. Furthermore, the glomerular filter showed properties of a negative charge barrier. Taken together, the present in vivo data may be interpreted to indicate that the endothelial glycocalyx-filled fenestrae are playing a greater role than previously thought, and the epithelial slit diaphragms a lesser role, in determining the sieving properties of the glomerular filtration barrier.


    APPENDIX A
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX A
REFERENCES

The fractional clearance data (theta ) were fitted to a two-pore model of membrane permeability (23, 34) using a weighted nonlinear least squares regression analysis. In detail, the function to be minimized was
SSQ<SUB><IT>w</IT></SUB> = <LIM><OP>∑</OP><LL>s</LL></LIM><LIM><OP>∑</OP><LL>1</LL><UL><IT>n</IT><SUB>s</SUB></UL></LIM><IT>W</IT><SUP>2</SUP><SUB>s</SUB> · <FENCE><FR><NU>&thgr;<SUB>exp<SUB>s, <IT>i</IT></SUB></SUB> − &thgr;<SUB>th<SUB>s, <IT>i</IT></SUB></SUB></NU><DE>&thgr;<SUB>exp<SUB>s, <IT>i</IT></SUB></SUB></DE></FR></FENCE><SUP>2</SUP> (A1)
where theta exp and theta th are experimentally and theoretically calculated theta , respectively, and the sum is extended to all the experimental points (ns) collected for each solute (s) considered. To correct for the different number of experimental points among the different solutes considered, the weight Ws was defined as
W<SUB>s</SUB> = 1 − <FR><NU><IT>n</IT><SUB>s</SUB></NU><DE><IT>N</IT></DE></FR> (A2)
where N is the total number of theta  measurements. To compensate for the extremely large range of experimental values (3 orders of magnitude from myoglobin to native albumin theta  values), the relative difference with respect to theta exp was introduced in place of the usual squared difference.

The estimated parameters were rs, A0/Delta X, and the fractional LpS accounted for by the large pores (alpha L). However, because the numerical values of these parameters differ by several orders of magnitude (9 from A0/Delta X to alpha L), a set of scaling multipliers was introduced, so that the minimization algorithm had to deal with parameters near to unity.

SE of the fitted parameters was assessed by calculating the variance-covariance matrix according to the method described by Smith et al. (29).


    ACKNOWLEDGEMENTS

We are grateful to Kerstin Wihlborg for skillful typing and editing of the manuscript. The expert technical assistance by Veronica Lindström (Dept. of Clinical Chemistry, University Hospital, Lund, Sweden) is acknowledged.


    FOOTNOTES

This study was supported by Swedish Medical Research Council Grant 08285 and by European Union Contract FMRX-CT98-0219.

This study has been published in abstract form (J Am Soc Nephrol 12: 503A, 2001).

Address for reprint requests and other correspondence: B. Rippe, Dept. of Nephrology, Univ. Hospital of Lund, S-211 85 Lund, Sweden (E-mail: Bengt.Rippe{at}njur.lu.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.

First published March 4, 2003;10.1152/ajprenal.00316.2002

Received 3 September 2002; accepted in final form 22 February 2003.


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