1 Department of Chemical Engineering and 2 Division of Bioengineering and Environmental Health, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139; and 3 Nephrology Division, Stanford University Medical Center, Stanford, California 94305
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ABSTRACT |
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Recent progress in relating the functional properties of the glomerular capillary wall to its unique structure is reviewed. The fenestrated endothelium, glomerular basement membrane (GBM), and epithelial filtration slits form a series arrangement in which the flow diverges as it enters the GBM from the fenestrae and converges again at the filtration slits. A hydrodynamic model that combines morphometric findings with water flow data in isolated GBM has predicted overall hydraulic permeabilities that are consistent with measurements in vivo. The resistance of the GBM to water flow, which accounts for roughly half that of the capillary wall, is strongly dependent on the extent to which the GBM surfaces are blocked by cells. The spatial frequency of filtration slits is predicted to be a very important determinant of the overall hydraulic permeability, in keeping with observations in several glomerular diseases in humans. Whereas the hydraulic resistances of the cell layers and GBM are additive, the overall sieving coefficient for a macromolecule (its concentration in Bowman's space divided by that in plasma) is the product of the sieving coefficients for the individual layers. Models for macromolecule filtration reveal that the individual sieving coefficients are influenced by one another and by the filtrate velocity, requiring great care in extrapolating in vitro observations to the living animal. The size selectivity of the glomerular capillary has been shown to be determined largely by the cellular layers, rather than the GBM. Controversial findings concerning glomerular charge selectivity are reviewed, and it is concluded that there is good evidence for a role of charge in restricting the transmural movement of albumin. Also discussed is an effect of albumin that has received little attention, namely, its tendency to increase the sieving coefficients of test macromolecules via steric interactions. Among the unresolved issues are the specific contributions of the endothelial glycocalyx and epithelial slit diaphragm to the overall hydraulic resistance and macromolecule selectivity and the nanostructural basis for the observed permeability properties of the GBM.
Darcy permeability; sieving coefficient; Ficoll; equilibrium partition coefficient
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INTRODUCTION |
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THE CONCEPT OF THE GLOMERULUS as a highly refined ultrafiltration device, capable of filtering large volumes of plasma while efficiently retaining proteins within the circulation, has long been one of the cornerstones of renal physiology. Although that basic view of glomerular function is due to earlier generations of researchers, efforts to achieve a quantitative understanding of glomerular filtration received a distinct stimulus some 30 years ago. Beginning about 1970, new animal models (e.g., the Munich-Wistar rat) and advances in micropuncture pressure measurement techniques permitted a much more direct examination of glomerular forces and flows in mammals than had been possible previously. Those and other developments have stimulated a large number of investigations into the dynamics of water filtration and the selective retention of macromolecules by the glomerulus in health and disease. A comprehensive review is available of results published through about 1990 (66).
Among the more recent lines of research are efforts begun in the early 1990s to relate the functional properties of the glomerular capillary wall to its unique structural features, on the cellular and even macromolecular level. This represents a significant departure from earlier analyses of glomerular barrier function by us and others, which mainly sought to express the available micropuncture and clearance measurements in terms of hydraulic permeabilities and effective pore sizes. In other words, in the 1970s and 1980s the glomerular capillary wall was regarded largely as a black box with certain measurable properties, whereas more recent biophysical analyses have sought to explain its permeability properties in terms of specific structures. This has been done by combining morphometric results, in vitro data using isolated glomeruli, and detailed hydrodynamic models of the capillary wall. Such work is the focus of this review.
As background, we begin with a brief overview of the structure and composition of the glomerular capillary wall. The permeability properties will be affected by features spanning a wide range of length scales, from the dimensions of cells to the dimensions of the macromolecules that form the basement membrane and junctional complexes (slit diaphragms). Those in the ~100- to 1,000-nm and ~0.1- to 10-nm ranges are conveniently labeled as "microstructural" and "nanostructural," respectively. Following the structural description is a section on water permeability, in which the main elements of the structure-based hydrodynamic models are discussed and their predictions compared with experimental findings in vivo. Emphasized there are insights into the reduced filtration capacity for water in several forms of glomerular disease. The last section concerns the selectivity of the glomerular barrier to macromolecules. Efforts to understand glomerular size selectivity in terms of structural models are reviewed, and various unresolved issues are discussed. One of the most controversial issues is the extent to which charge selectivity is important for glomerular barrier function. Also included is a discussion of recent findings concerning the effects of serum albumin on the sieving of macromolecular tracers.
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STRUCTURE AND COMPOSITION |
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Microstructural Idealizations
We focus here on structural representations that have been used in modeling glomerular permeability; a much more comprehensive discussion of glomerular anatomy is available elsewhere (55). The glomerular capillary wall is unusual in having three layers: a fenestrated endothelium, the glomerular basement membrane (GBM), and the foot processes of glomerular epithelial cells. Between the epithelial foot processes are "filtration slits" bridged by slit diaphragms. Because of the low water permeability of most cell membranes, it is generally accepted that glomerular filtrate follows an extracellular path: through the fenestrae, across the GBM, and through the slits (passing through the slit diaphragms). To describe this flow, Drummond and Deen (31) proposed that the glomerular capillary wall be viewed as an assembly consisting of many repeating subunits. The basic structural subunit, as shown in Fig. 1, consisted of a single filtration slit, an associated area of GBM, and several fenestrae. The key geometric quantities in this model are the width of the structural unit (W), the thickness of the GBM (L), the width of the filtration slit (w), the dimensions of a fenestra, and the number of fenestrae per filtration slit. Representative values gleaned from various morphometric studies in rats (1, 39, 57, 62, 87, 90, 92, 98, 107) are summarized in Table 1. Typical dimensions for rats are W = 360 nm, L = 200 nm, and w = 39 nm. The extent to which the GBM surfaces are blocked by cells is described by the fraction of the surface area occupied by slits (
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Data for healthy humans suggest a slit width similar to that in rats,
w = 43 nm (37) but a significantly larger
subunit width and GBM thickness, W = 500 nm and
L = 400 nm, respectively (58, 97). A
morphometric index used to describe slit spacing is the filtration slit
frequency (FSF), which is related to the subunit width by
W = (2/)(1/FSF); the factor 2/
accounts for the
random angle of sectioning (33).
Slit Diaphragm
Among the key nanostructural dimensions are those that describe the openings in the slit diaphragm. Figure 2A shows an enlarged view of the slit diaphragm oriented as in Fig. 1. The most frequently cited configuration for the slit diaphragm is that of Rodewald and Karnovsky (87), who described a structure consisting of a central filament oriented parallel to the podocyte membranes and regularly spaced bridge fibers, alternating from side to side, that connect the central filament to the membranes. This arrangement, which we term the "zipper" structure, is depicted in Fig. 2B. The reported dimensions of the openings were 40 × 140 Å. These dimensions are problematic in that they imply a much more size-selective barrier than that shown by functional measurements, as will be discussed. A simpler structure, motivated by the observations of Hora et al. (45), is shown in Fig. 2C. This "ladder" structure remains quite tentative, and specific dimensions for it are not available from electron microscopy.
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Recent efforts to elucidate the structure of the slit diaphragm have
centered on its component molecules, particularly the newly identified
protein nephrin. Nephrin has a molecular mass of ~150 kDa and has
been shown to be expressed exclusively by glomerular podocytes in the
slit diaphragm region (44, 89). Lack of proper expression
of the nephrin gene has been shown by Tryggvason and co-workers
(63, 102) to be linked to the congenital nephrotic
syndrome of the Finnish type, a glomerular disorder that results in
severe proteinuria and that is associated with normal GBM and the loss
of foot processes and slit diaphragms. Genetic analysis of the coding
region of the nephrin gene has demonstrated that it is a single-pass,
membrane-spanning protein with eight Ig motifs and a type III
fibronectin domain (102). It has been hypothesized that
nephrin molecules extending out from adjacent podocytes might interact
in a homophilic manner to form the zipper structure (102).
Such proposals remain speculative, as the interaction of nephrin with
other protein components of the slit diaphragm is not yet known. It has
been demonstrated that cultured podocytes form linking structures that
are similar to filtration slits in vivo and that these intercellular
linking structures contain the proteins zonula occludens-1,
P-cadherin, and -,
-, and
-catenin (82).
GBM
The GBM is a gel-like material that is 90-93% water by volume (21, 85). Structural integrity is conferred by a heteropolymeric network of type IV collagen, laminin, fibronectin, entactin, and heparan sulfate proteoglycan (59, 66). Collagen IV, a triple helical polypeptide, is thought to form an interconnected network of fibers within the GBM, to which other matrix components are attached. Laminin, an asymmetrical four-armed structure, is thought to play an important role in the structural integrity of the GBM and in its interactions with the cellular layers of the glomerular capillary wall. The sulfated glycoprotein entactin, or nidogen, binds to collagen IV, heparan sulfate proteoglycan, and laminin and thus may play an important role in linking GBM components to one another. Similarly, fibronectin, a 500-kDa glycoprotein, binds to laminin, collagen IV, and heparan sulfate proteoglycan, suggesting that it too may have a role in linking GBM constituents together. Heparan sulfate proteoglycan has been shown to comprise ~1% of the dry weight of the GBM (54). The predominant GBM proteoglycan is made up of a 400-kDa core protein called perlecan and four to five heparan sulfate chains bound to one end of the core protein (103). These anionic heparan sulfate chains are made of repeating disaccharide units of glucosamine and glucuronic acid (55).Endothelial Glycocalyx
The glycocalyx that covers the luminal surface of the endothelial cells and fills the fenestrae may also be an important determinant of glomerular permeability. This layer is thought to be composed principally of sulfated proteoglycans (95) and glycoproteins (94). Recent electron microscopy studies (88) demonstrated a 300-nm-thick filamentous surface coating that appeared to be present over both fenestral and interfenestral surfaces. The thicknesses of endothelial surface coatings reported by Rostgaard and Qvortrup (88) exceed those previously observed by other authors (65, 93) by a factor of three to five. This difference was attributed to a novel method of tissue fixation, combined with a treatment that enhanced micrograph contrast. ![]() |
FILTRATION OF WATER |
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Structure-Based Model
The structural unit depicted in Fig. 1 was used by Drummond and Deen (31) to formulate a hydrodynamic model for the filtration of water across the glomerular capillary wall. The objective of the model was to predict values of the effective hydraulic permeability (k). Because the three layers of the capillary wall act as resistances in series, the overall hydraulic permeability is related to those of the individual layers by
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(1) |
Finite-element solutions of Stokes' equation (the low-Reynolds-number
form of the Navier-Stokes equation) were used to characterize flow in
the epithelial filtration slits (30). The results
indicated that the slit diaphragm is the dominant resistance to water
flow between the foot processes, implying that the slit length is not an important parameter for water filtration. With the use of the zipper
structure, with all dimensions as given in Rodewald and Karnovsky
(87), the permeability of the slit diaphragm (in SI units)
was estimated as ks = 7.9 × 108
m · s
1 · Pa
1. Because what
is desired is a filtrate velocity (or volume flux) averaged over an
entire structural unit, and because the slits only occupy a fraction
s of the surface area, the epithelial permeability is kep =
s ks. With the use of the
representative dimensions for the rat given above,
s = 0.11 and kep = 8.6 × 10
9
m · s
1 · Pa
1. It was shown
that the resistances to water flow of the zipper and ladder structures
are similar, provided they are assumed to have the same ratio of wetted
cylinder area to cross-sectional area (30).
Finite-element solutions of Stokes' equation were used also to
characterize the hydraulic resistance of a water-filled fenestra (31). By using the dimensions given in Lea et al.
(62), the permeability of a single fenestra was estimated
as kf = 1.0 × 106
m · s
1 · Pa
1. With the
fenestrae occupying 20% of the filtering surface
(
f = 0.20), it was found that
ken =
f
kf = 2.0 × 10
7
m · s
1 · Pa
1. Comparing
this with the epithelial result, it is found that ken/kep
20. This
suggests that the dominant cellular contribution to k is
that of the slit diaphragms and that the water flow resistance of the
fenestrae is negligible. This assumes, however, that the flow
resistance of the glycocalyx is unimportant (see below).
Water flow through the GBM was described by Drummond and Deen
(31) using Darcy's law
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(2) |
Equation 2 was combined with that which describes local
conservation of mass ( · v = 0) and solved
for the idealized GBM geometry shown in Fig. 1 (31).
Although the actual fenestral openings are circular, a comparison of
three-dimensional finite-element solutions for circular openings with
two-dimensional analytical solutions for slitlike openings showed that
equivalent results were obtained if the value of
f was
the same. Moreover, for the relative dimensions typical of the GBM, it
was found that the infinite-series expression obtained from the
analytical solution was well approximated by
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(3) |
The main trends predicted by Eq. 3 are illustrated in Fig.
3, which shows the relative GBM
resistance to water flow for various combinations of
s,
f, and
nf. The parameter values used are those for the
normal rat (Table 1). The GBM resistance in vivo is predicted to be 2.3 times that of bare GBM. Decreases in
s,
f, and nf all exaggerate the
channeling phenomenon, thereby increasing the water flow resistance.
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Setting = 2.7 nm2 and using the dimensions for the
rat, found that kbm = 8.3 × 10
9
m · s
1 · Pa
1 Drummond and
Deen (31). Because kbm
kep
ken, it was
concluded that the GBM and epithelial resistances to water filtration
in the normal rat are about equal and that the resistance of the endothelium is negligible. From Eq. 1, the overall hydraulic
permeability was predicted to be k = 4.1 × 10
9
m · s
1 · Pa
1. This is well
within the range of values estimated from micropuncture measurements,
which is roughly from 3 × 10
9 to 5 × 10
9
m · s
1 · Pa
1
(31).
The hydraulic resistance of the GBM is proportional to 1/ (Eq. 3), and the
value used above is larger than more recent estimates, including
= 1.5 nm2 (34)
and
= 1.2 nm2 (9). Thus the GBM may
actually account for somewhat more of the overall resistance than
indicated. If one uses
= 1.2 nm2 instead of
= 2.7 nm2, the contribution of the GBM increases
from 50 to 69% of the total resistance. Although the overall hydraulic
permeability is then reduced by 38% to k = 2.5 × 10
9
m · s
1 · Pa
1, the predicted
value is still in reasonable agreement with the experimental range.
There are uncertainties also in the cellular contributions to the
hydraulic permeability. The value of ken quoted
above was computed by assuming that a fenestra is a short, water-filled channel of varying radius. An alternative model is that it is a
gel-filled channel, due to the endothelial glycocalyx. When that
possibility was explored by solving Brinkman's equation (related to
Darcy's law) in a fenestra, with = 2.7 nm2 as for
the GBM, ken was decreased to 1.3 × 10
8
m · s
1 · Pa
1
(31). That change alone decreases the overall hydraulic
permeability from 4.1 × 10
9 to 3.2 × 10
9
m · s
1 · Pa
1, with the
endothelium now accounting for 24% (instead of just 2%) of the total
resistance. The main obstacle to refining the estimate of
ken is the unknown
of the glycocalyx.
Whereas the hydraulic resistance of the endothelium may have been underestimated, depending on the actual properties of the glycocalyx, that of the epithelium may have been overestimated. As already mentioned, the zipper structure is far too "tight" a barrier to be consistent with the relatively large test macromolecules that appear in normal glomerular filtrate. Larger openings in the slit diaphragm would also tend to increase the value of kep. To refine models either for water flow or for macromolecule movement through the filtration slits, an improved representation of the slit diaphragm geometry is needed.
Uncertainties in the individual contributions notwithstanding, the success of the water flow model in predicting the overall hydraulic permeability suggests that the overall balance between the GBM and cellular resistances is approximately correct. Indeed, the tendency to underestimate the endothelial contribution may well have canceled a tendency to overestimate the epithelial contribution. In most of the applications to pathophysiological situations described below, the fenestral and slit diaphragm permeabilities are each assumed to be constant, and the main factor considered is the calculated change in kbm. Under those conditions, precisely apportioning the cellular resistance between the two layers is much less important than describing the effects of the cells on kbm.
Applications of Water Flow Model to Glomerular Disease
The first pathophysiological application of the water flow model was to adriamycin nephrosis in the rat (31). The morphometric and micropuncture results used were those of Miller et al. (69), who studied the effects of adriamycin administration in three groups of animals: group 1, no further treatment; group 2, four-fifths renal ablation; and group 3, low-protein diet. Relative to the values quoted above for normal rats, W was increased by factors of 5-7 (reflecting decreases in measured filtration slit frequency), and L was increased by factors of 1.5-2.5 (reflecting measured values of basement membrane volume divided by peripheral capillary surface area). Another prominent finding was the detachment of foot processes from as much as 4% of the capillary wall. That was modeled by considering two parallel pathways for water filtration, one with all structures present and the other withThe model has been applied also to human glomerular disease. In each of the four diseases studied to date, impairment of k appears to be the predominant cause of glomerular filtration rate (GFR) depression early in the course of the disorder. The conditions examined include minimal change, membranous, and diabetic nephropathies, and preeclamptic toxemia (33, 58, 79, 97). In each instance depression of GFR by 30-50% was associated with alterations in glomerular hemodynamics that should not have reduced the net ultrafiltration pressure and hence the GFR. By exclusion, we infer that GFR depression must have been due to a decline in the ultrafiltration coefficient (Kf). Kf is the product of glomerular hydraulic permeability and filtration surface area (Kf = kS), expressed either on a single-nephron or whole-kidney basis; single-nephron values are employed here.
In the human studies to be discussed, glomeruli obtained by biopsy were
subjected to morphometric analysis to determine L, FSF
(allowing calculation of W), filtration surface area per
glomerulus (S), and certain other quantities. The value of
S was computed from the product of filtration surface
density and glomerular volume (33, 97). Except where
indicated, the values of parameters employed in the water flow model
(ken, f,
nf,
, ks,
w) other than L and W were assumed to
be the same as the original set used for normal rats (31),
as given above. Control values of L and W were
provided by groups of subjects with normal glomeruli (living kidney
transplant donors). In the controls and in three forms of glomerular
injury (diabetic, minimal change, and membranous nephropathy),
transmission electron micrographs showed large and numerous endothelial
fenestrae, and the endothelial resistance to water flow was neglected.
In membranous (33, 97), minimal change (33),
and diabetic nephropathy (79), the main contribution to
the reduction in k was found to be the increase in
W. In preeclamptic toxemia, an observed reduction in the
size and number of fenestrae made the calculated endothelial
contribution important (58).
An example is provided by findings in a group of 15 patients with
membranous nephropathy. Each had a severe glomerular injury characterized by persistent nephrosis and a progressive decline in GFR
over a 2- to 5-yr period of observation ( 97). Glomerular structure and
ultrafiltration capacity were examined on two occasions, at the time of
presentation and diagnostic biopsy (baseline) and again after 2-5
yr. At baseline, glomerular volume was larger than control, and it was
estimated that S increased by some 40%. Membranous
nephropathy at this time was accompanied by an approximate doubling of
L and a roughly fourfold increase in W,
reflecting a marked widening of both the GBM and the epithelial foot
processes. Using Eqs. 1 and 3, it was found that
there was a marked depression of k, 0.79 ± 0.09 × 109
m · s
1 · Pa
1 in membranous
nephropathy vs. 2.8 ± 0.09 × 10
9
m · s
1 · Pa
1 in controls.
The corresponding values of Kf predicted by the model were 3.4 ± 0.7 nl · min
1 · mmHg
1 in
membranous nephropathy and 7.1 ± 0.6 nl · min
1 · mmHg
1 in
controls. This estimated 52% reduction in Kf
was sufficient to account for the observed reduction in GFR (56 ± 8 vs. 102 ± 2 ml/min in controls).
The later analysis (2-5 yr beyond baseline) revealed no further changes in FSF (or W), but there were increases in L to roughly four times that of control and reductions in S to ~30% below control values. The persistent nephrosis was associated with an additional, significant decline in GFR in each individual. Because k at this later time was computed to be not significantly different from that at baseline, it was concluded that the further reduction in GFR was attributable entirely to the reduced S. To summarize, the serial observations permit the conclusion that progressive hypofiltration in membranous nephropathy is a consequence of a biphasic loss of glomerular filtration capacity, consisting of an initial reduction in k that is later exacerbated by a loss of S (97).
Given that the GBM is a significant contributor to the overall water flow resistance, one might expect that the doubling of GBM width between biopsies in the membranous nephropathy patients would have lowered k even further below that of controls. However, with a very low FSF, as was the case in that disorder, much of the flow within the GBM is parallel to its surfaces, rather than directly across. With the path length for filtrate thereby determined largely by W, there is relatively little sensitivity of k to L. Thus FSF becomes the principal determinant of k when FSF is small enough. A similar observation was made in a comparison of results for membranous nephropathy and minimal change nephropathy (33). Similar values of FSF in the two groups led to similar predictions of k, despite approximately twofold larger values of L in membranous nephropathy. Because the measured values of S and of the hemodynamic determinants of GFR did not differ greatly, this explained the similar values of GFR in the two groups.
A group of glomerular diseases that fit loosely into the category of
"thrombotic microangiopathy" or "hemolytic uremic syndrome" can
lower GFR while having no discernable effect on the GBM or epithelial
foot processes. Rather, this group of glomerulopathies is associated
with substantial injury to glomerular endothelial cells. In subjects
with preeclamptic toxemia, which is an example of a thrombotic
microangiopathy, GFR was found to be depressed by 39% relative to
healthy gravid controls (58). Reductions in filtration
surface density due to mesangial interposition were partially offset by
glomerular hypertrophy, resulting in values of S that tended
to be slightly lower than in controls. Neither GBM thickness nor FSF
was altered, but there were extensive, dense, subendothelial deposits
of fibrinoid material that substantially lengthened the filtration
pathway (from fenestral interface to slit diaphragm). The
circumferential rim of endothelial cytoplasm was characterized by
swollen segments that were devoid of fenestrae. A morphometric analysis
of "en face" sections of endothelium by scanning electron
microscopy revealed that f was drastically reduced, from
0.16 in controls to 0.014-0.087 in the subjects with preeclamptic
toxemia. The fenestrae were also smaller, as evidenced by a reduction
in their area-to-perimeter ratio to one-half that of controls. From
this structural information, it was estimated that k was
reduced by ~30% in preeclamptic toxemia. Taken together with the
trend toward lower S, it was calculated that
Kf was likely to have been depressed by ~40%
in preeclamptic toxemia, similar to the reduction in GFR.
GBM Nanostructure and
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(4) |
With
0.1, as has been reported for GBM (21, 85),
realistic values for
(in the range of 1-2 nm2) are
obtained from any of the theoretical expressions if the fiber radius is
assumed to be ~1 nm (8). However, if
rf = 3-4 nm is employed, corresponding
to the radii of fibers visible in electron microscopic images, the
predicted value of
is an order of magnitude too large. This led to
the suggestion that GBM be modeled as a mixture of coarse and fine
fibers, the former corresponding roughly to collagen IV fibrils and the
latter to glycosaminoglycan chains (8, 34). Underlying
this suggestion is the presumption that the fine fibers would not have
been resolved in the electron micrographs. With coarse and fine fiber
radii of 3.5 and 0.5 nm, respectively, and roughly a 1:1 mixture (by
volume) of the two fiber types, it was possible to reconcile the
measured values of
and
with the electron microscopic appearance
of GBM. Parameter values for this two-fiber model of the GBM, which
should be viewed as quite tentative, are summarized in Table
2.
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Additional quantitative information on the composition and the spatial
arrangement of proteins and proteoglycans would be invaluable in
efforts to reach more definite conclusions about the nanostructural
basis for in the GBM. Analogous information is needed to estimate
in the endothelial glycocalyx and thereby better define the
endothelial resistance to water flow.
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FILTRATION OF MACROMOLECULES |
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General Relationships
This section begins with a discussion of physical phenomena that underlie efforts to relate macromolecule permeability to the structure of the glomerular capillary wall. Several key quantities are defined. In keeping with the microscopic viewpoint adopted for water filtration, this discussion focuses on the local sieving coefficient, which is the filtrate-to-plasma concentration ratio at a particular point along a capillary. This must be distinguished from the sieving coefficient for a whole kidney (or representative capillary), which is the average concentration in Bowman's space divided by that in afferent plasma. It is the average sieving coefficient that is accessible experimentally (e.g., from the fractional clearances of exogenous tracers). Even if the structure of the capillary wall is uniform along its length, the local sieving coefficient will vary with position, mainly because of the progressive increase in plasma protein concentration from the afferent to the efferent end. It has long been recognized that the resulting increase in oncotic pressure along a capillary will tend to slow filtration, which in turn will affect local sieving. Proteins may also have other effects on barrier performance, as will be discussed. The calculation of the average (measurable) sieving coefficient from local solute and volume fluxes (generally not measurable) has been described (e.g., Ref. 66). Although the local and average sieving coefficients are not identical, factors that affect the former will have a qualitatively similar influence on the latter.The relationship between the overall sieving coefficient at any
position along a capillary () and those of the individual layers can
be approximated as
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(5) |
Another important distinction between water filtration and
macromolecule sieving is that the individual
i values affect one another, whereas the
individual ki values could be computed
independently. Moreover, the
i values depend in general on the filtrate velocity, whereas the
ki values could be approximated as constants.
(Constancy of k assumes, of course, that the applied
pressures are not so large as to alter the structure of the capillary
wall). The interdependence of the layer sieving coefficients and the
effects of filtrate velocity are illustrated next by a somewhat
simplified model for transport in the GBM. As discussed later, an
extension of that approach is a central feature of a structure-based
model that has been proposed to describe glomerular size selectivity.
As in the application of Darcy's law (Eq. 2), the GBM will
be regarded as an isotropic medium, such as an array of randomly oriented fibers. In such a material the local flux (N) of an
uncharged macromolecule may be expressed as
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(6) |
The diffusivity and hindrance factors in Eq. 6 all depend on
molecular size. The standard measure of molecular size is the Stokes-Einstein radius (rs), because knowing it
is equivalent to knowing D. For a spherical
molecule of radius rs in water at 37°C, the
relationship is D
= (3.28 × 10
5 cm2/s)/rs (where
rs is in Å). In general, steric and
hydrodynamic interactions between a macromolecular solute and the fixed
polymeric fibers of a membrane or gel will cause
Kd and Kc to be less than unity, with both decreasing as rs increases. The
experimental estimation of these hindrance factors in GBM is discussed
later. Another property of a fibrous membrane or gel that influences transport and depends on rs is the equilibrium
partition coefficient (
). The partition coefficient is a
thermodynamic quantity that describes the tendency of steric and/or
electrostatic interactions to exclude macromolecules from the material.
As with the hindrance factors, it is typically less than unity and
decreases with increasing rs. As defined here,
if the GBM were in equilibrium with plasma, then C =
Cp, where Cp is the plasma concentration.
Steric exclusion from the GBM is important, but it appears that
electrostatic interactions are not (9). Although the
partition coefficient does not appear in Eq. 6, it enters
the analysis when concentrations within the GBM are related to those in
plasma or the other structures.
Assume for the moment that the GBM extends from z = 0 to z = L, that the solute concentration
depends only on z, and that the solute flux and fluid
velocity (magnitudes N and v, respectively) are
each constant. This "one-dimensional" model, involving just z, corresponds to a hypothetical GBM with fully accessible
surfaces (i.e., f =
s = 1). As will be seen later, only a
slight modification of the results is needed to describe the more
realistic situation where the surfaces are largely blocked by cells. In
the one-dimensional model, the solute concentration profile in the GBM
can be derived analytically for any specified values of
en and
ep. This allows the sieving
coefficient in the GBM to be evaluated. The result is
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(7) |
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(8) |
The dependence of bm on
ep predicted by
Eq. 7 is illustrated by the curve labeled "1-D model" in
Fig. 4. In these calculations Pe and
Kc were held constant at values
representative of a macromolecule with rs = 35 Å in rat GBM. It is seen that
bm is predicted to range from values above unity for a highly selective filtration slit
(
ep
0) to values below unity for a nonselective one
(
ep = 1). The behavior for highly selective slits
reflects concentration polarization within the GBM, as noted in Edwards
et al. (35). That is, a concentration increase in the
direction of flow arises to provide a diffusional driving force in the
other direction. The opposing contributions of diffusion and convection
in the GBM reduce N to what can be accommodated by the slit,
thereby maintaining the steady state. Inspection of Eq. 7
reveals that the upper limit of the polarization effect in the GBM is
bm
exp(Pe) for
ep
0. It is also
seen that GBM polarization disappears exactly (i.e.,
bm = 1) if
ep =
Kc, for any
Pe. Only for
ep >
Kc is
the slit permeable enough to allow the basement membrane to enhance the
overall selectivity (i.e.,
bm < 1), rather than degrade it. A final noteworthy aspect of Eq. 7 is that it
shows that
bm
1 as Pe
0, for any positive
values of
ep and
Kc. This is
an example of a well-known phenomenon in ultrafiltration, which is the
tendency for filtrate and retentate concentrations to equilibrate as
diffusion becomes more important. In this instance, the equilibration
is just across the GBM.
|
The simplified, one-dimensional analysis just discussed illustrates an
important, general point, which is that the individual sieving
coefficients depend on one another and on the relevant Péclet
number(s). Although the Péclet number discussed was that for the
GBM, analogous Péclet numbers for the fenestrae and filtration slits can be expected to influence en and
ep, respectively. Such effects have been discussed in
models of the slit diaphragm (32, 35). A consequence of
the dependence of the sieving coefficient on the Péclet numbers
is that great care must be taken in extrapolating results from one
experimental situation to another. For example, one cannot expect a
sieving coefficient measured for GBM in vitro to equal that in vivo,
even if the isolated GBM preparation is perfect. The thickness of a
filter made by consolidating GBM fragments will greatly exceed that of
a single layer of GBM and the filtrate velocity is unlikely to equal
that in vivo; both of these differences will affect Pe (Eq. 8). Moreover, the modifying effect of the epithelial sieving
coefficient will be absent.
Experimental Assessment of GBM and Cellular Contributions
As mentioned earlier, measurements of water filtration rates across filters prepared from isolated GBM have permitted the evaluation of its
|
The sieving results for Ficoll and Ficoll sulfate in protein-free
solutions were analyzed by Lazzara and Deen (61) to
estimate values of Kd and
Kc for GBM. The data were fitted using a
sieving relationship similar to Eq. 7 (but with
ep = 1) and assumed expressions of the form
![]() |
(9) |
![]() |
(10) |
The use of Eqs. 9 and 10 to make inferences about the glomerular capillary wall assumes, of course, that the isolated GBM was not functionally different from that in vivo. The possibility that GBM is altered during the isolation process has been examined using a variety of methods. Immunofluorescent microscopy of consolidated GBM filters demonstrated the presence of type IV collagen, laminin, and the core protein of heparan sulfate proteoglycan (27), the main components of GBM. The sulfated side chains of GBM proteoglycans are also present in GBM isolated using N-lauryl sarcosine to lyse cells (25), the procedure employed to obtain the data from which Eqs. 9 and 10 were derived (9). The permeability of GBM filters was not changed when a milder detergent, Triton X-100, which has been shown to preserve heparan sulfate proteoglycan, was used to lyse glomerular cells (25). That isolated GBM is relatively intact is suggested also by electron microscopy studies: the spatial distribution of cationic ferritin has been found to be similar to that in vivo (55).
A technical advance due to Daniels and co-workers (26, 36)
that has permitted the measurement of diffusional permeabilities for
macromolecules is the use of confocal microscopy to monitor the
movement of fluorescent tracers across segments of isolated glomerular
capillaries. Experiments have been performed with intact glomeruli,
freshly isolated from rats, and with glomeruli in which the cells have
been removed by detergent lysis, leaving only GBM. Thus it has been
possible to compare the diffusional permeability of intact capillary
walls (p) with that of bare GBM
(pbm). Diffusional permeabilities of
series barriers obey a resistance formula like Eq. 1, so
that
![]() |
(11) |
The experimental estimates of the GBM hindrance factors for Ficoll are
plotted in Fig. 6. The results for
Kd and
Kc derived from sieving data (Eqs. 9 and 10) are compared
with values of
Kd calculated from
pbm. The relationship between the diffusional permeability and diffusional hindrance factor is
pbm =
KdD
/L, where L (the GBM thickness) was taken to be 200 nm. The
agreement between the two independent estimates of
Kd is remarkably good, given the different
experimental preparations and the several assumptions required in
making this comparison. The finding that
Kc
Kd for Ficoll is qualitatively consistent
with data for globular proteins and Ficoll in agarose gels (49,
52, 53).
|
Using v = 4 µm/s as a typical average filtrate
velocity for the rat (corresponding roughly to single-nephron GFR = 40 nl/min), Pe calculated from Eqs. 8-10 ranges from
0.016 at rs = 20 Å to 0.22 at
rs = 50 Å. These small values of Pe
indicate that diffusion within the GBM is relatively rapid in vivo
(compared with convection), even for relatively large molecules. A
consequence of this is that concentration polarization within the GBM
will tend to be minimal, even if the filtration slits are highly
selective barriers. This tends to mitigate objections that are
sometimes made to a glomerular capillary "design" in which the
limiting barrier is the one farthest downstream. Although diffusion in
the GBM is rapid relative to convection, it is still much slower than
diffusion in water. This is indicated by the small values of
Kd in Fig. 6. For example,
Kd = 0.01 (the value for
rs = 35 Å) means that the diffusional
permeability of the GBM is only 1% of that of a film of water of
equivalent thickness.
Not considered in Fig. 6 are the possible effects of GBM
compressibility on macromolecule partition coefficients and diffusive or convective hindrance factors. In particular, the sieving data used
were obtained at an applied pressure of P = 60 mmHg
(9), whereas the diffusion experiments (36)
corresponded to
P = 0. The hydraulic permeabilities and/or
values of filters made from isolated GBM have been found to decrease
with increases in applied pressure (
P) (27, 34, 86,
106). Because f(
) in Eq. 4 decreases with
increasing
, one would expect
to decrease if compression of the
GBM forces out water and thereby increases the volume fraction of
solids. On the basis of theories for fiber matrices, increases in
are expected to also result in decreases in
(60, 71)
and Kd (49, 81). Experimental
results for proteins and Ficoll in agarose suggest that
Kc would decrease as well (52, 53).
Attempts have been made to model the effects of pressure on
Kd and
Kc
(34, 35), but these efforts are confounded by the lack of
an adequate theory for Kc in fibrous materials
and by the probable effects of BSA on the values of
for Ficoll
(61). The effects of BSA are an issue because BSA has been
present in some sieving experiments with isolated GBM, but not others.
The interpretation of pcell depends, of course, on the relative contributions of the endothelium and epithelium to the diffusional resistance of the intact capillary wall. Assuming that the cellular resistance resides in the slit diaphragm, and modeling that structure as a row of parallel cylinders (as in the "ladder" of Fig. 2), Edwards et al (36) found that the diffusion results could be explained by a cylinder spacing that followed a lognormal distribution, with small areas (~0.2%) devoid of cylinders. That representation of the cellular barrier was incorporated into later simulations of macromolecule filtration in vivo (35). The one significant difference was that in healthy subjects, at least, there was no evidence for "shunts" created by small areas of the slit diaphragm devoid of cylinders.
As already stated, it was found that sieving curves measured in
isolated GBM for Ficoll and its anionic derivative, Ficoll sulfate,
were indistinguishable. Only when the ionic strength of the solutions
was reduced below physiological levels, thereby amplifying the effects
of electrostatic interactions, was bm for Ficoll sulfate
less than that of neutral Ficoll (9). This finding of
little or no charge selectivity is generally consistent with other
studies of isolated GBM. That is, Bray and Robinson (11)
found only small differences in sieving curves for dextran and dextran
sulfate (DS), and Bertolatus and Klinzman (5) noted only
small differences in the filtration rates of native (anionic) and
cationized BSA. Procedures used in those laboratories to neutralize GBM
charge, including methylation of carboxyl groups (5) and reductions in pH from 7.4 to 5.7 (the isolectric point of GBM) (85) had little effect on the sieving of BSA. Similarly,
Daniels (25) found that treating the GBM with heparatinase
to remove heparan sulfate proteoglycan, adding protamine to neutralize
GBM polyanions, or reducing the experimental pH to the isoelectric point of the GBM or BSA had little or no effect on the sieving coefficient of BSA. Thus to the extent that the glomerular barrier is
charge selective, it is the cellular layers, and not the GBM, which
appear to be responsible. The charge selectivity of the intact
glomerular capillary wall is discussed below.
Structure-Based Model for Size Selectivity
With the structural unit depicted in Fig. 1 serving as a framework, and using experimental information on the transport of Ficoll in isolated GBM and intact capillaries (9, 34, 36), Edwards et al. (35) constructed a model for the filtration of uncharged macromolecules in vivo. The concentration field within the GBM was computed by combining Eq. 6 with the steady-state form of the solute conservation equation (
![]() |
(12) |
The hypothesis explored by Edwards et al. (35) is that the structure responsible for the cellular barrier to uncharged macromolecules is the slit diaphragm. As already mentioned, the slit diaphragm was modeled as a single row of cylindrical fibers of equal radius but nonuniform spacing. The advantages of postulating a nonuniform spacing were pointed out by Drummond and Deen (32), who developed a hydrodynamic model for the hindered transport of macromolecules through a single row of cylindrical barriers. If a lognormal distribution of spacings is adopted for the "ladder rungs" in Fig. 2, then many of the fiber spacings would be close to the dimensions reported in Rodewald and Karnovsky (87). Consequently, the hydraulic permeability can be made to match that of the zipper structure. Although infrequent, the larger spacings allow sufficient passage of large molecules to be consistent with diffusional results for Ficoll in isolated glomeruli (36) and fractional clearances of Ficoll measured in vivo (6, 75, 83). If the 40 Å wide openings of Rodewald and Karnovsky (87) applied throughout the slit diaphragm, then no molecule with rs > 20 Å would enter the filtrate, whereas Ficolls with rs > 60 Å are readily detectable in normal urine (6, 75, 83). Thus the lognormal distribution of spacings was an attempt to reconcile the electron microscopic appearance of the slit diaphragm with fractional clearance data in vivo.
In that the most restrictive part of the barrier was assumed to
be the slit diaphragm, it is not surprising that the sieving coefficients predicted by the model of Edwards et al. (35)
were very sensitive to the values chosen for the fiber radius and the fiber spacing parameters. Parameter values were found that provided very good fits to Ficoll data in normal rats (75, 83) and healthy humans (6), although the discrepancies in the
fractional clearances themselves precluded identification of a single
set that would closely match the results of any two studies. As already mentioned, it was unnecessary to postulate a shunt in the slit diaphragm in vivo. The values of the GBM hindrance factors were found
to be important mainly as they influenced Pe; that is, the ratio
Kc/Kd was much more
influential than either Kd or
Kc individually. This is a consequence of the
behavior of Eq. 7 for Pe < 1 and
ep
Kc, conditions that held in most of the simulations.
Simulations of the effects of hemodynamic perturbations on
sieving coefficients provide a clue that the model for size selectivity may need to be modified. That is, selective perturbations in afferent plasma flow rate (QA) were found to have almost no effect
on the average (observable) sieving coefficients (35).
This is in contrast to predictions for a one-layer capillary wall,
where the average for a capillary decreases with increasing
QA as a result of both the higher single-nephron GFR and
lower filtration fraction for water (66). The somewhat
surprising result for the composite barrier is explained by a tendency
for increased concentration polarization in the GBM to cancel the other
effects (35). Thus examining the dependence of sieving
curves on QA may provide insight into the amount of
concentration polarization actually present. There are no such data for
Ficoll, but increasing QA in rats by plasma volume
expansion was found to decrease the fractional clearances of dextrans
(15). This suggests that for dextran, at least, concentration polarization within the GBM may be absent. This raises
the possibility that the glycocalyx-filled fenestrae may have a greater
role in size selectivity than has been supposed, and the slit diaphragm
a lesser role. Similar experiments with Ficoll, a more ideal test
molecule than dextran, might clarify the situation. In addition to the
tentative nature of the assumption that
en
1, the
model of Edwards et al. (35) does not fully incorporate
recent findings concerning steric effects of plasma proteins on the
partitioning and sieving of tracers (see below). Finally, that model
was intended only to describe glomerular size selectivity, and not
charge selectivity.
Charge Selectivity Data
Research in the 1970s and 1980s led to the view that the glomerular capillary wall discriminates among macromolecules on the basis of their net charge as well as their size (66). The pattern seen was that, for a given rs and molecular conformation, anionic polymers passed through the capillary wall less readily than did neutral polymers, which in turn passed less readily than cationic polymers. Differences due to molecular charge tended to be diminished in proteinuric disorders. The inference was that fixed negative charges in one or more parts of the capillary wall normally make entry into and passage through the barrier less favorable for polyanions (such as albumin) than for neutral molecules of similar size and configuration. Much of the evidence for charge selectivity was based on comparisons between the fractional clearances in rats of dextran (uncharged) and DS (anionic) (e.g., Ref. 14). Other influential studies employed native (neutral) and anionic horseradish peroxidase (nHRP and aHRP, respectively) (e.g., Ref. 84). Technical concerns have been raised in recent years concerning both sets of test molecules, motivating a reexamination of the concept of charge selectivity. Indeed, arguments against glomerular charge selectivity are the main theme of a review by Comper and Glasgow (20). What follows is a summary of certain key issues and a review of the most recent findings.At least two factors may complicate the interpretation of fractional
clearance data for DS. First, it has been shown that DS binds to plasma
proteins (41, 68). This binding was studied extensively by
Guasch et al. (41), using ultrafiltration and equilibrium
dialysis experiments with 3H-DS and/or unlabeled DS added
to Krebs buffer solutions or to human serum. For the relatively small
sizes of 3H-DS examined, only some 45% of the activity in
serum was not protein bound. Use of total radioactivity to determine
the plasma concentration of a protein-bound tracer will tend to
overestimate the concentration of free tracer and therefore
underestimate its urinary clearance. Nonetheless, when corrections were
made for protein binding, the fractional clearance of 3H-DS
with rs = 15-18 Å in normal rats
(68) or humans (41) was still only
0.5-0.7, much smaller than that for dextran of similar size
(1). This charge selectivity was almost abolished in the nephrotic
syndrome, the fractional clearance of 3H-DS increasing from
0.68 in healthy humans to 0.95 in nephrotic patients (41).
Another concern with the use of DS is cellular uptake and intracellular desulfation, as examined in a series of studies by Comper and co-workers (12, 13, 22, 100, 104, 105). When 3H-DS was added to isolated kidney perfusates or administered intravenously to rats, most of the tritiated polymer in urine was found to be desulfated (12, 22, 104). This occurred without a significant change in molecular size (12, 22). Evidence was found for uptake of 3H-DS, but not uncharged dextran, by glomerular cells (100, 105), and it was argued that the glomerulus is a primary site for desulfation. Increases in the urinary clearance of intact DS with increasing DS concentration showed the uptake and/or desulfation to be saturable (12, 13, 104).
The significance of the cellular processing of DS depends on where the uptake occurs and the time required for intracellular levels to become constant. The half-time for accumulation of label in the glomeruli of isolated perfused kidneys (IPK) was <5 min (100), indicating that for clearance measurements done over much longer periods, time-dependent accumulation in the glomerulus will be unimportant. This is true for the studies by Mayer et al. (68) and Guasch et al. (41), where bolus doses of 3H-DS were followed by constant infusions, and sample collections were not begun until after 45-60 min of equilibration. Thus the rate at which the tracer crossed the glomerular barrier in those studies should have equaled its rate of appearance in urine, as assumed in the fractional clearance methodology. Under such steady-state conditions, if the cellular uptake and desulfation were downstream of the barrier (i.e., by epithelial cells from Bowman's space fluid), total tritium in urine (reflecting both intact and desulfated DS) would accurately reflect filtration of anionic DS and no new interpretation would be needed. Other possibilities include uptake by the foot processes from the filtration slits or GBM and uptake by the endothelial cells from the GBM or plasma. Potentially most significant is endothelial uptake of DS from plasma. If uptake by glomerular endothelial cells were rapid enough to compete with movement through the fenestrae, and if desulfation and release on the contraluminal side of the cells were slow, then entry of DS into the GBM would be slowed by the cellular processing. This would have the effect of reducing the fractional clearance of DS relative to uncharged dextran.
In support of the concept of DS processing in glomerular endothelial cells, Vyas et al. (105) cited evidence for endothelial endocytosis of sulfated polysaccharides in other organs. Moreover, after an intravenous bolus of 3H-DS in rats, some 78% of the label remaining in plasma was found by affinity chromatography to be desulfated within 2 h (22). However, the evidence tends to be ambiguous for uptake by glomerular endothelial cells specifically. Processing of DS by those cells was not rapid enough to allow detection of an increase in desulfated DS in perfusate collected from the IPK (22). The finding that DS isolated from glomerular digests (100) or vesicles (105) has a similar size distribution to that in plasma could mean that it is of endothelial origin, as argued, or that size-based fractionation occurs mainly at the level of the epithelium. Similarly, the finding of similar amounts of DS in vesicles isolated from filtering and nonfiltering perfused kidneys (105) is consistent with either cellular source. That is, the very small values of Pe estimated for the GBM (as discussed in Experimental Assessment of GBM and Cellular Contributions) imply that diffusion is rapid enough that water filtration will not greatly speed access of macromolecules to the epithelial cells.
The criticism of the data with HRP is based on the finding that aHRP is preferentially degraded in the kidney (76). Accordingly, the use of an enzymatic assay to detect aHRP in kidney tissue and urine leads to a systematic underestimate of its sieving coefficient, relative to that of nHRP. The apparent charge selectivity was reduced, but not eliminated, when radiolabels were employed (76, 77). The ratio of nHRP to aHRP sieving coefficients was reduced to two to three compared with a value of eight to nine in the original report (84).
We turn now to more recent studies by Haraldsson and co-workers, which provide additional evidence in favor of glomerular charge selectivity. Using the IPK preparation at 8°C to inhibit tubular activity, Ohlson et al. (73) found the fractional clearances of albumin and Ficoll of comparable size (rs = 36 Å) to be 0.0019 and 0.021, respectively. Using the cooled IPK preparation to examine the filtration of somewhat larger proteins (rs = 40-42 Å), Lindstrom et al. (64) showed that the fractional clearance of anionic lactate dehydrogenase (LDH) was less than that of a slightly cationic isoform.
In a comparison of the forms of HRP and LDH with differing charge,
variations in molecular shape are not an issue. However, Ficoll is
spherical and albumin is modeled more accurately as a prolate spheroid
with an axial ratio of ~3.3 (2, 48, 60, 99). To what
extent would that difference in molecular shape account for the 10-fold
difference in sieving coefficients between Ficoll and albumin? The link
between membrane partitioning and sieving (e.g., Eq. 7)
suggests that a partial answer would be provided by the theoretical
effect of molecular shape on in a random-fiber matrix such as that
used to represent GBM. Applying a recent excluded volume theory
(60) to the parameter values in Table 2, the results were
= 0.0234 for BSA and
= 0.0219 for Ficoll. This
difference is not only very small but is in the wrong direction to
contribute to the low sieving coefficient for albumin. Supporting the
conclusion that the nonspherical shape of albumin is of minor
importance are data for
Kd and
Kc in agarose gels of varying concentration,
which show little difference between the results for Ficoll and various
globular proteins, including BSA (50, 53).
Another recent finding with the cooled IPK is that reductions in the ionic strength of the perfusate decreased the fractional clearances of both aHRP and albumin, without affecting those of Ficoll (96). Because low ionic strengths amplify electrostatic interactions by reducing Debye screening, this was taken as evidence for functional, fixed negative charges. However, as with experiments with isolated GBM at reduced ionic strength (9), this shows only that charge was influential at the lower ionic strength. Because charge interactions will tend to be fully suppressed above a certain ionic strength (i.e., when the Debye length is very small relative to the spaces accessible to permeating macromolecules), examining normal and reduced ionic strengths does not exclude the possibility that the charges are fully screened under normal conditions. A more definite conclusion would be reached by showing that an ionic strength above the physiological elevates the fractional clearances of aHRP and albumin, making them more like those of a neutral test solute such as Ficoll.
A crucial aspect of the controversy over charge selectivity is the
manner and extent to which the glomerular barrier restricts the passage
of albumin. Two very different hypotheses have emerged. The
conventional view, recapitulated recently in Ohlson et al. (73,
74), is that the sieving coefficient for albumin is normally quite low, on the order of 104 to 10
3, due
in part to electrostatic interactions between albumin and fixed
negative charges in the glomerular capillary wall. An alternative hypothesis proposed in Osicka et al. (78) is that the
sieving coefficient of albumin is unaffected by charge and roughly
100-fold higher; using various drugs (including NH4Cl) to
inhibit tubular protein reabsorption in the IPK at 37 °C, they
inferred an albumin sieving coefficient of 0.07. This high sieving
coefficient was reconciled with the low concentrations of albumin
normally found in proximal tubule fluid by postulating a high-capacity
absorption pathway that returns intact albumin from tubular fluid to
plasma (78).
A critique of the alternative hypothesis for albumin handling is given
in Ohlson et al. (73), who measured fractional clearances of albumin and Ficoll in IPK preparations at both 8 and 37°C. Using
NH4Cl at 37°C, they too found a high fractional clearance for albumin (0.02), approaching that for similarly sized Ficoll under
those conditions (0.04). They argued that the apparent loss of barrier
selectivity for albumin in the IPK at 37°C, and especially the loss
of charge selectivity, is the result of irreversible glomerular injury
due both to hypoxia-reperfusion and to drugs used to inhibit tubule
function. They also criticized the concept of rapid reabsorption of
intact albumin, citing inconsistencies with the finding of Maunsbach
(67) that practically all albumin is degraded during
reabsorption. Finally, they noted the electron microscopic evidence of
Ryan and Karnovsky (91) that albumin is efficiently
excluded from the glomerular capillary wall, and micropuncture
measurements by Tojo and Hitoshi (101), which confirm that
albumin concentrations in early proximal tubule fluid are very low.
This last study is noteworthy in that a technique was devised to avoid
the difficult problem of sample contamination with subcapsular fluid;
the sieving coefficient estimated for albumin was 6 × 104 (101). We find all of these arguments persuasive.
To summarize our conclusions from the various experimental studies, the concept that charge selectivity contributes to the exclusion of albumin and other polyanions from glomerular filtrate remains viable, despite technical concerns. It is certain that DS is not as inert a tracer as once believed, and it is likely that earlier studies (e.g., with DS and aHRP) overestimated the effects of charge. Indeed, a major lesson has been how difficult it is to design experiments to test charge selectivity in vivo. Nonetheless, recent results with the IPK tend to reinforce, rather than negate, the conclusions from earlier fractional clearance studies in vivo.
Charge Selectivity Models
Structure-based models for the glomerular filtration of charged macromolecules, comparable to those discussed above for water and uncharged solutes, have not yet been developed. An early model for glomerular charge selectivity was based on the concept of Donnan exclusion from a homogeneous, charged membrane (29). Although able to describe certain experimental trends, that model has three aspects that are unrealistic. First, the Donnan approach treats permeating ions as if they were point charges, so that molecular size and shape are not accounted for in calculating the electrostatic interactions. Second, the Donnan model regards the fixed charge as being uniformly distributed within a fluid volume, rather than being localized on the surfaces of macromolecular fibers or cells. Third, the model does not distinguish one part of the capillary wall from another. For these reasons, the effective concentration of fixed, negative charges (Cm) derived by applying the Donnan model to fractional clearance data must be viewed with great caution. As noted previously (41), such values of Cm are valid only for limited comparative purposes, as when the same test molecule is used to assess differences in the glomerular capillary wall between two experimental conditions. The same value of Cm may not apply to other test molecules, due to size and/or shape differences (41, 66), and it is unlikely to correspond to a charge density of any part of the capillary wall determined by chemical assay.The limitations of the Donnan model merit reemphasis because the failure of Cm to correspond to a realistic charge density has been used as an argument against the possibility of glomerular charge selectivity (20, 21, 109). That argument is logically flawed, as may be seen by analogy. That is, pore models have been used successfully to correlate data on glomerular size selectivity, often yielding effective pore radii of ~50 Å (66), but there is no microscopic or compositional basis for the existence of straight, cylindrical pores of that size passing through the capillary wall. Arguing against charge selectivity on the basis of Cm values is akin to arguing against size selectivity on the basis of there being no anatomic correlates of pores. In other words, the microstructural and/or nanostructural limitations of the models, as applied to the glomerular capillary wall, do not invalidate the physiological data.
Ohlson et al. (74) recently presented a one-dimensional model (i.e., without cell coverage effects) in which purely charge-selective and size-selective barriers were placed in series. The Donnan approach was used to describe charge effects in the upstream part of the barrier (identified with the endothelial glycocalyx), and pore theory was used to model size selectivity in the downstream part (GBM and/or filtration slits). By exploring the idea that charge and size selectivity reside largely in different parts of the capillary wall, this work avoids one of the limitations of the early study noted above. A model has been developed to describe electrostatic effects on the partitioning of spherical macromolecules in random arrays of charged fibers (50). Because it accounts for molecular size and the localization of the fixed charges on fiber surfaces, this theory (or extensions of it) offer the prospect of overcoming the other limitations of the early model and of the Donnan model for the glycocalyx. Finally, by calling attention to what might be a crucial contribution of the endothelial glycocalyx, the work of Ohlson et al. (74) suggests that its role in water filtration and filtration of neutral macromolecules might also merit reconsideration.
Effects of Proteins on Sieving of Tracers
As already noted, Ficoll and Ficoll sulfate sieving coefficients measured in isolated GBM were found to be indistinguishable, at any given value of rs (9). However, the same study revealed a pronounced upward shift in the sieving curves of either tracer when BSA was present in the retentate at a concentration of 4 g/dl. (Due to concentration polarization in the stirred ultrafiltration cell, the BSA concentration at the upstream membrane surface was calculated to be higher, 6.2 g/dl.) The results for Ficoll, with and without BSA, are shown in Fig. 5. Because the hydraulic permeability of the GBM filters was unaffected by BSA, the shift in the sieving curves apparently was not due to an alteration of the intrinsic properties of the GBM (i.e., a result of binding of BSA to the membrane). An increase inThe hypothesis that BSA, as an abundant solute, could affect the
partitioning and sieving of a tracer (Ficoll or Ficoll sulfate) has
been examined recently in detail. This was done by first extending the
theory for partitioning in random fiber arrays, which had been limited
to dilute (71) or concentrated (38) solutions of a single, spherical solute, to include interactions among unlike macromolecular solutes (60). The theory for the sieving of
macromolecular tracers was then extended to allow for different values
of at the upstream and downstream surfaces of a membrane, which
would be a consequence of having different concentrations of a second, abundant solute (61). As shown by the curve labeled
"osmotic and partitioning" in Fig. 5, it was found that the
predicted effect of BSA on Ficoll partitioning was more than sufficient
to account for the remaining part of the upward shift in the Ficoll
sieving curve. At physiological concentrations, predictions for tracer sieving in the presence of BSA were found to be insensitive to the
assumed shape of the protein (sphere or prolate spheroid). For protein
mixtures, the theoretical effect of 6 g/dl BSA on the partitioning of
spherical tracers was indistinguishable from that of 3 g/dl BSA and 3 g/dl IgG. This effect of abundant proteins on the partitioning of
tracers has not yet been fully incorporated into simulations of
macromolecule filtration in vivo. Lacking the basis for a more precise
description, the model of Edwards et al. (35) assumed that
proteins would increase
of each tracer molecule by a constant factor.
Ohlson et al. (74) recently reported Ficoll sieving data in the IPK (at 8 °C) in the presence of either 1.8 or 5.0 g/dl albumin. The fractional clearances over much of the size range examined were significantly elevated at the higher protein concentration, qualitatively consistent with the effects described above.
Proteins may also have more specific effects on glomerular permeability. Orosomucoid is a serum protein that is thought to have a role in determining capillary permeability by maintaining and reinforcing the charge barrier (24, 43). Haraldsson et al. (42) and Johnsson and Haraldsson (51) demonstrated that orosomucoid influences the glomerular barrier by showing that the clearance of albumin in the IPK was four to five times lower when orosomucoid was present.
GBM Nanostructure and Macromolecule Filtration
As withIn an effort to model the sieving results for Ficoll (without BSA)
shown in Fig. 5, Bolton and Deen (8) represented the GBM
as an array of fibers of uniform radius. They evaluated
Kd using the theory of Ogston
(71) for
and that of Johnson et al. (49)
for Kd but chose to employ an empirical
expression for
Kc similar to Eq. 10. It was found that a fiber-matrix model based on a single
population of fibers could accurately predict both the sieving curve
for Ficoll and the value of
, but only if the volume fraction of
fibers was assumed to be unrealistically large. It was concluded that
fiber-matrix models based on a uniform fiber size do not adequately
relate the microstructure of the GBM to its permeability properties.
The success of the two-fiber model in describing
, as discussed in
GBM Nanostructure and Darcy Permeability, suggests that a
promising direction for future research is the development of analogous
hindered transport models.
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ACKNOWLEDGEMENTS |
---|
The collaboration of W. M. Deen with Dr. Barbara S. Daniels was important in much of the work described in this review, so that we have benefitted greatly from her insights.
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FOOTNOTES |
---|
Preparation of this review was supported by National Institute of Diabetes and Digestive and Kidney Diseases Grant DK-20368.
Address for reprint requests and other correspondence: W. M. Deen, Dept. of Chemical Engineering, 66-572, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139 (E-mail: wmdeen{at}mit.edu).
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