A gel-membrane model of glomerular charge and size selectivity in
series
Maria
Ohlson1,
Jenny
Sörensson1, and
Börje
Haraldsson1,2
Departments of 1 Physiology and 2 Nephrology,
Göteborg University, Göteborg 405 30, Sweden
 |
ABSTRACT |
We have analyzed glomerular sieving data from humans,
rats in vivo, and from isolated perfused rat kidneys (IPK) and present a unifying hypothesis that seems to resolve most of the conflicting results that exist in the literature. Particularly important are the
data obtained in the cooled IPK, because they allow a variety of
experimental conditions for careful analysis of the glomerular barrier;
conditions that never can be obtained in vivo. The data strongly
support the classic concept of a negative charge barrier, but separate
components seem to be responsible for charge and size selectivity. The
new model is composed of a dynamic gel and a more static membrane
layer. First, the charged gel structure close to the blood compartment
has a charge density of 35-45 meq/l, reducing the concentration of
albumin to 5-10% of that in plasma, due to ion-ion interactions.
Second, the size-selective structure has numerous functional small
pores (radius 45-50 Å) and far less frequent large pores (radius
75-115 Å), the latter accounting for 1% of the total hydraulic
conductance. Both structures are required for the maintenance of an
intact glomerular barrier.
capillary permeability; macromolecular transport; two-pore model
 |
INTRODUCTION |
ONE OF NATURE'S WELL KEPT
SECRETS is the intricate mechanism underlying the permselectivity
of the glomerular barrier. Normally, 180 liters of primary urine per
day is produced in healthy humans with minimal losses of proteins. In
fact, the causes for proteinuria, which is a hallmark of renal disease,
are most often completely unknown. In what are now classic studies,
Brenner and associates (2, 5, 11) used dextran to reveal
the size-, charge-, and shape-selective properties of the glomerular
membrane. However, the established theories of glomerular function have
recently been questioned because the use of dextrans may have certain
technical drawbacks (6).
Many researchers suggest the basement membrane to be the most
significant component of the barrier, whereas others suggest it to be
the podocytes. Indeed, there are genetic disorders that affect
components in these regions. For example, the newly discovered nephrin
has been found to be missing in hereditary nephrosis of the Finnish
type (27). However, if the principal barrier were to be
anywhere distal to the endothelial wall, this would require active
mechanisms for the return of huge amounts of protein. Indeed, such a
mechanism of "reuptake" of intact albumin from the proximal tubuli
has been proposed (38), but there is in fact no
experimental evidence to support it. In contrast, in a classic study,
Maunsbach (32) showed that practically all albumin
molecules taken up by the proximal tubules are degraded, a finding
still considered to be valid.
Most investigators have considered the glomerular wall to behave like a
membrane with functional pores of various dimensions, whereas others
have used the fiber matrix concept developed by Curry and Michel
(8). Alternatively, the barrier can be treated like a gel
having both size- and charge-selective properties (54). Such a gel concept can be regarded as an extension of the fiber matrix
model, and it has several interesting dynamic features not present in a
static membrane. The combined effects of charge and size in a single
structure result in highly complex equations. The first steps in such
an analysis were recently published for a fiber matrix
(23), but present equations for the effects on convection
must be improved (26). Indeed, the predictions of the
model do not seem to fit biological data (47).
In the present study the experimentally determined transglomerular
passage of neutral and charged solutes were analyzed by using various
theoretical models. The analysis led to the development of a new
integrative gel-membrane model that can predict transport of molecules
depending on their charge and size.
 |
THEORETICAL DEVELOPMENT |
This section begins with a description of the gel-membrane model
and how its parameters are determined. The equations for a gel-membrane
model of the glomerular capillary wall are then summarized.
The present gel-membrane model is composed of two separate barriers: a
negatively charged gel, which acts like an ion-exchange chromatography
column, and a second, size-selective membrane with two functional pore
pathways. The model assumes that there is no discrimination of
molecular size in the charged gel and no discrimination of charge in
the porous membrane. In addition, the model requires that the molecules
have a rather spherical shape. Under these conditions, the properties
of the two components of the glomerular barrier are readily calculated
from the fractional clearances (
) for neutral solutes with a range
of molecular sizes (e.g., Ficoll) and one or more anionic molecules
(e.g., albumin).
The following procedure is used for determining the gel-membrane model
parameters from clearance data of albumin and Ficoll. First, the
experimentally determined
-ratio for albumin and the size-matched
neutral Ficoll are inserted into Eqs. 1-5 below to give
the concentration of fixed charges within the gel compartment. Second,
calculated values from a two-pore model are fitted to experimentally
obtained urine over plasma (U/P) sieving data for Ficoll molecules of
different sizes [Stoke-Einstein radius
(aSE)12-72 Å] by using a nonlinear
regression analysis. There are four unknown parameters in the two-pore
model, namely, the small- and large-pore radii
(rs and rL), the
large-pore fraction of the hydraulic conductance (fL), and
the unrestricted pore area over diffusion distance
(A0/
x). The subsequent equations
(7-21) are used in the two-pore model to estimate the
as a function of molecular size. Finally, once the parameters of
the gel-membrane model have been determined, the fractional clearance
for any solute can be predicted from its size and charge.
Estimation of the Charge Density in the Gel
Assume a gel by the glomerular membrane with a homogenous
distribution of fixed charges of a certain density,
. The
concentration of an anionic solute will be lower in the gel than in
plasma due to ion-ion interactions (for details, consult Refs.
14, 53). Let us, for the sake of simplicity,
assume that there are only two ions present, sodium and chloride,
leaving the small contribution of other polyanions out of the
equations. Electroneutrality requires plasma sodium (NaP)
concentration to equal plasma chloride concentration (Clp)
plus the charges given by albumin (Alb; zA),
where p denotes the concentration in plasma
|
(1)
|
According to the Donnan equation, the intramembraneous
distribution of sodium (Namem) and chloride
(Clmem) will be
|
(2A)
|
where
E is the electrical potential difference
between plasma and the gel (mem); z is the valence of sodium
and chloride, zNa = +1 and
zCl =
1; R is the gas
constant; and T is the absolute temperature. Equation 2A can thus be reduced to
|
(2B)
|
In a membrane with a charge density of
, the chloride and
sodium concentrations must be in balance
|
(3)
|
Moreover, the gel-plasma partitioning of a charged solute,
X, with a net charge of zX is
directly related to the gel-plasma partitioning of chloride according
to
|
(4)
|
Thus, if the chloride concentration ratio is 0.9 and X
has a net charge of
20, then
Xmem/Xp equals
0.920; i.e., the gel concentration of X is 12%
of that in plasma. Hence the
of two differently charged solutes of
similar size, e.g., albumin and Ficoll36Å (F), is related
to the gel-plasma partitioning of chloride according to
|
(5)
|
To calculate the properties of the gel compartment, we must know
NaP, ClP, and Albp, the
experimentally determined fractional clearance ratio of albumin and
Ficoll (
ratio), and the net charge of these solutes
(zAlb and zF). For
albumin, the net charge, zAlb, is
23
(17), whereas it is 0 for Ficoll
(zF = 0) or
1 for FITC-Ficoll (3). There are three unknown parameters: the
of the
membrane, Namem, and Clmem. Thus a unique
solution can be found by solving Eqs. 2B, 3, and
5.
The analysis shows that there is an imbalance between the
concentrations of free ions in the gel and those in plasma. This imbalance will give rise to an electroosmotic pressure
(
el) (53) that amounts to
|
(6A)
|
where
el is given in millimeters mercury for ion
concentrations (in mM). As the gel
increases,
el
increases dramatically. At a
of 30 meq/l, the
El is
29 mmHg compared with 690 mmHg at
of 150 meq/l. The following
empirical function describes closely the relationship between
el (in mmHg) and
(in meq/l) in our perfused kidneys
|
(6B)
|
Once the
has been determined, the gel-plasma partitioning can
be predicted for any solute on the basis of its net charge by using
Eq. 4. Thus the concentration of a negatively charged solute
will be lower in the gel than in plasma. The size-selective porous
membrane will further reduce its concentration before the molecule
reaches Bowman's space. Hence, the effect of negative molecular charge
is to reduce the concentration of the solute before it reaches the pore entrance.
Estimation of the Size Selectivity
There are several theoretical models that describe the effects of
size on the passage of molecules across a membrane. In general, the
solutes are assumed to be spherical and uncharged. In this context,
aSE is used to describe solute size, because it
is derived from the free diffusion constant. The experimental data were
analyzed with the following size-selective models: one- or two-pore
analysis, normal or lognormal pore distribution models with or without
shunts, and a fiber matrix model with or without a shunt pathway. The various models gave qualitatively similar results as long as they were
heteroporous, whereas the homoporous equations were unable to simulate
the biological data. Therefore, the least complex heteroporous model,
i.e., the two-pore model (42), was chosen for further analysis.
For two-pore analysis, experimental sieving data for Ficoll molecules
of different radii (12-72 Å, ~100-250 data pairs) are compared with the modeled data by using a set of physiological equations. As mentioned above, the four unknown parameters
(rs, rL, fL,
and A0/
x) are determined by
iterative calculations using nonlinear regression analysis. The
procedure requires reasonable start values for the four parameters,
which will be modified by the nonlinear regression analysis to give the
best fit between experimental and modeled data. The best fit was
quantitated by using the residual square sum or using Powell's method
(see Ref. 36 for details).
First, the fluxes of fluid and solutes are calculated separately for
each pore pathway in heteroporous membrane. Thus the total hydraulic
conductance, LpS, equals that for the small (s) and the large (L) pores
|
(7)
|
where fL is the fraction of LpS
accounted for by the large-pore pathway. Because there only are two
pore pathways, fs + fL = 1. Moreover,
the reflection coefficient,
, gives important information about the
membrane properties. It approaches unity for an ideal semipermeable
membrane and is close to zero for extremely large pores when there is
no restriction at all. For a heteroporous membrane, the average
reflection coefficient,
, is given by
|
(8)
|
where the individual pore
values are calculated by using
Eq. 14 below.
LpS can be estimated from
|
(9)
|
where
P is the hydrostatic pressure difference across the
glomerular barrier,
is the average reflection coefficient for proteins, and
p is the colloid osmotic pressure of the
plasma proteins, assuming the oncotic pressure in Bowman's space to be zero.
P can be experimentally determined, but its absolute value has
little impact on the parameters in the two-pore model (Ohlson M,
Sörensson J, Lindström K, Blom A, Fries E, and Haraldsson B, unpublished observations).
The fluid flux, JV, can thus be estimated for
each pore pathway as
|
(10)
|
|
(11)
|
Second, the clearance for a solute (Cl) is calculated separately
for each pore pathway by using the following nonlinear flux equation
(42)
|
(12)
|
Where Pe is the Peclet number that describes the relative
contribution of diffusion and convection
|
(13)
|
For each pore pathway,
and PS must be determined.
This is readily done for spherical molecules (with given
aSE) in cylindrical pores, because the
restriction factors are described by the following equations using the
ratio of solute radius to pore radius (
) (4, 12). Other
often used equations (see Ref. 15, for
instance) give similar results.
Thus
over a wide range of
values is given by
|
(14)
|
where the restriction for convective solute transport,
W(
), is
|
(15)
|
Thus the hindrance factor for convective solute transport,
W (as well as the restriction for diffusion, H;
see Eq. 20), approaches unity as
0 and approaches
zero as
1 (complete exclusion from the pores). The partition
coefficient,
(
), in Eq. 15 (and Eq. 20)
describes the effects of steric exclusion from the membrane pores and
is expressed as
|
(16)
|
KS(
) and Kt(
)
have empirically (4) been described
as
|
(17)
|
|
(18)
|
PS (ml/min), required for the calculations of clearance
(Eq. 13), is given by
|
(19)
|
where A0/
x is the
unrestricted pore area over diffusion distance, H(
) is a
diffusive restriction factor, and
DaSE is the free diffusion constant
for the solute. Thus the diffusion of a solute is hindered in the
cylindrical pore by the function H(
), which in turn is
calculated as
|
(20)
|
where Kt(
) and
(
) are defined
above. The free diffusion coefficient at 37°C is related to
aSE of the solute
|
(21)
|
where
is viscosity, and N is the Avogadros number.
At 37°C, D (in cm2/s) is ~3.28 × 10
6/aSE, with
aSE expressed in nanometers.
The total clearance is the sum of the small- and large-pore clearances
(Cls + ClL), the calculations of which
require separate determinations of Jv,
PS, and
. Finally, the sieving coefficient,
, for a
neutral solute is obtained by dividing the total clearance by the
glomerular filtration rate (GFR). The latter requires that the tracer
molecule is neither taken up, secreted, bound, or degraded in the
tubular system. These conditions are met in the isolated kidneys
perfused at low temperature and in vivo for a few solutes, e.g., Ficoll.
How to Estimate the Combined Effects of Glomerular Charge and Size
Selectivity
When the functional parameters of the gel-membrane model have been
determined, the fractional clearance of any (spherical) molecule
X can be predicted on the basis of its size and charge. If
the solute is charged, its gel-to-plasma concentration ratio, Xmem/XP, is calculated by
using Eq. 4. The effect of molecular size is then calculated
by using Eqs. 7-21 to estimate the primary U/P for a
neutral solute. Finally, the combined effects of the charge and size
barriers in series on the sieving of a charged molecule give a
predicted fractional clearance of
Xmem/XP times U/P. Thus
in this model anionic molecules will have a lower concentration on the
"blood" side of the pores, resulting in a further decrease in their
urine concentration.
 |
EXPERIMENTAL METHODS |
In a previous paper from our group (34),
values
for Ficoll molecules with aSE of 12-72 Å and albumin (aSE = 36 Å) were estimated in
isolated perfused rat kidneys (for details, see Ref. 34).
Ficoll was chosen due to its spherical nonflexible shape and absence of
net molecular charge.
In the present paper three experimental groups were analyzed: isolated
perfused rat kidneys (IPK) at 8°C with 18 g/l of albumin in Tyrode
solution; IPK with similar solutions at 37°C; and IPK at 37°C with
50 g/l albumin in the perfusate. Multiple samples were analyzed in each
experiment as previously described in detail (34). The
experiments were conducted under controlled conditions, and the results
were analyzed according to the gel-membrane model as described in
THEORETICAL DEVELOPMENT. In the nonlinear regression analysis of the IPK data, a minimal value of 10,000 cm was used for
A0/
x.
For comparison, similar two-pore analysis was performed by using
previously published Ficoll data (see Table
1) on healthy and nephrotic humans
(1) and on intact rats (36, 37). Tables showing the exact distribution of Ficoll molecular radii and U/P-ratios can be found in the aforementioned papers.
 |
RESULTS |
Biological Data
Figure 1 shows the sieving
coefficient for Ficoll as a function of solute radius in IPK perfused
with albumin solutions. The three experimental groups differed in
temperature (8 or 37°C) and albumin concentration (18 or 50 g/l) but
were otherwise maintained under identical conditions. As can be seen
from Fig. 1, the urine-plasma concentration curves mainly differed for
molecules >35 Å. Thus there was an increased flux of larger Ficoll
molecules with increasing temperature and albumin concentration.

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Fig. 1.
The experimentally obtained sieving curves for Ficoll
during 3 control situations in the IPK. Bottom curve: data
from cooled isolated perfused kidney (cIPK) perfused with 18 g/l of
albumin solution at 8°C (n = 7, ).
Middle curve: data from 8 IPKs perfused with 18 g/l of
albumin solution at 37°C (gray squares). Top curve: data
from IPKs (n = 3, ) perfused with 50 g/l of albumin at 37°C. The 3 curves represent the best fit for the
calculated urine-plasma curve data from the 2-pore analysis for
A, B, and C, respectively.
|
|
Charge Selectivity
The theories of ion-ion interactions presented in
THEORETICAL DEVELOPMENT were applied to experimental data
(34). Thus an albumin concentration of 18 g/l (0.269 mM)
accounts for
6 meq/l of charge. For the sake of simplicity, the
ionic composition is assumed to be sodium chloride, leaving the small
contribution of other ions out of the equations. To obtain
electroneutrality in the perfusate, the Nap of 147 mM
requires the Clp to be 147
6 = 141 mM.
Fractional clearance ratios were calculated from the
for albumin
and for Ficoll of similar size (36 Å). Statistical analysis was
performed on the logarithmic values due to the uneven distribution of
data. Thus at 8°C the geometric mean of the
ratio was
18.7 (
6.9, +11.0, n = 7, which corresponds to an
average
of 43.1 meq/l). At 37°C the geometric mean of the
ratio was 7.6 (
2.3, +3.3, n = 8). The
average
at 37°C was 31.2 meq/l. Please note that the density of
fixed negative charges dramatically affects the distribution of charged
solutes within the charged membrane (or gel), as illustrated
in Fig. 2. The estimated
el in a gel structure with a
of 43 meq/l is close to
60 mmHg (see Eqs. 6A and 6B).

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Fig. 2.
The predicted effect of solute charge in a hydrated gel
with a charge density ( ) of 43 (solid line) or 100 meq/l (hatched
line). The vertical dotted lines represent 2 solutes with net charges
of 23 (e.g., albumin) and 0 (e.g., Ficoll), respectively.
|
|
The Two-Pore Model
The two-pore parameters for the three experimental situations are
shown in Fig. 3. For the cooled IPK
(cIPK), the estimated rs was 45.8 ± 0.4 Å, rL was 86.7 ± 2.1 Å, fL
was 0.82 ± 0.1%, and A0/
x
was 10,000 cm. The residual square sum (SS) was 0.226, and Powell's
2 was 0.095. For the IPK at 37°C,
rs was 46.8 ± 0.3 Å,
rL was 80.4 ± 0.7 Å, and fL
was 1.36 ± 0.1%. The SS was 0.139, and Powell's
2 was 0.075. For the IPK at 37°C with 50 g/l of
albumin in the perfusate, rs was 46.4 ± 0.4 Å, rL was 79.2 ± 0.7 Å, and fL was 3.50 ± 0.3%. The SS was 0.124, and Powell's
2 was 0.072. As shown in Fig. 3,
rs and rL were rather
similar in the three groups, whereas the number of large pores
(reflected by fL) increased with temperature and albumin
concentration. The best fit of the calculated U/P ratios from the
two-pore analysis is shown with the experimentally obtained U/P ratios
in Fig. 1.

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Fig. 3.
Two-pore model parameters in IPKs perfused with 18 g/l of albumin
solution at 8°C (hatched bars), 18 g/l of albumin solution at 37°C
(crosshatched bars), and 50 g/l albumin solution at 37°C (open bars).
The analysis is based on the sieving of Ficoll in the molecular radius
range 12-72 Å. Previously determined filtration pressures
(25) were used in the analysis.
|
|
The stability of the two-pore model can be demonstrated by analyzing
the Ficoll-sieving data in Fig. 1, assuming various
P. Figure
4 shows the two-pore parameters plotted
against effective filtration pressure. All parameters except
fL were rather insensitive to the assumed value of
P.
P has previously been determined in this experimental model
(25). Thus, in IPKs perfused with 18 g/l of albumin
solution at 8°C with a GFR of 0.2 ml · min
1 · g wet wt
1,
P
is close to 18 mmHg, which for a colloid osmotic pressure of 6 mmHg
would give a filtration pressure of 12 mmHg (see Ref. 25).
In IPKs perfused with 18 g/l of albumin solution at 37°C with a GFR
of 0.3 ml · min
1 · g wet
wt
1,
P will be close to 14 mmHg (filtration pressure 8 mmHg). Finally, in IPKs perfused with 50 g/l of albumin solution at
37°C with a GFR of 0.3 ml · min
1 · g
wet wt
1,
P will be close to 28 mmHg (filtration
pressure 8 mmHg).

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Fig. 4.
Two-pore model parameters plotted against assumed
filtration pressure. The analysis is based on the sieving of Ficoll in
IPK perfused with 18 g/l of albumin solution at 8°C ( ), 18 g/l of
albumin solution at 37°C (gray sqaures), and 50 g/l albumin solution
at 37°C ( ). Top and middle:
small- and large-pore radius, respectively. According to the previously
published pressure-flow relationship (25), the filtration
pressure in the 3 groups would be close to 12, 8, and 8 mmHg,
respectively. Bottom: the large-pore fraction of the
hydraulic conductance, fL, increased with filtration
pressure, temperature, and albumin concentration. The other pore
parameters were, however, rather constant.
|
|
Table 2 shows the results of applying the
two-pore model on glomerular sieving data for Ficoll from four
different studies (1, 34, 36, 37). The effective
filtration pressures presented in the cited studies were used in the
analysis. Note that the average pore values obtained are rather similar
in humans, rats in vivo, and in isolated perfused rat kidneys. Indeed,
the glomerular small-pore Peclet numbers are almost identical in the
different species in vivo and in the isolated rat kidneys both at 8 and 37°C (Ohlson M, Sörensson J, Lindström K, Blom A, Fries
E, and Haraldsson B, unpublished observations). The analysis of Peclet numbers shows that diffusion is the dominating transport force (Pe <1)
for molecules <30 Å in hydrodynamic radius, whereas convection dominates (Pe >1) for larger solutes.
The Integrative Gel-Membrane Hypothesis
The charge and size selectivity are easily brought together in an
integrated model with a negatively charged gel and a heteroporous membrane in series. The consequences of such a model in terms of
albumin concentrations and fluxes are shown in Table
3 and illustrated in the drawing denoted
as Fig. 5. According to the model, there
is actually not a true charge barrier. Instead, significant charge
selectivity is obtained because of the ion-exchange properties of the
negatively charged gel maintaining lower concentrations of ions in the
gel than in plasma. The gel-membrane model allows for predictions of
transglomerular passage based on molecular size and charge. Figure
6 illustrates the sieving coefficients (or
) for the glomerular barrier for solutes with different
molecular radii (16-72 Å) and z (+5 to
25); thus a
solute with a aSE of 36 Å and a z of
23 (e.g., albumin) is predicted to have a
of 0.002.

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Fig. 5.
A schematic drawing of the model of glomerular
permeability with charge and size selectivity in series.
Jv, the fluid flux across the membrane; arrows,
albumin molecules are indicated by the symbols. There is a Donnan
equilibrium between the blood and gel compartments. The gel contains
~40 meq/l of fixed negative charges. Hereby, the effective albumin
concentration at the "plasma side" of the membrane (M) will be 1/10
of the value predicted from a plasma sample. Restriction due to
molecular size in the membrane causes a further reduction of the
albumin concentration. See Table 3.
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Fig. 6.
The glomerular sieving coefficients for spherical solutes
with molecular radii of 16-72 Å and net charges between +5 and
25 meq/l, as predicted from the integrative charge- and
size-selective gel-membrane model.
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 |
DISCUSSION |
To treat renal disorders such as nephrotic syndromes, we must
understand the intricate glomerular barrier. The present paper is one
of the first attempts to describe both the charge and size selectivity
in one unifying model. We have found that size and charge effects must
be exerted by different components of the glomerular wall to explain
experimental data. Similar results were found when the gel-membrane
model was applied to glomerular sieving data from humans, intact rats,
IPK perfused at 37°C, and IPK perfused at low temperatures (8°C).
The latter model is particularly interesting from a physiological point
of view, because the experimental conditions can be modified in a
manner that never can be done in vivo. Thus unique information about
the glomerular barrier has been obtained by modification of perfusate
ionic composition (48), osmolarity (30),
temperature (34), and orosomucoid content (21,
24). In addition, the effects on the barrier of changing the
perfusion pressure and/or the GFR can be studied in detail. Below we
will discuss each of the functional components of the glomerular
barrier separately and in combination. Finally, we will address some
pathophysiological and clinical consequences of the analysis.
Our findings strongly support the classic concept of a highly
permselective glomerular barrier with considerable charge selectivity. Thus, when the fractional clearances for albumin and Ficoll, with similar aSE (36 Å), were analyzed by using
the equations given in THEORETICAL DEVELOPMENT, the gel
was 43 meq/l. This value is much lower than the 120-170 meq/l
(13) that can be calculated from dextran sulfate data.
Similar high values were obtained (
= 100-130 meq/l) when
the
was estimated from the clearance rates for horseradish
peroxidase (HRP) from Rennke and co-workers (40). However,
as indicated at the beginning of this study, the charge barrier was
probably overestimated by the use of sulfated dextrans. Similarly, the
enzymatic determination of HRP (40) probably overestimated
(38). Note that for albumin, this difference in
implies two orders of magnitude difference in fractional clearance (see
Fig. 2). Also, a
of 150 meq/l would give an
el, and
hence balancing, hydrostatic pressure of close to 700 mmHg (see
Eq. 6B). In contrast, a
of 43 meq/l gives rise to an
el of 60 mmHg, which is in the physiological range of pressure.
Thus the presently suggested gel
of 35-45 meq/l is similar to
that found by using native and charge-modified myoglobin
(52), lactate dehydrogenase isoenzymes (LDH)
(31), as well as native and charge-modified HRP
(48). Interestingly, Huxley and co-workers (22) estimated the
in single mesenteric capillaries
perfused with plasma and reported a value of 34 meq/l. Thus glomerular and peripheral (20) capillaries may have similar
charge-selective properties but differ in their
rs and rL. In contrast to
the studies cited above, low
(7, 38, 55) or absence of
a glomerular charge barrier (39) has been reported. The
apparent conflict regarding the charge barrier can, however, be
resolved if one assumes the charged gel to be sensitive to hypoxia, as
will be further discussed below.
We have applied several different size-discriminating models to
glomerular sieving data of Ficoll, which is a neutral and nonflexible
sphere. The heteroporous models (2-pore model, lognormal + shunt,
fiber matrix + shunt) gave qualitatively similar results, whereas
the homoporous equations were unable to simulate the biological data.
This is in accordance with previous studies on glomerular permeability
(1, 12, 19, 36, 37, 46) and, in fact, seems to apply to
almost all microvascular beds (41, 42). Because of its
less complex nature, the two-pore model was chosen for further analysis.
The
for larger Ficoll molecules increased during perfusion at
37°C and with high albumin concentration (see Fig. 1). This can be
due to an increased rL, an increased number of
large pores, and/or an increased convective flow through the large-pore
pathway. Analysis with the two-pore model revealed that the pore radii were rather stable, but the number of large pores increased with increasing temperature and albumin clearance (see Fig. 3). The two-pore
model describes the biological data just as well, or even better than,
any other theory. This is in agreement with Deen et al.
(12), who found that the two-pore model was superior to
all other models in describing their dextran data. They found, however,
an inverse correlation between two of the three unknown parameters in
the two-pore model, a phenomenon not observed in the present study.
The studies using Ficoll, reported in Table 2, gave similar results in
terms of rs and rL, with
one exception (36). Thus the rs is
45-50 Å, and the rL is
75-90 Å [61 Å in the study with a narrow range of Ficoll and
hence less sensitivity in the large-pore range (1)].
Moreover, the large-pore pathway seems to contribute to 1% of the
LpS. A similar rL
(110-115 Å) was recently reported from analysis of protein in
intact rats with inhibited tubular uptake (50). These
results are qualitatively similar to a large number of studies with
dextran (12, 28, 33, 46). However, the flexible nature of
the dextran molecule probably explains the numerical differences in
pore radii. The rL ~80 Å is only one-third of
that reported for other capillaries (42, 49). The
glomerular large pore is therefore far from a shunt and possesses both
size- and charge-selective properties (31).
In the present gel-membrane model, there are two distinct layers; the
gel discriminates due to molecular charge, and the membrane is neutral
and size selective. The reason for using two separate components is the
observation that charge and size selectivity may change independently
of each other, for example, when the ionic composition of the perfusate
is altered (48). The charged fiber matrix of Johnson and
Deen (23) presently represents the most extensive analysis
of the effects of molecular charge and size. However, it cannot predict
the effects on glomerular charge selectivity of reducing perfusate
ionic strength (47).
From a logistical point of view, the glomerular charge barrier should
ideally be placed at the endothelial level close to the plasma
compartment (29). Indeed, experimental evidence for this
was presented three decades ago, in a seldom cited but relevant paper
by Ryan and Karnovsky (44). Most investigators have
instead focused on the basement membrane as the morphological
counterpart to the charge barrier. Observations on isolated basement
membrane have revealed that these structures are rather nonselective
(3, 7, 10, 16, 18). However, all such studies assume that the basement membranes do not alter their properties during the preparation procedure (3). Recently, the endothelial
glycocalyx was suggested to be much thicker than previously thought,
i.e., almost twice as thick as the basement membrane. Thus electron micrographs taken after fixation with glutaraldehyde in fluorocarbons seem to preserve the glycocalyx better than glutaraldehyde-based fixative (43).
Placing the charge barrier in the endothelial glycocalyx has several
advantages. First, there is the logistical argument above. Second, it
could explain how charge selectivity can be affected by the plasma
composition, such as the beneficial effect of orosomucoid (21). Third, the glomerular
can reversibly be altered
by changes in the perfusate ionic strength (48), but not
by alterations in osmolality (30). Fourth, it can explain
why some investigators fail to demonstrate charge selectivity, because
the endothelial glycocalyx has been shown to be sensitive to
hypoxia-reperfusion in other vascular beds (9, 51).
In agreement with these observations, IPKs perfused at 37°C had
slightly less fixed negative charges (31 meq/l) compared with the
at 8°C (43 meq/l, n.s.). Erythrocyte-free perfusion is known to give
hypoxic tubular cell damage at 37°C (45). With other experimental approaches, involving reperfusion, the glycocalyx is thus
likely to be damaged, giving a reduced charge barrier, which then could
be almost abolished by the administrations of various toxins
(39). The apparently conflicting views of the glomerular
barrier could therefore be due to differences in experimental approach
affecting the delicate endothelial glycocalyx to various degrees.
Another virtue of a charged gel is that one would expect a Donnan
equilibrium to maintain a reduced concentration of negatively charged
solutes in the gel compared with that of plasma. However, such a
"self-rinsing" ability would most likely be impaired due to
concentration gradients and stagnant layers if there were to be
significant size discrimination in the gel.
The size-selective barrier is probably situated at the podocyte slit
membrane, having a large number of functional pores with 45 to 50 Å radii and a few pores with radii from 75 to 115 Å. Genetic or acquired
defects in the basement membrane may disturb endothelial function or
affect the three-dimensional glomerular structure, hence causing
proteinuria. However, we suggest that most nephrotic syndromes are
secondary to changes in the podocytes and/or in the endothelial glycocalyx.
To conclude, there is substantial evidence for the glomerular barrier
to be heteroporous with charge-selective properties in qualitative
agreement with the classic view. We extend the analysis and propose a
gel-membrane model with charge and size selectivity in series. The
charge selectivity is probably confined to a delicate endothelial
glycocalyx acting as an ion-exchange gel sensitive to perfusate flow,
pressure, and plasma composition. We have previously shown that
glomerular charge and size selectivity can be changed independently of
each other, which suggests that a different component is responsible
for the size barrier, most probably the podocyte slit membrane. The
glycocalyx has been shown to be highly sensitive to hypoxia-reperfusion
in other organs, and that may explain why some investigators have found
lower glomerular
. Indeed, we would suspect certain nephrotic
syndromes to be caused by changes in the hitherto completely neglected
and poorly understood glomerular endothelial glycocalyx.
 |
ACKNOWLEDGEMENTS |
This study was supported by the Swedish Medical Research Council
Grants 9898 and 2855, the Knut and Alice Wallenberg Research Foundation, the Ingabritt and Arne Lundberg Research Foundation, the
National Association for Kidney Diseases, the Göteborg Medical Society, and Sahlgrenska University Hospital Grant LUA-B31303.
 |
FOOTNOTES |
Address for reprint requests and other correspondence: B. Haraldsson, Dept. of Physiology, Göteborg Univ., Box 432, SE-405 30 Göteborg, Sweden (E-mail: bh{at}kidney.med.gu.se).
The costs of publication of this
article were defrayed in part by the
payment of page charges. The article
must therefore be hereby marked
"advertisement"
in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 9 May 2000; accepted in final form 10 October 2000.
 |
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