INVITED REVIEW
Mathematical models of renal fluid and electrolyte transport:
acknowledging our uncertainty
Alan M.
Weinstein
Department of Physiology and Biophysics, Weill Medical
College of Cornell University, New York, New York 10021
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ABSTRACT |
Mathematical models of renal
tubular function, with detail at the cellular level, have been
developed for most nephron segments, and these have generally been
successful at capturing the overall bookkeeping of solute and water
transport. Nevertheless, considerable uncertainty remains about
important transport events along the nephron. The examples presented
include the role of proximal tubule tight junctions in water transport
and in regulation of Na+ transport, the mechanism by which
axial flow in proximal tubule modulates solute reabsorption, the effect
of formate on proximal Cl
transport, the assessment of
potassium transport along collecting duct segments inaccessible to
micropuncture, the assignment of pathways for peritubular
Cl
exit in outer medullary collecting duct, and the
interaction of carbonic anhydrase-sensitive and -insensitive pathways
for base exit from inner medullary collecting duct. Some of these uncertainties have had intense experimental interest well before they
were cast as modeling problems. Indeed, many of the renal tubular
models have been developed based on data acquired over two or three
decades. Nevertheless, some uncertainties have been delineated as the
result of model exploration and represent communications from the
modelers back to the experimental community that certain issues should
not be considered closed. With respect to model refinement,
incorporating more biophysical detail about individual transporters
will certainly enhance model reliability, but ultimate confidence in
tubular models will still be contingent on experimental development of
critical information at the tubular level.
proximal tubule; distal tubule; collecting duct; sodium; potassium; chloride; acid/base
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INTRODUCTION |
IN THE PRESENTATION OF A PHYSIOLOGICAL
model, declaration of success typically comes with the demonstration of
faithful predictions of function in simulations of a number of
experiments. Arguably, one may endorse a standard of model presentation
in which the model builder shows not only what works but where the
model fails, or where it makes novel predictions that have yet to be
tested. In this regard, "model failure" may vary from small to
large, where "large" implies an important observation that just
cannot be captured by a reasonable model with realistic parameters. In some sense, this situation is the most interesting, because its resolution may provide new insights. In renal physiology, models of
glomerular filtration have probably enjoyed the closest working relationship with experimental data, initially representing
hemodynamics and subsequently examining issues of glomerular
permselectivity. The successes and limitations of these models have
recently been reviewed in this series (20). Perhaps the
oldest and most intense renal modeling effort has been to represent the
tubules and vasculature of the kidney medulla in antidiuresis and the
formation of a concentrated urine. The serious difficulties encountered
with representations of inner medullary function have been well
documented (56, 101) and will not be taken up here. With
respect to tubular models, the greatest attention has been given to the
proximal tubule, initially with regard to forces and routes of water
transport and subsequently focused on ion transport through the
transcellular pathway. More recently, segments of the distal nephron
have been modeled, and these simulations have been used to extrapolate
in vitro transport observations to tubules in vivo. It is the aim of
this review to survey models of renal tubular transport, specifically with regard to uncertainties encountered by the model builders. The
points of interest will be model limitations and the authors' responses, either to question experimental data or to propose testable
mechanisms that might render the models satisfactory.
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PROXIMAL TUBULE: WATER TRANSPORT |
Figure 1 is a schematic of the
proximal tubule epithelium, in which the lateral intercellular space
(LIS) is separated from luminal and peritubular solutions by the tight
junction (TJ) and basement membrane (BM). All of the early models of
proximal tubule function had focused on water transport, specifically
to try to understand the forces responsible for isotonic water
reabsorption and the pathways for transepithelial water flow (45,
79, 80, 91, 114). The last review of these issues here
(116) was principally concerned with the paracellular
pathway. Models of the proximal tubule had agreed that most of the
transepithelial water flowed through the LIS and out across the BM.
Points of disagreement among the models included 1) the
magnitude of the flow that arrived in the LIS via the TJ and via a
transcellular route across luminal and lateral cell membranes in series
and 2) the magnitude of the solute permeability of the
outlet BM (i.e., whether there was any significant resistance to solute
flux across this barrier). A finite solute permeability of the BM would
result in "middle compartment" behavior by the LIS. This refers to
active solute transport into the LIS across the lateral cell membrane,
creating a region of local hypertonicity, which acts to pull water from cell to LIS, and ultimately from lumen to cell. The net result is the
possibility of transepithelial reabsorptive water flux in the absence
of a transepithelial osmotic gradient (coupled water transport).
Furthermore, a finite solute permeability for the LIS BM would result
in solute polarization effects, namely, an overall epithelial water
permeability less than that of the cell membranes in series and an
overall epithelial solute reflection coefficient less than that of the
TJ and cell in parallel ("pseudo-solvent drag"). A previous model
had argued that large flows of isotonic water reabsorption could exist
despite relatively low proximal tubule water permeability if there were
substantial solute polarization within the LIS (114). In
the review (116), it was estimated that coupled water
transport was anywhere from 55-81% of isotonic water
reabsorption, depending on which of the experimental measurements of
overall epithelial water permeability one believed. Furthermore, it was
estimated that proximal tubule could transport water against an adverse
osmotic gradient (hypertonic lumen) of 8-23
mosmol/kgH2O. These predictions were subsequently tested
experimentally by Green et al. (37) using in vivo
microperfusion of rat proximal tubules and peritubular capillaries. It
was found that coupled water transport was ~75% of isotonic
transport and that the adverse osmotic gradient required to null volume
reabsorption was between 13.2 and 29.4 mosmol/kgH2O,
depending on the concentration of peritubular protein.

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Fig. 1.
Transport pathways across luminal and peritubular cell
membranes of rat proximal convoluted tubule cell. All of the
peritubular transport pathways shown on the basal surface also line the
lateral cell membrane and communicate with the lateral intercellular
space (LIS). There is a permeable tight junction. Adapted from Ref.
118.
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The fraction of reabsorptive water flow that actually traverses the
proximal tubule TJ is unknown. Arguments in favor of transjunctional water flow have included substantial solvent drag of ionic species (31, 44, 80); the appearance of streaming potentials with the application of an impermeant osmotic agent (30, 104);
and ionic permeabilities roughly in proportion to their mobility in free solution (49). More direct evidence for TJ water flux
in rabbit tubules came from Whittembury and associates (15, 34, 127), whose estimate of the water permeability of the
peritubular cell membrane indicated a transcellular water permeability
less than the overall epithelial tubular water permeability. In
the rat, evidence for TJ water flow was the observation of convective entrainment of sucrose, despite relatively small diffusional flux (126). An important discrepant observation was made by
Schnermann et al. (85), who found that mice, genetically
defective for the proximal tubule cell membrane water channel
aquaporin-1, had a reduction in proximal tubule epithelial water
permeability of nearly 80% compared with control mice. These data are
difficult to rationalize with significant TJ water permeability.
However, before one can fully assess the implications of this
observation, it must be acknowledged that there are no measurements of
proximal tubule solute reflection coefficients in any strain of mouse, so as yet we have no idea whether there is significant solute-water interaction that must be modeled in these tubules. Perhaps the most
direct measure of TJ water flow was the work of Kovbasnjuk et al.
(50), who were able to visualize standing concentration gradients of a fluorescent indicator trapped within the lateral interspaces of confluent Madin-Darby canine kidney cells. A sweeping away of marker from the neighborhood of the TJ would have indicated transjunctional convection, but none was observed in this tight epithelium.
Consistent with early observations, the first proximal tubule models
all included substantial TJ convective solute flux (45, 79, 80,
91, 114). Nevertheless, Rector and Berry (8, 74)
resisted ascribing substantial water flux to the TJ based on
pore-theoretic calculations that indicated that the junctions were not
large enough to allow anything but a small fraction of transepithelial
water flow. Preisig and Berry (72) measured the permeation
of sucrose and mannitol across the rat proximal tubule. Applying the
Renkin equations to their data, they computed the dimensions of the
"sucrose pore" and indicated that it could be responsible for at
most 2% of the tubular water permeability. These arguments provoked a
quantitative examination of whether apparent convective epithelial
solute flux could derive from solute polarization within the LIS
(115). Specifically, could one construct a model of
proximal tubule with just the right solute polarization to yield
realistic reflection coefficients? In the reconsideration of rat data
from Frömter et al. (31), all of the acceptable interspace models required substantial TJ convective Cl
flux. An important contribution to this discussion came with the
suggestion of Fraser and Baines (28) that the TJ might be represented as a fiber matrix, rather than as a collection of pores.
The critical feature of the fiber matrix equations is that for a given
solute permeability, the water permeability can be substantially
greater than that predicted from the Renkin equations. This formulation
was compatible with the permeabilities of rat proximal tubule, although
it was a phenomenologic equation and not based on the fine structure of
junctional strands. Most recently, Guo et al. (40)
returned to this problem and examined representations of the TJ as a
two-pore structure. It was found that an abundant small pore
(consistent with interstices between claudin-2 molecules) could be used
to represent small-solute permeability, and an infrequent large pore
(such as 18 × 100-nm breaks in the TJ strands) could be used to
represent sucrose permeability. This large pore could also be
responsible for a substantial fraction of proximal tubule water flow,
although it is not at all clear how such a pore could give rise to the
differences in reflection coefficients that have been observed between
Na+ and Cl
, or between Cl
and
HCO
. Ultimately, a true model of hindered transport,
which incorporates electrical effects, will be required to represent TJ
fluid and electrolyte fluxes.
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PROXIMAL TUBULE: REGULATION OF NA+
REABSORPTION |
Once the TJ had been established as a route for solute flux, an
hypothesis was advanced that the junction might be a key locus for the
regulation of proximal Na+ reabsorption. Lewy and Windhager
(57) demonstrated a correlation between single-nephron
filtration fraction and proximal tubule Na+ reabsorption
(57). Because a lower filtration fraction reduces protein
oncotic pressure within peritubular capillaries, they surmised that
this would lead to reduced capillary uptake of fluid from the renal
interstitium and LIS, and, hence, elevated interspace pressure. In
turn, this would produce a backflux of Na+ already
transported into the interspace, that is, backflux across the TJ into
the lumen. Before this proposal, it was known that proximal tubule
Na+ reabsorption was depressed during extracellular volume
expansion (22). In the intact dog, the ability to reverse
this natriuresis with infusion of hyperoncotic albumin indicated that
peritubular oncotic pressure could influence sodium reabsorption, and
Earley et al. (24, 63) had proposed that renal
interstitial pressure might be an intermediate variable. Micropuncture
experiments in the rat reproduced the findings in the dog, namely, that
depression of proximal sodium reabsorption that occurs with saline
infusion could be reversed by perfusion of the efferent arteriole with a solution whose protein is at the control concentration (10, 90). Microperfusion of both proximal tubules and peritubular capillaries in the rat showed that peritubular oncotic force sharply increased isotonic Na+ reabsorption, well beyond a simple
osmotic effect on water flux, thus suggesting a qualitative change in
the epithelium (38). The precise mechanism by which LIS
pressures modulate TJ sodium flux is uncertain. One possibility is that
with increased interstitial pressure there is junctional widening and
back-diffusion of sodium from interspace to lumen. Evidence from
several sources has documented increased junctional permeability with
volume expansion, both in Necturus (9) and in
the rat (88). A second possibility is that backflux of
sodium across the TJ occurs by convective flow. The TJs of leaky
epithelia are sensitive to hydrostatic pressures applied from the
contraluminal side, and volume expansion was found to decrease the
proximal tubule NaCl reflection coefficient (7). In this
regard, convective backflux across the tight junction of rat proximal
tubule has been invoked by Ramsey et al. (73) to explain
their observation that the luminal appearance of lanthanum deposited
within the renal interstitium is enhanced during saline volume expansion.
To examine the backflux hypothesis quantitatively, a mathematical model
of rat proximal nephron was developed, comprising tubular epithelium,
glomerulus, peritubular capillary, and interstitium (117).
In this model, the TJ was compliant in the sense that both junctional
salt and water permeability increased and the salt reflection
coefficient decreased in response to small pressure differences from
lateral interspace to tubular lumen. Although these compliance
properties were empirical, they provided a model in which a decrease in
peritubular protein concentration (which increased interspace
hydrostatic pressure) could open the TJ and produce a secretory salt
flux. This backflux was a combination of both diffusive and convective
terms and did not specifically require either component to dominate. In
this model of the TJ, once the interspace pressure fell below that of
the lumen, the junction closed and junctional properties were fixed.
The consequence of junctional closure is that beyond a certain value of
peritubular protein, one may expect little influence of peritubular
Starling forces on volume reabsorption. Figure
2 displays the results of calculations
when afferent arteriolar tone was varied, changing both glomerular
plasma flow and filtration fraction. What is shown in the log-log plot
are the changes in proximal reabsorption (APR) as a function of
filtration fraction (FF; Fig. 2A) or as a function of
glomerular filtration rate (GFR; Fig. 2B). Within the region in which the TJ are "open" and influenced by pressure, the relative changes in APR and FF are identical. However, when related to changes
in GFR, the fractional change in APR is only 41% (Fig. 2B).
This derives from the fact that (within the model glomerulus) increases
in renal plasma flow produce GFR increases even in the absence of
changes in glomerular capillary pressure, i.e., without any change in
filtration fraction. This model prediction was at odds with the nearly
perfect glomerulotubular balance that has been observed in the rat
kidney (86).

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Fig. 2.
Assessment of glomerulotubular balance during afferent
arteriolar constriction. The model is composed of a glomerulus,
peritubular capillary, interstitial compartment, and proximal tubule
with compliant tight junction and is solved for the case of a single
nonelectrolyte salt plus plasma proteins. A: a log-log plot
of predicted absolute proximal reabsorption (APR) as a function
of filtration fraction (FF). B: a log-log plot of APR as a
function of glomerular filtration rate (GFR). In the range of
lower GFR, the peritubular capillary protein concentrations are lower,
so that renal interstitial pressures are higher, and tight junctions
are open and modulated by pressure changes. The dotted lines are linear
regressions and indicate the sensitivity of APR to either FF or GFR.
Adapted from Ref. 117.
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A prerequisite for the precise glomerulotubular balance that has been
observed is that luminal fluid flow modulates epithelial Na+ reabsorption. This has been termed
"perfusion-absorption balance" (128) and has been
demonstrated in rat microperfusion studies (4, 41, 68,
78). One of the best illustrations of this phenomenon are the
micropuncture data of Chan et al. (17), in which a
three-fold increase in luminal perfusion rate (with trivial changes in
luminal HCO
concentration) produced a doubling of
the rate of HCO
reabsorption. It must be
acknowledged that examination of rabbit tubules in vitro did not show
flow-dependent reabsorption (13), but whether this is due
to species difference or to the preparation of tubules for perfusion in
vitro is not known. Although rat proximal tubules have been perfused in
vitro (32), flow-dependent reabsorption has not been
examined. In this regard, flow-dependent Na+ and
HCO
transport has been reported recently in mouse
tubules both in vivo and in vitro (23). The underlying
mechanism for flow-dependent changes in reabsorption has not been
established. At one point, the proximal tubule brush border had been
considered a possible unstirred layer. However, model calculations
indicated that there was unlikely to be any appreciable convective
stirring within this pile (5). More to the point, the
diffusion barrier between the bulk luminal fluid and the cell membrane
was not predicted to hinder Na+/H+ exchange
(52). Two studies raised the possibility that increases in
axial flow velocity recruit new transporters into the luminal membrane.
Preisig (70) examined recovery of cellular pH from an
acute acid load in vivo (ammonium pulse). With increases in luminal
flow rate, the pH recovery mediated by Na+/H+
exchange was enhanced. Maddox et al. (59) subjected rats
to acute changes in vascular volume to obtain hydropenic, euvolemic, and volume-expanded groups, with respective grouping according to
decreased, normal, and increased GFR. When brush-border membrane vesicles were prepared from each of these groups and
Na+/H+ kinetic parameters were assessed, it was
found that the Vmax determinations stratified in
parallel with GFR.
Ultimately, perfusion-absorption balance must derive from an afferent
sensor of fluid flow rate in series with a cascade of effector steps
that activate luminal transporters or insert new membrane transporters.
Model calculations (39) have indicated that the proximal
tubule microvilli are physically suitable to function as such a sensor.
A striking feature of proximal tubule epithelium is the observation
that the microvilli are remarkably uniform in height and form a highly
organized hexagonal array (64). Although the main function
that has been attributed to the brush border has been luminal membrane
area amplification, such regular organization is not necessary to
accommodate more transporters. However, the model in Guo et al.
(39) shows that such regularity in height and spacing is
highly advantageous if the microvilli are to function as a flow sensor,
because the bending deformation of the microvilli would be both small
and uniform. The critical component of this system may well be the
actin cytoskeleton, which is abundant within and beneath the brush
border (64). The model in Guo et al. (39)
describes how the actin filament bundle that is the central core of the
microvillus deforms under hydrodynamic loading. The proposed role for
the microvilli is that they can not only sense fluid drag forces but
are also capable of greatly amplifying these stresses as the forces are
transferred to the intracellular cytoskeleton. This is due to the
hydrodynamic torque exerted on the terminal web, where the actin
filament bundle within the microvillus attaches at its roots to the
main cell body. To serve the hypothesized function, the microvilli
should be relatively stiff structures that are able to transmit,
without significant bending, the torque due to the hydrodynamic drag
acting on the microvilli tips (113). In this scheme of
signal transduction, specific interaction between the proximal tubule
cytoskeleton and the apical cell membrane
Na+/H+ exchanger is a critical feature. In this
regard, Lamprecht et al. (55) have shown that the
Na+/H+ exchanger in brush-border microvilli is
linked via ezrin, a kinase anchoring protein, to the actin
cytoskeleton. Finally, implication of the cytoskeleton in the
flow-dependent modulation of luminal Na+ entry invites an
immediate means for coordinating peritubular solute exit in response to
changing throughput. In sum, model failure to represent a fundamental
aspect of glomerulotubular balance has been the impetus to formulate
testable hypotheses for regulation of proximal tubule Na+ transport.
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PROXIMAL TUBULE: CL REABSORPTION |
Proximal tubule Cl
reabsorption proceeds via both
paracellular and transcellular pathways (3). Evidence for
a transcellular component to Cl
flux includes
observations that in the absence of transepithelial electrochemical
driving force, there is still substantial Cl
reabsorption
(1) and that a substantial component of Cl
reabsorption can be blocked by specific inhibitors of membrane transporters (84, 110). The principal candidates for
luminal membrane Cl
uptake are all Cl
/base
exchangers, in which the base may be HCO
, hydroxyl,
formate, or oxalate (Fig. 1). A major advance in this inquiry came with
the finding by Karniski and Aronson (46) that formate
could catalyze Cl
uptake into proximal tubule
brush-border membrane vesicles, and, in the presence of a
vesicle-to-medium formate gradient, vesicle Cl
concentration could be driven above that of the ambient medium. In
rabbit proximal tubules perfused in vitro with a high-Cl
,
low-HCO
solution, addition of luminal formate (0.5 mM) increased volume reabsorption by 60% (84) and was
associated with a small increase in cell volume (82). In rat tubules perfused in vivo with the same high-Cl
solution, luminal formate increased volume reabsorption by 45% (110). This increase in volume and Cl
reabsorption could be blocked, not only by an inhibitor of the Cl
/HCO
transporter but also by an
inhibitor of the luminal membrane Na+/H+
exchanger (109). Underscoring the importance of the
Na+/H+ exchanger in this observation, the
effect of formate to enhance proximal Cl
reabsorption
(present in normal mice) was absent in Na+/H+
exchanger 3 (NHE3)-deficient mice studied with in vivo microperfusion (111). For formate-enhanced Cl
transport to
be significant, submillimolar concentrations of formate (and micromolar
concentrations of formic acid) must mediate reabsorption of a
substantial portion of the filtered Cl
load. The scheme
that has emerged is one in which cellular formate exchanges for luminal
Cl
, the formate is protonated to formic acid within the
tubular lumen, and formic acid recycles back into the cell. At minimum, the luminal membrane Na+/H+ exchanger is a
proton source, but it may be more tightly coupled to the formate flux
pathways (3).
Luminal membrane Cl
/ HCO
exchange has
been problematic for the modeling of proximal tubule. In model
simulations with a luminal membrane Cl
/
HCO
exchanger, the addition of formate produced cell
swelling, and increased cytosolic Cl
concentration,
(118). Unfortunately, variation of the density of the
Cl
/ HCO
exchanger had virtually no
effect on overall NaCl reabsorption along the tubular segment, whereas in similar simulations, the density of the
Na+/H+ exchanger had a powerful impact on NaCl
reabsorption; i.e., the rate of Na+ reabsorption was
clearly rate limiting (Fig. 3). In this
model, although transcellular Cl
flux was substantial, it
was only about one-half the estimate of paracellular Cl
flux. When the transcellular pathway was diminished, the forces favoring paracellular flux were augmented. In these model calculations, the luminal membrane permeability to formic acid was about one-third that of a lipid bilayer to CO2. Unfortunately, the only
measurement of the formic acid permeability of the proximal tubule cell
membrane is ~5% of the value selected for the model parameter
(71), and using the measured value, the recycling scheme
fails. This prompted a modeling investigation into the possibility that
the microvillous configuration of the proximal tubule brush border
could provide a diffusion barrier, so that the experimental assessment
of membrane formic acid permeability might have been artifactually low.
The result of these calculations was that the brush border only
depressed formic acid permeability measurement by ~10%; even if the
formic acid diffusion coefficient within the brush border were
one-tenth that in free solution, the permeability assessment would only be off by 25% (51). Additional calculations, which
included the diffusion of CO2 and the finite rate of
catalysis of carbonic anhydrase, confirmed the original estimates
(52). It is not clear how this proximal tubule model
should be modified to represent formate's enhancement of proximal
Cl
reabsorption. Certainly if formate were to directly
modulate the ion translocation rate through NHE3 (or NHE3 density), the overall transport effect could be achieved. However, this still leaves
unresolved the problem of how enough formic acid could be recycled back
into the cell despite a low membrane permeability.

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Fig. 3.
Proximal reabsorption of Na+,
Cl , and HCO predicted by an
electrolyte model of proximal tubule (Fig. 1). Perfusate and bath are
identical bicarbonate-Ringer solutions, and perfusion rate is 30 nl/min
into a 5-mm tubule segment. In the top panel, electrolyte
reabsorption is computed over a range of values for the activity of the
luminal NH /H+ exchanger. The arrow
indicates the reference value for this parameter. In the
bottom panel, the independent variable is the activity of
luminal Cl /HCO2 exchange. Adapted from Ref.
118.
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With respect to peritubular exit of Cl
, the early
electrophysiological data indicated only a small role for a conductive
pathway (6, 12, 14). Welling and O'Neil
(124) found that in rabbit proximal straight tubule the
conductive Cl
pathway in peritubular membrane could
account for ~6% of the total membrane conductance. However, after
cell swelling induced by a 150 mosmol/kgH2O hypotonic
osmotic shock, Cl
conductance increased to 20% of the
total peritubular membrane conductance. In rabbit proximal convoluted
tubule, cell volume was unaffected by changes in peritubular
Cl
concentration. However, prior hypotonic cell swelling
rendered the cell volume sensitive to peritubular Cl
concentration, and this effect was eliminated by application of a
Cl
channel blocker (83).
Electrophysiological study of rabbit convoluted tubule during osmotic
shock estimated the fractional Cl
conductance to increase
from 3 to a maximum of 16%, with relaxation to 8%. During these same
experiments, the fractional conductance of the
Na+-3HCO
pathway declined from 41 to 16%, with little change in the absolute conductance through this pathway (125). The data from this type of experiment give
some guidance for estimating the reabsorptive flux of Cl
through peritubular channels in rat experiments. If one assumes that
the peritubular membrane conductance under control conditions is 10 mS/cm2 (29), then the conductance of the
Na+-3 HCO
pathway is ~4
mS/cm2, and in the relaxation phase after cell swelling,
the steady-state Cl
conductance increased to 2 mS/cm2. For a peritubular membrane electrical potential of
75 mV, and cytosolic and peritubular Cl
concentrations
of 18 and 118 mM (16), respectively, the cytosolic Cl
potential is ~25 mV. Multiplication by the
steady-state Cl
conductance of the swollen cell, 2 mS/cm2, yields a Cl
current of 50 µA/cm2, or 0.5 nmol · s
1 · cm
2, or 25 pmol · min
1 · mm
1 for a
tubule with a 25-µm diameter. If in the conditions of these experiments, cytosolic Cl
had been doubled to 36 mM, then
the Cl
potential might have been as high as 45 mV, and
the conductive flux 45 pmol · min
1 · mm
1. These
estimates must be considered in light of the control volume fluxes of
2.5 nl · min
1 · mm
1
(110), which for isotonic transport corresponds to
Cl
reabsorption of 350 pmol · min
1 · mm
1. In
the experiments of Wang et al. (110), the application of DPC (which had no effect in control conditions) was able to abolish the
formate-induced 45% increase in volume reabsorption. This corresponds
to a reduction in Cl
flux by 160 pmol · min
1 · mm
1,
several-fold higher than the conductive maximum. In the mathematical model, the formate-induced increases in luminal Cl
entry
exited largely via the potent
Na+-2HCO
/Cl
exchanger
within the peritubular membrane (118).
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DISTAL NEPHRON: K+ SECRETION |
Micropuncture study of K+ handling by the rat kidney
has identified the accessible portion of the distal convoluted tubule (DCT) as the principal site for K+ secretion (61,
62). Further along the nephron, there is little change in
K+ flow, at least from a comparison of K+
delivery to the collecting duct (CD) with its appearance in the final
urine. In rats on a low-Na+ diet and treated with
mineralocorticoid, maneuvers designed to enhance renal K+
excretion, determinations of late distal fluid-to-plasma K+
concentration yielded a ratio of 3.8 (62). In a
microperfusion study, the limiting K+ concentration of rat
DCT has been estimated to be 13-15 mM by extrapolating between
secretory (10 mM) and reabsorptive (25 mM) luminal K+
concentrations (35). Perhaps the most direct determination of the limiting K+ concentration was the "stationary
K+ concentration" observed in a split drop, 30.6 mM under
control conditions (2). These values are about an order of
magnitude lower than urinary K+ concentrations of
antidiuretic rats on a control diet (61) and reflect the
fact that K+ secretion in the distal tubule precedes final
water abstraction from CD fluid. The idea of the CD as a
K+-passive conduit to the final urine stands in contrast to
observations of cortical CD (CCD) function in vitro, revealing that in
rabbit (66, 87, 97, 95) and rat tubules (81,
102), the CCD is a site of Na+ reabsorption and
K+ secretion, with transport enhanced by aldosterone and
antidiuretic hormone. Thus one issue is understanding the observed DCT
K+ concentrations in terms of the measured fluxes and
permeabilities of this segment, and a second issue is
rationalizing the CCD K+ fluxes in vitro with the
negligible K+ secretion in vivo.
The only mathematical model of rat DCT that has been developed was done
by Chang and Fujita (18, 19) and includes K+
fluxes and acid-base transport in this segment. The late DCT principal
cell, which is responsible for the K+ secretion of this
segment, is depicted in Fig. 4. Chang and
Fujita applied a novel method to obtain model parameters by devising a
penalty function that examined the results of simulations of several
different experiments, and notably none of the reference experiments
included measurements of the limiting DCT K+ concentration.
What their results show is that K+ secretion occurs
predominantly in the first half of the late DCT and then goes to zero
by the end of this segment, when luminal K+ concentration
reaches a limiting value of 15 mM (18). This represented
an approximately sixfold increase from the entering K+
concentration and reflects an approximate doubling of axial
K+ flow in conjunction with reabsorption of two-thirds of
the delivered water. Their model prediction for the limiting
concentration was derived from data obtained under control conditions
and thus appears realistic. A model of rat CCD by Weinstein
(122) was developed with parameters designed to yield
fluxes and permeabilities characteristic of tubules exposed to both
aldosterone and antidiuretic hormone stimulation. With these
parameters, the limiting K+ concentration for CCD was 23 mM. When simulations were run for a 2-mm tubule in which entering fluid
was hypotonic with 12 mM K+, there was rapid water
reabsorption to isotonicity, a prompt doubling of luminal
K+, and virtually no change in the axial flow of
K+. When entering K+ was 24 mM, the luminal
concentration was driven above 40 mM, and 23% of delivered
K+ was reabsorbed. This model was subsequently extended to
a model of the whole CD, by appending outer medullary (OMCD) and inner medullary (IMCD) segments (123). Under antidiuretic
conditions, the model predicted that ~80% of the K+
delivered to the CD would be reabsorbed; most of this flux occurred within the OMCD and was paracellular (Fig.
5). In these CD segments, the model
K+ permeabilities had been guided by experimental
measurements of rat tubules perfused in vitro: NH
permeability in OMCD (25) and K+ permeability
in IMCD (76). The most immediate rationalization of the
predicted CD K+ reabsorption with the micropuncture data is
that the tubules in vivo either have a greater K+ secretory
capacity or a lower K+ permeability, or both.

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Fig. 4.
Transport pathways across luminal and peritubular
membranes from the principal cell of the late distal convoluted tubule
of the rat. Adapted from Ref. 19.
|
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Fig. 5.
Electrolyte transport along the model collecting duct (CD) under
antidiuretic conditions. Left: luminal potential difference
(PD; mV) and the concentrations of Na+ and K+.
Right: volume flow and axial solute flows within all CD of a
single kidney. The abcissa is distance along the CD, with
x = 0 the initial cortical point, and cortical (CCD),
outer medullary (OMCD), and inner medullary (IMCD) CD accounting for 2, 2, and 5 mm of CD length. Peritubular conditions along the OMCD include
a doubling of interstitial NaCl and KCl; along the IMCD, there is no
change in interstitial NaCl, but urea increases from 20 to 500 mM and
KCl increases from 10 to 20 mM. Fluid reabsorption within the CCD,
OMCD, and IMCD is 32, 35, and 22% of entering flow. Luminal delivery
of NaCl and KCl is ~5 and 50% of that filtered, and overall about
two-thirds of the delivered Na+ and 80% of delivered
K+ is reabsorbed. K+ reabsorption occurs within
the OMCD and IMCD, due in part to transcellular uptake by luminal
H-K-ATPase but most importantly due to the concentration of luminal
K+ by water abstraction and diffusive backflux across the
tight junctions and within IMCD, luminal cation channels. Adapted from
Ref. 123.
|
|
Plasma HCO
concentration has a profound effect on
renal K+ handling, with metabolic alkalosis increasing
excretion (27, 75) and acidosis decreasing excretion
(103). Distal micropuncture by Malnic et al.
(60) localized much of this effect to the accessible DCT.
Microperfusion of this segment by Stanton and Giebisch
(93) established that the effect of HCO
concentration to modulate DCT K+ secretion derived from
peritubular events and not the luminal concentration. These workers
found a 65% increase in K+ secretion with alkalosis and a
50% decrease with acidosis, whereas the effects on Na+
transport were substantially less. Examination of rabbit CCD in vitro
confirmed that reduction in peritubular HCO
decreased K+ secretion, with little effect on
Na+ reabsorption, but with an increase in apical membrane
resistance (100). With respect to underlying mechanisms,
pH dependence of cation channels is a prime consideration, and in this
regard, Palmer and Frindt (67) patch clamped rabbit CCD
and demonstrated that alkalosis opened and acidosis closed the
Na+ channel of the luminal membrane. Wang et al.
(112) observed a comparable pH effect on the
small-conductance luminal K+ channel. For these channels,
there was an ~60% reduction in open probability as cytosolic pH was
reduced from 7.4 to 7.0. Strieter et al. (98, 99) used a
mathematical model of rabbit CCD to try to assess the relevance of the
channel kinetics to the pH effect on overall tubular K+
transport, and a summary of their observations is displayed in Table
1. Each section of the table shows the
ion fluxes and epithelial PD for three values of the peritubular
HCO
concentration,
CS(HCO
). When all permeabilities are
fixed or when luminal membrane K+ permeability
(P
) is the only pH-dependent permeability, peritubular HCO
engenders only trivial
changes in Na+ and K+ fluxes. When luminal
Na+ permeability (P
) is pH
dependent, alone or in combination with K+ permeability,
the modulation of K+ flux is substantial, but this comes
with an increase in Na+ reabsorption that appears to be too
high to be compatible with observation. Strieter et al.
(99) considered the possibility that, as in gallbladder
(130), tight junctional Cl
permeability
(P
), might decrease with alkaline pH.
This would act to hyperpolarize the epithelium, increasing K+ secretion while decreasing Na+ reabsorption,
so that when all three permeabilities are pH dependent, there is a
doubling of K+ secretion in going from acidosis to
alkalosis, with virtually no change in Na+ flux. Whether
there is such pH dependence of CCD TJ permeabilities remains to be
examined.
 |
CD: H+ SECRETION |
Net acid excretion by the kidney is determined within the CD as a
consequence of luminal proton secretion and buffer availability. Our
information about this derives from studies of CCD and OMCD segments in
vitro (albeit with significant uncertainty over extrapolation to
conditions in vivo), and to a limited number of micropuncture and
microcatheterization studies and far fewer perfusions of rat IMCD.
Recently, component models of rat CD segments have been concatenated to
yield a simulation of the complete structure, from cortex to papilla
(123). In this model, the OMCD emerges as the most
important site for CD acidification, and the
-intercalated cell of
this segment is shown in Fig. 6. In the
rat, when luminal HCO
is 24 mM, luminal membrane
proton secretion is apportioned 5:2 between the H-K-ATPase and
H+-ATPase transporters (33). Although
cytosolic carbonic anhydrase (CA) is present (58), there
is no membrane-bound luminal CA (11, 26). Luminal proton
secretion is balanced by peritubular base exit, which for OMCD is
almost exclusively HCO
, and it is believed that exit
is almost exclusively via AE1, the peritubular
Cl
/HCO
exchanger. The first evidence for this was the finding that rabbit OMCD proton secretion is eliminated by removal of peritubular Cl
or by application
of a stilbene inhibitor of AE1 (96). Confirming the
importance of Cl
/HCO
exchange are
experiments in which OMCD cell pH was monitored and in which removal of
ambient Cl
reduced peritubular HCO
permeability by 90% (42). Cl
that enters
via AE1 can exit the cell via peritubular Cl
channels.
Although the absolute conductance of the membrane is not known, it has
been established that the major conductive pathway is Cl
selective (47, 65). In the model OMCD, assignment of all Cl
exits to a peritubular conductive pathway did yield an
estimate for the absolute conductance of this pathway (~22
mS/cm2) but also provided a dilemma (121). The
model attempted to accommodate the fact that Cl
channels
typically have a HCO
permeability (54,
69) and used a conservative estimate of 1:8 for the
HCO
-to-Cl
permeability ratio. This
provided a peritubular exit pathway for HCO
that
carried about one-half of the generated HCO
. Thus in
this model, even when peritubular AE1 activity was reduced to near zero, model proton secretion decreased by only one-third. A
number of explanations could be invoked to rationalize this important discrepancy, but one attractive hypothesis is that a substantial portion of peritubular Cl
exits occurs via electroneutral
K-Cl cotransport and not all via Cl
channels. Koeppen
(48) had suggested the existence of this pathway to
rationalize the slow hyperpolarization of SITS-inhibited OMCD cells in
terms of loss of cell Cl
via an electroneutral pathway.
One additional appeal of this hypothesis is that it may also provide a
possible mechanism for blunting cell volume perturbations that are
predicted to accompany any changes in flux through the luminal
H-K-ATPase (121).

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Fig. 6.
Transport pathways across luminal and peritubular
membranes from an intercalated cell of the rat OMCD. Adapted from Ref.
121.
|
|
The IMCD cell, like that of the proximal tubule or thick
ascending limb of Henle, must coordinate both Na+
reabsorption and H+ secretion within a single cell type. A
schematic is shown in Fig. 7
(119). The Na+ fluxes are variable but can be
perhaps nearly as large as those of the proximal tubule (21,
89) and occur without generating a significant transepithelial
PD (36, 43). In view of the reports of thiazide inhibition
of IMCD Na+ reabsorption (77, 129), a luminal
Na-Cl cotransporter appears to be the dominant pathway. To accommodate
this large transcellular Cl
flux, along with the
observation that the peritubular membrane conductance is predominantly
K+ (92), a peritubular K-Cl cotransporter has
been included in the model cell. Luminal membrane H-K-ATPase has been
identified as the major proton transporter (108). As in
rat OMCD, cytosolic CA is present (58) but not within the
luminal membrane (11, 106). Peritubular base exit may
occur as HCO
, via a
Cl
/HCO
exchanger and is thus
susceptible to inhibition with CA inhibition (53, 94).
What has been noteworthy about IMCD is a second mechanism for
peritubular base exit, which has been identified by Wall
(105), and involves ammonia recycling. In this scheme,
peritubular NH
enters on the Na-K-ATPase in
competition for K+ (107), elevates cytosolic
ammonia, and thus promotes diffusive exit of NH3.
Predictions from this mechanism are that base exit and thus luminal
acid secretion 1) should have a CA-insensitive component
that would vary directly with peritubular NH
concentration; 2) should vary inversely with peritubular
K+ concentration; and 3) should vary directly
with the rate of IMCD Na+ reabsorption (i.e.,
Na+ flux through the Na-K-ATPase). In the model IMCD, this
scheme was represented with competition of K+ and
NH
on the Na-K-ATPase, and the first prediction was
realized (120). Inhibition of proton secretion by
peritubular K+ was stronger than expected, because
increasing K+ also produced an increase in cell
Cl
(via K-Cl cotransport) and thus also inhibited the
CA-sensitive component of base exit. The predicted effect of
Na+ reabsorption on proton secretion turned out to be false
(at least in the model) and the results of that calculation are shown
in Fig. 8 (120). In this
simulation, the abcissa for all panels is luminal NaCl concentration,
from 2 to 110 mM. Figure 8A indicates cytosolic conditions,
and Fig. 8C shows the rate of luminal H+
secretion via the H-K-ATPase. Figure 8B, left,
displays the peritubular membrane fluxes of NH
via
the Na-K-ATPase and K+ channels
(GNH4), and in Fig. 8B,
right, are peritubular HCO
fluxes
(GHCO3) via
Cl
/HCO
exchange and Cl
channels. Over the range of luminal NaCl concentrations, the peritubular pump rate for Na+ varied from 0.9 to 6.1 nmol · s
1 · cm
2. In these
calculations, however, there was virtually no change in luminal
membrane H+ secretion (Fig. 8C) or in cell pH
(Fig. 8A, left). Reference to Fig. 8B,
left and right shows that the changes in
Na+ transport led to opposing effects on
NH
cycling and HCO
exit. As
luminal entry of NaCl decreased, there was a decrease in cytosolic
Cl
(Fig. 8A, right) and thus
increased peritubular HCO
exit via the
Cl
/HCO
exchanger (Fig. 8B,
right). Thus this model predicted that with these two base
exit mechanisms operating in parallel, acid secretion would be stable
over a wide range of IMCD Na+ transport. At present,
dissected and perfused IMCD do not transport Na+ well, if
at all, and in situ peritubular conditions are not easily assessed, so
that the prospects for subjecting these model predictions to testing
appear distant.

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Fig. 8.
Impact of luminal Na+ on predicted acid
secretion by a model of rat IMCD epithelium (Fig. 7). Peritubular
conditions are representative of the outer-inner medullary junction.
The abcissa for each panel is luminal NaCl concentration, which varied
from 2 to 110 mM. A: cytosolic conditions. B:
peritubular (Peritub.) membrane fluxes of NH via the
Na-K-ATPase and K+ channels
(GNH4; left) and
peritubular HCO fluxes via
Cl /HCO exchange and Cl
channels. C: rate of luminal proton secretion via the
H-K-ATPase. Adapted from Ref. 120.
|
|
 |
CONCLUSION |
It should be clear that there remains considerable uncertainty as
to our ability to model renal tubular function. The issues presented
here can be formulated as specific questions: How much proximal tubule
water flux traverses the TJ? What is the role of proximal TJs in the
regulation of Na+ reabsorption? Which luminal cell membrane
transporters of proximal tubule have flow-dependent changes in density,
and what is the signaling pathway? What are the important transcellular
pathways for proximal tubule Cl
flux, and which
transporters are modulated by formate? Do CD K+ fluxes and
tubular permeabilities measured in vitro correspond to those in vivo?
What are the Cl
exit pathways in OMCD, and in particular,
is a K-Cl cotransporter important? Does variation in H-K-ATPase
activity in OMCD produce derangements in cell volume, or is there
coordinate activation of other pathways? Does the IMCD shift base exit
between CA-dependent and CA-independent mechanisms to maintain stable
proton secretion in the face of variable Na+ fluxes? This
list of questions hardly exhausts the uncertainties that have come to
the fore in the published model investigations. Some of the issues have
had intense experimental interest well before they were cast as
modeling problems, but some truly did arise out of model exploration.
What should also be clear is that some of these questions are
quantitatively very important; i.e., the essence of some phenomena have
not been captured, and this is not just an effort to fine-tune a nearly
completed picture. What must also be acknowledged is that, for all its
obvious value to understanding the kidney, structural information alone
will not suffice to answer many of our most important questions, and there is no escape from the conclusion that additional functional data
are required. It may be legitimate to question whether existing experimental technology is up to the task, or whether new techniques are necessary. However, at the level of detail considered here, the
available numerical methods and computing power are certainly up to the
task of simulating renal tubular transport. With respect to model
refinement, incorporating more biophysical detail about individual
transporters will no doubt enhance model reliability, but ultimate
confidence in these tubular models will still be contingent on critical
experimental information to be developed at the tubular level.
 |
ACKNOWLEDGEMENTS |
This work was supported by Public Health Service Grant
1-RO1-DK-29857 from the National Institutes of Health.
 |
FOOTNOTES |
Address for reprints and other correspondence: A. Weinstein, Department of Physiology and Biophysics, Weill Medical
College of Cornell University, 1300 York Ave., New York, New York 10021 (E-mail: alan{at}nephron.med.cornell.edu).
10.1152/ajprenal.00330.2002
 |
REFERENCES |
1.
Alpern, RJ,
Howlin KJ,
and
Preisig PA.
Active and passive components of chloride transport in the rat proximal convoluted tubule.
J Clin Invest
76:
1360-1366,
1985[ISI][Medline].
2.
Amorim, JBO,
and
Malnic G.
V1 receptors in luminal action of vasopressin on distal K+ secretion.
Am J Physiol Renal Physiol
278:
F809-F816,
2000[Abstract/Free Full Text].
3.
Aronson, PS,
and
Giebisch G.
Mechanisms of chloride transport in the proximal tubule.
Am J Physiol Renal Physiol
273:
F179-F192,
1997[Abstract/Free Full Text].
4.
Bartoli, E,
Conger JD,
and
Earley LE.
Effect of intraluminal flow on proximal tubular reabsorption.
J Clin Invest
52:
843-849,
1973[ISI][Medline].
5.
Basmadjian, D,
Dykes DS,
and
Baines AD.
Flow through brushborders and similar protuberant wall structures.
J Membr Biol
56:
183-190,
1980[ISI][Medline].
6.
Bello-Reuss, E.
Effect of catecholamines on fluid reabsorption by the isolated proximal convoluted tubule.
Am J Physiol Renal Fluid Electrolyte Physiol
238:
F347-F352,
1980[Abstract/Free Full Text].
7.
Bentzel, CJ,
and
Reczek PR.
Permeability changes in Necturus proximal tubule during volume expansion.
Am J Physiol Renal Fluid Electrolyte Physiol
234:
F225-F234,
1978[Abstract/Free Full Text].
8.
Berry, CA.
Water permeability and pathways in the proximal tubule.
Am J Physiol Renal Fluid Electrolyte Physiol
245:
F279-F294,
1983[Abstract/Free Full Text].
9.
Boulpaep, EL.
Permeability changes of the proximal tubule of Necturus during saline loading.
Am J Physiol
222:
517-531,
1972[Free Full Text].
10.
Brenner, BM,
Troy JL,
and
Daugharty TM.
On the mechanism of inhibition in fluid reabsorption by the renal proximal tubule of the volume-expanded rat.
J Clin Invest
50:
1596-1602,
1971[ISI][Medline].
11.
Brown, D,
Zhu XL,
and
Sly WS.
Localization of membrane-associated carbonic anhydrase type IV in kidney epithelial cells.
Proc Natl Acad Sci USA
87:
7457-7461,
1990[Abstract].
12.
Burckhardt, BC,
Sato K,
and
Frömter E.
Electrophysiological analysis of bicarbonate permeation across the peritubular cell membrane of rat kidney proximal tubule. I. Basic observations.
Pflügers Arch
401:
34-42,
1984[ISI][Medline].
13.
Burg, MB,
and
Orloff J.
Control of fluid absorption in the renal proximal tubule.
J Clin Invest
47:
2016-2024,
1968[ISI][Medline].
14.
Cardinal, J,
Lapointe JY,
and
Laprade R.
Luminal and peritubular ionic substitutions and intracellular potential of the rabbit proximal convoluted tubule.
Am J Physiol Renal Fluid Electrolyte Physiol
247:
F352-F364,
1984[Abstract/Free Full Text].
15.
Carpi-Medina, P,
Gonzalez E,
and
Whittembury G.
Cell osmotic water permeability of isolated rabbit proximal convoluted tubules.
Am J Physiol Renal Fluid Electrolyte Physiol
244:
F554-F563,
1983[Abstract/Free Full Text].
16.
Cassola, AC,
Mollehauer M,
and
Frömter E.
The intracellular chloride activity of rat kidney proximal tubular cells.
Pflügers Arch
399:
259-265,
1983[ISI][Medline].
17.
Chan, YL,
Biagi B,
and
Giebisch G.
Control mechanisms of bicarbonate transport across the rat proximal convoluted tubule.
Am J Physiol Renal Fluid Electrolyte Physiol
242:
F532-F543,
1982[Abstract/Free Full Text].
18.
Chang, H,
and
Fujita T.
A numerical model of the renal distal tubule.
Am J Physiol Renal Physiol
276:
F931-F951,
1999[Abstract/Free Full Text].
19.
Chang, H,
and
Fujita T.
A numerical model of acid-base transport in rat distal tubule.
Am J Physiol Renal Physiol
281:
F222-F243,
2001[Abstract/Free Full Text].
20.
Deen, WM,
Lazzara MJ,
and
Myers BD.
Structural determinants of glomerular permeability.
Am J Physiol Renal Physiol
281:
F579-F596,
2001[Abstract/Free Full Text].
21.
Diezi, J,
Michoud P,
Aceves J,
and
Giebisch G.
Micropuncture study of electrolyte transport across papillary collecting duct of the rat.
Am J Physiol
224:
623-634,
1973[Free Full Text].
22.
Dirks, JH,
Cirksena WJ,
and
Berliner RW.
The effect of saline infusion on sodium reabsorption by the proximal tubule of the dog.
J Clin Invest
44:
1160-1170,
1965[ISI].
23.
Du, ZP,
Weinstein AM,
Weinbaum S,
and
Wang T.
Stimulation of Na and HCO3 absorption by increasing tubular flow rate in mouse proximal tubules (Abstract).
FASEB J
16:
A54,
2002.
24.
Earley, LE,
Martino JA,
and
Friedler RM.
Factors affecting sodium reabsorption by the proximal tubule as determined during blockade of distal sodium reabsorption.
J Clin Invest
45:
1668-1684,
1966[ISI][Medline].
25.
Flessner, MF,
Wall SM,
and
Knepper MA.
Permeabilities of rat collecting duct segments to NH3 and NH
.
Am J Physiol Renal Fluid Electrolyte Physiol
260:
F264-F272,
1991[Abstract/Free Full Text].
26.
Flessner, MF,
Wall SM,
and
Knepper MA.
Ammonium and bicarbonate transport in rat outer medullary collecting ducts.
Am J Physiol Renal Physiol
262:
F1-F7,
1992[Abstract/Free Full Text].
27.
Franglen, GT,
McGarry E,
and
Spencer AG.
Renal function and the excretion of potassium in acute alkalosis.
J Physiol
121:
35-45,
1953[ISI].
28.
Fraser, WD,
and
Baines AD.
Application of a fiber-matrix model to transport in renal tubules.
J Gen Physiol
94:
863-879,
1989[Abstract].
29.
Frömter, E.
Solute transport across epithelia: what can we learn from micropuncture studies on kidney tubules?
J Physiol
288:
1-31,
1979[ISI][Medline].
30.
Frömter, E,
and
Gessner K.
Active transport potentials, membrane diffusion potentials and streaming potentials across rat kidney proximal tubule.
Pflügers Arch
351:
85-98,
1974[ISI][Medline].
31.
Frömter, E,
Rumrich G,
and
Ullrich KJ.
Phenomenologic description of Na+, Cl
and HCO
absorption from proximal tubules.
Pflügers Arch
343:
189-220,
1973[ISI][Medline].
32.
Garvin, JL,
and
Knepper MA.
Bicarbonate and ammonia transport in isolated pefused rat proximal straight tubules.
Am J Physiol Renal Fluid Electrolyte Physiol
253:
F277-F281,
1987[Abstract/Free Full Text].
33.
Gifford, JD,
Rome L,
and
Galla JH.
H-K-ATPase activity in rat collecting duct segments.
Am J Physiol Renal Fluid Electrolyte Physiol
262:
F692-F695,
1992[Abstract/Free Full Text].
34.
Gonzalez, E,
Carpi-Medina P,
and
Whittembury G.
Cell osmotic water permeability of isolated rabbit proximal straight tubules.
Am J Physiol Renal Fluid Electrolyte Physiol
242:
F321-F330,
1982[Abstract/Free Full Text].
35.
Good, DW,
and
Wright FS.
Luminal influences on potassium secretion: sodium concentration and fluid flow rate.
Am J Physiol Renal Fluid Electrolyte Physiol
236:
F192-F205,
1979[Abstract/Free Full Text].
36.
Graber, ML,
Bengele HH,
Schwartz JH,
and
Alexander EA.
pH and PCO2 profiles of the rat inner medullary collecting duct.
Am J Physiol Renal Fluid Electrolyte Physiol
241:
F659-F668,
1981[Abstract/Free Full Text].
37.
Green, R,
Giebisch G,
Unwin R,
and
Weinstein AM.
Coupled water transport by rat proximal tubule.
Am J Physiol Renal Fluid Electrolyte Physiol
261:
F1046-F1054,
1991[Abstract/Free Full Text].
38.
Green, R,
Windhager EE,
and
Giebisch G.
Protein oncotic pressure effects on proximal tubular fluid movement in the rat.
Am J Physiol
226:
265-276,
1974[Free Full Text].
39.
Guo, P,
Weinstein AM,
and
Weinbaum S.
A hydrodynamic mechanosensory hypothesis for brush border microvilli.
Am J Physiol Renal Physiol
279:
F698-F712,
2000[Abstract/Free Full Text].
40.
Guo, P,
Weinstein AM,
and
Weinbaum S.
An ultrastructural model for the tight junction (TJ) strands in rat proximal tubule epithelium (Abstract).
FASEB J
16:
A53,
2002.
41.
Häberle, DA,
Shiigai TT,
Maier G,
Schiffl H,
and
Davis JM.
Dependency of proximal tubular fluid transport on the load of glomerular filtrate.
Kidney Int
20:
18-28,
1981[ISI][Medline].
42.
Hays, SR,
and
Alpern RJ.
Basolateral membrane Na+-independent Cl/HCO3 exchange in the inner stripe of the rabbit outer medullary collecting tubule.
J Gen Physiol
95:
347-367,
1990[Abstract].
43.
Hayslett, JP,
Backman KA,
and
Schon DA.
Electrical properties of the medullary collecting duct in the rat.
Am J Physiol Renal Fluid Electrolyte Physiol
239:
F258-F264,
1980[Abstract/Free Full Text].
44.
Hierholzer, K,
Kawamura S,
Seldin DW,
Kokko JP,
and
Jacobson HR.
Reflection coefficients of various substrates across superficial and juxtamedullary proximal convoluted segments of rabbit nephrons.
Miner Electrolyte Metab
3:
172-180,
1980[ISI].
45.
Huss, RE,
and
Marsh DJ.
A model of NaCl and water flow through paracellular pathways of renal proximal tubules.
J Membr Biol
23:
305-347,
1975[ISI][Medline].
46.
Karniski, LP,
and
Aronson PS.
Chloride/formate exchange with formic acid recycling: a mechanism of active chloride transport across epithelial membranes.
Proc Natl Acad Sci USA
82:
6362-6365,
1985[Abstract].
47.
Koeppen, BM.
Conductive properties of the rabbit outer medullary collecting duct: inner stripe.
Am J Physiol Renal Fluid Electrolyte Physiol
248:
F500-F506,
1985[Abstract/Free Full Text].
48.
Koeppen, BM.
Electrophysiology of collecting duct H+ secretion: effect of inhibitors.
Am J Physiol Renal Fluid Electrolyte Physiol
256:
F79-F84,
1989[Abstract/Free Full Text].
49.
Kottra, G,
and
Frömter E.
Functional properties of the paracellular pathway in some leaky epithelia.
Exp Biol
106:
217-229,
1983.
50.
Kovbasnjuk, O,
Leader JP,
Weinstein AM,
and
Spring KR.
Water does not flow across the tight junctions of MDCK cell epithelium.
Proc Natl Acad Sci USA
95:
6526-6530,
1998[Abstract/Free Full Text].
51.
Krahn, TA,
Aronson PS,
and
Weinstein AM.
Weak acid permeability of a villous membrane: formic acid transport across rat proximal tubule.
Bull Math Biol
56:
459-490,
1994[ISI][Medline].
52.
Krahn, TA,
and
Weinstein AM.
Acid/base transport in a model of the proximal tubule brush border: impact of carbonic anhydrase.
Am J Physiol Renal Fluid Electrolyte Physiol
270:
F344-F355,
1996[Abstract/Free Full Text].
53.
Kraut, JA,
Hart D,
and
Nord EP.
Basolateral Na-independent Cl-HCO3 exchange in primary cultures of rat IMCD cells.
Am J Physiol Renal Fluid Electrolyte Physiol
263:
F401-F410,
1992[Abstract/Free Full Text].
54.
Kunzelmann, K,
Gerlach L,
Froebe U,
and
Greger R.
Bicarbonate permeability of epithelial chloride channels.
Pflügers Arch
417:
616-621,
1991[ISI][Medline].
55.
Lamprecht, G,
Weinman EJ,
and
Yun CH.
The role of NHERF and E3KARP in the cAMP-mediated inhibition of NHE-3.
J Biol Chem
273:
29972-29978,
1998[Abstract/Free Full Text].
56.
Layton, HE,
Knepper MA,
and
Chou C.
Permeability criteria for effective function of passive countercurrent multiplier.
Am J Physiol Renal Fluid Electrolyte Physiol
270:
F9-F20,
1996[Abstract/Free Full Text].
57.
Lewy, JE,
and
Windhager EE.
Peritubular control of proximal tubular fluid reabsorption in the rat kidney.
Am J Physiol
214:
943-954,
1968[Free Full Text].
58.
Lonnerholm, G,
and
Ridderstrale Y.
Intracellular distribution of carbonic anhydrase in the rat kidney.
Kidney Int
17:
162-174,
1980[ISI][Medline].
59.
Maddox, DA,
Fortin SM,
Tartini A,
Barnes WD,
and
Gennari FJ.
Effect of acute changes in glomerular filtration rate on Na+/H+ exchange in rat renal cortex.
J Clin Invest
89:
1296-1303,
1992[ISI][Medline].
60.
Malnic, G,
de Mello Aires M,
and
Giebisch G.
Potassium transport across renal distal tubules during acid-base disturbances.
Am J Physiol
221:
1192-1208,
1971[Free Full Text].
61.
Malnic, G,
Klose RM,
and
Giebisch G.
Micropuncture study of renal potassium excretion in the rat.
Am J Physiol
206:
674-686,
1964[Abstract/Free Full Text].
62.
Malnic, G,
Klose RM,
and
Giebisch G.
Micropuncture study of distal tubular potassium and sodium transport in rat nephron.
Am J Physiol
211:
529-547,
1966[Free Full Text].
63.
Martino, JA,
and
Earley LE.
Demonstration of a role of physical factors as determinants of the natriuretic response to volume expansion.
J Clin Invest
46:
1963-1978,
1967[ISI][Medline].
64.
Maunsbach, AB,
and
Christensen EI.
Functional ultrastructure of the proximal tubule.
In: Handbook of Physiology. Renal Physiology. Bethesda, MD: Am Physiol Soc, 1992, sect. 8, vol. I, chapt. 2, p. 41-107.
65.
Muto, S,
Yasoshima K,
Yoshitomi K,
Imai M,
and
Asano Y.
Electrophysiological identification of alpha and beta-intercalated cells and their distribution along the rabbit distal nephron segments.
J Clin Invest
86:
1829-1839,
1990[ISI][Medline].
66.
O'Neil, RG,
and
Helman SI.
Transport characteristics of renal collecting tubules: influences of DOCA and diet.
Am J Physiol Renal Fluid Electrolyte Physiol
233:
F544-F558,
1977[Abstract/Free Full Text].
67.
Palmer, LG,
and
Frindt G.
Effects of cell Ca and pH on Na channels from rat cortical collecting tubule.
Am J Physiol Renal Fluid Electrolyte Physiol
253:
F333-F339,
1987[Abstract/Free Full Text].
68.
Peterson, OW,
Gushwa LC,
and
Blantz RC.
An analysis of glomerular-tubular balance in the rat proximal tubule.
Pflügers Arch
407:
221-227,
1986[ISI][Medline].
69.
Poulsen, JH,
Fischer H,
Illek B,
and
Machen TE.
Bicarbonate conductance and pH regulatory capability of cystic fibrosis transmembrane conductance regulator.
Proc Natl Acad Sci USA
91:
5340-5344,
1994[Abstract].
70.
Preisig, PA.
Luminal flow rate regulates proximal tubule H+-HCO
transporters.
Am J Physiol Renal Fluid Electrolyte Physiol
262:
F47-F54,
1992[Abstract/Free Full Text].
71.
Preisig, PA,
and
Alpern RJ.
Contributions of cellular leak pathways to net NaHCO3 and NaCl absorption.
J Clin Invest
83:
1859-1867,
1989[ISI][Medline].
72.
Preisig, PA,
and
Berry CA.
Evidence for transcellular osmotic water flow in rat proximal tubules.
Am J Physiol Renal Fluid Electrolyte Physiol
249:
F124-F131,
1985[Abstract/Free Full Text].
73.
Ramsey, CR,
Berndt T,
and
Knox FG.
Effect of volume expansion on the paracellular flux of lanthanum in the proximal tubule.
J Am Soc Nephrol
9:
1147-1152,
1998[Abstract].
74.
Rector, FC, Jr,
and
Berry CA.
Role of the paracellular pathway in reabsorption of solutes and water by proximal convoluted tubule of the mammalian kidney.
In: The Paracellular Pathway, edited by Bradley SE,
and Purcell EF.. New York: Josiah Macy Jr. Foundation, 1982, p. 135-157.
75.
Roberts, KE,
Magida MG,
and
Pitts RF.
Relationship between potassium and bicarbonate in blood and urine.
Am J Physiol
172:
47-54,
1953[ISI].
76.
Rocha, AS,
and
Kudo LH.
Water, urea, sodium, chloride, and potassium transport in the in vitro isolated perfused papillary collecting duct.
Kidney Int
22:
485-491,
1982[ISI][Medline].
77.
Rocha, AS,
and
Kudo LH.
Factors governing sodium and chloride transport across the inner medullary collecting duct.
Kidney Int
38:
654-667,
1990[ISI][Medline].
78.
Romano, G,
Favret G,
Federico E,
and
Bartoli E.
The effect of intraluminal flow rate on glomerulotubular balance in the proximal tubule of the rat kidney.
Exp Physiol
81:
95-105,
1996[Abstract].
79.
Sackin, H,
and
Boulpaep EL.
Models for coupling of salt and water transport.
J Gen Physiol
66:
671-733,
1975[Abstract].
80.
Schafer, JA,
Patlak CS,
and
Andreoli TE.
A component of fluid absorption linked to passive ion flows in the superficial pars recta.
J Gen Physiol
66:
445-471,
1975[Abstract].
81.
Schafer, JA,
and
Troutman SL.
Potassium transport in cortical collecting tubules from mineralocorticoid-treated rat.
Am J Physiol Renal Fluid Electrolyte Physiol
253:
F76-F88,
1987[Abstract/Free Full Text].
82.
Schild, L,
Aronson PS,
and
Giebisch G.
Effects of apical membrane Cl
-formate exchange on cell volume in rabbit proximal tubule.
Am J Physiol Renal Fluid Electrolyte Physiol
258:
F530-F536,
1990[Abstract/Free Full Text].
83.
Schild, L,
Aronson PS,
and
Giebisch G.
Basolateral transport pathways for K+and Cl
in rabbit proximal tubule: effects on cell volume.
Am J Physiol Renal Fluid Electrolyte Physiol
260:
F101-F109,
1991[Abstract/Free Full Text].
84.
Schild, L,
Giebisch G,
Karniski LP,
and
Aronson PS.
Effect of formate on volume reabsorption in the rabbit proximal tubule.
J Clin Invest
79:
32-38,
1987[ISI][Medline].
85.
Schnermann, J,
Chou C,
Ma T,
Traynor T,
Knepper MA,
and
Verkman AS.
Defective proximal tubular fluid reabsorption in transgenic aquaporin-1 null mice.
Proc Natl Acad Sci USA
95:
9660-9664,
1998[Abstract/Free Full Text].
86.
Schnermann, J,
Wahl M,
Liebau G,
and
Fischbach H.
Balance between tubular flow rate and net fluid reabsorption in the proximal convolution of the rat kidney.
Pflügers Arch
304:
90-103,
1968[ISI][Medline].
87.
Schwartz, GJ,
and
Burg MB.
Mineralocorticoid effects on cation transport by cortical collecting tubules in vitro.
Am J Physiol Renal Fluid Electrolyte Physiol
235:
F576-F585,
1978[Free Full Text].
88.
Seely, JF.
Effects of peritubular oncotic pressure on rat proximal tubule electrical resistance.
Kidney Int
4:
28-35,
1973[ISI][Medline].
89.
Sonnenberg, H.
Medullary collecting-duct function in antidiuretic and in salt- or water-diuretic rats.
Am J Physiol
226:
501-506,
1974[Free Full Text].
90.
Spitzer, A,
and
Windhager EE.
Effect of peritubular oncotic pressure changes on proximal tubular fluid reabsorption.
Am J Physiol
218:
1188-1193,
1970[Free Full Text].
91.
Spring, KR.
A parallel path model for Necturus proximal tubule.
J Membr Biol
13:
323-352,
1973[ISI][Medline].
92.
Stanton, BA.
Characterization of apical and basolateral membrane conductances of rat inner medullary collecting duct.
Am J Physiol Renal Fluid Electrolyte Physiol
256:
F862-F868,
1989[Abstract/Free Full Text].
93.
Stanton, BA,
and
Giebisch G.
Effect of pH on potassium transport by renal distal tubule.
Am J Physiol Renal Fluid Electrolyte Physiol
242:
F544-F551,
1982[Abstract/Free Full Text].
94.
Star, RA.
Basolateral membrane sodium-independent Cl/HCO3 exchanger in rat inner medullary collecting duct cell.
J Clin Invest
85:
1959-1966,
1990[ISI][Medline].
95.
Stokes, JB.
Potassium secretion by cortical collecting tubule: relation to sodium absorption, luminal sodium concentration, and transepithelial voltage.
Am J Physiol Renal Fluid Electrolyte Physiol
241:
F395-F402,
1981[Abstract/Free Full Text].
96.
Stone, DK,
Seldin DW,
Kokko JP,
and
Jacobson HR.
Anion dependence of rabbit medullary collecting duct acidification.
J Clin Invest
71:
1505-1508,
1983[ISI][Medline].
97.
Stoner, LC,
Burg MB,
and
Orloff J.
Ion transport in cortical collecting tubule; effect of amiloride.
Am J Physiol
227:
453-459,
1974[Free Full Text].
98.
Strieter, J,
Stephenson JL,
Giebisch GH,
and
Weinstein AM.
A mathematical model of the cortical collecting tubule of the rabbit.
Am J Physiol Renal Fluid Electrolyte Physiol
263:
F1063-F1075,
1992[Abstract/Free Full Text].
99.
Strieter, J,
Weinstein AM,
Giebisch GH,
and
Stephenson JL.
Regulation of potassium transport in a mathematical model of the cortical collecting tubule.
Am J Physiol Renal Fluid Electrolyte Physiol
263:
F1076-F1086,
1992[Abstract/Free Full Text].
100.
Tabei, K,
Muto S,
Furuya H,
Sakairi Y,
Ando Y,
and
Asano Y.
Potassium secretion is inhibited by metabolic acidosis in rabbit cortical collecting ducts in vitro.
Am J Physiol Renal Fluid Electrolyte Physiol
268:
F490-F495,
1995[Abstract/Free Full Text].
101.
Thomas, SR.
Cycles and separations in a model of the renal medulla.
Am J Physiol Renal Physiol
275:
F671-F690,
1998[Abstract/Free Full Text].
102.
Tomita, K,
Pisano JJ,
and
Knepper MA.
Control of sodium and potassium transport in the cortical collecting duct of the rat. Effects of bradykinin, vasopressin, and deoxycorticosterone.
J Clin Invest
77:
132-136,
1986.
103.
Toussaint, C,
and
Vereerstraeten P.
Effects of blood pH changes on potassium excretion in the dog.
Am J Physiol
202:
768-772,
1962[Abstract/Free Full Text].
104.
Tripathi, S,
and
Boulpaep EL.
Cell membrane water permeabilities and streaming currents in Ambystoma proximal tubule.
Am J Physiol Renal Fluid Electrolyte Physiol
255:
F188-F203,
1988[Abstract/Free Full Text].
105.
Wall, SM.
NH
augments net acid secretion by a ouabain-sensitive mechanism in isolated perfused inner medullary collecting ducts.
Am J Physiol Renal Fluid Electrolyte Physiol
270:
F432-F439,
1996[Abstract/Free Full Text].
106.
Wall, SM,
Flessner MF,
and
Knepper MA.
Distribution of luminal carbonic anhydrase activity along rat inner medullary collecting duct.
Am J Physiol Renal Fluid Electrolyte Physiol
260:
F738-F748,
1991[Abstract/Free Full Text].
107.
Wall, SM,
and
Koger LM.
NH
transport mediated by Na-K-ATPase in rat inner medullary collecting duct.
Am J Physiol Renal Fluid Electrolyte Physiol
267:
F660-F670,
1994[Abstract/Free Full Text].
108.
Wall, SM,
Truong AV,
and
DuBose TD, Jr.
H+,K+-ATPase mediates net acid secretion in rat terminal inner medullary collecting duct.
Am J Physiol Renal Fluid Electrolyte Physiol
271:
F1037-F1044,
1996[Abstract/Free Full Text].
109.
Wang, T,
Egbert AL, Jr,
Abbiati T,
Aronson PS,
and
Giebisch G.
Mechanisms of stimulation of proximal tubule chloride transport by formate and oxalate.
Am J Physiol Renal Fluid Electrolyte Physiol
271:
F446-F450,
1996[Abstract/Free Full Text].
110.
Wang, T,
Giebisch G,
and
Aronson PS.
Effects of formate and oxalate on volume absorption in rat proximal tubule.
Am J Physiol Renal Fluid Electrolyte Physiol
263:
F37-F42,
1992[Abstract/Free Full Text].
111.
Wang, T,
Yang C,
Abbiati T,
Shull GE,
Giebisch G,
and
Aronson PS.
Essential role of NHE3 in facilitating formate-dependent NaCl absorption in the proximal tubule.
Am J Physiol Renal Physiol
281:
F288-F292,
2001[Abstract/Free Full Text].
112.
Wang, W,
Schwab A,
and
Giebisch G.
Regulation of small-conductance K channel in apical membrane of rat cortical collecting tubule.
Am J Physiol Renal Fluid Electrolyte Physiol
259:
F494-F502,
1990[Abstract/Free Full Text].
113.
Weinbaum, S,
Guo P,
and
You LD.
A new view of mechanotransduction and strain amplification in cells with microvilli and cell process.
Biorheology
38:
119-142,
2001[ISI][Medline].
114.
Weinstein, AM.
A nonequilibrium thermodynamic model of the rat proximal tubule epithelium.
Biophys J
44:
153-170,
1983[Abstract].
115.
Weinstein, AM.
Convective paracellular solute flux: a source of ion-ion interaction in the epithelial transport equations.
J Gen Physiol
89:
501-518,
1987[Abstract].
116.
Weinstein, AM.
Modeling the proximal tubule: complications of the paracellular pathway.
Am J Physiol Renal Fluid Electrolyte Physiol
254:
F297-F305,
1988[Abstract/Free Full Text].
117.
Weinstein, AM.
Glomerulotubular balance in a mathematical model of the proximal nephron.
Am J Physiol Renal Fluid Electrolyte Physiol
258:
F612-F626,
1990[Abstract/Free Full Text].
118.
Weinstein, AM.
Chloride transport in a mathematical model of the rat proximal tubule.
Am J Physiol Renal Fluid Electrolyte Physiol
263:
F784-F798,
1992[Abstract/Free Full Text].
119.
Weinstein, AM.
A mathematical model of the inner medullary collecting duct of the rat: pathways for Na and K transport.
Am J Physiol Renal Physiol
274:
F841-F855,
1998[Abstract/Free Full Text].
120.
Weinstein, AM.
A mathematical model of the inner medullary collecting duct of the rat:acid/base transport.
Am J Physiol Renal Physiol
274:
F856-F867,
1998[Abstract/Free Full Text].
121.
Weinstein, AM.
A mathematical model of the outer medullary collecting duct of the rat.
Am J Physiol Renal Physiol
279:
F24-F45,
2000[Abstract/Free Full Text].
122.
Weinstein, AM.
A mathematical model of rat cortical collecting duct: determinants of the transtubular potassium gradient.
Am J Physiol Renal Physiol
280:
F1072-F1092,
2001[Abstract/Free Full Text].
123.
Weinstein, AM.
A mathematical model of rat collecting duct. I. Flow effects on transport and urinary acidification.
Am J Physiol Renal Physiol
283:
F1237-F1251,
2002[Abstract/Free Full Text].
124.
Welling, PA,
and
O'Neil RG.
Ionic conductive properties of rabbit proximal straight tubule basolateral membrane.
Am J Physiol Renal Fluid Electrolyte Physiol
258:
F940-F950,
1990[Abstract/Free Full Text].
125.
Welling, PA,
and
O'Neil RG.
Cell swelling activates basolateral membrane Cl and K conductances in rabbit proximal tubule.
Am J Physiol Renal Fluid Electrolyte Physiol
258:
F951-F962,
1990[Abstract/Free Full Text].
126.
Whittembury, G,
Malnic G,
Mello-Aires M,
and
Amorena C.
Solvent drag of sucrose during absorption indicates paracellular water flow in the rat kidney proximal tubule.
Pflügers Arch
412:
541-547,
1988[ISI][Medline].
127.
Whittembury, G,
Pas-Aliaga A,
Biondi A,
Carpi-Medina P,
Gonzalez E,
and
Linares H.
Pathways for volume flow and volume regulation in leaky epithelia.
Pflügers Arch
405:
S17-S22,
1985[ISI][Medline].
128.
Wilcox, CS,
and
Baylis C.
Glomerular-tubular balance and proximal regulation.
In: The Kidney: Physiology and Pathophysiology, edited by Seldin DW,
and Giebisch G.. New York: Raven, 1985, p. 985-1012.
129.
Wilson, DR,
Honrath U,
and
Sonnenberg H.
Thiazide diuretic effect on medullary collecting duct function in the rat.
Kidney Int
23:
711-716,
1983[ISI][Medline].
130.
Wright, EM,
and
Diamond JM.
Effects of pH and polyvalent cations on the selective permeability of gallbladder epithelium to monovalent ions.
Biochim Biophys Acta
163:
57-74,
1968[ISI][Medline].
Am J Physiol Renal Fluid Electrolyte Physiol 284(5):F871-F884
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