Am J Physiol Renal Physiol
279: F468–F481, 2000.
Inner medullary lactate production and accumulation:
a vasa recta model
S. RANDALL THOMAS
Institut National de la Santé et de la Recherche Médicale Unité 467,
Necker Faculty of Medicine, F-75015 Paris, France
Received 17 September 1999; accepted in final form 15 May 2000
glucose; descending vasa recta; blood flow; urine concentrating mechanism; anaerobic glycolysis
Address for reprint requests and other correspondence: S. R.
Thomas, INSERM U.467, Necker Faculty of Medicine, F-75015
Paris, France (E-mail: [email protected]).
F468
Glossary
AVR
DVR
IMVR
IM
OM
IMBF
IMCD
LDL
LAL
N(x)
cGLU
cLAC
Fji
Ji
PGLU
PLAC
ksh
x
L
␴i
ascending vasa recta
descending vasa recta
inner medullary vasa recta
inner medulla
outer medulla
DVR
inner medullary blood flow (⫽FV
(0))
inner medullary collecting duct
long descending Henle’s loop
long ascending Henle’s loop
number of DVR at depth x
glucose concentration
lactate concentration
tubular flow of i in tube j (pmol/min)
transmural flux of i (pmol 䡠 min⫺1 䡠 mm⫺1)
glucose permeability across DVR
lactate permeability across DVR
coefficient for exponential decay of N(x)
distance from OM/IM border (mm)
distance to papillary tip
reflection coefficient of solute i
Subscripts and Superscripts
i
j
glucose, lactate, or volume
DVR, AVR, or SH (for shunt flows)
the possibility that countercurrent
recycling of lactate produced continually in the renal
inner medulla (IM) by anaerobic glycolysis might lead
to an axial gradient of interstitial osmoles.1 By serving
as “external osmoles” (i.e., external to the tubular
fluid), such osmoles could contribute to the single effect
for countercurrent multiplication in the IM (20).
The extent to which a metabolically produced external solute can accumulate an axial interstitial (and
vasa recta) concentration gradient by countercurrent
exchange will depend on at least four factors: its rate of
production within the medulla, its descending vasa
recta permeability (a high value favors recycling), inner medullary blood flow (IMBF) (low IMBF favors
THIS STUDY EXPLORES
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.
1
I am not speaking here of the intracellular osmolytes that protect
IM cells from the high external urea and salt concentrations.
0363-6127/00 $5.00 Copyright © 2000 the American Physiological Society
http://www.ajprenal.org
Downloaded from http://ajprenal.physiology.org/ by 10.220.33.4 on June 18, 2017
Thomas, S. Randall. Inner medullary lactate production and accumulation: a vasa recta model. Am J Physiol
Renal Physiol 279: F468–F481, 2000.— Since anaerobic
glycolysis yields two lactates for each glucose consumed
and since it is reported to be a major source of ATP for
inner medullary (IM) cell maintenance, it is a likely source
of “external” IM osmoles. It has long been known that such
an osmole source could theoretically contribute to the
“single-effect” of the urine concentrating mechanism, but
there was previously no suggestion of a plausible source. I
used numerical simulation to estimate axial gradients of
lactate and glucose that might be accumulated by countercurrent recycling in IM vasa recta (IMVR). Based on measurements in other tissues, anaerobic glycolysis (assumed
to be independent of diuretic state) was estimated to consume ⬃20% of the glucose delivered to the IM. IM tissue
mass and axial distribution of loops and vasa recta were
according to reported values for rat and other rodents.
Lactate (PLAC) and glucose (PGLU) permeabilities were
varied over a range of plausible values. The model results
suggest that PLAC of 100 ⫻ 10⫺5 cm/s (similar to measured
permeabilities for other small solutes) is sufficiently high
to ensure efficient lactate recycling. By contrast, it was
necessary in the model to reduce PGLU to a small fraction
of this value (1/25th) to avoid papillary glucose depletion
by countercurrent shunting. The results predict that IM
lactate production could suffice to build a significant
steady-state axial lactate gradient in the IM interstitium.
Other modeling studies (Jen JF and Stephenson JL. Bull
Math Biol 56: 491–514, 1994; and Thomas SR and Wexler
AS. Am J Physiol Renal Fluid Electrolyte Physiol 269:
F159–F171, 1995) have shown that 20–100 mosmol/
kgH2O of unspecified external, interstitial, osmolytes
could greatly improve IM concentrating ability. The
present study gives several plausible scenarios consistent
with accumulation of metabolically produced lactate osmoles, although only to the lower end of this range. For
example, if 20% of entering glucose is consumed, the model
predicts that papillary lactate would attain about 15 mM
assuming vasa recta outflow is increased 30% by fluid
absorbed from the nephrons and collecting ducts and that
this lactate gradient would double if IM blood flow were
reduced by one-half, as may occur in antidiuresis. Several
experimental tests of the hypothesis are indicated.
GLYCOLYSIS AND THE URINE CONCENTRATING MECHANISM
The present study uses a mathematical model of
inner medullary vasa recta (IMVR), first, to discover
conditions under which lactate produced by IM anaerobic glycolysis might accumulate a significant axial
concentration gradient and, second, to propose experimental tests of this idea. Using a conservative estimate
of IM glycolytic lactate production, based on glycolytic
rates measured in the kidney and in other tissues, I
calculate projected axial IM gradients of lactate and
glucose for a range of assumed vasa recta permeabilities to lactate and glucose. I also briefly treat the case
of species with different percentages of long loops
reaching all the way to the papillary tip. I find it
plausible that lactate accumulation could be considerable in the deep IM, though volume uptake from the
nephrons (resulting in part from the metabolic osmole
production) will limit the tendency. It remains for one
to apply this idea in medullary models incorporating
the nephrons and collecting ducts explicitly to see how
this extratubular metabolic osmole production might
affect salt and urea recycling and, thus, the IM osmotic
gradient.
MODEL DESCRIPTION
Since the nephron is essentially impermeable to
small sugars, glucose and lactate are distributed only
among the interstitium, the microcirculation, and of
course the cytoplasm of IM cells (i.e., interstitial cells,
epithelial cells, and cells of the capillary walls). If, in
addition, we consider only the steady state, we can
estimate IM recycling and accumulation of glucose and
lactate using a simple model of IMVR, lumping the
interstitium with ascending vasa recta (AVR) and excluding nephrons and collecting ducts. The important
parameter with respect to the question of a single effect
for the IM axial osmotic gradient is the interstitial
concentration of supposed external osmoles, but interstitial concentrations are hard to handle both experimentally and theoretically. I thus limit this modeling
study to consideration of steady-state glucose and lactate flows in descending vasa recta (DVR) and AVR,
with a conservative range of estimated glycolytic rate
within the IM, assumed here not to depend on diuretic
state. The “AVR” represent the interstitium as well as
ascending vasa recta. Previous models specifically investigating vasa recta flow and exchange (14, 15, 34,
56) addressed the relative importance of hydrostatic
vs. osmotic pressure, protein oncotic force, dissimilarity between DVR and AVR, likely roles of water channels and urea transporters, importance of varying
number of vessels with medullary depth, and other
issues. Compared with those earlier models, the
present study adopts a simpler model, since it addresses the simpler issue of accumulation by recycling
of solutes excluded from the nephrons.
Mass balance constraints require that total glucose
consumption and lactate production in all cells within
a slice of medulla at a given depth x must, in the steady
state (and independent of considerations of reduced
numbers of vessels with depth), equal the net differ-
Downloaded from http://ajprenal.physiology.org/ by 10.220.33.4 on June 18, 2017
accumulation by minimizing washout; Ref. 53), and
volume uptake from the nephron system. It has long
been known that energy for the buildup of the IM
osmotic gradient could theoretically be supplied not
only by recycling of urea and NaCl (the crux of the
“passive hypothesis”; Refs. 30 and 52) but alternatively
(or in addition) by “external,” or interstitial, osmoles
(24, 31, 37, 46), that is, solutes present in interstitial
fluid but not in tubular fluid of the loop of Henle or
collecting duct. Using a detailed three-dimensional
model of rat medulla to estimate the amount of such
external osmoles needed to boost concentrating ability,
we calculated (55) that 100 mosmol/kgH2O of interstitial osmolytes would considerably increase the axial
IM osmotic gradient. The literature has remained
mute as to the identity or possible source of such
hypothetical interstitial osmoles, which would have to
be produced continuously within the IM and recycled
downward by the vasa recta to accumulate significantly toward the papilla.
I recently proposed (54) that IM glycolysis may contribute to such a pool of external osmoles, since it is
known that in the relatively hypoxic (49) IM, a large
fraction of the energy for cell metabolism is supplied by
anaerobic glycolysis (32, 47), which yields two lactate
molecules (and two protons) for each glucose molecule;
that is, anaerobic glycolysis produces net osmoles as a
matter of course. Anecdotally, this phenomenon is the
reason for corneal swelling under hypoxic conditions
(27).
Having suggested that IM metabolic osmole production may contribute to the IM single effect for urine
concentration, one immediately wonders how the effect
would depend on the animal’s diuretic state. It seems
unlikely that cell metabolism in the IM, which is just
housekeeping since there is no known active epithelial
transport in this region except in the collecting ducts,
should vary with the organism’s water balance; that is,
there is no reason to suppose a priori that IM glycolytic
rate should vary as a function of the animal’s salt and
water balance, so its involvement in the concentrating
mechanism appears hard to rationalize. However,
studies of the IM microcirculation (e.g., 19, 35, 36, 50,
62) have shown that the IM blood supply may vary in
response to perturbations of the organism’s water balance, being reduced under antidiuretic conditions.
Also, it is clear from earlier modeling studies [see
review by Stephenson (53)] that net flow rate through
a countercurrent exchange system determines the extent to which intrinsic osmole production will build up
an axial gradient, with low flow being favorable to
steeper gradients.
The crux of my conjecture is thus: first, that intrinsic
metabolic osmole production may be sufficiently high
and IM blood flow sufficiently low, especially in antidiuresis, to result in significant osmole accumulation by
countercurrent exchange, and second, that this could
contribute importantly to the urinary concentrating
mechanism. The present work addresses the first of
these.
F469
F470
GLYCOLYSIS AND THE URINE CONCENTRATING MECHANISM
N(x) ⫽ N(0)e ⫺k shx
(1)
with ksh ⫽ 1.213 mm⫺1. Thus, compared with the
number of tubes entering the IM, the fraction of tubes
reaching the papillary tip is 1/128 for L ⫽ 4 mm at the
tip and x ⫽ 0 at OM/IM border.
Other species have different proportions of tubes and
vessels extending to the tip. I investigate possible implications of this by running simulations with different
values of ksh.
The number of entering DVR, N(0), was nominally
set at 128, so the simulation represents behavior of a
system that gives a single DVR at the papillary tip.
Qualitatively, the model behavior is in fact independent of the numerical value chosen for this parameter,
depending instead on the loop distribution, determined
Fig. 1. Schematic representation of the
steady-state model of IMVR. Dotted walls for
AVR indicate that it represents interstitium
as well as AVR. See Glossary for complete
description of abbreviations.
by ksh. Everything is scaled to this assumption, in
particular, glycolytic glucose consumption (and lactate
production) is expressed as percent of glucose inflow,
and DVR volume reabsorption and net volume uptake
into AVR from nephrons and collecting duct are expressed as percent of DVR inflow. By this strategy, the
model can represent kidneys containing any number of
vasa recta simply by varying the medullary length
and/or the factor describing the exponential decrease of
their number with depth (ksh).
Inflows. Baseline volume flow into DVR is set to 3.75
nl 䡠 min⫺1 䡠 tube⫺1, the DVR flow at the OM/IM border in
(57). The glucose and lactate concentrations entering
the IM DVR are set at 10 and 2 mM, respectively, i.e.,
cGLU(0) ⫽ 10 mM, cLAC(0) ⫽ 2 mM.
Mass balance considerations. Conservation of matter
in the steady state requires that in any slice of IM
extending from depth x1 to depth x2, with x2 ⬎ x1, we
must have, taking glucose flows as an example, the
following: (rate of glucose entry into the slice) ⫺ (rate of
glucose exit from the slice) ⫽ (rate of glucose conversion to lactate within the slice), i.e., accounting for both
DVR and AVR flows through the slice and noting that
ascending flows carry a negative sign
DVR
AVR
DVR
AVR
(x 1 ) ⫺ F GLU
(x 2 )) ⫺ (F GLU
(x 2 ) ⫺ F GLU
(x 1 ))
(F GLU
⫽
兰
x2
(2)
J gly(x) dx
x1
For lactate balance, since each converted glucose molecule yields two lactate molecules, we have the following: (rate of lactate exit from slice) ⫺ (rate of lactate
Downloaded from http://ajprenal.physiology.org/ by 10.220.33.4 on June 18, 2017
ence of vasa recta glucose and lactate outflows and
inflows through the slice, so by restricting the analysis
to the steady state, one sidesteps the difficulty of estimating glucose and lactate distributions between cell
cytoplasm and interstitium. As stated above, I make
the further assumption that AVR concentrations are
equal to interstitial concentrations. This model thus
says nothing about intracellular glucose or lactate concentrations. Figure 1 schematically depicts the model.
Since in vivo flows and concentrations are unknown
at the OM/IM border, I set up the baseline case according to predictions of our recent calculations with a
three-dimensional model of the whole medulla (54, 57).
Anatomy. DVR and AVR are assumed to diminish
exponentially in number along the IM toward the tip of
the papilla according to the same relation as in our
earlier models and in conformity with reported rat
anatomy (28), i.e.
GLYCOLYSIS AND THE URINE CONCENTRATING MECHANISM
entry into slice) ⫽ 2 ⫻ (rate of glucose conversion to
lactate within slice), i.e.
DVR
AVR
DVR
AVR
(F LAC
(x 2 ) ⫺ F LAC
(x 1 )) ⫺ (F LAC
(x 1 ) ⫺ F LAC
(x 2 ))
2
兰
⫽
x2
(3)
J gly(x) dx
x1
Integrating all the way to the tip from any point x, and
given the continuity condition at the papillary tip,
namely
F iDVR(L) ⫽ ⫺F iAVR(L), for i
⫽ volume, glucose, or lactate
(4)
DVR
AVR
(x) ⫹ F GLU
(x) ⫽
F GLU
兰
L
J gly dx
(5)
x
and net lactate production from x to the tip is
DVR
AVR
⫺(F LAC
(x) ⫹ F LAC
(x))/2 ⫽
兰
L
J gly dx
(6)
x
In particular, for the IM as a whole
DVR
AVR
(0) ⫹ F GLU
(0) ⫽ ⫺
F GLU
⫽
兰
DVR
AVR
F LAC
(0) ⫹ F LAC
(0)
2
(7)
L
J gly dx
0
From this, it is straightforward to show that the
maximum rate of osmole addition to the IM from anaerobic glycolysis, if all the glucose were converted to
AVR
lactate, in which case FGLU
(0) ⫽ 0, would equal the
rate of entry of glucose into the IM in the DVR. The
actual IM rate of glycolysis must be only a fraction of
this maximum.
Prediction of the gradients of glucose and lactate
concentration along the vasa recta is the purpose of
what follows.
Estimate of glycolytic rate. Although extraction of a
consensus estimate for IM glycolytic rate from the
literature is subject to the usual difficulties, the following two facts seem clear: the IM is relatively hypoxic
[PO2 ⬃10 Torr (33)], and anaerobic glycolysis supplies a
substantial part of the energy budget, with lactate
clearly being produced in the IM, whereas it is consumed in the cortex (3), although complete dependence
of IM on anaerobic glycolysis is a myth (10). In what
follows here, I attempt a best, albeit conservative,
estimate of fractional IM glucose consumption.
Quoting from Ross and Guder (47), p. 393: “The high
rate of glycolysis observed in [rat] papillary slices corresponds to the highest local activity of hexokinase. It
may be calculated that this enzyme activity, expressed
in terms of dry weight of tissue, exceeds by a factor of
2 the maximum rate of glycolysis which has been
recorded, i.e., 800–1,000 ␮mol/hr/g dry weight lactate
production under anaerobic conditions.” Their table II
shows about 100 ng dry weight/mm tubule, so this
converts to 1.67 pmol 䡠 min⫺1 䡠 mm of tubule⫺1, which I
consider an extreme upper limit on glucose consumption.
To compare glucose consumption with its delivery
rate, I consider a minimal group, served by each DVR,
to correspond roughly to seven tubule equivalents, as
follows: DVR, two AVR, long descending limbs (LDL),
long ascending Henle’s loops (LAL), IM collecting ducts
(IMCD), plus some interstitial cells. I thus estimate
maximal glycolytic rate of a minimal group as roughly
seven times that of one tubule, or 11.7 pmol 䡠
min⫺1 䡠 mm⫺1. This need must be met by the input from
one DVR: given my base case assumptions of 10 mM
glucose and 3.75 nl/min inflow rate to DVR entering
the IM, the glucose supply for each group is 37.5
pmol/min. This rough estimate of maximal metabolic
glucose consumption thus implies that all entering
glucose would be consumed in a group of length 4 mm,
the IM length of the longest loops in a rat kidney.
However, in the rat kidney, most long loops turn back
before reaching the papillary tip. Integration over the
whole depth of IM using our assumed loop distribution
for rat kidney (Eq. 1, above) predicts a maximal total
IM consumption of 25% of the entering glucose. This
equals the estimate made by Ruiz-Guinazu et al. (48).
An alternative approach to estimation of IM glycolytic rate is to estimate IM energy requirements. A
minimal estimate (it ignores basic cell metabolism
needs) can be based on measurements of total IMCD
sodium transport, since IMCD are the only demonstrated site of IM active transepithelial transport.
These measurements were recently summarized in association with a model of IMCD transport (table 4 of
Ref. 58). Taking a conservative estimate of reabsorption of, say, 2% of filtered Na⫹ from the IMCD and
glomerular filtration rate (GFR) of 500 ␮l/min gives
500 ␮l 0.140 ␮mol Na⫹
1.4 ␮mol Na⫹
⫻
⫻ 0.02 ⫽
min
␮l
min
If anaerobic glycolysis were the only source of ATP (but
see below), and given transport of 3 Na⫹ per ATP and
production of 2 ATPs per glucose, then this would
amount to consumption of ⬃240 nmol glucose/min, or
1.6 ␮mol 䡠 min⫺1 䡠 g wet wt⫺1 of IM, if the IM represents
10% of a 1.5-g rat kidney. This is higher than direct
measurements of lactate production in rabbit medulla
(32), which reported values of 0.2 ␮mol 䡠 min⫺1 䡠 g wet
tissue⫺1 in the presence of oxygen and 0.4
␮mol 䡠 min⫺1 䡠 g wet tissue⫺1 under N2 perfusion, but it
is much lower than measured anaerobic lactate production in guinea pig medulla, namely 6.2
␮mol 䡠 min⫺1 䡠 g wet tissue⫺1 (from Refs. 18 and 13, cited
in Ref. 10). We can compare these consumption rates to
an estimate of IM glucose delivery rate as follows.
Estimates of papillary plasma flow (PPF) in antidiuretic rats range from 0.3–0.5 ml 䡠 min⫺1 䡠 g wet tis-
Downloaded from http://ajprenal.physiology.org/ by 10.220.33.4 on June 18, 2017
we have net glucose consumption from any depth x to
the tip equal to
F471
F472
GLYCOLYSIS AND THE URINE CONCENTRATING MECHANISM
dF
DVR
v
dx
(x)
⫽ ⫺J v(x) ⫺ k shF DVR
(x)
v
DVR
dF GLU
(x)
DVR
(x)
⫽ ⫺J GLU(x) ⫺ k shF GLU
dx
DVR
dF LAC
(x)
DVR
⫽ ⫺J LAC(x) ⫺ k shF LAC
(x)
dx
dF
AVR
v
(x)
dx
dF
AVR
GLU
dx
(x)
⫽ ⫹J v(x) ⫹ k shF
DVR
v
(x) ⫹ J
ABS
V
where N(x) is the number of DVR at depth x (Eq. 1),
PGLU and PLAC are permeabilities to glucose and lactate, ␴GLU and ␴LAC are reflection coefficients (both set
at 0.5 here), and concentrations of solute i in tube j are
c ij (x) ⫽
J GLY(x) ⫽ N(x)
⫺c
(x)
J LAC(x) ⫽ N(x)P LAC(c
DVR
LAC
⫺c
AVR
LAC
DVR
AVR
(c GLU
⫹ c GLU
)
2
)
DVR
AVR
(c LAC
⫹ c LAC
)
⫹ (1 ⫺ ␴ LAC)J v(x)
2
兰
L
e ⫺ k shx dx
0
(12)
1 ⫺ e ⫺ k shL
⫽ V maxN(0)
k sh
where L is the total length of the IM. Solving this for
TOT
Vmax and expressing JGLY
as a fraction GlyFract of
total baseline glucose delivery, FDVR
(0), we obtain
G
)
⫹ (1 ⫺ ␴ GLU)J v (x)
(11)
Thus glycolytic rate will be virtually equal to Vmax
except for extremely low glucose concentrations. In
practice, for exploration of model behavior, I wanted to
specify Vmax values that would result in specified fractions of total glucose consumption (rather than specifying glycolytic rates per unit tissue volume or per mm
AVR
of medullary depth). To this end, assuming Km cGLU
for
all x, substituting from Eq. 1 for N(x), and integrating
over the whole IM, total glucose consumption is
TOT
J GLY
⫽ V maxN(0)
where kshFDVR
(x) is shunt transfer of i from DVR to
i
AVR at depth x (59). Ji(x) terms are the diffusional
transfers (pmol 䡠 min⫺1 䡠 mm⫺1) and osmotic volume
flow (nl 䡠 min⫺1 䡠 mm⫺1) at x from all DVR to AVR.
Treating the capillary walls as a single barrier (i.e., no
distinction here between transcellular and paracellular transport), we have for glucose and lactate fluxes
J GLU(x) ⫽ N(x)P GLU(c
AVR
V maxc GLU
(x)
AVR
K m ⫹ c GLU(x)
(8)
AVR
dF LAC
(x)
DVR
(x) ⫹ 2J gly(x)
⫽ ⫹J LAC(x) ⫹ k shF LAC
dx
AVR
GLU
(10)
Since volume flux along the DVR (Jv(x)) depends on
forces not represented in this model, it cannot be calculated explicitly here. Jv(x) is thus taken to be an
explicit fraction (30% as baseline value) of entering
flow, distributed over the length of the IM in proportion
to the number of DVR at each depth. Simulations were
run for various fractional volume fluxes.
To avoid unrealistic glycolytic glucose consumption
in the event that glucose concentration falls locally to
zero in the course of numerical analysis, I describe
glycolytic rate simply with a first-degree MichaelisMenten equation, saturable as a function of AVR glucose concentration, setting Km very low (0.1 mM) and
Vmax equal to estimated local glycolytic rate
DVR
(x) ⫺ J gly(x)
⫽ ⫹J GLU(x) ⫹ k shF GLU
DVR
GLU
F ij (x)
F jv(x)
(9)
V max ⫽
TOT
k shJ GLY
N(0)(1 ⫺ e ⫺ k shL )
k sh
(GlyFract 䡠 FGDVR(0))
⫽
N(0)(1 ⫺ e ⫺ k shL )
(13)
ABS
In like manner, JV
(x), the volume reabsorbed from
LDL and IMCD, was distributed in proportion to the
number of DVR (assumed equal to the number of LDL)
at each depth
J VABS ⫽ k VN(x)
(14)
By analogy with the treatment of the glycolytic Vmax, I
express total IM volume absorption as a proportion of
ABS TOT
DVR
entering blood flow, i.e., (JV
)
⫽ VolFract 䡠 FV
(0),
Downloaded from http://ajprenal.physiology.org/ by 10.220.33.4 on June 18, 2017
sue⫺1 (4, 16, 25, 40). If glucose concentration in blood
entering the IM is 10 ␮mol/ml (i.e., 10 mM), then
glucose delivery to IM is around 3 to 5 ␮mol 䡠 min⫺1 䡠 g
wet tissue⫺1, or double to triple the above estimate of
minimal expenditure. Thus it would appear that glucose (via anaerobic glycolysis) could in principle suffice
as the IM energy supply. Nonetheless, despite the
relative hypoxia of the IM, anaerobic glycolysis is in
fact only responsible for perhaps one-third of the energy supply (6).
Based on these considerations, I adopt a baseline
glucose consumption of 20% of IM delivery and investigate a wider range of values in the sensitivity studies
reported below.
System equations. The model treats steady-state
flows and exchanges of volume, glucose, and lactate
along DVR and AVR. The interstitium and cells (epithelial and interstitial) are assimilated with AVR. I
assume that glucose consumed by cellular glycolysis is
supplied from AVR and that the resulting lactate is
recovered into AVR/interstitium. Also included is net
volume reabsorption into the AVR from LDL and
ABS
IMCD, designated as JV
(x).
The system is subject to the continuity condition at
the papillary tip (Eq. 4) and is described by the following system of six differential equations
F473
GLYCOLYSIS AND THE URINE CONCENTRATING MECHANISM
and following the development of Eq. 13, we obtain an
expression for kv
kV ⫽
k sh
(VolFract 䡠 FVDVR(0))
N(0)(1 ⫺ e ⫺ k shL )
(15)
“Baseline” Permeabilities and Constants
⫺1
⫺1
PLAC ⫽ 100 ⫻ 10 cm/s ⫽ 33.93 nl 䡠 min 䡠 mm tube (for
radius ⫽ 9 ␮m)
PGLU ⫽ 4 ⫻ 10⫺5 cm/s
␴GLU ⫽ ␴LAC ⫽ 0.5
ksh ⫽ 1.213 mm⫺1
N(0) ⫽ 128 (arbitrary)
Glycolytic rate parameters
Vmax is calculated to obtain a desired fractional glucose
consumption
Km ⫽ 0.1 mM
Initial Conditions
(0) 3.75 nl 䡠 min⫺1 䡠 DVR⫺1
(0) 10 mM
(0) 2 mM
DVR
V
DVR
GLU
DVR
LAC
F
c
c
DVR, descending vasa recta.
(16)
where i is volume, glucose, or lactate. Ideally, score
equals zero. Using the initial conditions for the three
DVR inflows FDVR
(0) and guesses for the three AVR
i
outflows FAVR
(0),
the
equations were integrated from 0
i
to L (Mathematica’s function NDSolve, which switches
automatically between a non-stiff Adams method and a
stiff Gear method, based on LSODE). Using Mathematica’s LinearSolve function (which uses LU decomposition), the error vector, score, from Eq. 16 is used
with a numerically determined Jacobian matrix, JAC,
to solve for a corrections vector, s, to the guesses for
FAVR
(0) according to
i
JAC 䡠 s ⫽ ⫺score
(17)
Improved guesses for AVR flows at x ⫽ 0 are obtained
by adding the corrections vector s to the previous
guesses. The system is again integrated from x ⫽ 0 to
L, and score is recalculated. This cycle is repeated until
the maximum of score is ⱕ10⫺5. Typically only two or
three iterations were needed to reach a solution. As a
post hoc check on the quality of the solutions, mass
balance at each depth is verified based on conservation
of glucose equivalents, i.e., according to
(
Table 1. Baseline parameter values
and initial conditions
⫺5
F iDVR(L) ⫹ F iAVR(L)
⫽ score
F iDVR(0)
F GDVR(x) ⫹
) (
)
F DVR
(x)
F AVR
(x)
L
L
⫹ F GAVR(x) ⫹
⬇0
2
2
(18)
The maximum of this sum was typically less than
10⫺15 pmol 䡠 min⫺1 䡠 mm⫺1.
RESULTS
Logically, the main factors influencing IM accumulation of metabolically produced lactate should be: 1)
the rate of glycolysis; 2) PLAC, the lactate permeability
of DVR, which should be sufficiently high to efficiently
recycle lactate to the papilla instead of having it carried out in the AVR; 3) blood flow into the IM, which
should be low to favor accumulation instead of washout, especially if glycolytic rate is insensitive to the
animal’s water balance state; and 4) the amount of
volume absorption from the nephrons and collecting
ducts, which will tend to dilute the interstitial lactate
Downloaded from http://ajprenal.physiology.org/ by 10.220.33.4 on June 18, 2017
Parameter values. Table 1 gives baseline parameter
values (in dimensions of most literature reports as well
as in the dimensions used for the present model).
In the absence of measurements of DVR permeabilities to lactate and glucose (PLAC and PGLU), I set the
baseline value for PLAC at 100 ⫻ 10⫺5 cm/s, which is
midway between the measured DVR permeabilities to
NaCl and urea used in our recent simulations of the
whole rat medulla (57). During the simulations, it
became immediately necessary to reduce the glucose
permeability well below this value to avoid convergence problems due to near zero glucose concentrations. Baseline PGLU was thus set 25-fold lower than
PLAC. Whether this requirement reflects reality remains to be seen; certainly such low permeability for
glucose across the vasa recta wall contradicts the general assumption that such vessels are very leaky to
small solutes. Around these baseline values, simulations were run over a wide range of PLAC and PGLU
values. It is interesting in this context to cite Kean et
al. (26): “It should be pointed out that anaerobic metabolism of the renal medulla in vivo, although a satisfactory explanation for the metabolism by which energy is made available despite probable deprivation of
oxygen, still poses the significant problem of substrate
delivery to the tissue for this type of metabolism. If
oxygen exchanges across the limbs of the vasa recta,
thereby depriving the deeper portions of the medulla,
why does not glucose also exchange in a similar manner?”
JvABS baseline value is set at 30% of flow into IM
DVR. This is the value reported by two studies in
antidiuretic rats based on measurement of vasa recta
protein concentration at the base and tip of the papilla
(38, 63). However, values as high as 117% have been
reported (21). This is a crucial parameter for lactate
accumulation, as the results below show, but proper
investigation must be done in a model of the full medulla that includes not only vasa recta but also
nephrons and collecting ducts.
Numerical solution. I programmed Mathematica to
solve this nonlinear system of ordinary differential
equations by simple shooting, which also amounts to
multidimensional Newton-Raphson (43). Briefly, the
system of six equations and six unknowns (Eq. 8) was
solved subject to three initial conditions (flows into
DVR) at x ⫽ 0 and three boundary conditions at L,
where L is the depth at the papillary tip. The three
boundary conditions are continuity relations on the
flows at the hairpin turn, normalized by the entering
flow rate
F474
GLYCOLYSIS AND THE URINE CONCENTRATING MECHANISM
and increase the washout rate by increasing AVR flow
rate.
Glycolytic rate. Figure 2 shows baseline model behavior for overall glycolytic glucose consumption of 0 to
40% by steps of 5%. The volume flow profiles (Fig. 2, A
and B) show the 30% net increase of volume flow due to
assumed uptake from the nephrons and IMCD and the
30% fall of single-vessel DVR flow due to the assumed
baseline rate of DVR volume flux. Note that volume
flows here are not coupled to glucose and lactate concentrations (see MODEL DESCRIPTION, above). As glycolytic rate increases, glucose concentration falls and
lactate rises. Note that the fall of glucose concentration
even for glycolytic rate of zero is due to dilution by
incoming volume from the nephrons (JvABS in the model
equations).
Volume absorption from nephrons. The effect of varying JvABS is shown in Fig. 3 for absorption rates from 10
to 90% of DVR inflow. This fluid absorption is seen to
significantly reduce the accumulation of a lactate gradient. As an indication that this range spans physiological values, it can be easily shown that IMCD volume reabsorption of 1 or 2% of GFR corresponds to
25–50% of PPF, assuming a filtration fraction of 25%
and PPF equal to 1% of renal blood flow.
Fig. 3. Effect of increasing volume absorption from nephrons and collecting
ducts on glucose and lactate concentration profiles. JvFract was 10, 30, 50, 70,
or 90% of IM DVR inflow rate; arrows
indicate increasing volume absorption.
Other parameters are at baseline values.
Reduction of IMBF. Figure 4 shows the effects of
reducing IMBF, under the assumption that tissue glucose consumption is not affected by the change of blood
flow. Lactate accumulation is seen to dramatically increase as IMBF falls to one-half its baseline value. The
predicted lactate profiles clearly suggest that IMBF
may play an important role in the extent of lactate
accumulation.
Lactate permeability. The effect of increasing PLAC
from 0 to its baseline value in steps of 10% is shown in
Fig. 5. As is clear from the tendency seen in the lactate
profiles, higher values lead to no further improvement
of lactate accumulation. That is, given the baseline
assumptions, there is no reason to postulate specialized lactate transport systems that would increase its
effective permeability above the values measured in
IMDVR for salt and urea. On the other hand, lactate
permeability would have to be less than half that of
salt and urea before its efficient recycling would be
compromised.
Glucose permeability. As mentioned above, it was
necessary in the present simulations to drastically
reduce glucose permeability to assure its delivery to
the deep medulla. That is, higher values resulted in
glucose shunting, much as outer medullary oxygen
Downloaded from http://ajprenal.physiology.org/ by 10.220.33.4 on June 18, 2017
Fig. 2. Profiles of volume flow and solute concentration along IM, for varying
glycolytic rates. Vmax was varied to
yield 0% to 40% consumption of delivered glucose, as indicated on the
curves; 20% consumption will be
adopted as the baseline value for subsequent simulations. All other parameters were set to baseline values. For
this and subsequent Figs. 3–9, solid
curves show values for DVR, dashed
curves for AVR. A: total volume flow
(normalized by delivered flow rate),
showing that outflow from AVR is 30%
higher than DVR inflow, due to assumed volume uptake from nephrons.
B: volume flow per vessel (normalized
by delivered flow rate per vessel),
showing DVR volume flux equal to 30%
loss over the length of the IM; sn, single vessel. C: glucose concentration
profiles; fall of glucose concentration at
0% consumption is due to dilution by
volume uptake from nephrons. D: lactate concentrations.
GLYCOLYSIS AND THE URINE CONCENTRATING MECHANISM
F475
shunting leads to hypoxia in the IM. Figure 6 illustrates this behavior.
Jv along DVR. Since this model does not include
solutes other than glucose and lactate and also ignores
hydrostatic and oncotic pressures, volume flux along
the DVR could only be treated by assuming some ad
hoc profile. The results shown in Fig. 7, where volume
loss along the DVR was varied from 0 to 40% of delivery rate, indicate that this is not a crucial parameter
with respect to glucose or lactate profiles. Simulations
Fig. 5. Effect of lactate permeability
(PLAC) on glucose (cGLU) and lactate concentrations (cLAC). PLAC was increased
from 0 to 100% of baseline value by steps
of 10%. Other parameters are at baseline
values (except PGLU ⫽ PLAC/25). Bottom:
lactate concentrations at papillary tip vs.
PLAC (expressed as percentage of baseline
value). Top: glucose and lactate profiles
from x/L ⫽ 0 to 1.0.
Downloaded from http://ajprenal.physiology.org/ by 10.220.33.4 on June 18, 2017
Fig. 4. Effect of reducing inner medullary blood flow (IMBF) on glucose (cGLU) and lactate concentrations (cLAC).
IMBF was reduced from 100% to 50% of its baseline value. Absolute glucose consumption was held constant.
Bottom: glucose and lactate concentrations at the papillary tip (mM) vs. IMBF (expressed as percentage of baseline
IMBF). Top: glucose and lactate profiles from x/L ⫽ 0 to 1.0.
F476
GLYCOLYSIS AND THE URINE CONCENTRATING MECHANISM
(not shown) with reflection coefficients of 0 (instead of
0.5) for both glucose and lactate showed that the increased solvent drag had only a minor effect on the
profiles.
Percentage of early returns. All simulations up to
here have assumed a conic papilla like that of the rat,
with only a small fraction (1/128) of IM tubes reaching
the papillary tip. Many species of rodents have longer
papillae with a greater proportion of tubes extending to
the region near the tip. In Psammomys, for example,
about 40% of nephrons enter the IM and nearly all of
these run essentially the whole length of the very long
papilla. In such papillae, since metabolic rate must be
Fig. 7. Effect of fractional DVR volume loss. Volume
flux out of DVRs was varied from 0 to 40% of entering flow rate. As a function of normalized medullary
depth, top shows total (left) and single-vessel (right)
volume flows (expressed as fraction of entering
flow), and bottom shows profiles of glucose and lactate concentrations.
proportional to the amount of tissue, it seems reasonable to assume that glycolytic lactate production must
consume a greater fraction of entering glucose. Also,
one would anticipate that, with a longer papilla, lactate
accumulation by countercurrent recycling would be
favored. To get some idea how well the present model
reflects this hunch, I ran a series of simulations with
decreasing values of ksh, the factor for exponential
decrease of the number of vessels. As a starting point,
I chose a Vmax giving 20% glucose consumption for
baseline ksh value (this percentage increases as the
proportion of long vessels increases). Figure 8 (A and
B) shows the resulting profiles for various values of ksh.
Downloaded from http://ajprenal.physiology.org/ by 10.220.33.4 on June 18, 2017
Fig. 6. Effect of glucose permeability
on glucose and lactate profiles. Bottom:
glucose concentrations at papillary tip
vs. PGLU (expressed as fraction of baseline PLAC). PGLU was varied from 0.01–
0.085 ⫻ baseline PLAC. All other parameters were held at baseline values,
with glucose consumption at 20% of
delivery rate. Top: glucose and lactate
profiles from x/L ⫽ 0 to 1.0.
GLYCOLYSIS AND THE URINE CONCENTRATING MECHANISM
F477
It is seen that lactate accumulation is favored by an
increased proportion of long loops. Table 2 gives, for
each value of ksh, the percentage of long loops attaining
the papillary tip and the corresponding percentage of
delivered glucose converted to lactate.
Alternatively, one may ask how glucose and lactate
profiles would differ in kidneys having identical overall
glucose consumption but different loop distributions.
Figure 8C shows the results of such a simulation in
which glucose consumption was held constant at 20%
of delivery rate. The main effect one sees is better
delivery of glucose to the papilla when more vessels
extend deeper. Lactate profiles are unaffected by the
changing loop distribution.
Reflection coefficients. To test the sensitivity to assumed reflection coefficient values, I varied ␴GLU and
␴LAC independently from 0 to 1.0. Figure 9 shows the
results. The glucose profile is seen to depend somewhat
on ␴GLU, but the lactate profile is essentially independent of ␴LAC, mainly because baseline lactate permeTable 2. Effect of various ksh values on percentage of
loops reaching papillary tip and percentage of
delivered glucose conversion
ksh Divisor
% Loops to Tip
% Total Glucose Conversion
1
2
3
4
5
0.78
8.8
19.8
29.7
37.9
20
36
48
56
62
See Eq. 1 for reference. These values correspond to curves in Fig.
8, A and B.
ability is sufficiently high to assure nearly identical
DVR and AVR lactate concentrations, i.e., solvent drag
of lactate is negligible compared with lactate diffusion.
DISCUSSION
Our earlier modelling study (55) suggested that 100
mosmol/kgH2O of external osmoles would suffice to
significantly boost the concentrating mechanism. Jen
and Stephenson (24) suggested that an even smaller
amount, around 20 mosmol/kgH2O, might suffice. The
present results suggest that IM lactate production
could conceivably furnish substantial levels of such
external osmoles but that lactate accumulation to concentrations as high as 100 mM seems unlikely. To my
knowledge, Dell and Winters (12), working with dog
kidney, did the only experimental study aimed at evaluation of a possible IM gradient of lactate concentration. In their thoughtful study, they not only demonstrated a corticomedullary lactate gradient (lactate
concentration doubling from base to tip in normal and
diuretic dogs) but also attributed it to “countercurrent
exchange between afferent and efferent limbs of the
vasa recta” and speculated that the most likely source
was anaerobic glycolysis. More thorough theoretical
evaluation of this possibility will necessitate its inclusion in a model of the full medulla, including flows not
only of glucose and lactate but also of urea and NaCl in
both nephrons and blood vessels, to account explicitly
for enhanced volume absorption from descending limbs
and collecting ducts, which will in turn affect the recycling of salt and urea among nephrons and vessels.
Downloaded from http://ajprenal.physiology.org/ by 10.220.33.4 on June 18, 2017
Fig. 8. Effect of different loop distributions. The
factor ksh was divided by 1, 2, 3, 4, or 5, changing the
fraction of loops that extend into the deepest papilla
(see text and Table 2). Arrows indicate increasing
number of loops reaching the papilla. A: total (left)
and single-vessel (right) flows as a function of IM
depth. B: glucose and lactate profiles: glucose consumption was proportional to number of loops at
each depth, i.e., it increased as ksh decreased. C:
glucose and lactate profiles: glucose consumption
held constant at 20% for all values of ksh.
F478
GLYCOLYSIS AND THE URINE CONCENTRATING MECHANISM
Fig. 9. Effect of ␴GLU and ␴LAC on glucose and lactate profiles. Glucose (top)
and lactate (bottom) reflection coefficients were varied from 0 to 1.0. Other
parameters at are baseline values.
then high external concentrations imply high cellular
concentrations (and acidity?) as well, since these transporters are passive and reversible. This issue warrants
investigation.
Experimental tests. In the end, of course, the relevance or irrelevance of metabolically produced osmoles
to the concentrating mechanism is an experimental
question. To my knowledge, only one attempt has been
made to measure papillary glucose and lactate concentrations. In 1961, Ruiz-Guinazu et al. (48) enzymatically measured glucose and lactate concentrations in
micropuncture samples of vasa recta blood collected at
the tip of golden hamster papillae. They found glucose
concentration diminished by about one-third and lactate concentration doubled compared with arterial
blood (aorta), but to obtain sufficient sample volume
they had to collect for up to 30 min. Perhaps because of
perturbations due to the long collection times, osmolality in their vasa recta samples was only about threefold plasma osmolality (based on their freezing-point
depression measurements). These data thus support
IM lactate production from glucose, but the values
seem too low to contribute significantly to the single
effect. It would be interesting to repeat these measurements (in frankly antidiuretic animals), since there are
now micro-enzymatic methods for measuring glucose
and lactate in nanoliter samples.
Besides this technically demanding measurement of
glucose and lactate concentrations in papillary interstitium, it will be relevant to search for specialized
transport paths favoring lactate transport. These
should be located in plasma membranes of interstitial
cells and on basolateral membranes of epithelial cells
of the nephrons and collecting ducts. Obvious first
candidates are members of the recently cloned family
Downloaded from http://ajprenal.physiology.org/ by 10.220.33.4 on June 18, 2017
To put things in scale, it is useful to compare total IM
glucose delivery to the amount of urea dumped into the
papilla from IMCD. Based on numbers from our threedimensional models (54, 57), the present assumed delivery of glucose to the IM amounts (in osmolar equivalents) to about 9% of the filtered load of urea (FLu). If
about 40% of FLu is dumped into the interstitium from
the IMCD, conversion of 20% of total delivered glucose
to lactate would represent generation in the IM of only
about 4% as many lactate osmoles as urea osmoles.
Nonetheless, it must be kept in mind that the sugars
exert their full osmotic force across nephron walls
(intratubular concentration near zero and tubular reflection coefficient of 1.0), whereas urea is highly permeable (thus only a small concentration difference), so
the relative contribution of each milliosmole of interstitial lactate to an “external osmole” single effect will
be much greater than a milliosmole of interstitial urea.
Acid production. In addition to lactate, anaerobic
glycolysis also produces protons, one for each lactate
molecule, so it is natural to wonder whether the steady
IM glycolysis poses an acid-base problem. I suggest
that it does not, since the small production of protons
would presumably be buffered immediately by ambient
HCO3⫺ or ammonia. Even if papillary lactate accumulation by recycling is increased during progressive onset of antidiuresis by reduction of blood flow or by
increased DVR lactate permeability, this will presumably have no effect on the rate of local production of
protons and lactate.
This does, however, raise the issue of lactate and
proton exit from cells in the papilla, whose surroundings may have high lactate concentration. If the cells
are equipped with one-to-one coupled lactate-proton
transporters [MCT family of transport proteins (44)],
GLYCOLYSIS AND THE URINE CONCENTRATING MECHANISM
pocket mouse, spiny mouse) or succulent plants (Psammomys) and have very long papillae in which the number of IM nephrons and vessels remains nearly constant almost to the tip. Although these species can
concentrate their urine better than the rat, at least one
study showed that papillary urea concentration is not
correlated with urine osmolality (22). Even in the rat,
it has been reported (5) that NaCl concentration was
not correlated with urine osmolalities above 1,500
mosmol/kgH2O. It is thus tempting to speculate that
although the kidneys of species that elaborate the most
concentrated urine are somewhat paradoxical in the
context of the classic hypothesis, their long, thick papillae, with presumably correspondingly abundant cell
metabolism throughout their length, would appear to
be consistent with an important single effect for metabolic osmoles such as lactate. Relevant to this point is
the observation, pointed out by Beuchat (7, 8) in her
exhaustive review of the relationships between kidney
size, metabolic rate, and urinary concentrating ability,
that small animals have a higher mass-specific metabolic rate than do larger animals, although the relationship varies among individual organs.
As a final thought, I suggest that if metabolic osmole
production does turn out to participate importantly in
the urinary concentrating mechanism (through regulation of IMBF or by some other means), then it also
adds another mode of separation of renal regulation of
water balance, salt balance, and urea balance.
The manuscript was considerably improved thanks to suggestions
of two diligent referees.
Parts of this work were previously presented in abstract form.
REFERENCES
1. Bankir L and Kriz W. Adaptation of the kidney to protein
intake and to urine concentrating activity: similar consequences
in health and CRF. Kidney Int 47: 7–24, 1995.
2. Bankir L and de Rouffignac C. Urinary concentrating ability:
insights from comparative anatomy. Am J Physiol Regulatory
Integrative Comp Physiol 249: R643–R666, 1985.
3. Bartlett S, Espinal J, Janssens P, and Ross BD. The influence of renal function on lactate and glucose metabolism. Biochem J 219: 73–78, 1984.
4. Bayle F, Eloy L, Trinh-Trang-Tan MM, Grunfeld JP, and
Bankir L. Papillary plasma flow in rats. I. Relation to urine
osmolality in normal and Brattleboro rats with hereditary diabetes insipidus. Pflügers Arch 394: 211–216, 1982.
5. Beck F, Dörge A, Rick R, and Thurau K. Intra- and extracellular element concentrations of rat renal papilla in antidiuresis. Kidney Int 25: 397–403, 1984.
6. Bernanke D and Epstein FH. Metabolism of the renal medulla. Am J Physiol 208: 541–545, 1965.
7. Beuchat C. Metabolism and the scaling of urine concentrating
ability in mammals: resolution of a paradox? J Theor Biol 143:
113–122, 1990.
8. Beuchat CA. Body size, medullary thickness, and urine concentrating ability in mammals. Am J Physiol Regulatory Integrative
Comp Physiol 258: R298–R308, 1990.
9. Bonen A, Baker SK, and Hatta H. Lactate transport and
lactate transporters in skeletal muscle. Can J Appl Physiol 22:
531–552, 1997.
10. Cohen JJ. Is the function of the renal papilla coupled exclusively to an anaerobic pattern of metabolism? Am J Physiol
Renal Fluid Electrolyte Physiol 236: F423–F433, 1979.
11. Cupples WA. Renal medullary blood flow: its measurement and
physiology. Can J Physiol Pharmacol 64: 873–880, 1986.
Downloaded from http://ajprenal.physiology.org/ by 10.220.33.4 on June 18, 2017
of monocarboxylate transporters (MCT1, MCT2, . . .)
(44), which serve in other tissues to couple lactate and
proton exit from glycolyzing cells (e.g., 9, 17, 23, 29, 39,
41, 45, 60). Although some of these have been reported
in kidney tissue, their precise locations and regulation
have not yet been studied.
It will also be interesting to look further into the
correlation of IMBF with urinary concentrating ability.
Although some studies have shown that IMBF is reduced by almost 50% in antidiuresis (4), others showed
only slight sensitivity of urinary concentrating ability
to medullary blood flow (11).
Conclusion. The picture that emerges here is that IM
glycolytic lactate production in the range of reported
values is probably sufficiently high and vasa recta
recycling sufficiently efficient to result in an osmotically significant corticomedullary lactate gradient. The
extent to which this external osmole production amplifies concentrating ability remains to be explored in full
medullary models. It is hoped that the present work
will serve as a guide for such studies as well as a
stimulus for experimental tests of this idea.
I conclude with a few more general remarks. The
countercurrent arrangement of nephrons and blood
supply was an evolutionary innovation that permitted
animals to move into arid ecological niches (20, 51, 61),
but we see now that it also posed problems for the
supply of nutrients for the cells in the deep medulla.
First, plasma skimming and shunting of O2 from descending vessels to the avid salt pumps of the outer
medullary thick ascending limbs lead to hypoxia below
a certain depth (42, 49), necessitating reliance on anaerobic glycolysis for metabolic maintenance of cells
deeper in the medulla (32). By nature’s serendipity,
this may have provided an alternative single effect (the
proposition in the present work), namely, a source of
metabolically produced osmoles, thereby favoring continued lengthening of the papilla for progressively
more concentrated urine. That said, the suggestion
must not be taken too narrowly, since the relationship
across species among papillary length, percentage of
long loops, and number of nephrons per unit body
weight is far from straightforward (2). Nonetheless, for
very long papillae (as in certain desert species) or for
high IM metabolic rates, I do predict that DVR glucose
permeability must be low in order not to starve the
deepest regions by glucose shunting.
This suggested role in the concentrating mechanism
for metabolically produced osmoles suggests a nuanced
interpretation of the role of urea. In omnivores like the
rat, and in carnivores [such as cat and dog, both with
100% long loops (2)] maintenance of urea balance and
maintenance of water balance are arguably intimately
linked, in the manner suggested by the classic passive
hypothesis (according to which, the dumping of a relatively small amount of urea from the terminal collecting ducts serves efficiently as external osmoles in the
drastically reduced volume of the rat papilla) and in
relation to dietary protein intake (1). However, most of
the desert rodents that have been studied eat a lowprotein diet of dry seeds (Mongolian gerbil, jerboa,
F479
F480
GLYCOLYSIS AND THE URINE CONCENTRATING MECHANISM
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
54.
55.
56.
57.
58.
V1 and V2 receptors. Am J Physiol Regulatory Integrative Comp
Physiol 269: R193–R200, 1995.
Niesel W and Röskenbleck H. Möglichkeiten der Konzentrierung von Stoffen in biologischen Gegenstromsystemen. Pflügers
Arch 276: 555–567, 1963.
Pallone TL, Yagil Y, and Jamison RL. Effect of small-solute
gradients on transcapillary fluid movement in renal inner medulla. Am J Physiol Renal Fluid Electrolyte Physiol 257: F547–
F553, 1989.
Pellerin L, Pellegri G, Martin JL, and Magistretti PJ.
Expression of monocarboxylate transporter mRNAs in mouse
brain: support for a distinct role of lactate as an energy substrate
for the neonatal vs. adult brain. Proc Natl Acad Sci USA 95:
3990–3995, 1998.
Peterson LN. Time-dependent changes in inner medullary
plasma flow rate during potassium-depletion. Kidney Int 25:
899–905, 1984.
Philp NJ, Yoon H, and Grollman EF. Monocarboxylate transporter MCT1 is located in the apical membrane and MCT3 in the
basal membrane of rat RPE. Am J Physiol Regulatory Integrative Comp Physiol 274: R1824–R1828, 1998.
Prasad PV and Epstein FH. Changes in renal medullary PO2
during water diuresis as evaluated by blood oxygenation leveldependent magnetic resonance imaging: effects of aging and
cyclooxygenase inhibition. Kidney Int 55: 294–298, 1999.
Press WH, Flannery BP, Teukolsky SA, and Vetterling
WT. Numerical Recipes. The Art of Scientific Computing. Cambridge, MA: Cambridge University Press, 1986.
Price NT, Jackson VN, and Halestrap AP. Cloning and
sequencing of four new mammalian monocarboxylate transporter (MCT) homologues confirms the existence of a transporter
family with an ancient past. Biochem J 329: 321–328, 1998.
Ritzhaupt A, Wood IS, Ellis A, Hosie KB, and ShiraziBeechey SP. Identification of a monocarboxylate transporter
isoform type 1 (MCT1) on the luminal membrane of human and
pig colon. Biochem Soc Trans 26: S120, 1998.
Röskenbleck H and Niesel W. Gekoppelte Gegenstromsysteme als Modell der konzentrierenden Niere. Pflügers Arch
277: 316–324, 1963.
Ross BD and Guder WG. Heterogeneity and compartmentation in the kidney. In: Metabolic Compartmentation, edited by H.
Sies. New York: Academic, 1982, p. 363–409.
Ruiz-Guinazu A, Pehling G, Rummrich C, and Ullrich KJ.
Glucose- und Milchsäurekonzentration an der Spitze des vasculären Gegenstromsystems im Nierenmark. Pflügers Arch 274:
311–317, 1961.
Schurek HJ. Kidney medullary hypoxia: a key to understanding acute renal failure? Klin Wochenschr 66: 828–835, 1988.
Silldorff EP, Kreisberg MS, and Pallone TL. Adenosine
modulates vasomotor tone in outer medullary descending vasa
recta of the rat. J Clin Invest 98: 18–23, 1996.
Smith HW. From Fish to Philosopher. The Story of Our Internal
Environment. Boston, MA: Little Brown, 1953.
Stephenson J. Concentration of urine in a central core model of
the renal counterflow system. Kidney Int 2: 85–94, 1972.
Stephenson JL. Urinary concentration and dilution: models.
In: Handbook of Physiology. Renal Physiology. Bethesda, MD:
Am Physiol Soc, 1992, sect. 8, vol. 2, chapt. 30, p. 1349–1408.
Thomas SR. Cycles and separations in a model of the renal
medulla. Am J Physiol Renal Physiol 275: F671–F690, 1998.
Thomas SR and Wexler AS. Inner medullary external osmotic
driving force in a 3-D model of the renal concentrating mechanism. Am J Physiol Renal Fluid Electrolyte Physiol 269: F159–
F171, 1995.
Wang W, Parker KH, and Michel CC. Theoretical studies of
steady-state transcapillary exchange in countercurrent systems.
Microcirculation 3: 301–311, 1996.
Wang X, Thomas SR, and Wexler AS. Outer medullary anatomy and the urine concentrating mechanism. Am J Physiol
Renal Physiol 274: F413–F424, 1998.
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.
Downloaded from http://ajprenal.physiology.org/ by 10.220.33.4 on June 18, 2017
12. Dell RB and Winters RW. Lactate gradients in the kidney of
the dog. Am J Physiol 213: 301–307, 1967.
13. Dickens F and Weil-Malherbe H. Metabolism of normal and
tumour tissue: a note on the metabolism of medulla of kidney.
Biochem J 30: 659–660, 1936.
14. Edwards A and Pallone TL. Facilitated transport in vasa
recta: theoretical effects on solute exchange in the medullary
microcirculation. Am J Physiol Renal Physiol 272: F505–F514,
1997.
15. Edwards A and Pallone TL. A multiunit model of solute and
water removal by inner medullary vasa recta. Am J Physiol
Heart Circ Physiol 274: H1202–H1210, 1998.
16. Eloy L, Grunfeld JP, Bayle F, Bankir L, Ramos-Frendo B,
and Trinh-Trang-Tan MM. Papillary plasma flow in rats. II.
Hormonal control. Pflügers Arch 398: 253–258, 1983.
17. Gerhart DZ, Enerson BE, Zhdankina OY, Leino RL, and
Drewes LR. Expression of the monocarboxylate transporter
MCT2 by rat brain glia. Glia 22: 272–281, 1998.
18. György P, Keller W, and Brehme T. Nierenstoffwechsel und
Nierenentwicklung. Biochem Z 200: 356–366, 1928.
19. Hansell P. Evaluation of methods for estimating renal medullary blood flow. Renal Physiol Biochem 15: 217–230, 1992.
20. Hargitay B and Kuhn W. Das Multipikationsprinzip als
Grundlage der Harnkonzentrierung in der Niere. Zeitschrift
Elektrochemie 55: 539–558, 1951.
21. Holliger C, Lemley KV, Schmitt SL, Thomas FC, Robertson CR, and Jamison RL. Direct determination of vasa recta
blood flow in the rat renal papilla. Circ Res 53: 401–413, 1983.
22. Imbert M and de Rouffignac C. Role of sodium and urea in the
renal concentrating mechanism in Psammomys obesus. Pflügers
Arch 361: 107–114, 1976.
23. Jackson VN, Price NT, and Halestrap AP. cDNA cloning of
MCT1, a monocarboxylate transporter from rat skeletal muscle.
Biochim Biophys Acta 1238: 193–196, 1995.
24. Jen JF and Stephenson JL. Externally driven countercurrent
multiplication in a mathematical model of the urinary concentrating mechanism of the renal inner medulla. Bull Math Biol
56: 491–514, 1994.
25. Karlberg L, Kallskog O, Ojteg G, and Wolgast M. Renal
medullary blood flow studied with the 86Rb extraction method.
Methodological considerations. Acta Physiol Scand 115: 11–18,
1982.
26. Kean EL, Adams PH, Winters RW, and Davies HC. Energy
metabolism of the renal medulla. Biochim Biophys Acta 54:
474–478, 1961.
27. Klyce SD. Stromal lactate accumulation can account for corneal
oedema osmotically following epithelial hypoxia in the rabbit.
J Physiol (Lond) 321: 49–64, 1981.
28. Knepper MA, Danielson RA, Saidel GM, and Post RS.
Quantitative analysis of renal medullary anatomy in rats and
rabbits. Kidney Int 12: 313–323, 1977.
29. Koehler-Stec EM, Simpson IA, Vannucci SJ, Landschulz
KT, and Landschulz WH. Monocarboxylate transporter expression in mouse brain. Am J Physiol Endocrinol Metab 275:
E516–E524, 1998.
30. Kokko JP and Rector JFC. Countercurrent multiplication
system without active transport in inner medulla. Kidney Int 2:
214–223, 1972.
31. Kuhn W and Ramel A. Aktiver Salztransport als möglicher
(und wahrscheinlicher) Einzeleffekt bei der Harnkonzentrierung
in der Niere. Helv Chim Acta 42: 628–660, 1959.
32. Lee JB, Vance VK, and Cahill JGF. Metabolism of C14labelled substrates by rabbit kidney cortex and medulla. Am J
Physiol 203: 27–36, 1962.
33. Leichtweiss HP, Lubbers DW, Weiss C, and Baumgartl H.
The oxygen supply of the rat kidney: measurements of intrarenal
PO2. Pflügers Arch 309: 328–349, 1969.
34. Marsh DJ and Segel LA. Analysis of countercurrent diffusion
exchange in blood vessels of the renal medulla. Am J Physiol
221: 817–828, 1971.
35. Mattson DL and Cowley AW Jr. Kinin actions on renal papillary blood flow and sodium excretion. Hypertension 21: 961–
965, 1993.
36. Nakanishi K, Mattson DL, Gross V, Roman RJ, and Cowley AW Jr. Control of renal medullary blood flow by vasopressin
GLYCOLYSIS AND THE URINE CONCENTRATING MECHANISM
59. Wexler AS, Kalaba RE, and Marsh DJ. Three-dimensional
anatomy and renal concentrating mechanism. I. Modeling results. Am J Physiol Renal Fluid Electrolyte Physiol 260: F368–
F383, 1991.
60. Wilson MC, Jackson VN, Heddle C, Price NT, Pilegaard H,
Juel C, Bonen A, Montgomery I, Hutter OF, and Halestrap
AP. Lactic acid efflux from white skeletal muscle is catalyzed by
the monocarboxylate transporter isoform MCT3. J Biol Chem
273: 15920–15926, 1998.
F481
61. Wirz H, Hargitay B, and Kuhn W. Lokalisation des Konzentrierungsprozesses in der Niere durch direkte Kryoskopie. Helv
Physiol Acta 9: 196–207, 1951.
62. Yang S, Silldorff EP, and Pallone TL. Effect of norepinephrine and acetylcholine on outer medullary descending vasa recta.
Am J Physiol Heart Circ Physiol 269: H710–H716, 1995.
63. Zimmerhackl B, Robertson CR, and Jamison RL. Fluid
uptake in the renal papilla by vasa recta estimated by two
methods simultaneously. Am J Physiol Renal Fluid Electrolyte
Physiol 248: F347–F353, 1985.
Downloaded from http://ajprenal.physiology.org/ by 10.220.33.4 on June 18, 2017