Inner medullary lactate production and urine-concentratingmechanism: a flat med - 《American Journal of Physiology》美国生理学杂志干细胞之家



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发表于 2009-4-21 13:23 |只看该作者 |倒序浏览 |打印

作者：StéphaneHervy and S. RandallThomas作者单位：Institut National de la Santé et de la RechercheMédicale Unit 46 Necker Faculty of Medicine, University ofParis  F-75015 Paris, France $ G& l2 ?9 K' W. Y% l. @% e

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      【摘要】
   We used a mathematical model to explorethe possibility that metabolic production of net osmoles in the renalinner medulla (IM) may participate in the urine-concentratingmechanism. Anaerobic glycolysis (AG) is an important source of energyfor cells of the IM, because this region of the kidney is hypoxic. AGis also a source of net osmoles, because it splits each glucose intotwo lactate molecules, which are not metabolized within the IM.Furthermore, these sugars exert their full osmotic effect across theepithelia of the thin descending limb of Henle's loop and thecollecting duct, so they are apt to fulfill the external osmole rolepreviously attributed to interstitial urea (whose role is compromisedby the high urea permeability of long descending limbs). The present simulations show that physiological levels of IM glycolytic lactate production could suffice to significantly amplify the IM accumulation of NaCl. The model predicts that for this to be effective, IM lactaterecycling must be efficient, which requires high lactate permeabilityof descending vasa recta and reduced IM blood flow during antidiuresis,two conditions that are probably fulfilled under normal circumstances.The simulations also suggest that the resulting IM osmotic gradient isvirtually insensitive to the urea permeability of long descendinglimbs, thus lifting a longstanding paradox, and that this high ureapermeability may serve for independent regulation of urea balance.
      【关键词】 urineconcentrating mechanism anaerobic glycolysis lactate mathematical model
   INTRODUCTION7 l$ ]! \1 e$ q& C: |4 O, `3 [
4 A1 J+ {" n2 K  _6 x
THE DRIVING FORCE, or "single effect," behind the development of theinner medullary osmolality gradient that serves to concentrate urineduring its final passage along the collecting ducts has still not beenadequately explained. As has so often been the case, it is worthwhileto quote an early paper by Carl Gottschalk (and Karl Ullrich)( 11 )$ ]6 w* M0 r! }% \8 x0 V# o1 o( S
9 B; z4 K7 K7 U; [
Solute production in the inner medulla. As firstsuggested by Ullrich ( 43 ), the liberation of osmoticallyactive solute, as in the acidifying mechanism or anaerobic metabolismof glucose, would contribute to the osmolality in inner medulla. Itseems unlikely, however, that this is the sole mechanism responsible for the increasing tonicity in the inner medulla, and it is even moredifficult to attribute the increase in sodium concentration in thisarea to such a mechanism. Quantitative considerations make it apparentthat solute production alone could not explain the entire urinaryconcentrating process, and this need not be seriously entertained inview of the known activity of the thick ascending limb of the loop ofHenle.
' k$ z( l- [1 k0 P; n6 z; h& f
Given these doubts about significant papillary lactateaccumulation, which were supported by the earlier in vivo micropuncture results of Ruiz-Guinazu et al. ( 30 ), this idea was quietly abandoned." y+ q4 W) m' ]) r9 l  ^

We know now that the active transport of the medullary thick ascendinglimb (MTAL) is limited to the outer medulla (OM), leaving open thequestion of the single effect in the inner medulla (IM). The presentmodeling study explores exactly the possibility mentioned byGottschalk, illustrating a scenario by which, in answer to his doubts,the metabolically produced osmoles do not themselves constitute theosmotic gradient but rather serve to amplify papillary NaClaccumulation. We have proposed that metabolic production of net osmoles( 39, 42 ), and in particular lactate production byanaerobic glycolysis (AG) ( 41 ), might constitute asignificant contribution to the IM single effect. It is wellestablished both that the inner medulla is hypoxic ( 7, 32 )and that lactate accumulates within the IM ( 8, 31 ).( x. }0 t( x3 N! {" e6 t( A
7 ]' E7 U' A, x8 a
In a simple model of the inner medullary vasa recta ( 41 ),we previously calculated that lactate from AG could plausibly accumulate to significant levels within the papilla, givenphysiological estimates of glycolytic rate and IM blood flow. In thepresent work, we use a so-called "flat" model of the full medullato further explore the hypothesis that this recycling of IM lactate mayhelp generate the IM osmotic gradient. This model includes not only vasa recta but also loops of Henle and collecting ducts. It is "flat", as opposed to three-dimensional (3-D), in that it assumes all structures at each level are bathed by a common interstitium, inthe manner of classic "central core" models [although thedescending vasa recta (DVR) are treated here as full-fledged tubes, notgrouped with the ascending vasa recta (AVR)]. It is well established( 25, 47 ) that such flat (or "one-dimensional" orcentral core) models cannot explain the steep IM osmotic gradientobserved in antidiuretic rodents while respecting measured permeabilityvalues, the main problem being the high measured urea permeability oflong descending limbs, P u LDL, in the IM( 6, 25 ).7 h: G3 U0 K  {4 T" X2 ~7 V; x. P

Here, we show that addition of glucose and lactate to such a model (inaddition to the usual NaCl and urea) and the conversion of 15-20%of entering glucose to lactate (each consumed glucose is converted byAG to 2 lactates, thus generating net osmoles) result in a sizeableosmotic gradient that is essentially insensitive to the P u LDL.. B6 U0 B2 g/ a
  |4 S3 }1 i, }
MODEL DESCRIPTION
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The steady-state medullary model used here, illustrated in Fig. 1, includes vasa recta (DVR and AVR),short and long Henle loops [descending (SDL and LDL) and ascending(SAL and LAL)], and collecting ducts (CDs) and treats flows of volume,NaCl, urea, glucose, lactate, and (only in the CD) KCl. It is thus asystem of 35 nonlinear, ordinary differential equations (5 flowvariables along 7 tubular structures). The AVR serve to represent theinterstitium surrounding all the structures. Rather than using explicitinclusion of equations for transport along the distal tubules, inflowto the outer medullary collecting duct (OMCD) is calculated from flowsexiting at the top of the ascending limbs (AHL), based on physiologicalconstraints representing the action of virtual distal tubules (see Inputs and Boundary Conditions ).9 w" X4 b$ z* d1 z; V. `" L
+ \3 S/ R$ x5 I$ G' R
Fig. 1. Schematic diagram of the model. The ascending vasa recta (AVR)represent the interstitium, which bathes all structures equally atevery level. F v, volume flow; C NaCl,C urea, C glu, and C lac : NaCl, urea,glucose, and lactate concentration, respectively; DVR,descending vasa recta; LDL and LAL, long descending limb and longascending limb, respectively; SDL and SAL, short descending limb andshort ascending limb, respectively; LDL and LAL, long descending limband long ascending limb, respectively; CD, collecting duct; OS and IS,outer stripe and inner stripe, respectively; UIM and LIM, upper innermedulla and lower inner medulla, respectively; OM and IM, outer medullaand inner medulla, respectively.9 x" v* z# k  ~

This model corresponds closely to our 3-D models ( 39, 44 ),with the following exceptions.) N$ ?* C: u1 a. p9 B; W$ o* x
* C1 F6 g" K# z6 G
1 ) It is "flat" instead of 3-D; i.e., all exchange amongtubes passes via a common interstitial space instead of beingdistributed among neighboring structures according to their relativeplacement within each region.! d" Q+ }8 \/ e7 v& z

2 ) We have added glucose and lactate as full-fledged solutesand treated conversion of glucose to lactate (stoichiometry 1:2) withinthe IM "interstitium," assimilated here to the AVR; this representsglycolytic lactate production by all cells of the IM. The lactate thusproduced must transit by the interstitium because it is not consumedwithin the IM ( 26 ). See Thomas ( 41 ) for acomparison of our baseline glycolytic rate with available biochemical data from kidney and other tissues. Within the nephrons, we assume thatglucose and lactate concentrations are near 0 (as is generally reportedafter the end of the proximal tubule). As explained further below, weuse the glucose solute within the nephron to formally representnonreabsorbable solutes, setting their initial concentration at 1 mM atthe entry to LDL and SDL (see Tables 3 and 5 ).

3 ) KCl is added to the fluid flowing into the collectingducts [a feature common to a previous model by Layton et al.( 25 )].
# Q, m# h- {6 H$ y* D: I$ t
Topology7 [/ a2 N4 B2 z' M# f; V
' O9 Z' _) }- D+ U/ T
Each type of tube is represented by a single, lumped tubularstructure, whose circumference at each depth reflects the total numberof such tubes at that depth. Within the IM, flows in the longdescending vasa recta (LDV) and in LDL are shunted directly to the longascending vasa recta (LAV) and LAL, respectively, in proportion to thenumber of tubes that return at each depth. Here, we adopt the sameaxial exponential loop distribution as in our recent 3-D medullarymodels ( 39, 44 ), based on the reported anatomy of ratkidney ( 13, 21 ). To be explicit, the number of tubes, j, at depth x within the IM, i.e., for x OM/IM, is given by j (x)=N j (0)e −k sh ( x−x OM/IM ), g2 v2 ?$ k& Z# O$ T) E: R0 @
' \$ G/ J& U, @, p4 G
( 1 )
9 X* q  K0 q3 d' W! {/ V
with the factor describing the exponential decrease in theirnumber with depth ( k sh ) = 1.213 mm 1 for vasa recta and Henle's loops and k sh = 1.04 mm 1 for IMCD, and N (0) is the number entering the IM. Thus, compared with thenumber of tubes entering the IM, the fraction of vasa recta andHenle's loops reaching the papillary tip is 1/128 for an IM thicknessof 4 mm, and over the same distance, 64 OMCDs converge to a singleexiting collecting duct. Also in conformity with the 3-D models,two-thirds of the descending vasa recta turn back within the innerstripe of the OM (we call these the SDV), and the remaining third (theLDV) extend at least part way into the IM, their number diminishingexponentially as explained above. The SDV and LDV are distinctstructures in the WKM-type 3-D models, but in this flat model they arelumped into a single structure, the DVR. For the whole system, thebasic scaling factor is N CD, 0 (=64), the number of OMCD entering the OM. Table 1 gives the numbers of tubes at eachdepth according to this scheme.

Table 1. Numbers of tubes at each depth6 P1 z1 E- c" e, b

Because species other than the rat have different proportions oftubes and vessels extending to the tip ( 2 ), everything isscaled to the assumption of a single exiting CD. By this strategy, themodel can represent kidneys containing any number of nephrons simply byvarying the medullary length and/or the factor describing theexponential decrease in their number with depth( k sh ).

Although it has long been recognized as a crucial parameter forconcentrating ability, the total IM blood flow relative to total flowin the nephrons is not established in the literature due to thedifficulty of measuring it. We explore this in the parameter studies.

System Equations
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The equations describing the changes in flows and concentrationswith depth in each tube are identical to those used in earlier models.System variables are the axial tubular flows of water and solutes.Concentrations of solutes i in tubes j arecalculated from the ratio of solute flow to volume flow,C i j = F i j /F v j. As in Thomas ( 41 ), shunt flows from descending tube j to the corresponding ascending tube at depth x are given by j sh ( x ) = F j i ( x ) N j ( x )   d N j ( x ) d x =k sh F j i ( x ),

( 2 ). O# Q; ~! l6 e
% {  ?9 `4 h1 ]7 }4 n+ \
We then have the following system of differential equations,adopting the usual convention that descending tubule flows are positiveand ascending flows are negative dF LDL v ( x ) d x = − J LDL v ( x ) −k sh F LDL v ( x9 n5 @  N  I( q. F# P- d9 @0 R

dF LDL i ( x ) d x = − J LDL i ( x ) −k sh F LDL i ( x3 D5 p' X2 ?/ N
- f5 i, L3 h" q5 n. l, }. r0 J
( 3 )

dF LAL v ( x ) d x = − J LAL v ( x ) +k sh F LDL v ( x( V: O% E' B7 b4 T) g- G1 ~( X& w  K1 G8 @

dF LAL i ( x ) d x = − J LAL i ( x ) +k sh F LDL i ( x ) −J LAL i,&ensp; pump ( x
3 E: S3 }! d0 ]- G! \" N
( 4 )% s+ G& V' {8 i8 @
7 U4 A0 X2 h% J$ V0 `' \
dF SDL v ( x ) d x = − J SDL v ( x
% Y9 V# A1 R. [
dF SDL i ( x ) d x = − J SDL i ( x$ y5 d& O$ A1 P% W1 ?: W; D3 p, w) \

( 5 )* ?  p1 V, L4 Y* Q2 k' D, y

dF SAL v ( x ) d x = − J SAL v ( x4 Q3 C& y0 Y, p% I

dF SAL i ( x ) d x = − J SAL i ( x ) −J SAL i,&ensp; pump ( x+ X7 V' \! p4 ~, f3 o

( 6 )

dF CD v ( x ) d x = − J CD v ( x

dF CD i ( x ) d x = − J CD i ( x ) −J CD i,&ensp; pump ( x
9 ^3 P6 F3 c1 R! {" N
( 7 )
6 b3 T" H/ b' A8 B1 P' [3 j  e
dF DVR v ( x ) d x = − J DVR v ( x ) −k sh F DVR v ( x" h5 U3 Q, i8 Y9 a4 r6 }  b
* J2 g2 c, G0 j
dF DVR i ( x ) d x = − J DVR i ( x ) −k sh F DVR i ( x
* B9 O1 C" J  I1 e" U. R! D
( 8 )
  M. @8 M: ]9 _+ z2 |6 g
where in each case i refers to NaCl, urea, glucose, or lactate.4 C; i* c3 L- q- |
  ?! v9 u/ Q7 t- `: ^3 o
In these equations, transmural fluxes of volume and solute i out of tube j are given by j v ( x ) = A j Lp j &ensp;. n! o0 Z. H6 v

∑ i =1 4 &ensp;RT&sfgr; j i [C AVR i ( x ) − C j i ( x

( 9 )
( J, N/ }1 R2 M5 [1 q
j i (x)=A j P j i [C j i ( x ) − C AVR i ( x9 V2 `% d. G" L: k6 D
, c0 C) L6 I& C
J j v ( x )(1 −&sfgr; j i ) C j i ( x ) + C AVR i ( x ) 25 b* Q' @( d  }

j i,&ensp;pump = A j &ensp;  Vm j i C j i ( x ) K m j i + C j i ( x )
- g! v& e: M  a# [, _
The AVR concentrations here also represent the interstitialconcentrations surrounding all the other tubes. Notice also that thereis no mention in the above equations of glycolytic conversion ofglucose to lactate. This is because the conversion is limited to the"interstitial space," i.e., the AVR. The AVR concentrations andvolume flow were calculated from the constraint of global mass balance,as follows.0 U" Z* i; n$ z+ ~0 C# w9 L

Conservation of mass for the medulla as a whole in the steady state( 35 ) says simply that, at any depth x, thealgebraic sum of flows of type i in all tubes j (taking flows to be positive toward the papilla and negative away fromthe papilla) must equal the exit rate of i from the terminalcollecting duct minus the total amount of i synthesized from x to the papillary tip, x = L : ∑ j &ensp;F j i ( x )  =  F CD i ( L ) −' R/ q1 \. B% C1 W4 Z
8 h* x# ^" C1 t) D. w9 b* U6 `) u8 C
∫ x L &ensp;S j i ( x )d x

( 10 )

where flows at level x are taken to be 0 in tubes thatdo not extend all the way to x. The S i j term is, of course, 0 everywherefor NaCl and urea and applies only in the AVR/interstitium for lactateand for glucose (for which it is negative, because glucose is consumed).9 E: P0 f. Y' L' |/ ]7 y" q

As in our earlier vasa recta model ( 41 ), we specify thetotal IM glycolytic glucose consumption, J gly,tot, as a percentage of total glucoseinflow into DVR, and the rate of glycolysis at a given depth is thenscaled to the number of vasa recta at that depth. To be specific,calling the fractional glucose consumption J rx,fract, we have gly,&ensp;tot =J r x,&ensp; fract &ensp;F VR glu
; J4 e& A# H& w8 T' `9 T
( 11 )
& y) ?5 s1 P6 b3 w% ~* m3 _# q, }
which is used to calculate K gly, theglycolysis rate per tube and per millimeter gly = k sh J gly,&ensp;tot N DVR (0)[1 −e −k sh ( L−x OM/IM ) ]: W+ o' Y, W. s5 E4 ]

( 12 )3 B4 n# L& T. J
6 m" B! d8 Y2 P) W* q
Because in this model glucose is converted to lactate only withinthe IM, we have within the OM (i.e., for x x OM/IM ) ∫ x L &ensp;J gly ( x )d x=J gly,&ensp;tot

( 13 )( p9 A0 M: m- W/ S: |5 m3 ]2 H
* @$ }4 r2 e) e$ U* u. U! @
and within the IM (i.e., for x OM/IM ) ∫ x L &ensp;J gly ( x )d x
; E3 c/ Z. W! Y3 M' n3 z- o
( 14 )
! _# ~7 [  U( k( s
=K gly N DVR (0) e − k sh ( x − x OM/IM ) −e − k sh ( L − x OM/IM ) k sh

Boundary conditions at the bottoms of loops are based on tubeconnectivity, where E indicates the end of tube j, i.e., at the tips of Henle's loops and at the bottom of vasa recta j v (E) = −F j +1 v& A3 S5 l7 c3 _3 _
' N8 h0 e1 K" ~
j i (E) = −F j +1 i! Y3 s8 d% d' Z. G/ N6 K0 |
1 p; }, O# _' B  h
( 15 )$ ^8 U0 s1 o+ h

In general, it is considered that there are no sources or sinks(except glycolysis, for lactate and glucose), that hydrostatic pressureplays a negligible role compared with osmotic pressure forces, and thataxial diffusion is negligible relative to convective flow of solutes[these last 2 assumptions were discussed in Moore and Marsh( 28 )].# \" r  {- N5 _
. E6 Q  ~. {& }6 W
Baseline Parameter Values

The baseline parameter values follow those of our earlier 3-Dmodel ( 39, 44 ) as closely as possible and aregiven in Table 2. K m for the pump equation in Eq. 9 wastaken as 50 mM." C1 p! l9 p* R* q; i

Table 2. Values of baseline membrane parameters# r% A: S$ }9 f" M: s/ h( C
$ N4 {" F# u1 J5 n
High-Urea Permeability Parameter Values
: n8 A2 s( J' ?
To further explore the impact of high urea permeability of LDL( P u LDL ), we also used a second parameter set(taken from Table 2 in Ref. 25 ), which was based mainly onpermeability measurements in Henle's loops of chinchilla (although some of the values are from the rat literature, because there is not acomplete set of measurements for chinchilla). The chinchilla has beenreported to concentrate its urine as high as 7,600 mosM ( 46 ). We will call this the"high- P u " parameter set. Table 4 shows thevalues that are different from the baseline set. Here, we did not adoptthe high value of LDL salt permeability used by Layton et al.( 25 ).2 T  K3 c; `0 y" t! n

Inputs and Boundary Conditions7 N! c/ G" L/ v- n

The inputs to the system are the volume flows and soluteconcentrations at the entry into the LDL and SDL and into the vasa recta. F v LDL and F v SDL were set at 10 nl · min 1 · nephron 1 basedon a single-nephron glomerular filtration rate (SNGFR) of 30 nl/min andratio of inulin concentration in tubular fluid to that in urine[(TF/P) inulin ] of 3 at the end of the proximal tubule.F v into vasa recta was set at 7.5 nl · min 1 · tube 1 (as inRef. 39 ). For the LDL and SDL, entering concentrations ofurea, glucose, and lactate were set at 10 mM, 1 µM, and 1 µM, respectively. For the vasa recta, entering concentrations of urea, glucose, and lactate were set at 5, 5, and 2 mM, respectively. NaClconcentrations were calculated from these, assuming global entering fluid osmolality of 263 mosM and an osmotic activity coefficient for NaCl of 1.82 ( 45 ).

Inputs to the OMCD. Rather than include distal tubules explicitly, the entry to thecollecting ducts is calculated from flow and concentrations at the topof the SDL and LDL, based on constraints deduced from the literature.To calculate the volume flow and four concentrations into the OMCD, weneed five constraints. In particular, the following was assumed.- V( `9 A0 G9 d" a4 A' X
! I6 T- b+ y+ t' x$ i
1 ) Fluid entering the OMCD is isosmotic to plasma and isassigned the value Osm CD, 0 = 263 mosM.
, g* F) s1 s9 j  E
2 ) A specified fraction, u fac = 0.85, of urea is delivered to OMCD [i.e., the distal tubulesreabsorb (1 u fac ) of the urea delivered to earlydistal tubules].

3 ) NaCl concentration entering the OMCD has a fixed value,C S CD (0) = 35 mM; glucose andlactate flows are conserved along the virtual distal tubules, i.e.,their flows into OMCD equal the sum of their flows out of the LAL and SAL.
: o. S% _  }2 r
We also assume that KCl enters the OMCD at the fixed concentrationC K CD (0) (= 20 mM) but that itsabsolute flow rate, F K CD = C K CD (0) F v CD (0), then remains unchangedalong the rest of the CD, and its concentration at depth x is then C K CD ( x ) = F K CD /F v CD ( x ). This is usedalong with the other solute concentrations to calculate the osmoticdriving force for water flux across the CD wall.
& v. g0 v& s) Q1 g1 R" r
Thus, to be explicit, we can solve for volume flow entering the OMCD,F v CD (0), by rearranging the equation for totalosmolality CD,&ensp;0 = 1.82&ensp;[C CD S (0) + C CD K (0)] + u fac [F SAL u (0) + F LAL u (0)] + [F SAL glu (0) + F LAL glu (0)] + [F SAL lac (0) + F LAL lac (0)] F CD v (0)  j+ b" i  `, f* |9 ^
9 \! A& Y5 ]" p* q
( 16 )! @, w8 o' l, I2 c( q5 P2 l

thus obtaining CD v (0) = u fac [F SAL u (0) + F LAL u (0)] + [F SAL glu (0)&emsp; &emsp; + F LAL glu (0) + [F SAL lac (0) + F LAL lac (0)] Osm CD,&ensp;0 − 1.82&ensp;[C CD S (0) + C CD K (0)]2 e6 C( A6 F% r  Q4 i, w1 k/ C: t
" T& U$ e: p: r/ g% Z9 R
( 17 )
) B# o- W* D$ {2 l3 b. K
We then have, for the other values entering the OMCD CD u (0) = u fac [F SAL u (0) + F LAL u (0)] / F CD v7 R$ S: E+ A' h" _5 W7 h
; U9 h) d% q/ d3 I7 |$ N
CD glu (0) = [F SAL glu (0) + F LAL glu (0)] / F CD v

( 18 )3 i7 C3 q2 u, a' y9 w) m, o( y
3 m" Q$ d8 o! l  g, ~
CD lac (0) = [F SAL lac (0) + F LAL lac (0)] / F CD v
  P" s) J% S/ F- |$ b
where we take the absolute values of the flows exiting theascending limbs.7 V/ \' |& \6 b' @$ y+ z
  B% W# F! e' b3 K4 p) ]4 R: t; j% m
Numerical Solution

The system was solved using a method based on that described byStephenson et al. ( 35 ) and used by us in an earlier model with six cascading nephrons ( 40 ). The differentialequations are approximated by finite difference equations centered inspace. If we consider tube j to be divided into n slices, then the space-centered finite difference equations betweennodes k-1 and k are F j i ( k- 1) − F j i ( k ) &Dgr;x = − J j i ( k-
: T4 E9 z& }0 o5 V% V
( 19 )

where i represents flows of volume, NaCl, urea,glucose, or lactate. Thus the fluxes J i j areevaluated at the middle of the interval ["midpoint method" ( 38 )], on the assumption that concentrations in themiddle of the interval are the arithmetic average of the concentrations at k-1 and k.- D4 G, f6 E% }
7 v( A/ v$ D. I: I
The solution proceeds as follows. An initial guess is made for theinterstitial/AVR concentrations, then these are taken as fixed, andgiven the defined input volume flow and solute flows for LDL and SDLand for the DVR, the equations for each tube are integrated stepwise[we used a spatial chop of 120 slices (121 nodes)] in the directionof flow using Newton's method on the system of five finite differenceequations and five unknowns (F v and 4 concentrations,C i ) and using an analytically calculated Jacobian matrix. We found it advantageous to use a much stricter errortolerance ( 10 ) on these "tubular" iterations thanwas necessary on the "global" iterations. Using the relative valuesfor tubular flows and concentrations, F v AVR ( k ) is calculated tosatisfy global mass balance at each mesh node by applying Eq. 10 to volume flow and rearranging to obtain AVR v ( x ) = F CD v ( L ) − [F DVR v ( x ) + F LDL v ( x ) + F LAL v ( x2 M4 x" _) i) k( b' J( M
# n; n( u+ V, ^# @! X) z; |  i
( 20 )5 _, a( |+ d6 n; k, [# f% o

+ F SDL v ( x ) + F SAL v ( x ) + F CD v ( x" K# X+ e3 I; W
3 d: r. F8 l; S1 g' `$ c
Then, using these AVR volume flows, one checks for global massbalance for each solute at each discrete depth. This gives thefollowing "scores," which would ideally equal 0. These are therelative deviations from an ideal solution NaCl ( x ) = F CD NaCl ( L ) −&Sgr; j &ensp; F j NaCl ( x ) F LDL NaCl (0)* a2 D3 V% Y/ T0 R. y% Y

( 21 )
' {) V3 f/ c+ o7 j- `
urea ( x ) = F CD urea ( L ) −&Sgr; j &ensp; F j urea ( x ) F LDL urea (0)- v  S' I: \/ `

glu ( x ) = F CD glu ( L ) −&Sgr; j &ensp; F j glu ( x ) +∫ L x &ensp;J gly ( x )d x F LDV glu (0)
: L' \* D5 i& t/ d
lac ( x ) = F CD lac ( L ) −&Sgr; j &ensp; F j lac ( x ) − 2 &ensp;∫ L x &ensp;J gly ( x )d x F LDV lac (0): s% ~  S" |6 K" R5 R" f$ i7 F" E

If the maximum relative deviation is less than 10 6,we have a solution. If not, then a global Jacobian is constructednumerically by varying each interstitial/AVR concentration in turn (thevariation used here was 10 4 times the concentration inquestion) and reintegrating the system. This Jacobian matrix and theerror vector based on Eq. 21 are then used to solve for acorrections vector s to the interstitial concentrations byLU decomposition ·s=9 R1 F) r0 X! Q3 t# H

( 22 )

This global Newton iteration is repeated until global convergenceis achieved (i.e., until global mass balance is respected to within ourchosen error tolerance).: k6 z5 W* I7 ^
8 R1 g* o3 l6 P" Y" H
RESULTS
; D0 |+ s2 S- x6 e2 @2 A1 i
Here, we present the results of several key simulationsdemonstrating the effect of IM metabolic osmole production (glyocolytic conversion of glucose to lactate) in the flat medullary model describedabove. Using the baseline parameter set (Table 2 ), we show thatconversion of 15% of the glucose entering the medulla suffices toengender a sizeable IM osmotic gradient, mainly by amplifying the IMrecycling of NaCl. We also show that this simulated osmotic gradient isessentially unaffected by raising the urea permeability of the thindescending limbs even to values several times higher than thosereported in the microperfusion literature. Then, using a set ofparameters corresponding more closely to the chinchilla kidney, whichhas an even higher value of P u LDL than therat, we show that urea can accumulate to levels closer to observedvalues and yet still be independent of the lactate effect on NaCl recycling.( _3 e* f; K- s+ M
/ [0 r* {4 p: _; p% V, }
In addition to these key results, we show some results from a partialsensitivity analysis, concerning in particular the predicted role of IMblood flow as the potential regulator of the importance of glycolyticosmole production for the concentrating mechanism, and the sensitivityto lactate and glucose permeabilities of the IM DVR.4 _2 ?! ~& g- |5 `6 Q

Increasing Glycolytic Rate
" ~3 V# B5 A6 ?- W. q" @
As shown in Fig. 2, the modelpredicts that conversion of 15% of entering glucose to lactate wouldlead to the establishment of a sizeable IM osmotic gradient, whereas inthe absence of glycolytic lactate production we obtain the classicresult for flat medullary models with a passive IM and high P u along the LDL, namely, the frank absence ofan IM osmotic gradient.

Fig. 2. Effect of glycolytic rate ( A and B ) on thecorticopapillary osmolality profile using the baseline parameter set(Table 2 ). The osmolality of long ascending limbs of Henle's loop(LAL) is slightly less than that of all other tubes.  e' n5 R) W  C; }3 \( H' E
9 ?: {3 v, A, A$ g' y8 F1 Z
Figure 3 shows the composition of thesimulated IM osmotic gradient along the AVR/interstitium. We see that asmall accumulation of lactate toward the papilla leads to greatlyincreased recycling of NaCl but not of urea.$ V, @6 g3 I# ^* B; z% _/ p
; Y, q  _& I, v0 W7 u
Fig. 3. Composition of total osmolality along the medulla in the absence( A ) and presence ( B ) of glycolysis.
! A; P7 t' G0 K: U6 l- h
Table 3 gives numerical values from these simulations for solute concentrationsand (TF/P) inulin at key points along the nephrons, usingthe baseline parameter set. Actual simulations had 120 spatial chopsand were run in double precision. Complete tabulated output isavailable from the authors. Two details should be noted: 1 )the solute labeled "glucose," and to which the nephron isimpermeable, was used here to represent nonreabsorbable solutes, set at1 mM at the entry of LDL and SDL and progressively concentrated alongthe nephron by water withdrawal. However, this tactic is only a partialremedy for the problem (typical of flat models) that(TF/P) inulin rises (i.e., flow rate diminishes) tounphysiological values in the distal nephron and along the collectingducts. We contend that this problem is due to the lack, in the flatmodel, of correct recycling paths that exist in real kidneys thanks to the vascular bundles, and we expect that proper handling must thus bedone in 3-D models. Note, however, that the results with thehigh- P u parameter set (Table 5 ) give morephysiological (TF/P) inulin values; 2 )(TF/P) inulin is a misnomer for the vasarecta, wherein this table simply gives values for the ratio of initialvolume flow to vasa recta flow at given points along the tubes(normalized per tube).' a* x' m; B" ^% c! ~; v. z3 A
% p7 V' ]6 y9 _  Z
Table 3. Results, using baseline parameters, for simulations with 0 or 15%conversions of glucose to lactate within IM interstitium
1 t- y! Y3 m1 O5 ~9 N0 m  y/ \
Effect of Medullary Blood Flow and Inner Medullary Blood Flow
) B/ H$ l/ w  ]6 b! N( A1 Z1 v
It has long been appreciated that the tradeoff between efficientIM solute recycling and washout must depend on the rate of total bloodflow vs. total nephron flow in the IM, but there exists no convenientmethod for experimental determination of this ratio. At least one studydid describe a videomicroscopic method for determination of papillaryblood flow ( 18 ), but the authors did not report the IMnephron flow for comparison. We explored this relationship with our model.' @. o0 V( c; a( D2 |+ F8 D
" k- D3 ~4 d* i  z2 D
Figure 4 A shows the strongrole predicted for the absolute rate of medullary blood flow (MBF). Inthis series of simulations, we increased total MBF up to double itsbaseline value (keeping simulated GFR constant). Over this range, theratio of IM blood flow (IMBF) to total volume flow entering the IM inthe nephrons and collecting ducts also nearly doubled, increasing from1.2 to 2.2. At the same time, the IMBF/MBF ratio increased from 0.126 to 0.177. As shown in Fig. 4 A, the osmotic gradient wasnearly eliminated by doubling MBF.7 X  r- S) S3 \; u2 Z, j  H/ P

Fig. 4. Effect of varying total medullary blood flow (MBF; A ) orits fractional distribution between the outer medulla (OM) and innermedulla (IM; B ). Absolute glycolytic rate was held constant.In the right panel, the ratio of IM blood flow (IMBF)/MBF varied from13 to 24%; the steeper gradients are for lower ratios.
  l) Z& n- r8 n) z1 G* _3 i. W# b
Figure 4 B shows the effect of redistribution of MBF between OM and IM,with no change in total MBF. We see that although a simpleredistribution of MBF in favor of the IM has a negative effect on theIM osmotic gradient, this effect is rather small over the range we wereable to explore here. For these simulations, we increased the fractionof vasa recta entering the IM from one-third to one-half of the totalnumber of vasa recta. As indicated in the figure, this resulted ineffective IMBF/MBF ratios from 0.126 to 0.19 (comparable to the changein Fig. 4 A ), but the ratio of IMBF to nephron flow increasedonly from 1.2 to 1.77. Taken together with the results of Fig. 4 A, these results suggest that mere redistribution of MBFbetween OM and IM is less effective than variation of absolute MBF as ameans of affecting the osmotic gradient. In the absence of experimentaldata, it remains to be seen to what extent these results will carryover to more complete 3-D models.! [3 a0 J9 o# U2 D3 O" X

Note that in this series of simulations the absolute amount of lactateproduction was maintained at the baseline level of 15% (i.e.,conversion of 15% of entering glucose to lactate). This is in keepingwith our basic, conservative assumption that the IM metabolic rate isindependent of the animal's hydrosmotic state. Data on this questionare limited, especially in antidiuresis. Bernanke and Epstein( 4 ) found that high urea concentrations depressed IMglycolysis, and it has been found ( 8, 31 ) that osmoticdiuresis actually increased IM lactate compared with antidiuretic controls. Also, Tejedor et al. ( 37 ) showed in dog kidneysthat papillary collecting ducts metabolize glucose to lactatestoichiometrically (1:2) when incubated under anaerobic conditions butthat the ratio falls to 1:1.6 under aerobic conditions.
6 S5 z; f/ R+ C0 V
DVR Lactate Permeability' G2 v! k, E" m, U
1 l, @- Q- ]0 V" D5 A+ _( ?) s1 i3 y
Figure 5 shows that the IM osmoticgradient induced by IM lactate production is quite sensitive to the DVRlactate permeability. That is, efficient lactate recycling is necessaryto obtain the effect on the osmotic gradient. The values in this seriesof simulations are in the range of measured DVR permeabilities to othersmall solutes such as NaCl and urea (see Table 2 ), suggesting one need not postulate specific DVR lactate transporters to raise lactate permeability to effective levels. However, as explained in the nextsubsection, the model predicts that DVR glucose permeability must bevery low to deliver sufficient glucose to the IM. If this is the case,one would also expect passive permeability to lactate to be low. Thusif lactate is indeed recycled efficiently by IM vasa recta, one mayexpect to find specific lactate transporters. In any case, the presentresults suggest that variation in DVR lactate permeability over thisrange, by whatever means, would exercise strong control over theimportance of lactate production for the IM osmotic gradient.

Fig. 5. Sensitivity of AVR/interstitial osmolality to DVR lactatepermeability ( P lac ).
1 @) {$ Q( O3 v- i7 z( H0 [
DVR Glucose Permeability' e' Q) B4 r, m; W

As shown in Fig. 6 (and values inTable 2 ), this model predicts that glucose delivery to the deep IMwould be compromised unless DVR glucose permeability is very much lowerthan that measured in capillary beds of other tissues. In other words,the papilla will starve due to glucose shunting unless DVR permeabilityis limited. This was anticipated by Kean et al. ( 20 )and suggests surprising selectivity of an epithelium that haslong been considered to be essentially perfectly leaky to smallsolutes. This prediction calls for experimental verification. Figure 6 B shows that the profile of lactate concentration isunaffected by DVR glucose permeability.
  A- P5 @4 [! _& I8 H7 |
Fig. 6. Sensitivity of total osmolality ( A ) andglucose ( B ) and lactate ( C ) profiles to DVRglucose permeability. Osmolality is in mosM; concentrations are in mM.Baseline glucose permeability of DVR was multiplied by factors0-1.0, as indicated. In B and C, solid linesshow flow down the DVR, and dashed lines show flow up the AVR.5 ], E/ P0 |# v8 K
9 @. q: ]$ y+ e( b
High P u LDL6 T% j! i; ]0 n" ?
3 y% r* D% r- Y7 v1 K. ?
We explored the role of P u LDL in thismodel using both the baseline parameter set of Table 2 (based on measurements for the rat kidney and also chosen to facilitate comparison with earlier 3-D models) and a parameter set (see Table 4 )based on values reported for the chinchilla kidney [as reported inLayton et al. ( 25 )], which has an an even higher P u LDL than the rat." b5 W4 `6 P/ S0 c: ^, Y

Table 4. Values of alternative membrane parameters7 E; a1 k* Z* K& S, C) R
1 h2 r9 ]" |$ |; H* h. k" L0 K
Figure 7 shows, for both parameter sets,that the gradient engendered by IM lactate production is affected onlyto a small extent by the value of P u LDL. Forthe baseline parameter set, raising P u LDL leads to a slight decrease in IM osmolality gradient, and for thehigh- P u parameter set the gradient actuallyincreases with increasing P u LDL. Detailedresults from the high- P u simulation are given inTable 5. This relative insensitivity of the IM osmolality gradient to P u LDL is a keyresult, because the high measured value of P u LDL ( 6, 13, 15 ) has long been recognized as a major incompatibility with therequirements of the classic "passive hypothesis."/ G* e( g* Q1 G3 M! P8 T

Fig. 7. Effect of LDL urea permeability ( P u LDL )on the profile of total osmolality. Glycolytic glucose consumption was15%. A : baseline parameter set. B : high-ureapermeability (high- P u parameter set).1 `( e# ^: R9 T& j- W. g2 i8 i
* o8 ^; A8 V' h9 A1 N/ B4 }8 T
Table 5. Results, using high-P u parameters, for simulations with 0 or 15% conversion of glucose to lactate within IM interstitium

Figure 8 shows the constitution of theinterstitial osmolality in the absence and presence of glycolyticconversion of 15% of entering glucose using thehigh- P u parameter set. By comparison withresults in the baseline model (Fig. 3 ), urea here constitutes a muchgreater fraction of IM osmolality, and although the main effect oflactate production is still seen on the NaCl gradient, ureaaccumulation is also increased.

Fig. 8. Effect of glycolytic lactate production on interstitial osmolalitywith high- P u parameter set (Table 4 ). Glycolyticglucose consumption was 0 or 15%, as indicated. A and B : profiles of total osmolality in all structures. C and D : contributions of urea, NaCl, and lactateto interstitial osmolality.) W; }' w; [- t2 k% v: Q

Fractional excretion of urea. Urea excretion in the rat ranges from ~20-60% of the filteredurea load ( 1 ). Failure to reproduce this observed level of urea excretion while accumulating urea to the high levels observed inthe IM has been a longstanding problem in medullary modeling studies.The present simulations show that the introduction of glycolyticlactate production does not solve this problem in the case of the ratparameters of our baseline simulation, because one can calculate fromthe values in Table 3 (using our assumption that half of the filteredurea is reabsorbed by the proximal convoluted tubule) that fractionalexcretion of urea (FE u ) is only 4% without IM glycolysisand falls to 2% when 15% of entering glucose is converted to lactate.However, in the case of the high- P u parameter set, with its higher P u LDL and otherparameter changes, FE u (calculated from results of Table 5 )is 19% in the absence of glycolysis and 15% when simulated glucoseconversion is raised to 15%, values that are much closer tothe physiological range. We also see from Tables 3 and 5 that ureaconstitutes only ~10% of the osmoles at the papillary tip insimulations with the baseline parameters but reaches 30% with thehigh- P u parameter set, compared with typicalvalues of ~50% in antidiuretic animals.

Concentrating work. Another apparent improvement associated with thehigh- P u parameter set is an increase ineffective concentrating work (Fig. 9 ). For the case of 15% glucoseconversion, urine flow rate increases by 227% using thehigh- P u parameter set compared with the baseline simulation [i.e., (U/P) inulin = 1,409/620.7],whereas urine osmolality falls by only 22%. We can relate these valuesto the net osmotic concentrating work as follows.; Z# X+ g7 |1 x! o4 @, F. b# _
" G; ]0 s! c2 L: M, o7 o: \
Fig. 9. Comparison of osmotic work calculated using Eq. 26 forour simulations (baseline and high- P u ) and fordata from several micropuncture studies in rats, hamsters, and Psammomys. The labels refer to the literature references(see Table 6 ).. B  `  s$ d4 C$ y1 N% E. D  B
% D6 \9 n/ J8 D4 E7 L9 z% S& b
Considering the kidney as a black box that does purely osmoticconcentrating work, the free energy change associated with excretion of each milliosmole of concentrated urine is conc =RT&ensp; ln&ensp; U osm P osm$ a. U) ~( V3 G0 |  c5 A$ D1 w) e
" |+ G- [2 E7 y, o- z
( 23 )4 G: ?% k" h! W" ?; c) y6 {6 a
" G+ a7 k7 c9 |5 {( r, j
where RT = 2.5773 J/mmol at 37°C, andU osm and P osm are urine and plasmaosmolalities, respectively. The absolute osmotic work accomplished (theactual energy cost will of course be higher; see Ref. 36 )is obtained by multiplying this by the osmolar excretion rate, N = V × U osm, where V isurine flow rate. Thus conc =N&ensp;RT&ensp; ln&ensp; U osm P osm
$ a# E" F9 Q# P: Q: [
( 24 )

For comparison of our simulation results withexperimental results from the literature in various species, wenormalize this by the GFR W &cjs1171; conc = N GFR &ensp; RT&ensp; ln&ensp; U osm P osm# Q0 C$ {/ z( h& G
1 d1 u) X  @2 j: ~0 d8 H, F
( 25 )8 i" J% G9 O  b( t  D7 T2 R

where the overbar indicates the normalized value. This can be mademore convenient, in terms of experimentally measured parameters, byincorporating the (U/P) inulin as follows. Substituting the definition of N from above and because(U/P) inulin = GFR/ V, we have GFR = V × (U/P) inulin. Thus Eq. 25 becomes W &cjs1171; conc = U osm (U/P) inulin &ensp;RT&ensp; ln&ensp; U osm P osm

( 26 )0 |  _% f/ u6 @" z; x2 h
4 t8 j% l5 L3 t8 U, |
For U osm in milliosmoles per liter, Eq. 27 gives the normalized concentrating work in joules per liter.* g  _7 Y, k6 v6 u# k- A7 N) i

Table 6 presents calculations of thenormalized work of concentration for our results from Tables 3 and 5 at15% glucose consumption along with some literature values forantidiuretic animals. These are plotted in Fig. 9. The simulationresults are below all the literature values, indicating that althoughincorporation of glycolytic lactate production in this flat model canexplain the generation of an IM osmotic gradient, it does notaccomplish a comparable amount of concentrating work, even using thehigh- P u parameter set.) x6 q0 Y8 `, ], E* D

Table 6. Osmotic work calculated using Eq. 26 for our simulations (baseline andhigh P u ) and for data from several micropuncture studiesin rats, hamsters, and Psammomys3 C0 k7 E1 o' }% w0 a/ q$ W$ w0 x
# c  Z# L1 F  l( G4 Z9 o' C; r
DISCUSSION4 D7 E3 h/ N3 Z! t# W4 T. t8 K7 b

Our results show that if the glycolytic rate is set to 0, thismodel, like all previous models whether flat or 3-D, does not developan IM osmotic gradient using reported permeability values and a passiveIM. Adding glucose-to-lactate conversion builds an osmotic gradientwithin the IM, and this gradient is only marginally sensitive to theurea permeability of the terminal IMCD.
' X0 I- t0 \$ z' c; a
When Hargitay and Kuhn ( 14 ) introduced the countercurrentmultiplication hypothesis in 1951, they carried out their formal analysis using a hydrostatic pressure difference but carefully explained that in the kidney the actual driving force was more likelyto be "electroosmotic." Later in the 1950s, Kuhn and Ramel ( 23 ) settled on active salt transport from ascending todescending limbs as the most feasible single effect, and then Nieseland Röskenbleck ( 29 ) briefly considered the ideathat interstitial "external" osmoles might also supply a singleeffect; also, the idea that IM glycolysis might participate wasinvestigated once by in vivo micropuncture ( 30 ), but theidea was abandoned in favor of active transport from the ascendinglimbs. During the 1960s, it gradually became clear that althoughvigorous active salt transport occurs from the MTAL in the OM, this isnot the case in the IM. Thus was posed the enigma that the steepest and major portion of the medullary osmotic gradient is established in theIM with no apparent means of support.
: i% G+ z4 w' v) X0 F. P
The "passive" or "SKR" hypothesis, introduced in 1972 byStephenson ( 34 ) and by Kokko and Rector ( 22 ),astutely proposed that the metabolic effort spent in the outermedullary MTAL could serve indirectly for the establishment of the IMosmotic gradient if not one but two solutes were recycled, namely, NaCland urea. Permeabilities of individual nephron segments were unknown at the time, but the SKR hypothesis made specific predictions that mustobtain if urea in fact serves the proposed external osmole role. Inparticular, IM LDL must have very low urea and salt permeabilities andhigh water permeability and LAL must be more permeable to NaCl than tourea. Under these conditions, they predicted that the urea that entersthe deep medullary interstitium from the collecting ducts will drawwater from LDL, thereby concentrating their luminal solutes, especiallyNaCl, which will then diffuse passively out of the water-impermeableascending limbs on the way back up, thus providing an osmotic singleeffect with no local expenditure of metabolic energy. Subsequentmeasurement of tubular permeabilities by in vitro microperfusion was indirect conflict with these predictions; e.g., P u LDL was found to be low in the rabbit,which does not develop a highly concentrated urine, but quite high inspecies with well-concentrated urine, such as the chinchilla( 6 ) and the rat ( 15 ).4 v: r3 {) m4 y5 N, W
, K6 q# {0 t( x; p8 T
The model proposed here is the first to reconcile these permeabilitydata with an appreciable IM NaCl gradient, although it still gives nosatisfactory explanation for the observed IM urea gradient. The centralnew feature is that metabolically produced osmoles play the rolepreviously attributed to urea. Because the loops of Henle andcollecting ducts are essentially impermeable to glucose and lactate(their permeabilities have not been measured, but their normalconcentrations in the urine are very low and there is no evidence fortheir reabsorption in segments past the proximal tubule), the externalosmoles contributed by lactate production can exert their full osmoticeffect across the epithelium of the descending limb and collectingduct. The effective accumulation of lactate in the deep IM will befavored by reduced IMBF [known to be the case in antidiuresis( 3 )] and high DVR lactate permeability. Concerning thelatter, it remains to be seen whether there are specific lactatetransporters in DVR and, if there are, whether they are regulated bylocal or systemic signals. Specific transporters of the MCT family areresponsible in other tissues for one-to-one coupled exit of lactate andprotons from cells undergoing anaerobic glycolysis ( 12 ),and the MCT-2 isoform has been localized to basolateral membranes ofouter MTAL ( 9 ), but their localization and the regulationof their expression in IM structures remain to be characterized.

Although our simulation results with this flat model provide supportfor the possible contribution of metabolically produced osmoles in theurine-concentrating mechanism, it is still clear that this model fallsshort of being a definitive explanation. Comparison of the results inTables 3 and 5 for simulations with the two different parameter setsindicates that the problem remains complicated. Although a thoroughsensitivity analysis to explain the differences is beyond the scope ofthe present study (we believe this would be more approriate in thecontext of a 3-D model treating the vascular bundles and otheranatomical details), some indications are possible.& `0 X8 m8 i. [& R: D6 v

Several symptoms are visible in the numerical results given in Table 3,the most notable being the high (TF/P) inulin value in theterminal CD. It reaches 1,400 here, whereas reported physiological values above several hundred are uncommon. This problem is typical offlat, central core-type models. Nonetheless, as seen in Table 5, thehigh- P u parameter set performs much better bythis criterion. In addition, FE u increases here to 15%,whereas it is only 2-4% in the baseline case.
/ C6 s. B! `% ?; K& X
Inspection of the model's behavior suggests that this and otherproblems stem from the impossibility, in such flat models, ofaccommodating the additional recycling paths available in real kidneysthanks to the vascular bundle arrangement of the inner stripe. Ourinclusion of nonreabsorbable solutes (represented as "glucose" inthe nephrons) only partially addresses this problem. It is alsointeresting to note in this context that thehigh- P u parameter set gives more physiologicallevels of flow [(U/P) inulin = 620, and end distal(TF/P) inulin = 39] while still attaining aconsiderable osmotic gradient. This issue thus awaits implementation ina 3-D model for further clarification.
2 C7 q# t, |+ f6 t
Suggestions for experimental tests. 1 ) Given modern micromethods for enzymatic analysis oflactate (and urea and glucose) concentrations in nanoliter samples, itwould be worthwhile to repeat the in vivo papillary vasa recta micropuncture experiments of Ruiz-Guinazu et al. ( 30 ).Collection of the microliter volumes of fluid required by them forenzymatic analysis required long collection times that necessarilycompromised the medullary gradient. It should now be possible to do themeasurements in frankly antidiuretic animals. 2 ) Our resultsstrongly suggest that the glucose permeability of the DVR must beuncharacteristically low (compared with vessels in other tissues) toefficiently deliver glucose to the deep medulla, i.e., to avoid IM"hypoglycemia" by the same countercurrent-exchange effect that isresponsible for the IM hypoxia ( 19 ). Measurement of DVRglucose and lactate permeabilities would require in vitromicroperfusion. 3 ) Our results (Fig. 5 ) suggest that IMaccumulation of lactate would be optimal only if DVR lactatepermeability is considerably higher than measured DVR permeabilities toNaCl and urea. This opens the possibility that there may be specificlactate transporters in DVR epithelium. It would be interesting tosearch for such transporters and, if any are found, to see whether theyare sensitive to local autocrine or paracrine factors or to thehormones involved in antidiuresis and regulation of IMBF.
1 S. Y- [# \5 P3 o5 [
In conclusion, this flat-model exploration of a possible role forIM metabolic osmole production in the urine-concentrating mechanismfurther confirms the feasibility of the idea that we first explored ina simple vasa recta model ( 41 ). Not only is this the firstscenario to reconcile the high measured P u LDL with the establishment of an IMosmotic gradient, but it also suggests a role for the previouslyparadoxical high P u LDL; that is, by allowing Henle's loops to participate in urea recycling, it favors the papillary accumulation of urea. Thus in this scenario, the regulation of urea balance may be uncoupled from a primary role insalt or water balance. This would make sense from a comparative physiological standpoint, considering that many of the rodents havingthe highest concentrating ability have a vegetarian diet ( 2 ), so their urea load is less than that of omnivorousspecies like the rat. What's more, the papillae of such species aretypically much longer and have a higher fraction of nephrons extendingdeep into the papilla than does the rat kidney. These two features seemed paradoxical in the context of the urea-centered SKR hypothesis based on the rat kidney, but they make sense for the presenthypothesis, because the additional tissue mass should provide moremetabolic osmoles, and the greater papillary length should improvelactate trapping by recycling ( 41 ). These issues and theshortcomings of the present flat model should be further explored in3-D models of the medulla to explore the advantages of the additionalrecycling pathways afforded by the vascular bundles.. z# ~7 K8 v4 o3 z) W4 G

ACKNOWLEDGEMENTS$ B0 L+ ^# n( @6 M; b1 ^3 @7 f/ E  [
! y6 ^  d2 |" w- f
This study was financed by the general operating funds of InstitutNational de la Santé et de la Recherche Médicale Unit 467 and the Necker Faculty of Medicine, University of Paris 5.$ ~8 h( ]5 x8 X, F
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