Pfliigers Arch. 360, 25--44 (1975) 9 by Springer-Verlag 1975

The Hydraulic Conductivity of the Rat Proximal Tubular Wall Determined with Colloidal Solutions A. E. G. Persson, J. S c h n e r m a n n , B. A gerup, a n d N.-E. E r i k s s o n Department of Physiologic and Medical Biophysics, Biomedical Center, University of Uppsala, Sweden, and Physiologisches Institut, Universit/~t Miinchen, Germany Received June 20, 1975 Summary. The hydraulic conductivity of the rat proximal tubular wall was determined using colloidal solutions perfused in short (50--200 tzm) (SMP) or long (90--2000 fxm) (LMP) proximal tubular segments. In SMP human serum albumin (HSA) or polyvinylpyrrolidone (PVP) was added to rafflnose solutions. A L v of 0.019 nl 9rain-1 9 -1 9 I-Ig-1 was found when high colloid concentrations were used while values of 0.055--0.092 were found when low colloid concentrations were used. In other experiments, the Lv was determined by perfusing short tubular segments with pure raffmose solutions. A value of 0.015 n l . rain-1- ram-1, mm Hg -I was found. This is twice the value found when rafflnose solutions were perfused through long tubular segments and it is concluded that the short microperfusion technique overestimates Lp with a factor of two. When microperfusions of long tubular segments were conducted, PVP was added to an equilibrium solution consisting of NaC1 (110 raM) and raffinose (80 raM). L~was found to be 0.018--0.021 when high colloid concentrations were used, while a value of 0.029 was found when a low colloid concentration was used. As found in both SMP and LMP a decrease in Lp's with increasing colloid concentrations indicates that a significant influence of radial concentration differences is highly probable. I t is therefore suggested that the highest Lp derived when using the lowest colloid concentrations represents the best estimate. With this Lv value (0.03--0.05 nl 9rain-1. mm -1. mm l:fg-1) and the existing transtubular hydrostatic and oneotic pressure difference it can be calculated that these passive forces might constitute the driving force for 1/a of the fluid reabsorbed in the proximal tubule.

-

-

K e y words: Proximal Tubule -- Microper/usion Technique - - Colloidal Solutions Hydraulic Conductance.

A n impressive a r r a y of e x p e r i m e n t a l evidence indicates t h a t p r o x i m a l t u b u l a r n e t fluid a b s o r p t i o n is affected b y changes i n the p e r i t u b u l a r hydrostatic a n d oneotie pressure. A t t e m p t s to ascribe this effect to a direct Starling-like action of loeritubular physical forces have n o t been u n d e r t a k e n since the m a g n i t u d e of the h y d r a u l i c c o n d u c t a n c e a p p e a r e d to exclude a direct c o n n e c t i o n b e t w e e n pressure a n d flux changes. However, it is to be noted, t h a t evidence from other epithelia a n d m e m b r a n e s

26

A . E . G . Persson et at.

p o i n t s to t h e p o s s i b i l i t y of a c o r r e l a t i o n b e t w e e n t h e g e n e r a t e d flux a n d t h e q u a l i t y of t h e force u s e d to p r o d u c e t h e fluid m o v e m e n t [4, 7, 20, 35]. These results i m p l y t h a t h y d r a u l i c c o n d u c t a n c e across c o m p l e x b a r r i e r s m i g h t n o t be a well defined q u a n t i t y , b u t m a y v a r y as a f u n c t i o n of t h e force. Since h y d r a u l i c c o n d u c t a n c e of t h e p r o x i m a l t u b u l a r e p i t h e l i u m has been m e a s u r e d w i t h low m o l e c u l a r weight p a r t i c l e s such as raffinose or m a n n i t o ] [26, 34] a n a t t e m p t was m a d e to assess its value b y m e a s u r i n g t h e t r a n s t u b u l a r w a t e r flux p r o d u c e d b y colloid osmotic p r e s s u r e gradients. As t h e results c l e a r l y d e m o n s t r a t e t h i s a p p r o a c h is c o m p l i c a t e d b y t h e fact t h a t t h e i n d u c e d w a t e r fluxes g e n e r a t e b o u n d a r y effects due t o i n t e r n a l n o n - m i x i n g . H o w e v e r , a t sufficiently low colloid concent r a t i o n s t h e h y d r a u l i c c o n d u c t a n c e was f o u n d to be higher t h a n prev i o u s l y a s s u m e d . F r o m t h e s e m e a s u r e m e n t s i t was c o n c l u d e d t h a t t h e existing t r a n s t u b u l a r h y d r o s t a t i c a n d oneotie pressure difference d r i v e s a significant f r a c t i o n of t o t a l n e t fluid r e a b s o r p t i o n .

Methods The experiments were performed on male albino rats of the Sprague-Dawley strain with a body weight of 250--350 g. The animals were anesthetized with Inaetin (ll0mg/kg BW) and placed on a serve-regulated heating pad which maintained body temperature at 37.5 ~ Catheters were introduced into the right jugular vein and the right common carotid artery for recording of the blood pressure. The left kidney was dissected free and fixed with cotton wool in a Lucite holder. The kidney surface was continuously bathed with warm mineral oil to avoid drying of the kidney surface. Throughout the experiment isotonic saline was infused at 0.3 ml/hr 9 100 g t~W to restore fluid losses. Micropuneture experiments were performed by use of a Leitz double headed stereomicroseope. Two different series of experiments were performed. 1. Perfusions over a short segment length (50--200 ~m) (short microperfusions, SMP). 2. Perfusions over a longer segment length (90--2000 ~m) (long microperfusions, LMP). 1. The SMP-technique described by Ullrich et al. [33] was carried out by two operators as follows. A random proximal tubular segment was punctured with an oil filled pipette and subsequent segments of the same convolution were identified by injecting small oil droplets. An 8 ~m tipped pipette connected to a micropeffusion pump was then introduced into a long superficial segment downstream of the initial puncture site. Tubular flow was blocked by injecting an oil block whose position was carefully controlled by quantitative aspiration of the filtrate. A timed quantitative collection of the perfusate was then made in the distal end of the long superficial segment. The length of the perfused tubule was measured with an ocular micrometer. The perfusion rate used was 15 ill. rain-1. In the short mieroperfusion experiments the following perfusion solutions were used: a) HSA-High Raffinose. Solutions of this type were made up with HSA and dissolved in a 236 m3s raffinose solution. The sodium concentration was in all solutions corrected to 25 mM sodium, The solutions were made to contain 0.5 and 15 g-~ HSA.

Hydraulic Conductance of R a t Proximal Tubular Wall

27

b) HSA-Low Ra//inose. Solutions of this type were made up with HSA dissolved in a 180 mM raffinose solution. The sodium concentration was in all solutions 25 mM and the p H was corrected to 7. The HSA concentrations used were 5, 10 and 15 g-~ c) PVP-Low Ra/]inose. Solutions of this type were made from PVP (dialyzed) dissolved in 152 mM rafflnose solutions. The sodium concentrations in all solutions were about 1 mlYL The p H was corrected in all solutions to 7. PVP concentrations were 4, 7.5, 10 and 15 g-~ d) NaCI-Ra//inose. This solution contained 110 mM NaC1 and 130 mM raffinose. 2. The LMP-technique was performed in the same way only that the length of the perfused tubule was determined by injecting on oil column whose length was measured in a long surface segment with an ocular micrometer. This oil column was then shifted until it reappeared in another segment so that also the length of the segments not visible on the surface could be assessed. The perfusion solutions used in the long microperfusion experiments were: e) PVP-NaC1. Solutions of this type contained 110 mM NaC1 used to dissolve 10, 14 and 17 g-~ PVP. /) PVP-NaCl-Ra/]inose. Consisted of 110 mM NaC1 ~- 80 mM raffinose used to dissolve 3.8, 7.5 or 10 g-~ PVP. Two different colloid preparations were used in these studies: a) Human serum albumin (ttSA), freezedried, and dialyzed against distilled water for 3 days at + 4 ~ and contained in mg per g protein: Na 2.5, C1 0. b) Polyvinylpyrrolidone (PVP) (Mean molecular weight 28000) dialyzed against distilled water for 3 days at + 4 ~ using cellophane dialysis tubing. Inulin-l~C was added to the perfusion solutions as a volume marker. The collected samples and standard samples taken directly out of the perfusion pipette after every or every other micropcrfusion wore transferred to a constant bore glass capillary for volume determination. They were then iniected into glass vials for liquid scintillation counting. The scintillation cocktail contained 7 g butyl-PBD (Ciba, Switzerland), 100 ml BBS 3 (Beckman, U.S.A.) and 300 ml of 99.9~ ethanol added to 1000 ml of toluene. The liquid scintillation counter used was a Beckman LS 250. In some experiments of the second series the sodium concentration of the perfusate was determined using a mieroflamephotometer as described by 0berg etal, [23]. The net flux, Jr, was calculated from [ I~Cx -- 1) where

g , = l?x\ l--~-Co

[?x is the collected fluid flow rate and laCx/laCo is the ratio between the inulin-~C activity in the collected and perfused fluid.

Calculations The hydraulic conductivity determined with the short mieroporfusion technique was calculated as follows: The hydraulic water permeability (Lp) was calculated as L~ ~ Jv/~ where oncotie pressure (z) was calculated from the colloid concentrations by application of the Landis-Pappenheimer equation (z = 2.8 C + 0.18 C~ + 0.012 Ca) for HSA [15] and the Vink equation (~ = 6.7 C -[- 1.31 C~ + 0.109 Ca) for PVP [36], where C denotes albumin or P V P concentrations in g-~ and ~ the colloid osmotic pressure in mm I-Ig. The use of Landis-Pappenheimer equation to calculate the albumin oncotic pressure at a p H of 7.0 and an electrolyte concentration of 25 to 50 mM might result in a pressure value 10--15% less than the true pressure due to a

28

A . E . G . Persson et al.

Donnan effect [29]. As the changes in volume were relatively small no correction was made for changes in concentration occurring during the sojourn of the perfusion fluid in the tubule [33]. I n long mieroperfnsions using solutions 5 the colloid concentration in the perfnsed fluid was calculated as if no leakage of protein occurred. The hydraulic conductivity was only calculated for the experiments of the series using solutions of type 6. This calculation was carried out as follows. The driving forces for fluid transfer across the tubular wall in these experiments can be expressed by:

Pn = Po~ + Pc~ -- ~

(1)

where Pn is the net driving pressure across the tubular wall, Poi is the osmotic pressure of the raffinoso solution in the tubular lumen, and P a is the colloid osmotic pressure inside the tubule. The symbol 6 with the dimension of pressure includes all other driving forces which act to move fluid in either direction. When colloids are absent from a perfusion solution, containing 80 mM raffinose and 100 mM NaC1, no net movement of fluid or NaO1 across the proximal tubular wall occurs. I n this condition, ~ signifies the driving force for fltlid absorption which is exactly balanced by the force due to an 80 mlV[ raffinose solution inside the proximal tubular lumen. The value of 6 depends on the reflection coefficient for raffinose a as the pressure of the raffinose solution can be expressed as Po~ = a P~TCo (X)

(2)

where a is the reflection coefficient for rafflnose, I~T has its usual meaning and Co (X) is the concentration of raffiuose. The colloid osmotic pressure of ]?VP was calculated according to the general expression: Pe~ = a Cc (X) -]- fl [Co (X)] z + y [Ce (X)] a

(3)

where Cc (X) is the colloid concentration and a, fl and ~, are the virial coefficients, determined by u [36] to be 6.7, 1.31 and 0.109 respectively. The influence of radial concentration gradients is neglected, but will be discussed later. The solute concentration at distance X along the perfused tubule can be obtained from the relation: (0) G (x) = G (o)- ~ ( x ) (4) where Cs (X) and 1? (X) denote solute concentration and flow rate at distance X and Cs (0) and l? (0) the corresponding initial values. This equation is valid if the solute molecules do not leak across the tubule wall. The fluid entering the tubule has a flow rate of 1~(0), a colloid concentration C~ (0) and a rafflnose concentration of Co (0). After a perfused distance X the fluid has the flow rate l? (X) and the colloid and raffinose concentrations are C~ (X) and Co (X) respectively. When fluid has moved further a distance 3 X , the flow rate is ~z(X 4- AX). Assuming that the tubule has a cylindrical shape and that the solutes within the tubular segment do not leak out, the rate of the fluid leaving a small disc with a thickness of LIX and radius r can be expressed as ?(X+3X)=

~(X)+AX'L.'P.

where Lv is the hydraulic conductivity of the wall. This gives

d ? (X) dX

--L~'P~.

(5)

tlydranlic Conductance of Rat Proximal Tubular Wall

29

Substitution of Eq. (2) and (3) into 1 and then 1 into 5 yields: ~ ? (x)

dX

--Lp [aI%TCo(X)+~C~(X)+fl[Ce(X)]~4-Z[Cc(X)]3--~]. (6)

Writing both Co ( X ) and Cc (X) according to Eq. (4) gives: d? (X)

_ L~

aRT

ex

oo (o). P- (o)

7 (~

oo (o). P- (o)

+ ~'

r, (x)

This differential equation was integrated numerically using the fourth order Rtmge-Kutta method with a step length of g ~zm [14].

Results I n the short mieroperfusion experiments using t y p e i solutions, shown in Fig. 1, the net fluid flow was directed into the tubular lumen. The n u m b e r of observations for 0,5 and 15 g-~ I-ISA were 15, 20 and 23 respectively. The equation for the regression line was calculated to be J v = - - 0.055 ~ -- 0.72 (r = 0.54) where ,Iv denotes the net fluid flux (n]. rain -1. m m -1) and oncotie pressure (ram Hg). The slope of the regression line was significantly different from 0. The microperfusions with t y p e 2 solutions yielded the results shown in Fig.2. The solution contMned 180 ram raffinose with 5, 10 or 15 g-~ HSA. The sodium concentration was 25 mM in all solutions. The lower

Jv

1

1

(hi. mm.min )

236mM Raffinose

+2

0 50

" ' \ ~ {5g~~

100

150 {ram Hg)

Oncotic Pressure

-5

-10 Fig. 1. The net fluid flow (Jr) as a function of the colloid osmotic pressure of HSA dissolved in a 236 mM raffinose solution. The interrupted line is the calculated regression line

3O

A. E. G. Persson et al.

t.,

Jv 1 -~ ( n!. rnr~ rain )

+5

180 mM Raffinose

.. ~15g%1 I

I

l

I',_I I I "50. "-,

I

I'

I II~0

I

I

Hg)" Oncofic Pressure iSOI(mrn

-5

-10

Fig. 2. The net fluid flow (Jr) as a function of the colloid osmotic pressure of HSA dissolved in a 180 mM raffinose solution. The interrupted line is the calculated regression line

colloid concentrations caused influx of fluid into the tubule. The regression line for all data was J v ~ - 0 . 0 9 2 ~ - ~ 4.0 (r = 0.54). The number of observations for 5, 10 and 15 g-~ HSA were 11, 9 and 12, respectively. Experiments with type 3 solutions are represented in Fig. 3. There was a relatively large difference between the fluid fluxes at the low concentrations used, whereas smaller differences were found at the higher concentrations. The regression line for all data was Jv = --0.019 ~- 10.3 (r -~ 0.55), while the linear regression for the lower concentrations 4 and 7.5 g-~ was J v = - 0.075~ + 17.4 (r ~ 0.47). For 4, 7.5, 10 and 15 g-~ P V P the number of observations were 13, 31, 29 and 24 respectively. To calculate if there was a significant difference in slopes at different oncotic pressures the mean slopes from 3 animals where both 4 and 7.5 g-~ P V P was used were compared to the mean slopes from 6 animals in which 10 and 15 g-~ P V P were used. I t was found t h a t the former slopes were significantly (P < 0.001) higher than the latter slopes. I t should be pointed out t h a t the slopes from different animals with the same concentration difference did not v a r y much although the magnitude of flows varied resulting in the relatively large scatter of data shown in Fig. 3. These results seem to indicate t h a t the hydraulic conductivity of the tubular wall m a y be dependent upon the magnitude of the colloid concentration acting as a driving force. The hydraulic conductivity of the proximal tubular wall determined with the colloids t t S A and P V P as the osmotically active substances was

IIydraulic Conductance of Rat Proximal Tubular Wall

31

152 mM Raffinose

\\ +10

.~

g0lo)

\\ "\..

\ " "--\,T

*5

"-

T

& (I0g%)

\

0

i

100

..

!

I ........

:

I'~'"".~. "" I

500

i

--.,.. ... --.

800

(rnm.Hg) Oncotic Pressure

-5

Fig. 3. The ne~ fluid flow (J~) as ~ function of the colloid osmotic pressure of PVP dissolved in a 152 m ~ raffiuose solution. The interrupted lines are the calculated regression lines for She two lower colloid concentration solutions and for all solutions, respectively

found to v a r y between 0.019 nl 9rain-: - r a m - : 9 Hg -1 and 0.092 nl 9 rain -1- r a m - : , m m H g -1 (Table 1). To correlate these measurements ~ 4 t h those obtained using mannitol or raffinose as the osmotically active substance in long microperfusions [26, 34] a type 4 solution was used. Assuming a reflection coefficient for raffinose of 1.0, the hydraulic conductivity was calculated to be 0.015 n l . r a i n - : , m m - : . m m H g _4:0.009 S.E. (n = 31). I n the first series of long perfusion experiments using solution of t y p e 5 an a t t e m p t was made to measure hydraulic conductance analogous to the method described b y Ullrich et al. [34]. I n this technique water permeability is derived from the attainment of plasma osmolar:ty in equilibrium solutions (110 mM NaC1-F 80 mM raffinose) made hypotonic or hypertonic b y removal or addition of raffinose. I n earlier experiments it was found t h a t a similar situation of steady state at zero net flux is created when tubules contained a solution of about 110 mM NaC1 + 14 g-~ P V P [25]. B y elevating or reducing the P V P concentration to 17 and 10 g-~ respectively solutions were made hypersonic or hypotonic and the approach of the osmotic equilibrium concentration was measured. The results are diagrammatically presented in Fig.4. As indicated b y a change in the cMcutated colloid concentration in the perfused fluid a small outflux was observed with a P V P concentration of

32

A. E. G. Persson et al. Table 1. Summary of results (short microperfusions)

Solution

Hydraulic conductivity (L~) nl 9rain-1. mm -1. mm Hg -1

l. HSA dissolved in 236 mM rafflnose solution with sodium correction in concentrations of 0.5 and 15 g-~ Whole slope (0--15 g-~ ) (low colloid cone.)

0.055

2. Dialyzed HSA dissolved in 180 m~s raffinose solution in concentrations of 5, 10 and 15 g-~ Whole slope (5-- 15 g-~ ) (low colloid cone.)

0.092

3. Dialyzed PVP dissolved in. 153 m ~ raffmose solution in concentrations of 4, 7.5, 10 and 15 g-O/o

Whole slope (4--15 g-~ ) (low and high colloid cone.) initial slope (4--7.5 g-~ ) (tow colloid cone.)

0.019 0.071

4. Raffinose 130 m)s in 110 mM NaCI solution

0.015

PVP (g%) Z, 9 1 4 9

i

16

9

9

9

9

9

9

mm

m-m9

m

m

m

14

i

B

9

9

12

m

10

I

I

I

500

I

I

I

-

~

~

1000

~

J

~

~(~m)

Perfused tubular length

Fig.4. The calculated PVP concentration in the perfused fluid as a function of the perfused tubular length using a perfusion solution consisting of 10 g-~ PVP (.), 14 g-~ PVP (.) and 17 g-~ PVP (A) dissolved in 110 mM NaC1

Hydrat~tic Conducta~nceof l~a,t Proximal Tubular Wail

33

14 g-~ Thus, the osmotic equilibrium concentration must be slightly higher than that found in the earlier study, a difference which is possibly due to a somewhat different distribution in molecular weights of the P V P brands. A much greater outflux was found when the PVP concentration was 10 g-C/0, while the direction of water flow was reversed with a PVP concentration of 17 g-0/0. I f a PVP concentration of 15 g-O/ois assumed go represent, osmotic equilibrium it is evident from inspection of Fig.~ that neither the outflux nor the influx is large enough to give rise to this concentration even after perfusion distances of more th~n I000 ~zm. When raffinose was used as the osmotically active substance osmotic equilibrium occurred a.fter 1000 ~m [34]. Using solution k~-t)e 6 the followings results were obtained. The length of the perft~sed tubules ranged from 90 ~2000/ira. The mean perfusion rates in the perfusion solutions containing 3.8 g-C/0, 7.5 g-C/o, and 10 g-~ PVP were (means ~ S . E . ) 16.2 ~ 0 . 3 nl/min, 16.1/=0.4 nl/min, and 16.1 :~::0,5 nl/min respectively. Fluid flow was directed into the tubule in all three situations. Tubular hydraulic conductance was evaluated by using Eq. (7) in the following way. Since t:'(0), I~(X), and (X) were measured and the constant ~ can be determined as described above, only L~ and O'raff are unknown variables. These parameters are determined by fitting Eq. (7) to the experimental values using the least, squares method. The error in the measurement of the independent variable (X) is small justii:ying the use of this method. The fitting procedure was performed as follows. Values, ranging from 0--1 in increments of 0.t are assigned to the reflection coefficient for raffinose, Craft. Taking one of the values for ffraff, a number of values within a wide range for L~ was assumed and the deviation of the experimental findings from the values calculated by using equation (7) was examined. In this manner, the best value for L~ was obtained for each O'raff by the criterion of accepting the value at which the sum of least squares of the deviations was minimal. Next, the smaltes~ least squares values were plotted against ffraff- The vaiue of ~rar~ corresponding to the smallest, of all the minima was accepted as the best measure of the reflection coefficient. The best ~a.tue for Lz~ at this O-raft WaS &1SO accepted. One typical fit for L~ at an assumed r of 0.6 for raffinose using the perfl~sion solution consisting of 80 m N raffinose, i l 0 m M NaC1 and 10 g-O/0 PVP is shown in Fig. 5. The sums of the least squares are plot~ted against values for L~. The least scatter was obtained at a Lp value of 0.018 n l . rain -i 9 mm -~ 9mm Hg -i. The upper panel in Fig. 6 shows the best values of Lv for the different values of ~r for raffinose using the solution containing 10 g-~ PVP~ The lower panel in :Fig. 6 shows the sum of least squares plotted against the different assumed ~rarr values. I t can be seen that even though each Lp 8 Pfli~gers Arch., VoI. 860

A. E. G. Persson et al.

34

Sum of [east squares

\

\

10

I~ o

I

I

I

I

1,0

I

I

e./Q/I

I

I

I

1,5

I

l

I

L

I

2,0

L

I

I

2,5 102

I

Lp

Fig.& Shows a t y p i e a l fit for Lp at an assumed ~ of 0.6 for raffinose using the perfusion solution containing 10 g-~ PVP. On the ordinate is the sum of the least squares

/

102. Lp

.//

2,5

2,0

./,/" 1,C'

i

i

i

i

f

i

i

t

]

i

o,s

1,o

1C -Sum of least squares

I

I

/

I

I

0)5 L

_.

OR

~

~

F

~ 1,0 OR

Fig.& Upper panel. Shows the best values for Lv for different d:s for raffinose using the 10 g-~ PVP solution. Lower panel. Shows the sum of least squares plotted against different assumed 6: s for raffinose

Hydraulic Conductance of Rat Proximal Tubular Wall

35

Table 2. Summary of results (long microperfusions) PVP g-~

6 raffinose (fitted)

L~ nl 9min -1 9 (fitted)

3.8 7.5 10

0.2 0.5 0.6

0.029 0.021 0.018

-1 9mm Hg

No. 8 13 25

value was obtained as that which had a minimal scatter at the given (~raff there is an overall minimum value of all these minima at a (~rarf of 0.6. At this (rraffvalue, L~ was determined to be 0.018 nl 9 rain -I 9 -I -mm fig -~ illustrated in the upper panel. Thus using the perfusion solution containing i0 g-~ PVP a (~raff of 0.6 and L~ of 0.018 were accepted as the values for the two unknown quantities. The same fitting procedure was repeated for each group of experiments using 7.5 g-~ PVP and 3.8 g-0/0 PVP added to the ii0 mM NaCI and 80 mM raffinose solution. I n Table 2, the best values are given ibr each group of experiments. Using 7.5 g-~ P V P in the perfusion solution araff was 0.5 and L~ was 0.021 nl 9 rain -1 9 -~ 9 m m H g -1. Using 3.8 g-~ P V P , the values for ara~f and L~ were 0.2 and 0.029 n l . rain -1 9 -1 9 t I g -1. F r o m these values it appears that with decreasing PVP concentration there is an increase in Lp and a decrease in (~raff. Hydraulic conductance measured with raffinose or mannitol as the osmotically active substances [26, 34] equalled 0.008--0.009 nl 9 rain -~ 9 m m -~ 9 Hg -I which is substan~ tially lower t h a n the values obtained in the present s t u d y using P V P as the driving osmotic particle species. To test the relevance of the fitting of Eq. (7) to the experimental data, flow rates at each tubular length were calculated with the optimal values for Lp and araff. Thus, the difference between the calculated flow rates a n d the initial flow rate, Vcalc, can be compared to the measured difference between these variables, Vmeas. There was good agreement between measured and calculated flow rate changes when the best fitting values for Lp and ar~ff are used. The regression lines for the solutions containing 10 g-~ 7.5 g-~ a n d 3.8 g-~ P V P were y = 1.0 x --0.12 (r=0.9), y~ 1.1x--0.15 ( r = 0 . 7 ) , and y = 1 . 1 x - - 0 . 0 8 (r == 0.7). None of these slopes were significantly different from the line of identity. I n contrast, when a O'raff of 0.9 and the corresponding Lp of 0.024 nl 9 min -~ . m m -1 9 m m H g -1 was used for the calculation of Vealc in the 10 g-~ P V P group the regression line for these d a t a was y -= 1.5 x -- 0.99 (r = 0.89) and the slope is significantly different from the line of identity. Thus, these values for Lp and (Yraffdo not represent a good fit between the experimental points and Eq. (7). 3*

36

A.E.G. Persson et al.

To test whether a solution consisiting of 110 mM i~aC1 and 80 mM raffinose was an equilibrium solution, microperfusions with a perfused tubular length of 400--1000 ~zm were carried out. The mean net outflux through the tubular wall was 0 . 0 9 • rain -1 . r a m -~ (~=S.E.) (n ---- 15) not significantly different from zero. In some of the long perfusion experiments the sodium concentration was measured. The mean concentration difference for sodium between the perfusion and perfused fluid was 4.4 =k 1.5ram (S.E.) (n ~ 35) which was not significantly different from zero. Thus there was no significant change in the sodium concentration during the perfusions. Discussion

Evidence from both in vivo and in vitro experiments indicates that proximal tubular fluid absorption depends to some extent upon peritubular oncotic and hydrostatic pressure [3, 18, 31]. The mechanism of absorption change is usually related to one of the possible consequences of altered uptake of the tubular reabsorbate into the pcritubular capillaries. Lewy and Windhager [18] have proposed that accumulation of fluid within the interstitium induces a rise of interstitial and intercellular pressure and that the altered interspace geometry affects absorption in an unknown way. The necessity to ascribe the absorption change to such an indirect effect of transepithelial physical forces is based on the earlier finding that proximal tubular hydraulic permeability is too low to relate the pressure and flux changes directly [26, 34]. However, the assessment of hydraulic conductance in other biological tissues suggests that this conclusion may be misleading. ]in such different barriers as the squid axon sheath [35], the dog gastric mucosa [20], and the endothelium of brain capillaries [4, 7] the hydrostatic pressure has been found to produce a much larger water flux than the equivalent osmotic pressure generated by small molecular weight particles. Since relatively impermeant particle species were chosen for these experiments, this difference may not only represent the influence of a low reflection coefficient of the osmotic particle at this particular boundary. Furthermore, a nonspeciflc increase in the membrane permeability due to the hydrostatic pressure elevation was excluded in the experiments of Vargas by the observation that the electrical resistance and glycerol outflux were only modestly changed [35]. I t should be realized that proximal ~ubular hydraulic conductance was derived from raffinose or mannitol induced water fluxes while normally only oncotic and hydroStatlc pressure differences exist across the tubular wall. Thus, if proximal tubular L v depends also on the quality of the force used to create water fluxes, the changes in adsorption produced by a certain change of

Hydraulic Conductance of Rat Proximal Tubular Wall

37

transtubular Starling forces cannot be predicted from the hydraulic conductance measured with osmotic pressure differences. Therefore an attempt was made to derive a value for proximal tubular Lp from colloid osmotically induced water fluxes.

Short Microper/usions (SMP) The microperfusion technique used in these experiments is similar to that described by Ullrich [33]. The advantage of this method is that the short contact time tends to minimize changes in the composition of the perfusion solution. Since the sodium concentration in all perfusion solutions is lower than the equilibrium concentration, sodium flows rapidly into the perfusion solution. However, as found by Ullrich [33], the rate of sodium influx is constant regardless of the rate and direction of the net water flow. This implies that it is not necessary to consider different sodium concentrations in the perfusion fluid when calculating the hydraulic conductivity. For this calculation the colloid concentration was assumed not to change significantly along the perfused segment. Using raffinose as the driving force in short microperfusions experiments (SMP) hydraulic conductivity was higher than reported by several laboratories using long tubular segments [5, 17, 26, 32, 34]. I t has been noted earlier that unidirectional outflux of radioactive sodium [21] or chloride [27] was higher in the immediate vicinity of the perfusion pipette. Since the formation of a dead-end loop proximal to the perfusion pipette was avoided in our study it is possible that the increase in permeability was indeed caused by the micropuncture intervention as suggested by Morel and Murayama [21]. However, when colloids were used as driving force in the same type of experiments Lp was found to be 4--6 times the raffinose value. As can be seen in Table 1 there was a tendency for L~ to decrease with higher colloid concentrations (Table 1, solution 3). This observation may be related to differences in the viscosity of the perfusion solutions. With increasing viscosity the internal mixing rate is reduced so that radial gradients in colloid concentration are generated. Hydraulic conductance will therefore be underestimated when more concentrated colloid solutions are used. Consequently, the best approximation of Lp is probably obtained with solutions of low colloid concentration. This value is 4--6 times higher than the Lp determined from raffinose induced water fluxes and 7--10 times higher than found by Ullrich et at. [34] and Persson and Ulfcndahl [26] using long tubular microperfusions with raffinose or mannitol (Table 3). Due to the methodical influence of SMP on tubular permeability it is difficult to compare the "colloidal" Lp directly to the "osmotic" Lp determined in LMP. I f the relationship between "colloid" and "rafflnose" Lp, is the

A.E.G. Persson et al.

38

Table 3. Comparson between Lp's obtained by others to those obtained in this study Osmotically active solute

Raffinose

Lp nl. rain-1 9

-i 9

short (< 200 ~xm)

long (> 200 ~zm)

0.007 [ref. 32] 0.015 (type 4)

0.009 [rcf. 5, 15, 313 0.010 [ref. 30] 0.004 Lsl [ref. 9] 0.003 Lp2 [ref. 9]

l~annitol Colloid, low cone.

Hg-i

0.008 [ref. 25] 0.055 (type 1) 0.092 (type 2) 0.077 (type 3)

Colloid, high cone.

0.029 (type 6)

0.021 (type 6) 0.018 (type 6)

same in long and short microperfusions a value of 0.03--0.05 nl rain -1 9 -i 9mm Hg -1 may be a reasonable estimate of the true colloidal Lv. 9

Long Microper/usion ( L M P ) Determination of the hydraulic conductance of the proximal tubular wall with colloidal solutions in long microperfusions is complicated by problems related to the properties of colloid solutions. In a first series of experiments an attempt was made to derive L~ from the attainment of osmotic equilibrium analogous to the method of Ullrich et al. [34]. We have shown earlier that luminal application of a solution containing 110 mM NaC1 and 14 g-~ of PVP generates a steady state situation of zero net sodium and water fluxes [25]. In theory then, it should be possible to derive Lv from water fluxes induced by making this "equilibrium solution" hypo- or hypertonic by removing or adding PVP. However, even after perfusion distances of more than 1000 tzm osmotic equilibrium was not reattained as predicted from the findings of Ullrieh et al. [34]. This observation most clearly indicates that rapid initial water fluxes create a local osmotic equilibrium at the luminal membrane. Internal non-mixing in highly concentrated colloidal solutions prevents attainment of osmotic equilibrium in the center core of the fluid column. Consequently a technique had to be developed which allowed Lp to be estimated with considerably lower colloid concentrations. I n these ex-

Hydraulic conductance of gat Proximal Tubular Wall

39

periments an equilibrium solution consisting of 110 mM NaC1 and 80 mM raffinose was used which was made hypertonie by adding small amounts of PVP. For the derivation of L~ in this experimental situation a theoretical treatment was applied which considered the presence of two relatively impermeant solutes. When long tubular segments are perfused considerable volume changes occur which amounted to as much as 200/0 of the initial perfusion rate. Consequently, the total osmotic force exerted by raffinose and PVP is significantly altered and the extent to which raffinose and PVP respectively contribute to net volume flux cannot a priori be estimated. To derive Eq. (7) we made the assumptions that the sodium concentration remains unchanged and that a solution consisting of 100 mM NaC1 and 80 mM raffinose does not induce a net fluid flux. The validity of both assumptions was verified in additional experiments which confirmed the earlier findings of Kashgarian et al. [13]. Thus, the presence of 80 mM raffinose exactly balances all other forces which tend to move fluid in either direction across the tubular wall. Furthermore, one ,nay assume that the sum of these forces, b, remains unchanged when a net fluid flux across the tubular wall is induced by adding colloids to the pcrfusion solution. Functional integrity of the tubular cells in the presence of colloids is suggested by normal transepithelial concentration gradients for sodium in colloid containing stationary fluid columns [25] and by normal net fluxes in segments after exposure to high colloid concentrations. As summarized in Table 2 Lv's determined with this technique varied between 0.018 and 0.029 n] 9rain -1 9mm -1 9mm Hg -1. As already noted in SMP experiments higher values of Lp are associated with lower colloid concentrations. One may safely assume that the reason for this correlation is again related to the dependency of unstirred layer generation on fluid viscosity. Ideally then, hydraulic conductivity should be attained with infinitely low colloid concentrations. Since this is technically unfeasible the best approximation of Lp, in our opinion, is obtained with the lowest colloid concentrations. Thus, a proximal tubular L~ of 0.029 nl 9rain -1 9mm -1 9mm Hg -1 probably approaches the true Lp although is still may represent an underestimation. This value is reasonably close to that obtained in SMP if one considers the likelihood that SMP experiments arc associated with an increase of both "raffinose" and "colloid" Lp. Furthermore, from the change in net fluid flux induced by changes of luminal hydrostatic pressure we have recently estimated a value for "hydrostatic" Lp of about 0.04 nl 9rain -~ 9mm -1. mm g g -1 [30]. Thus, results obtained with three different techniques are consistent with our contention that hydrostatic and colloid osmotic pressure gradients are more efficient in driving fluid across the proximal tubular epithelium than equivalent pressures exerted by raffinose.

40

A.E.G. Persson eta/.

Included in Table 2 is the result that the reflection coefficient for raffinose was as low as 0.2 when the lowest colloid concentration was used. This result is in agreement with the observed differences in osmotic efficiency between raffinose and colloids. The general assumption that the reflection coefficient for raffinosc is close to unity in the proximal tubule [34] is mainly based on the finding of a relatively low permeability for raffinose (10 -5 c m . see -i) [8]. However, the proximal tubule is a complex structure, and the relationship between permeability and refection coefficient is not predictable with certainty. Hill suggested [t 1] that the reflection coefficient may be low even when there is no solute leakage if the permeation depth into the pore is taken into consideration. In Nccturus proximal tubules, a reflection coefficient for raffinose of 0.51 was found by Benzel et al. [2]. Recently Green et al. [9] have reported results which in two aspects appear to be in contradiction to our conclusions. In split-drop experiments they failed to observe a clear quantitative relationship between intratubular colloid concentration and degree of inhibition of fluid transport. To analyse droplet shrinkage Green et al. [9] traced the outline of the droplet along the external limits of the brush border. The outlined tracings were then cut out and weighed, a procedure which will give information about the Volume of the droplet. According to most authors, however, net flux is not proportional to volume but to surface area or length of the investigated segment. We have recalculated a tubule of 100 ~m length and 19 ~xm radims and found that the initial tl/, including a meniscus correction according to Nakajima et al. [22] and Gy6ry [10] would be 250/0 higher than the one obtained by Green et al. [9]. When the droplet shrinks the meniscus correction will give rise to a progressive increase in difference. At a distance of one diameter between the top of the oil menisci the corrected tl/, will be 500/0 longer. The tl/, curve configuration will show a progressively slower outflux with time as found by Persson et al. [25]. Thus, it is likely that a progressive net flux inhibition would have been detected in the experiments of Green et al. [9] if the analysis would have included a meniscus correction. Furthermore, Green et al. [9] reported measurements of hydrantie conductivity with two methods. Using the method of Ullrich e t a [ . [34] they reported a value of 0.0026 n l . rain - i . mm - i " mm Hg -i (Lv~) which is only one third of the value reported by other investigators [5, 17, 26, 32, 34]. Green et al. [9] suggested that the perfiisions of very long segments explained this difference, since the hydraulic conductance may be increased in the first 200 ~m of the microperfused tubule. If this is the case one would predict a length dependent hydraulic conductance. However, Green et al. [9] found a linear relation between osmotic equilibration and perfusion distance, which indicates that the increase in

Hydraulic Conductance of Rat Proximal Tubular Wall

41

hydraulic conductance in the first portion of the perfused tubule is not large enough to measurably affect determinations of longer segments. An alternative explanation would be that their technique of simultaneous capillary and tubular microperfusion might have induced a change in the tubular-capillary pathways. I t is possible that the high capillary perfusion rate of 1 ~I/min m a y have alt3rcd tubulo-eapillary transfer dynamics as is also indicated by a study of ~gerup [1], who found that a high capillary perfusion rate was associated with a decrease in reabsorptive rate. T h a t such a mechanism m a y have contributed to their results is supported by the measured permeability for raffinose of 6.3 9 10 -s cm/sec which is six times the value reported earlier by Gertz [8]. Thus, their result of an inefficiency of luminally applied colloids on net flux m a y be partly caused by a different methodology without implying that their technique is necessarily inferior. Assuming t h a t the proximal tubular epithelium does not significantly rectify transepithelial water flux [34] an a t t e m p t can be made to estimate the fraction of total net flux which could be driven by transtubular hydrostatic and oncotic pressure gradients. Such estimation requires knowledge of the magnitude of transepitheliM physical force gradients. Since the pathways for fluid transport are unknown it is difficult to describe the forces available for fluid movement. From eleetronmieroscopieal studies [24] it appears t h a t a significant portion of the basal surface of the tubule is in close contact with the capillary endothelium. I t is possible therefore t h a t the tubular absorbate is transported into the capillary by two distinct transport routes. A fraction of the fluid m a y be transferred directly from basal labyrinth across an ultrathin interstitum into the bloodstream while another fraction m a y have to pass a wide interstitial space. The forces acting on tubulo-capillary fluid flow along the first p a t h w a y correspond mainly to the mean oncotic pressure of the peritubular blood of about 28 m m Hg [12]. I n addition, a small hydrostatic gradient in the same direction appears to exist [6, 39]. Hydraulic forces available for fluid transport from tubular lumen into the interstitium have been assessed by pressure measurements in the subcapsular space [37, 39]. In these experiments a combined hydrostatic and oneotic pressure gradient across the tubular wall of about 24 m m Hg was found. Thus, whatever the p a t h w a y for bulk fluid flow m a y be, a hydraulic force of 24--30 m m t t g is available to drive fluid across the tubular epithelium. Average values of SN-GFR, T F / P inulin ratios, and tubular length are 30 nl 9 rain -~ [38], 2.0 [16, 19], and 5 m m [28]. Thus, net fluid flow in the proximal tubule averages about 3 nl 9 min -~ 9m m -1. With a hydraulic conductance of 0.03 --0.04 nl. rain -1. ram -1 9m m Hg -1 as found in this study a flow of about 0.8--1.0 nl. min -1" m m -1 could be maintained whieh represents a fraction of 25--30~ of total net fluid absorption.

42

A . E . G . Persson et al. References

1. Agerup, B. : Influence of peritubular hydrostatic and oncotic pressures on fluid reabsorption in proximal tubules of the rat kidney. Acta physiol, scand. 93, 184--.194 (1975) 2. Benzel, C. J., Davies, M., Scott, W. W., Zatzman, M., Solomon, A. K. : Osmotic volume flow in the proximal tubule of 1Neeturus' kidney. J. gem Physiol. 51, 517--533 (1968) 3. Brenner, B.M., Falchuk, K . H . , Keimowitz, R . I . , Berliner, R . W . : The relationship between capillary protein concentration and fluid reabsorption by the renal proximal tubule. J. clin. Invest. 48, 1519--1531 (1969) 4. Coulter, N. A. : Filtration coefficients of the capillaries of the brain. Amer. J. Physiol. 195, 459--464 (1958) 5. Di Bona, G. F. : Effect of magnesium on water permeability of the rat nephron. Amer. J. Physiol. 228, 1324--1326 (1972) 6. Falchuk, K. H., Berliner, R. W. : Hydrostatic pressures in peritubular capillaries and tubules in the rat kidney. Amer. J. Physiol. 220, 1422--1426 (1971) 7. Fenstermacher, J. D., Johnson, J. A. : Filtration and reflection coefficients of the rabbit blood-brain barrier. Amer. J. Physiol. 211, 341--346 (1966) 8. Gertz, K . H . : Transtubulare Natriumchloridfliisse und Permeabilit~it fiir :Nichtelektrolyte im proximalen und distalen Konvolut der Rattenniere. Pflfigers Arch. ges. Physiol. 278, 336--356 (1963) 9. Green, R., Windhager, E. E., Giebisch, G. : Protein oncotic pressure effects on proximal tubular fluid movement in the rat. Amer. J. Physiol. 226, 265--276 (1974) 10. Gy6ry, A.Z.: Reexamination of the split-oil droplet method as applied to kidney tubules. Pfliigers Arch. 324, 328--343 (1971) 11. Hill, A. E. : Osmotic flow and solute reflection zones. J. theor. Biol. 86, 255--270 (1972) 12. Kallskog, 0., Wolgast, IV[.: Driving forces over the peritubular capillary membrane in the rat kidney during antidiuresis and saline expansion. Acta physiol, seand. 89, 116--125 (1973) 13. Kashgarian, M., StSckle, H., Gottshalk, C.W., Ullrich, K. J. : Transtubular electrochemical potentials of sodium and chloride in proximal and distal renal tubules of rats during antidiuresis and water-diuresis (Diabetes Insipidus). Pflfigers Arch. ges. Physiol. 277, 80--106 (1963) 14. Kunz, K. S.: :Numerical analysis. :New York: McGraw Hill Book Co. Inc. 1957 15. Landis, E. M., Pappenheimer, J. R.: Echange of substance through capillary walls. I n Handbook of Physiology, Circulation, Washington, Am. Physiol. Soc., Vol. II, p. 974 (1963) 16. Landwehr, D., Sehnermann, J., Klose, 1%. M., Giebisch, G. : Effect of reduction in the filtration rate on tubular sodium and water reabsorption. Amer. J. Physiol. 215, 687--695 (1968) 17. Lassiter, W . E . , Frick, A., l~umrich, G., Ullrich, K . J . : Influence of ionic calcium on the water permeability of proximal and distal tubules in the rat kidney. Pfliigers Arch. ges. Physiol. 285, 90--95 (1965) 18. Lewy, J. E., Windhager, E. E. : Peritubular control of proximal tubular fluid absorption in the r~t kidney. Amer. J. Physiol. 214, 943--954 (1968)

Hydraulic Conductance of Rat Proximal Tubular Wall 19. Lowitz, H. D., Stumpe, K. O., Ochwald, B.: Natrium und Wasserresorbtion in den verschiedenen Abschnitten des Nephrons beim experimcntellen renalen Hochdruck der Ratte. Pfliigers Arch. 304, 322--335 (1968) 20. ~Ioody, F. G., Durbin, R. P. : Water flow induced by osmotic and hydrostatic pressure in the stomach. Amer. J. Physiol. 217, 255--261 (1969) 21. Morel, F., lVIurAyama, Y.: Simultaneous measurement of unidirectional and net sodium fluxes in microperfused rat proximal tubules. Pflfigers Arch. 320, 1--23 (1970) 22. Nakajima, K., Clapp, J. R., Robinson, R. R. : Limitations of the shrinking-drop micropunctnre technique. Amer. J. Physiol. 219, 345--357 (1970) 23. 0berg, A., UlfenduhI, I-I. R., Wallin, G. : An integrating flame photometer for simultaneous microanalysis of sodium and potassium in biological fluids. Analyt. Biochem. 18, 543--558 (1967) 24. Pedersen, J. C., ~r A. B. : Ultrastructurat characteristicsofperitubular capillaries and interstitium in rat renal cortex. J. Ultrastruct. Res. 42, 401 (1.973) 25. Persson, A. E. G., Agerup, B., Schnermann, J. : The effect of luminal application of colloids on rat proximal tubular net fluid flux. Kidney Int. 2, 203--213 (1972) 26. Persson, E., Ulfendahl, H. R.: Water permeability in rat proximal tubules. Acta physiol, scand. 78, 353--363 (t970) 27. Radt,ke, H.W., Rumrich, G., Kloss, S., Ullrich, K. J. : Influence of luminal diameter and flow velocity on the isotonic fluid absorption and a6Cl permeability of the proximal convoluted tubule of t,he rat kidney. Pfliigers Arch. 824, 288-- 296 (1971 ) 28. Rector, F. C., Brunner, F. P., Seldin, P. W. : Mechanism of glomerulo-tubular balance. J. clin. Invest. 45, 590--611 (1966) 29. Scatchard, G., Batchelder, A. C., Brown, A.: Preparation and properties of serum and plasma proteins. VL Osmotic equilibria in solutions of serum albumin and sodium chloride. Amer. chem. Soc. 68, 2 (1946) 30. Schnermann, J., Persson, A. E. G., Agerup, B,: Correlation between luminal hydrostatic pressure and proximal tubular fluid reabsorption in the rat ki(~b]ey. Pflfigers Arch. ges. Physiol. 350, 145--t65 (1974) 3t. Spitzer, A., V~'indhager, E. E. : Effect, of peritubular oneotie pressure changes on proximal tubular fluid reabsorptiou. Amer. J. Physiol. 218, 1188--1193 (1970) 32. Stolte, H., Brecht, J . P . , Wiederhol% hL, Hierhottzer, K . J . : Einflul3 yon Adrenalectomie and Glucocortieoiden auf die Wasserpermeabilit~t eorticaIer Nephronabsctmitte der Rattenniere. Pfliigers Arch. ges. Physioh 299, 99--127 (1968) 33. Ullrich, K. J. : Renal transport of sodium. Proc. 3rd Int. Congr. Nephrol. Washington 1966, vol. 1, pp. 48--61. Basel-New York: Karger 1967 34. Ullrich, K. J., Rumrich, G., Fuehs, G. : Wasserpermeabilitiit und transtubularer WasserfluB corticaler Nephronabschnitte bei verschiedenen Diureseznstgnden. Pfliigers Arch. ges. Physiol. 280, 99--119 (1964) 35. Vargas, F. F.: Filtration coefficient of the axon membrane as measured with hydrostatic and oncotie methods. J. gen. Physiol. 51, 13--27 (1968) 36. Vink, I-I.: Precision measurements of osmotic pressure in concentrated polymer solutions. Europ. Polymer J. 7, 1411--1419 (1971)

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37. Wolgast, M., Persson, E., Schnermann, J., Ulfendahl, It., Wunderlich, P. : Colloid osmotic pressure of the subcapsular interstitial fluid of rat kidney during hydropenia and volume expansion. Pfliigers Arch. 840, 123--131 (1971) 38. Wright, F. S., Giehisch, G.: Glomerular filtration in single nephrons. Kidney Int. 1, 201--209 (1972) 39. Wunderlich, P., Persson, E., Schnermann, J., Ulfendahl, H., Wolgast, M.: Hydrostatic pressure in the subeapsular interstitial space of rat and dog kidney. Pfliigers Arch. 328, 307--319 (1971) Dr. A. E. G. Persson Institute of Physiology and Medical Biophysics, BMC, Box 572 S-751 23 Uppsala Sweden