AMERICAN JOURNAL OF PHYSIOLOGY Vol. 228, No. 2, February 1975. Printed

Nonelectrolyte pathway

in U.S.A.

permeability

in Necturus proximal

of the paracellular tubule

CHRISTINE ALBACHTEX BERRY AND EMILE L. BOULPAEP Defiartment of Physiology, Yde University School of Medicine, New Hacen, Connecticut 06510

BERRY, CHRISTINE ALBACHTEN, AND EMILE L. BOWLPAEP. Nonelectrolyte permeability of the paracellular pathway in Necturus proximal tub&. Am. J. Physiol. 228(2): 581-595. 1975.-Micropuncture experiments were performed on Necfurus proximal tubule using stationary microperfusion and microrecollection techniques. The transepithelial movement of the extracellular marker, sucrose, was used to investigate the passive permeability of the paracellular shunt pathway under steady-state conditions, during spontaneous reabsorption and water flow induced by an external osmotic gradient, Measurements were made of the sucrose permeability ( PS), efflux, net Aux, and of net volume flow. True P, determined in the absence of net volume flow and transepithelial gradient was 0.96 1W6 cm s-4 Both ouabain and isotonic volume expansion decreased shunt P,. During reabsorption, solute-coupled water Aow increased apparent P, and net sucrose flux equalled efflux. Osmotic water flow from lumen to plasma decreased apparent PS, with net sucrose flux equal to efflux; whereas osmotic flow from plasma to lumen increased apparent P, but no net flux was observed. It is concluded that changes in P, can be interpreted as relative alterations of the tight junction and the lateral spaces and that a portion of the volume flow from lumen to plasma proceeds via the tight junction. paracellular sucrose flux; solute-solvent

shunt pathway; passive transport; tight junctions; intercellular space; coupling; ouabain; volume expansion

transepithelial osmotic flow;

SINCE THE WORK OF Ussing and Windhager (41) demonstrated the existence of a transpithelial shunt pathway in parallel with and essentially independent of the active sodium transport pathway in frog skin, considerable effort has been directed toward resolving the intraepithelial site and functional properties of shunts in oriented epithelia. In Necturus proximal tubule, a low-resistance epithelium, recent morphological (48-49) and electrophysiological (5, 7-9) evidence indicates that the anatomical location of the electrical shunt is the tight junctions and the lateral intercellular spaces and that this paracellular pathway is the major route for passive ion transport. In addition, there are some suggestions of a significant paracellular permeability to nonelectrolytes (9) and water (5). As net salt and water reabsorption across the proximal tubular epithelium depends on the balance between active transport processes and passive permeation mechanisms, the passive permeability characteristics of the paracellular shunt pathway are of considerable interest. Changes in paracellular conductance and permeability have been shown to occur during conditions known to alter net solute

and fluid reabsorption (9). However, the structural elements of the paracellular pathway responsible for its permeability characteristics have remained in question because of the inability to distinguish between the relative contributions of the tight junctions and the lateral spaces. Furthermore, the extracellular channel provides a site where the flows of solute and solvent might interact. Direct evidence for solute-solvent or solute-solute coupling within the intercellular fluid compartment is lacking in proximal tubule, although such frictional interactions have recently been demonstrated in frog skin (20, 2 1, 39), toad skin (6, 40), and frog jejunum (28). In the present study on Necturus proximal tubule, the factors governing the transepithelial permeability of the nonelectrolyte sucrose are examined. Sucrose has been shown to distribute only in the extracellular space of Necturus kidney (50-51) and thus can be used to investigate the passive permeability characteristics of the shunt pathway. In addition, sucrose transfer is independent of electrical potential+ Sucrose permeability, efflux, and net flux were determined under steady-state conditions and during reabsorptive and bulk osmotic water flow. Changes in total sucrose permeability are interpreted in terms of relative alterations of the tight junction and lateral intercellular space m The net sucrose flux was observed to be dependent on the magnitude and direction of net volume flow. No evidence was found for coupling between the flux of sucrose and that of sodium or urea. The results suggest that a significant portion of the net volume flow from lumen to plasma crosses the epithelium via the tight: junction-lateral intercellular space route. METHODS

Animal

Pre$cwation

In vivo (9) and doubly perfused (8) kidneys of Neclurus maculosus were prepared as previously described. The comz>osition of the vascular infusion and perfusion solutions is shown in Table 1. To attain a cinstant plasma sucrose concent ;ration of 10 mM, preliminary experiments were performed to determine the appropriate initial and sustaining doses of sucrose to be administered to the in vivo preparation. An initial volume of 1 M sucrose Ringer necessary to bring the extracellular fluid space (26.8 % body wt (37) in control and 29.5 % body wt in 10 % extracellular volume expansion) to 10 mM was injected. For infusion rates of .l ~1 min-l g-l body wt in control and 1

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532 TABLE

C, 1.

Vmdar

k$sion Glucose, g/ii ter

Solution

and Perfusion sohtzbns PVP, g/ii ter*

Heparin, ml/ii ter

In vivo kidney Infusion control Infusion volume expansion Uoublyfierfused

Perfusion Perfusion ouabain Perfusion

S”iEe9

Other

35.0 11 .O

+

20 20

2 ‘2

lO*O 10.0

+ PEG

0.4

20

2

10.0

State of Animal,

In vivo, Perfused, In vivo, steady Perfused,

kidney

0.4 0.4

2. Tubular

TABLE

4,10-4 M ouabain+ 80 g/liter PEG$

volume expansion, ~1 min-l g- l body wt in extracellular thL sustaining concentration of the infusion solution was estimated from the expected sucrose excretion rate (27) and tested experimentally by chemical sucrose analysis of blood samples collected over several hours. The initial dose equilibrated after 30 min. A sucrose infusion concentration of 35 mM in control and 11 mM in volume exr>ansion administered at the above rates maintained the plasma sucrose concentration at 10 mM. All experiments included plasma sucrose analysis of blood collected at 30-min intervals. Micro@mclure The general method used for preparation of split droplets has been described previously (9). However, in the present experiments the split droplets were relatively long, filling one-third to one-half of the proximal tubular volume, to insure an adequate volume of recollected fluid for analysis. Two techniques differing in the site of the initial injection were used. In technigue A, oil was injected into the straight segment of the late proximal tubule and split by means of a second pipette containing the tubular perfusion solutions. The downstream oil droplet was immobilized in the intermediate segment, while the upstream oil droplet remained mobile and able to move in response to fluid reabsorption. The injection of additional oil distally sealed the injection site and advanced the split droplet to the early proximal segment for observation and recollection. This technique has been shown to provide maximal pressure transmission and optimal mobility of the upstream oil droplet (22). To insure against tubular collapse, technique A was applied to reabsorbing Ringer droplets. All other experiments were performed using technique B in which oil was injected into the early proximal tubule distal to the nephrostome. The luminal perfusion solution was introduced slightly downstream. The droplet was kept in place by immobilization of the downstream oil column with back pressure from an oil pipette. The composition of the tubular perfusion solutions is

BERRY

AND

E.

perfusion sohh’ons --

Capillary,

Cl-, mM

PEG, g/liter

64.5 70.8 70.8

62.1 68.4 68.4

80 76 76

80.3

79.9

55

100.5 100.5

98.1 98.1

PEG,

100.5

98.1

hypertonic

100.5

98.1

200 mM

100.5

98.1

control, steady state control, steady state volume expansion, state ouabain, steady state

BOULPAEP

-~

Naf, mM

Tubule

L.

.-

Other

Gmp r1 In vivo, Perfused, Group

All solutions bubbIed with 97.5% 02 and 2.5% C& All solutions contain IVecturus Ringer solution: Naf, 100.5 mM; K+, 2.5 mM; Cl-, 98.1 mM; HC03-, 10 mM; HzPOd-, 0.5 mM; Ca++, 1.8 mM; Mg++, 1 .O mM. pH = 7.4. * PVP polyvinyl pyrolidione, GAF Corporation, Plasdone C, average mol wt 40,000. + Ouahain octahydrate formula weight-679; Sigma Chemical Company. $ Polyethylene glycol, average mol wt-15-20,000. Matheson, Coleman and Bell, East Rutherford, N. J.

A.

control, control,

Ringer Ringer

III

Perfused, hypertonic Ringer Perfused, control, PEG + Ringer Perfused, control, urea + Ringer

80 200 mM urea

All solutions contained: K +, 2.5 mM; HCOS-, 10 mM; &PO4-,, 0.5 n-M; Gaff, 1.8 mM; Mg”‘, 1.0 mM; sucrose-14C, 10 mM; dextran-“H, 48 mg/liter. Sucrose-14C, sp act - 6.45 mCi/g, New England Nuclear, Boston, Mass. DextranJH, average mol wt 15-17,000, sp act - 417 mCi/g, New England Nuclear, Boston, Mass.

summarized in Table 2. Solutions in group I were used to measure sucrose fluxes at constant tubular fluid volume and concentration difference. The osmolar difference between Ringer and the equilibrium NaCl concentration was made up with polyethylene glycol (PEG). The osmotic pressure of freshly prepared PEG solutions was determined empirically from the replacement concentration which resulted in no net volume flow. Eighty grams per liter PEG replace 70 mosmol ?VaCl. In group 11, Necturus Ringer solution was used to examine the effect of fluid reabsorption on sucrose movement. Solutions in group 111 were used to investigate the effects of bulk osmotic water flow on transepithelial sucrose movements and to test for anomalous solute movement. All tubular perfusion solutions contained 10 mM sucrose- W and dextran-3H as a volume marker. Since the sucrose concentration in the peritubular capillaries was maintained at 10 mM, there was no initial sucrose concentration difference between lumen and plasma. The split droplet was recollected after contact times ranging from 30 s to 40 min. Localization of the pipette tip within the tubular lumen was confirmed by an initial injection of a small droplet of oil. After recollection the tip was sealed with stained oil in situ or with surface oil. Collected tubular fluid samples, 15-30 nl, were immediately transferred onto a siliconized dish and kept under

Analysis of Tubular

Fluid SampEes

Total sucrose concentration. A method of analyzing picomolar quantities of sucrose was not available; however, a fluorometric method for the determination of nanogram quantities of inulin has been used in micropuncture laboratories (43). The chemical similarities between inulin, (fructose) n, and the disaccharide sucrose, glucose-fructose, suggested that the inulin procedure might be applied to su crose- The

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PAKACELLULAR

PEKMEABILITY

OF

THE

PROXIMAL

583

TUBULE

stable fluorescent chromophore on which the inulin assay depends is formed from the combination of the ketone group of fructose with dimedone in the presence of orthophosphoric acid (1). The fructose moiety of sucrose forms this same chromophore, but the procedure is less sensitive for sucrose than for inulin. Since this method is essentially new, the preparations and procedure will be described in detail. The dimedone reagent was prepared daily by dissolving 0.5 g dimedone (3,5-dimethyl-l , 3-cyclohexanedione) in 25 ml phosphoric acid. Constant-bore microcapillaries (Drummond Scientific Co.), 100 pl, were boiled for 30 min in 25 YO concentrated HNOZ, rinsed repeatedly in distilled water, and dried at 100°C. To retain the dimedone reagent at the end of the microcapillary during sample transfer, one end was pressed against filter paper wetted with Desicote (Beckman Instruments, Fullerton, Calif.). Sucrose standards from 0 to 500 mg/ 100 ml were prepared in solutions identical to tubular perfusion solutions except that the 10 mM sucrose-14C were replaced with unlabeled sucrose of varying concentration. In the micromethod used for tubular fluid sample analysis, the microcapillaries were secured horizontally in a holder and their siliconized end was filled with dimedone reagent from a Z-p1 constriction pipette. Unlabeled sucrose standards, time 0 radioactive standard, and tubular fluid samples were introduced into the dimedone reagent using a constriction pipette of approximately 10 nl. Standards were always pipetted in triplicate; the number of sample aliquots was determined by the size of the recollected droplet. The microcaps were sealed at their unfilled end, spun in a microcentrifuge, and sealed at their other end. Adequate mixing was insured by repeated centrifugation. Finally, samples and standards were boiled for 10 min in a water bath before reading on an Aminco Fluoromicrophotometer. The sample sucrose concentration was determined by interpolation from the standard curve and expressed as the ratio of concentration in the collected to that injected. The accuracy in determining the total sucrose concentration can be estimated from the range of fluorescence readings in replicates of a single standard. The coefficient of variation for triplicate aliquots of the sucrose-14C standard was 3.7 & .6% (n = 24). The sucrose concentration of the sucroseJ4C time 0 standard is expected to be 10 mM; the measured chemical sucrose concentration was in good agreement, lo-45 =t 0.33 mM (n = 24). The macromethod used to determine nlasma sucrose concentration differs from the micromethod in the amount of reagents and samples used. Twenty-five microliters of plasma or Ringer sucrose standards were added to 100 ~1 of 3 Yc trichloroacetic acid to precipitate plasma proteins. Fifty microliters of the supernatant were added to a tube containing 1 ml of dimedone reagent and thoroughly mixed. Plasma sucrose concentrations read from the standard curve were 9.7 % 0. I mM (n = 20) Sucrose-W and dextran-3H. Radioactive counting was done on the same sample aliquot used to measure chemical sucrose concentration. Microcapillaries containing the sucrose-W time 0 standards and tubular fluid samples were cut, and the open end was placed in a polyethylene

scintillation vial containing 0.5 ml of distilled water and spun in a centrifuge. Five milliliters of scintillation fluid (PPO 7 g, POPOP 50 mg, naphthalene 50 g in 1 liter dioxane) were added to the samples for double-label counting of 14C and 3H to a probable error of less than 1 %. Appropriate radioactive standards were used for counting corrections. The concentration of tracer sucrose and tracer dextran was expressed as the ratio of the counts in the collected sample to that injected. The recovery of radioactivity from split droplets depended on the technique employed. Recoveries were tested using the shortest possible contact time which would simulate experimental conditions; steady-state solutions for which no volume change is expected were used. In technique A, the tubular perfusion solution is injected in a late segment and collected in an early portion. The minimum time required to advance a droplet from injection to collection site was 2.5 min; technique B droplets were injected and collected in an early segment after similar contact times. Dextran recovery using technique A, 68.6 + 3.0 % 7) was significantly (P < ,005) less than in technique ( i, L.7 31 1.0% (n = 6); however, the concentration ratio of tracer sucrose after correction for apparent volume change was not significantly (P < 95) different; technique A = 89.0 A= +09 Yo, technique B = 90.2 =t 1.8 Yo. Low recoveries of isotope were found not to be caused by adsorption of label to puncturing or transfer pipettes, but could be due to mixing with unlabeled fluid trapped within the br#ush border. In technique A exposure to a longer segment of tubule as the split droplet is moved from a late: to an early segment might enhance the intervening dilution of label as compared to technique B. The identity of the calculated rate of tracer sucrose loss after correction for the dextran recovery using techniques A and B indicates that the loss is identical for both isotopes so that the ratio of r4C/3H is not significantly altered. Since, as shown below, it is this ratio that is actually used to evaluate the sucrose permeability, these results are not affected by the apparent dilution of tracers and no correction is necessary. The dextran recoveries obtained from short contact times provide a correction factor for the calculation of net sucrose flux and net volume flow. CALCULATIONS

Tubular fluid ship to time

volume

VI bears

an exponential

relation-

where k is the rate constant (s-l) and VI0 is the volume. The k was determined from the regression of ln V1,/V10 against time .

1 = In C3H -

In F 10

wo1t

initial slope

(2)

where C3H0] and [“Ht] are the initial and final dextran concentrations corrected for tracer loss. The net volume flux, Jv (expressed as nl cm+ s-l), is given by k(V)/(A) where A is area. Assuming a straight cylindrical split

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584 droplet

c. A. BERRY of constant

radius

r

where Thus,

7 J = 1 ln C3HOl V

f

PI t = P&3

t

= -hh/(kz1

+ ha)

\

b3 s2

k21

Peritubular Plasma

P

.

Jt7 -J

indistinguishable system. Using flux of sucrose

2

I s1

(51

k13- ?I1 ercellu Space

kl2

. s3

k32

J2Y 21

-J

32

1. Schematic illustration of 3-compartment series system consisting of tubular lumen (I), intercellular space (Z), and peritubular Auid (3) compartments. S1, S2, and SB denote amount of solute in individual compartments. k 12, k21, and k23, ka2 are rate coefficients across tight junction (a) and effective intercellular space membrane (B), respectively. J i j are unidirectional fluxes. FIG.

1.

(7) Using

equations 4 and 7 1 h r P, = - In - f ho 2

(8)

Ps was calculated from the regression line relating r/2 In (P1,/Plo) to time. Using equations6 and 7, Ji3 can be calculated. In some experimental conditions, Cl varied with time. However, changes in sucrose concentration were small so that the integration of sucrose concentration over time can be closely approximated by the arithmetic mean.

,f i3=-r [1,: 1Gt+Go

J

2

2

10

(9)

Cl0 is the initial sucrose concentration in the lumen, in millimoles per liter. Ji3 was determined from the slope of the regression line relating r/2 [In(P1t/Plo)] (Cl f + C&o)/2 to time. By definition the net sucrose flux, J&, is

J8net

=

lvli!

[Cl

-

GOVlO]ltA

UN

where A = Z/Y~I. Substantial changes in volume were observed in some experimental conditions, thus the logarithmic mean volume VI must be used to approximate the integration of volume over time.

(4)

The three-compartment analysis becomes experimentally from the two-compartment equation 6 of APPENDIX 1, the unidirectional from lumen to plasma, Ji3 is

Lumen

Cl is the sucrose concentration in compartment the transepithelial sucrose permeability P,

(3)

where P1 t and PI0 are the amounts of tracer in the luminal compartment at times t and 0, respectively. The rate corate coefficients efficient k13 (s-l) contains individual

J ;3=

E. I;, BOULPAEP

[3H,32

In order to calculate sucrose efflux and permeability, the compartmental model that reproduces the kinetics of tracer disappearance from the lumen must be determined. Anatomicaiiy it is possible that four compartments are involved in the transfer of sucrose across the proximal tubular epithelium. Besides the lumen and plasma, both the epitheIia1 cell and the lateral intercellular spaces could participate. Nec~us cell membranes are impermeable to sucrose (50, 51) so that the cellular fluid space can be disregarded as part of the transepithelial transport path. The transfer of sucrose from lumen to plasma must then proceed through the lateral intercellular spaces and should be described by a three-compartment series system consisting of tubular lumen (I), intercellular space (Z), and peritubular fluid compartment (3) as shown schematically in Fig. 1. A similar system has been analyzed by Curran and Solomon (14). The tight junction is represented by the barrier Q, the intercellular fluid compartment is assumed to be well mixed, and the total interspace resistance to sucrose flow is assigned to an effective intercellular space membrane, & In the system under investigation, the volume of the middle compartment is small relative to compartments I and 3. Under these conditions, as shown in APPENDIX I, the rate of tracer disappearance from the lumen is described by a single exponential

ha

AND

v,

Jiet

was calculated into equation IO.

=

from

v1t

-

ho

W)

In (Vl t/V10) substitution

of equations 2 and II

The fluxes and permeabilities measured in these experiments varied from tubule to tubule and from animal to animal under the same experimental conditions. Therefore, the following averaging procedure has been used. A time block which evenly distributed the population of recollected samples was chosen. The mean time and mean for the measured quantities were calculated for the resulting groups. All calculations and statistics are done using grouped data. In no condition was the intercept of the least-square regression line through the data points significantly different from zero; therefore, regression slopes were determined by assuming that the lines passed through the origin. Statistical differences were evaluated according to the Student f test. Significance was accepted at the 0.05 level. RESULTS

True Sucrose Permeability

and Effect of Physiologic State

Transepithelial sucrose net flux, efflux, and permeability were measured in vivo and in doubly perfused kidneys, and the effects of isotonic volume expansion and ouabain

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PARACELLULAR

PERMEABILITY

OF

THE

PROXIMAL

poisoning were examined. The results summarized in Table 3, group I, confirm the existence of a steady state in these experiments; net volume flow, JV, and net sucrose flux, Jiet, did not differ significantly from zero in any of the conditions tested. Under these conditions, the proportionality constant relating the sucrose flux from lumen

-10 h

s

-20

I

l

8 \ -ci E

I

I

I

0

h

I

1

I

I

500

1500

1000

585

TUBULE

0

to plasma to the sucrose concentration in the lumen corresponds to a true thermodynamic permeability coefficient. As shown in equation 8, the permeability coefficient is evaluated from the slope of the line relating In (PIt/PIO)r/2 to time. Figure 2 shows this plot for all data obtained under steady-state conditions. The data obtained from four animals under control conditions using the in vivo preparation are depicted in Fig- 2A. As indicated in Table 3, group I, the permeability coefficient calculated from these data was 0.959 lO+ cm/s. Fig. 2B shows similar results for five doubly perfused animals under control conditions. The permeability coefficient, 0.608 1W6 cm/s, is significantly (P < .OOl ) less than the value observed in vivo. The unidirectional sucrose fluxes from lumen to plasma corresponding to these permeability coefficients are given in Table 3, group I. Since net sucrose flux is essentially zero, sucrose influx is equal to sucrose efflux. The lower sucrose permeability observed in the doubly perfused preparation as compared to in vivo results agrees with electrical resistance measurements (23) Transepithehal specific resistance, which is principally a measure of shunt resistance, is appreciably higher in the perfused coefficients preparation than in vivo. The permeability of other solutes measured in Necturus proximal tubule are TABLE 3. Net u&me flow (S,), sucrose permeability sucrose ej?ux (J1;& and sucrose net j%x (&t) Animal,

Capillary,

Tubule

Jv (10-9 liter

control,

steady

+o l 0003 ~0.0012* (n = 7) -0.0003 *o .0025* (n = 5) -0.0019

cm-2 s-1)

Grolql I In vivo, state

In viva, volume expansion, steady state In vivo, state

0

control,

zt0,0027* (n = 4)

Perfused, steady

control, state

Perfused, steady

ouabain, state

Group 11 In vivo, control,

Perfused, Ringer

c I 0

+0.0014

*o .OOO7” (n = 6) -0.0022 &O .OOO6* (n = 4)

Ringer

(6)

I -10

steady

I

t

I

I

1

1

I

1

500

I

I

IOpo Time

1

I

1

.I

control,

1

1500

bcl

FIG. 2. Sucrose permeability. Semilogarithmic plot of experimentally measured quantities (cm) as a function of time (s) Slope of line, as calculated from equation 8, corresponds to true sucrose permeability coefkient. Number in parentheses below each mean point is number of tubules represented. Bars are & 1 SE. A: in vivo, control, steady state; PB = 0.959 lo+ cm/s. 3: perfused, control, steady state; PS = 0.608 lO+ cm/s. C: in viva, control, steady state expansion, steady w; P* = 1.12 10B6 cm/s and in vivo, volume state (A); P, = 0.77 lOus cm/s. D: perfused, ouabain, steady state; PS = 0.415 1o-6 cm/s, l

Group 111 Perfused, control, Ringer + hypertonic PEG Perfused, hypertonic PEG, Ringer Perfused, Ringer urea * Not

control, + 200 mM significantly

- 1 12 zto .093 (n = 4) -0.775 ztO.006 (8 = 3) l

+0 .342 ho.041

(n = 7) - 1 .86.5 =to*31 (n = 3) +1 l 77 Zto.14 (n = 4) different

from

Ps (10-S cm S-l>

0.959 Ito .097 (n = 7)

(Ps>,

J,“, (10-12

mol cm-2s~1)

-9.60 ztO.98 (n = -7.65

7)

0.765 zt0.0725 (n = 5) 1.118 zto.0995 (n = 4) 0.608 Zto.015 (n = 6) 0.415 +o .037 (n = 4)

-11.12 Ztl .o (n = 4) -5.94 zkO.152 (n = 6) -4.36 ztO.465 (n = 4)

1.30 l o* 101

-12.5 ~tl.06

(n = 6) 1.29 Zto .072 (n = 5)

ho.725 (n = 5)

(n = 6) -11.2 ztl l Ol

(n = 5)

1.45

3&t

m-l2

mol cm2 s-1)

2.65 *2.2* (n = 7) -4.67 *4*5* (n = 5) -5.15 *3 l 64* (n = 4) 1.57 &0.835* (n = 6)

-I*77 zt .98” (0 = 4)

-12.6 Al.42

(n = 6) -11.4 &I .8

(n = 5)

-13.7 -0.064 Ito. zto.252* (n = 7) (n = 7) (n = 7) 0*92.5 -10.1 -12.4 AO.014 Ito. It4.27 (n = 4) (n = 4) (n = 4) Time de- b Time Time dependent dependpendent ent Ito.

zero.

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586

C.

A.

NaCl 3.04 10V6 cm/s (9), raffinose 0.54 lO+ cm/s (9), and mannitol 0.44 10m6 cm/s (53). On the basis of their free solution diffusion coefficients, the expected ranking of permeabilities is PNaC 1 > Pmannitol > PSuCrOse> PraffinoseWith the exception of mannitol, this sequence appears to hold. However, a strict comparison is not entirely justified because the previous studies were not performed under steady-state conditions. Figure 2C demonstrates the effect of isotonic volume expansion on sucrose permeability in two in vivo animals. An initial control period was followed by a period of isotonic volume expansion. The slope of the line depicting the control data (e) is significantly (P < .02) steeper than that obtained during volume expansion (A). As indicated in Table 3, group 1, P, decreased following volume expansion from 1.12 1OW6 to 0.77 lO+ cm/s. The effect of 4 lO+ M ouabain on sucrose permeability w&s examined in three animals using the doubly perfused kidney preparation. The experiment was begun after waiting 90 min for the poison to exert its maximal inhibitory effect. The results of these experiments are shown in Fig. 2D. Table 3 shows that P, decreased significantly (P < .OOl) from the control value of 0.608 10M6 to 0.415 lOA6 cm/s. Effect of Solute-Coupled Water Flow on A#arent Permeability and on Net Sucrose Flux

J net=

P,AC,

+

c,(l

-

c)JV

W)

where G is the reflection coefficient of the total epithelium for sucrose and the lumen to plasma sucrose flux by:

Jfs3

=

KG

+ h(1

- o)Jv

Time

AND

E.

L.

BOULPAEP

(ted

Sucrose

In this group of experiments net flows of volume and solute, mainly sodium chloride, occur. Half-times of reabsorption (@) can be calculated (9) during the period of constant volume flow from the data depicted in Fig. 3A. The values, 32 min in vivo and 40 min in the perfused kidney, are comparable to those found by other investigators (3, 9, 34, 53). Assuming that all solute interactions with net sucrose flux can be considered negligible, the total sucrose flux under these conditions can be expressed by: S

BERRY

W)

where c13 refers to the mean concentration. Equation I4 indicated that the coefficient relating the unidirectional sucrose flux to the luminal sucrose concentration is no longer the true thermodynamic sucrose permeability, but contains a term relating sucrose flow to volume flow. The apparent sucrose permeability defined as s J 13 = r.+g(l -g)Jy u5) C1 1 becomes equal to the true sucrose permeability PS only ifa = 1. Table 3, group 11 shows that the calculated apparent permeability coefficients were 1.3 1Oh6 and 1.29 1 Oh6 cm/s for eight in vivo and four doubly perfused animals, respectively. These values are significantly (P < .025 for in vivo and P < .OO 1 for doubly perfused) greater than the corresponding coefficients obtained under steady-state con-

J13 =* Jnet=x

Time FIG. 3. In vivo, control, fluid volume (A) and luminal against time (s). C: fluxes

(set)

Ringer. Logarithm of relative tubular sucrose concentration (mM, B) plotted (pmol/cm2 s) vs. time (s). Bars & SE.

ditions. The observation of an increased apparent permeability coefficient in the presence of net fluid reabsorption is in agreement with the measurements of Windhager et al. (53) on mannitol fluxes. Extrapolation from their data to canditions of zero net volume flow yields a mannitol permeability of 0.44 lo-” cm/s, whereas a similar calculation made under conditions of net volume efflux corresponds to a mannitol permeability of 0.914 lo-” cm/s. As indicated in Fig. 3B, the concentration of sucrose in the lumen decreases significantly with time in spite of the fact that the total volume of the tubular fluid is decreasing (Fig. 3A). This behavior is illustrated more clearly in Fig. 3C, which shows that throughout the time course of the experiment the net sucrose flux does not differ significantly from the unidirectional flux from lumen to plasma. In other words, during solute-coupled water flow there appears to be no detectable flux of sucrose into the lumen in spite of the fact that the sucrose concentration in the plasma is 10 mM. Table 3, grotip 11 shows that this is also the case in the perfused preparation.

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PARACELLULAR

PERMEABILITY

OF

THE

PROXIMAL

587

TUBULE

EJect of Osmotic Gradients on Apparent Sucrose Permeability and Sucrose Fluxes All experiments in this group were done on the doubly perfused kidney and included Ringer in the luminal solution establishing the perfused preparation in group II as the control with which comparisons were made. The results presented in group XX revealed that during solute-coupled water flow the luminal sucrose concentration decreased and that the sucrose influx was essentially zero. Further investigation of the effect of net water movement on sucrose fluxes showed that flux depends on the magnitude and direction of net volume flow. Figure 4C shows that when volume flow was directed from lumen to plasma, the net sucrose flux was not significantly different from the sucrose efflux. In other words, the sucrose flux from plasma to lumen was zero, as also observed during reabsorptive flow. However, Fig. 4B shows that the luminal sucrose concentration increases during osmotic flow from lumen to plasma, indicating that the sucrose concentration of the reabsorbate was lower during bulk osmotic flow than during solute-coupled flow. In addition, Table 3, group 111 shows that the magnitude of net volume flow is greater in the former condition than in the latter. These observations suggest a smaller degree of interaction between sucrose flux and net volume flow. When the luminal solution was made hypertonic with 80 g/liter PEG, volume flow directed from plasma to lumen resulted in no net sucrose flux as shown in Fig. 5C. Figure 5, A and B, further illustrates this point. The decrease in luminal sucrose concentration is a direct result of the increased volume of fluid within the tubule. As indicated in Table 3, group 111 hypertonic PEG solutions significantly altered the apparent sucrose permeability; the effect depended on the locus of the hypertonic medium. In the absence of a hypertonic environment, the apparent sucrose permeability . was 1.29 lOA6 cm/s. The -addition of 70 mosmol PEG to the luminal solution resulted in a significant (P < ,025) increase to 1.45 10m6 cm/s, whereas perfusion of the peritubular capillaries with the hypertonic PEG solution caused a significant (P < .Ol) decrease in apparent sucrose permeability to 0.925 IO+ cm/s. These results are in agreement with the effect of changes in the osmolarity of the extracellular environment on the paracellular shunt conductance in Necturus proximal tubule studied by Windhager et al. (52). Their measurements showed a decrease in conductance during luminal hypertonicity, whereas an increase was observed when the aorta was perfused with hypertonic raffinose solutions. A similar correlation was observed for sucrose permeability, suggesting that sucrose permeation occurs through the electrical shunt path whose conductivity was altered by the tonicity changes. Following the addition of 200 mM urea to the luminal solution, Table 3, group III shows that the net volume flow was from plasma to lumen, as was the net sucrose Aux (Fig. 6A) - Clearly sucrose-urea coupling as previously described in the frog and toad skins (6, 20, 21, 39, 40) was not observed in Necturus proximal tubule. Anomalous solute movement would require a net flux of sucrose from

0

-0.6

r

A

L I

I

I

I

I

I

1

1

I

400

-20

-

Isec)

313’9

c

X

Jnst IX

T

II

1

I

X I

1

1

0

4. Perfused,

1

1

1

500 Time

FIG.

I

800

Time

0 < z a ‘E -fO i 2 5 c

I

hypertonic

PEG,

bed Ringer.

Legend

as in

Fig.

3.

lumen to plasma when net volume flow was from plasma to lumen. Further interpretation of the effects of luminal urea hypertonicity on sucrose fluxes and permeability can be made on a qualitative basis because time-dependent changes of the parameters under investigation preclude a quantitat ive an al ysis. Figure 6B shows the plot of a gainst time. The relationship is nonlinear In O&%Jr/2 making the calculation of a single apparent sucrose permeability unjustified. One can estimate the apparent sucrose permeability from the tangent of the curve. Clearly cLps” increases then decreases. Figure 6A shows that lumento-plasma sucrose flux follows a similar pattern. These results are most likely due to decreasing luminal tonicity because in a split droplet of finite volume the degree of luminal hypertonicity decreases with time due to net volume flow driven by the osmotic gradient and to urea diffusion down its concentration gradient from lumen to plasma.

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588

C.

A.

BERRY

AND

E.

L.

BOULPAEP

J13 =* Jnst =X

1

1

I

0

400

I

800

Time (WC)

1 (4)

t It

1

t

I

0

11

I

III

control,

I

loo0 Tim8

FIG. 5. Perfused, as in Fig, 3.

I

500

Ringer

I1

J

-10 L

1500

I

(St%)

+

i

I

I

1

PEG.

Time

Legend

In the cell model proposed for the proximal tubular epithelium (7), there are four possible transepithelial permeation routes. First, solutes and solvent may bypass the epithelial cells and permeate solely via the paracellular pathway. Second, permeant molecules may pass from one side of the epithelium to the other exclusively through the epithelial cells. Finally, transport may proceed via a pathway involving both cellular and paracellular routes. Since Whittembury (50, 51) has shown that Necfurus cell membranes are essentially impermeable to sucrose, the transepithelial flux of sucrose must proceed through the paracellular shunt pathway. However, this shunt pathway cannot be considered a single passive barrier, but must be treated as a series array of elements, in principle involving the tight junction, lateral intercellular space, and basement membrane. In the absence of other flows the rate of sucrose transfer through the shunt will be determined by the conductances of the series elements. However, in the presence of other flows, the rate can be affected by frictional interactions between sucrose flow and concurrent solute or solvent

flows through the same show that sucrose flow the ensuing discussion points: 1) the nature of flow, and 2) the nature flux on the magnitude Nuture of Rate-Limiting

1

I

bed urea. A: fluxes Semilogarithmic as a function of

FIG. 6. Perfused, control, Ringer + hypertonic (pmol/cm2 s) vs. time (s). B: sucrose permeability. plot of experimentally measured quantities (cm) time (s). Numbers and bars as in Fig. 2.

DISCUSSION

1 (51

I

500

0

hypertonic

1

pathway. The results of this study was altered by solvent flow. Thus will consider two fundamental the rate-limiting barrier to sucrose of the dependence of net sucrose and direction of net volume flow.

Barrier

to Paracellular

Mute

Flow

Interfretation of tracer kinetics. As pointed out in APPENDIX 1, the fact that the experimental data can be fitted adequately by a single exponential does not permit any decision regarding the nature of the rate-limiting barrier(s) to sucrose flow. Three interpretations are compatible with the theoretical analysis. Inspection of equation 5 shows that if kz 1 is small and k23 is large the rate of tracer disappearance from the lumen is determine,d by the barrier a in Fig. 1; if i&l is large and k 23 is small the single effective barrier to sucrose flow from lumen to plasma is the barrier p; if kzl and k23 are similar both a and p contribute and the

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PARACELLULAR

PERMEABILITY

OF

THE

PRBXTMAL

TUBULE

paracellular pathway behaves as a series barrier to sucrose flow from lumen to plasma. When net volume flow is directed from lumen to plasma, only the first interpretation kzl

barrier

1

1

(16)

+ Ps(ls) + G can be calculated P =-

AD d

from un

where P is the sucrose permeability (cm/s), D is the free solution diffusion coefficient, A is the relative surface area available for permeation, and d is the effective path depth. The relative contribution of the basement membrane to total P, can be neglected since it is thin, 0.26 pm (lo), and the relative surface area equals 1.45 times the luminal area if luminal diameter is 110 pm and cell length is 25 pm (9) If diffusion is unrestricted (D, = 5.2 IO+ cm2 s-l), Pscbm) calculated from equation 17 would be 29 cm s-l, several orders of magnitude greater than the values of P, observed in this study. This conclusion is supported by observations that the basement membrane is highly permeable to low molecular weight solutes and water, and is unaffected if in fact only the estimated 10 % of the basement membrane surface area which is exposed to the lateral intercellular and basal labyrinth is available for sucrose permeation (46). Both the tight junction and lateral intercellular space require further consideration as possible sites of restriction to sucrose flow. For an average interspace width of 2 lo-” cm and a total linear length of cellular circumference per centimeter epithelium of 800 cm/cm2 (9), A in equation 17 is 1.6 10m3 cm/cm2 epithelium. The effective depth of the interspace is the cell height, 25 10e4 cm (12, 47). From these data and the free solution diffusion coefficient for sucrose, Ps(ls) is calculated to be 3.33 10m6 cm/s. As shown in Table 3, group I total sucrose permeability P, was 0.96 IO+ cm/s in vivo, control steady state. The overall

589

shunt sucrose permeability is lower than the predicted lateral space permeability; therefore, P, cannot be interpreted solely in terms of the lateral space. Substitution of 1 /Ps(bm), gives K and K(I,) into equation 16, neglecting a value for the permeability of the tight junction, P,, of I .35 10B6 cm/s. Thus under these conditions, the permeability of the paracellular pathway to sucrose is controlled by both the tight junction and the lateral space with about 70 % of the resistance provided by the tight junction. Effect of physiological conditions on true sucrose permeability. The absence of a sucrose influx during net volume flow from lumen to plasma suggests that P, can only be ininterpreted in terms of the tight junction; in other words under these conditions. Table 3, group 11 shows PS = Ps(tj) that P, in vivo, control, Ringer and in perfused, control, Ringer was 1.3 1OV6 and 1.29 lo+ cm/s, respectively. The agreement between the value of Ps of 1.35 10m6 cm/s predicted above from considerations of lateral space geometry and those measured during solute-coupled water flow supports the interpretation that under steady-state conditions P, measurements include a contribution from both the lateral space and the tight junction and that during volume flow from lumen to plasma P, measures P dt W fn addition, the agreement suggests that P, is constant in steady-state conditions and during reabsorption and that Psctj 1 is the same in vivo and in perfused kidney preparations. Table 3 shows that P, determined in perfused, control, steady state was significantly lower than the same value obtained in vivo. Since P,ctj> can be considered constant, the differences in P, must be due to changes in P S(ll3~~ If psCtj) under steady-state conditions is identical during solute-coupled water flow, 1.3 IO+ cm/s, to Ps(tj) equation 16 predicts that P, in the perfused preparation equals 1.2 lOA6 cm/s. The change in P,(r,, is probably associated with changes in the geometric dimensions of the lateral space. The average interspace width can be estimated from equation 17 where A = (width X 800 cm)/cm2 epithelium and the assumption that sucrose diffusion is unrestricted in the lateral space; the effective length can be considered constant. P,, and the reflection coefficient of this barrier for sucrose, g. The differential equation describing these processes can be solved to yield the following equation describing luminal sucrose concentration as a function of time, as given in APPENDIX

J;1 =

z

12

-

8

A.

BERRY

AND

IL

L.

2,

6

(eQua t’ton

19) where P’, is an apparent sucrose permeability or Jil = PsctijC2’ (equation 20) where The second C2’ is an effective sucrose concentration. term of equation 18 describes the quasisteady state, and the first term describes the time course of approach to this distribution from the initial conditions. When net volume flow is zero, the paracellular shunt pathway can be considered a homogenous compartment with a sucrose concentration, Cz, of 10 mM. Under these conditions Clt is constant and equal to 10 mM; no net flux is observed. However, in the presence of net volume flow, a net sucrose flux was observed. When net volume flow was from lumen to plasma, the net sucrose flux was essentially equal to the sucrose efflux; there was no detectable sucrose influx. This result requires either that effective concentration of sucrose C2’ immediately adjacent to the antiluminal side of the tight junction is significantly less than 10 mM or that apparent permeability PLltj, is decreased in the space-to-lumen direction. Such alterations in Psctj> or CS could occur only if a significant portion of the net volume flow from lumen to plasma proceeds through the tight junction. Indeed, junctional volume flow might have two simultaneous effects, both reducing backflux J&: 1) a sweeping effect that will tend to decrease the effective sucrose concentration Cz in the lateral spaces, and 2) a streaming effect in the tight junction that will tend to reduce P, for backflux requiring usage of an apparent sucrose permeability. It is not possible at present to decide whether volume flow through the tight junction affects CZ or P,(tj), but a combination of these factors will determine the degree of sucrose backflux J&. As indicated in the results, Ji1 is essentially zero during lumen-to-plasma volume flow. Under these conditions equation 18 reduces to PL(tj)C2

Clt

=

Cl0

e-2/r(Ps(tj)+aJvJ

t

(23

The tubular radius, r, the sucrose permeability of the flow JV were tight junction P, (tj 1, and the net volume measured experimentally* If we assume that the reflection coefficient c is equal to 1, the expected luminal sucrose concentration as a function of time can be calculated. Figure 7 shows that equation 21 essentially reproduces the experimentally determined concentration of sucrose in the lumen. However, a reflection coefficient of 1 and a backflux Jil of 0 do not provide unique fits to the experimental data. In this study sucrose influx was not measured directly but was evaluated from the difference between sucrose efflux and net flux. Were the net flux overestimated by 20 % J$ in viva, control Ringer would be 2.5 pmol/cm2 se

1 0

I

I

600

I

I

1200 Time (set)

I

j

1800

1

1

2400

FIG. 7, Comparison of experimentally determined of sucrose within lumen during lumen-to-plasma volume flow (symbols) as a function of time with values calculated using equation 21 (lines), Parameters r/Z, P,(t, j,), and JV were experimentally determined; gs was assumed to be 1. A = perfused, hypertonic PEG, Ringer; T/Z = 26.4 low4 cm, Ps(t,j.) = 0.9 lo-” cm/s, Jy = - 1.9 10B6 cm/s. control, Ringer, r/2 = 26.7 10B4 cm, Pa(tj) = 1.3 lo-6 X = perfused, lo-” cm/s. l = in vivo, control, Ringer; r/a = cm/s, JV = -0.78 31.4 10V4 cm, Ps(tj) = 1.3 10B6 cm/s, Jv = - 1.12 10-G cm/s.

Substitution of this value into equation 18 and evaluation of Cl at t = 2,000 s shows that a theoretical fit to the experimental data would result if the reflection coefficient were approximately .7. The total epithelial reflection coefficient for sucrose has not been measured in Necfurus proximal tubule; however, apparent reflection coefficients for raffinose of 0.5 1 and for mannitol of 0.79 have been determined (4). On the basis of these results, a value of 0.7 for sucrose is reasonable. In conclusion even assuming large errors in the determination of sucrose influx, the experimentally observed changes in sucrose concentration are compatible with a relatively high overall sucrose reflection coefficientWhen net volume flow was directed from plasma to lumen, no net flux was observed with PEG as the osmotic agent, whereas a net sucrose influx was observed with urea. Figure 5, A and B, shows that during luminal PEG hypertonicity the luminal sucrose concentration decreased in direct proportion to the tubular fluid volume increase. Under these conditions no interaction between fluid and sucrose flows were observed, suggesting different transepithelial pathways. In addition the average concentration gradient for sucrose between lumen and plasma was considerably less than 1 mM. Such a small concentration gradient cannot be expected to result in a detectable net influx during the course of the experiment. On the other hand, during luminal hypertonicity with 200 mM urea, Fig. 6A shows that initially the net flux was not significantly different from 0, but that a net influx was measured at later times. The fundamental difference between urea and PEG hypertonicity can be related to the magnitude of the net volume flow. Table 3, group III shows that Jy = +0.3 nl/cmz s when 70 mosmol PEG + Ringer was present in the tubular lumen and JV = + 1.8 nl/cm2 s with 200 mosmol urea + Ringer. Initially, the tubular fluid volume increased 20 % and the luminal sucrose concentration decreased by the same factor, establishing a sucrose concentration gradient between plasma and lumen

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PARACELLULAR

PERMEABILITY

OF

THE

PROXIMAL

of at least 2 mM. If 90 % of the observed increase in shunt permeability was contributed by the tight junction, then P sttjl is 1.46 lo+ cm/s. Under these conditions, a 2 mM concentration gradient will result in a net influx of 30 pmol/ cm2 s, a value 3 times greater than observed. When volume flow is from plasma to lumen, the net flux can be described adequately if all of the flow proceeds via the epithelial cells. On the basis of morphologic data, Bentzel et al. (5) have also suggested that the epithelial cells are the major pathway of the solvent influx into the tubular lumen in Necturus. In addition, cell shrinkage has been observed in frog skin following mucosal hypertonicity (19) and in fact has been suggested to account for the increased shunt permeability between cerebrovascular endothelial cells when exposed to hypertonic urea perfusion (33). In summary, under steady-state conditions and during plasma-to-lumen bulk osmotic flow, the sucrose permeability of the paracellular shunt pathway is determined by both the tight junction and lateral space. Changes in the total sucrose permeability have been interpreted in terms of relative alterations of these parameters. On the other hand, during lumen-to-plasma volume flow, the sucrose permeability of the shunt pathway is determined only by the tight junction. The effect of lumen-to-plasma volume flow on the net sucrose flux can be described by the existence of a low effective sucrose concentration within the interspace, due to the sweeping effect of flow through the lateral spaces and the streaming effect of flow through the junctional complex. The results indicate that solvent flow from lumen to plasma crosses the epithelium via the lateral intercellular spaces rather than through the cells. In addition a significant percentage of the flow probably passes through the tight junction into the interspaces, the remainder probably first crossing the luminal and then lateral membranes enroute to the interspaces* On the other hand, when net volume flow is directed from plasma to lumen, the results suggest that only a small percentage if any of the solvent Aow proceeds via the paracellular pathway, indicating that volume flow from plasma takes primarily a cellular route. Solvent-solute coupling and junctional water flow suggest the possibility of passive transport of other solutes from lumen to plasma. The extent of such coupling depends on the reflection coefficient of the tight junction for the solute and the percentage of volume flow that crosses this barrier. The model suggests that all proximal tubular transport processes might be interdependent. Transport processes currently considered entirely active may in fact be partially passive. APPENDIX

X2

=

-%(klz

B2

P1 is the

amount

+ kzl + ku) +h+h)

--lo(k12 =

+

hoh

+

of tracer +ss

% d(krz d(h

in

(0 the

luminal

+ kzl + k23)2 +

kzl

-I- k23)2 -

compartment 4k12k23 4k12k23

x2)/(x1 x,)/(x1

ho = amount the rate compartment

of tracer in the luminal coefficient (s-l) for sucrose j and defined by

where J i j is the and Vi, Ai, and in compartment i, Cl = Ct, and

-

x2)

(4)'

x,)

(5)

compartment transfer from

Jii = k .-Vi I’ Ai

at t = 0. kij

= i to

compartment

Ci

(6)

unidirectional flux from compartment i to compartment j, Ci are the volume, area, and sucrose concentrations respectively. Under steady-state conditions J 12 = J 21, Al = AZ; thus the rate coefficient k2l is defined by

(7)

k 21 = kl2

The ratio of the volume of the Iuminal compartment, VI, to the interspace volume, VT, can be estimated from their average dimensions. The interspace volume, as calculated for a rectangular solid with length = 800 cm/cm2 epithelium (37) width = 2 101~ cm and effective depth = 25 low4 cm (12, 47), is 4 n&km2 epithelium; whereas the luminal volume, as calculated for a right, circular cylindar of an average radius of 70 lo-’ cm, is 3,820 nl/cm2 epithelium. Vi is several orders of magnitude larger than VZ; therefore, k2l >> k12. Under these conditions the three-compartment series analysis predicts a single exponential with an intercept not significantly different from -1. Equations 2 and 3 can be combined to yield, x1+

x2

=

-h

x1 - x2 = - dh

+

h

+

(8)

k23)

+ kzl + M2 - 4klzkea

(9)

if Xl

Equation

10 holds

then

>> x2,

if k 12 is relatively

X1 + X2 rv XI small

x2

ua

and if

4-hk23 k 12 the inequality of the size of k23. If k23 > kl2* If k23 >> This is always true since k2 1 >> be true and equations 9 and 5 are

of equation II is insured independent then 4k12k23 < k212. This is always k21, then 4klzk23 > X2 will always approximated by

Since AI >> X2, (k12 -I- k21 + k23j2 >> 4hJC23

and XI = (klz + kzl i- k2& Since kzl >> k12, X1 >> k12 and B2 approaches PI* and B1 approaches 0. Thus, when compartment 2 of Fig. 1 is small compared to I and 3, the rate of tracer disappearance is described by a single exponential, as shown in equation 4 of METHODS. APPENDIX

2

The net sucrose

flux is defined

1.

PI = B1eXlt + B&t

XI = -iW12

Br =

by the following

8 3 net

The simultaneous differential equations of the analysis (14) that describes tracer flow in a three-compartment system can be solved to yield equation 1. The rate of disappearance of tracer from the luminal compartment is described by two exponentials.

in which

593

TUBULE

J Assuming

c

B net

= PAC

= Cl and equating

equations

1 dS, =---A dt + c(1 equations

-

a)Jv

(2)

1 and 2 yields

where P&j) is the apparent sucrose permeabil .ity measured from to 1 Using the identities V r/A 1 = r/2 and S 1 =f C IV 1, simplification of equation 3 gives r

2

l

(2) (3)

dG -dt

2

-

Pi(tj)

2

G - - Cl (Ps(tj> + Jv g> 7

1

Downloaded from www.physiology.org/journal/ajplegacy at Tulane University (129.081.226.078) on February 13, 2019.

r

(4)

594 which

C. has

Gt

=

the

Go

solution

-

I11

e-2/r

(ps(tj)+cJ,)t

+

+ aJv

8Ujl

[

APPENDIX

J

p

s

J 21 -Psctj> +

AND

E,.

L.

BOULPAEP

gJv

for 800 depth,

3 functional

slit

width

can P s(G)

be estimated e D’Act

from

eguation

i,/d

I-,

-

1 -

D’

= D

1 +

b/42) 3.4

(a/w/2j2

L

x) is the a is the

free solution molecular

diffusion coefficient radius of sucrose, 5.2

-I

one

real

solution,

w =

14.4

A.

17

where Ps{tj) is the observed sucrose permeabihty of the tight junction, 1.3 1OV6 cm/s; D’ is the restricted sucrose diffusion coefficient in the junctional cleft due solely to the proximity of apposed cellular membranes and defined by Pappenhcimer et al. (32).

where cm2/s;

BERRY

tanguiar hlit width; A (t j) is the relative surface area available permeation and is equal to 1, the Iinear length of tight junction, cm/c@ (9), times the slit width, w; and d is the junctional 4,600 A (13). Th e simplifiezl equation

has The

A.

I $or sucrose, 5.2 A, and w is the

(2) 10s6 rec-

We are indebted to Dr. Peter F. Curran for valuable suggestions throughout this work and to Dr. Gerhard Giebisch for critical reading of the manuscript. This investigation was supported by Public Health Service Research Grant 5-ROl-AM13844 from the National Institute of Arthritis, Metabolism, and Digestive Diseases + Present address of Christine Albachten Berry; Dept. of Medicine, University of California Medical School, San Francisco, Calif. Address all reprint requests to : E. L. BouIpaep, Yale University School of Medicine, Dept. of Physiology, New Haven, Conn. 06510. Received

for publication

10 May

1974.

REFERENCES 1. 2.

3.

4.

5.

6. 7.

8.

9.

10.

11. 12.

13.

14.

15,

16.

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