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Chapter 18 Ionic Conductance of the Cell Membranes and Shunts of Necturus Proximal Tubule
CURRENT TOPICS I N MEMBRANES A N D TRANSPORT, VOLUME
13
Chapter 18 Ionic Conductance of the Cell Membranes and Shunts of Necturus Proximal Tubule GENJtRO K I M U R A A N D KENNETH R . S P R t N G Lahoraton*of Kidney & Electrolyte Metmholiswi Natiotiul Heart. Lutig. and Blood Institute National Itrstitutes of Heulth Bethrsda, Maryland
I . Introduction . . . . . . . . . . . . . . . . . . . .
265
. . . . . . . . . . . . . . . . . . . 266 H I . Estimating k 21 and h 23 . . . . . . . . . . . . . . . . . 267 11. Estimating h I 2
IV. V. VI. VII. VII1. IX.
Estimation of Basolateral Membrane Permeabilities and Conductances . . 269 Estimation of Luminal Membrane Ionic Conductances . . . . . . . 270 Estimation of Shunt Permeabilities and Ionic Conductances . . . . . 270 Electrical Analog Model . . . . . . . . . . . . . . . . 272 Membrane Resistances . . . . . . . . . . . . . . . . 272 Summary . . . . . . . . . . . . . . . . . . . . 274 274 References . . . . . . . . . . . . . . . . . . . .
1.
INTRODUCTION
Analysis of ion tracer fluxes into the cells of the proximal tubule is hampered by the presence of paracellular shunts. The unidirectional flux of most ions is largely through the extracellular route, and steady-state tracer movements often yield little information about the movement of substances across the cells. We describe an analytical method by which the rate constants of the luminal and basolateral membrane may be calculated from measurements of luminal tracer disappearance. In previous experiments (6) it was shown that the initial flux of tracer Na out of the Nec~rrrrrrsproximal tubule lumen was the sum of the fluxes into 265
266
G. KIMURA AND K. R. SPRING
the cell across the luminal membrane and into the shunt across the tight junction. A similar result was obtained for the movement of tracer chloride (5). The tracer disappearance data are analyzed with a compartment model. Necturus proximal tubule may be represented as a three-compartment, series-parallel system (6) containing (i) lumen, (ii) cell, and (iii) extracellular fluid (ECF) including the shunt arranged as shown in Fig. 1. The rate of tracer disappearance from the lumen is given by d Q i ( t ) / d t = -(kn
f ki3)
Q i < t >+ kziQz(t) + k31Q3(1)
(1)
where Q l ( t )is the quantity of tracer in compartment i at time t, and kij is the rate constant for the flux from compartment i to j. Since the tracer is diluted and washed away quickly by the capillary perfusate, Q 3 ( t )is assumed to be equal to zero. II. ESTIMATING k l z
Equation (1) can be solved in the form of the two exponentials (fast and slow components): Q l ( t ) / Q l ( O )= bIexp(Alt) ibzexP(Azt)
(2)
where b i is the intercept and At is the slope for each exponential, and Q l ( 0 )is the tracer quantity in the lumen at time zero. Since Q z ( t )is also zero for the first few moments after the tracer is introduced into the lumen, the initial rate of tracer disappearance is given by dt dele
1
= t=o
-(k12
+ k13)Q1(0)
k23 k32
k'3 ! k31
! I
Shunt (3)
267
PROXIMAL TUBULE CONDUCTANCE
FIG. 2. Tracer disappearance curves. The logarithm of the ratio of tracer "CI activity in re-collected luminal droplets to that in original perfusate, log[Ql(t)l/[Ql(0)], is plotted as a function of the time elapsed after introduction of tracer into the tubule lumen. Lines I , 11, and 111 are the initial, fast, and slow components, respectively, obtained by least-squares fit of exponentials. A droplet of equilibrium N a T I was introduced into proximal tubules, while capillaries were perfused with CI Ringer's solution. [From Kirnura and Spring (S).]
Thus the initial slope, ho, of tracer disappearance is equal to - ( k l z + kI3). When the lumen is filled with a solution containing 36Cl, the tracer disappearance curves conform to the above equations ( 5 ) . Figure 2 shows the disappearance of luminal 36Cl as a function of time after droplet injection. Line I on the figure is used to calculate the initial rate of tracer disappearance for determination of (k12 + k 1 3 )by Eq. (3). The shunt permeability is determined independently (9,and once the shunt rate constant, k13, is known, a value for k , 2 , the rate constant for movement from lumen to cell, may be obtained by subtraction. 111.
ESTIMATING k Z 1and k 2 3
The rate of change of the quantity of tracer in the proximal tubule cell is given by
d Q 2 ( t ) / d t= k l z Q l ( t ) -
WZl + k 2 d Q z ( t ) + k 3 , Q 3 ( t )
( 4)
In luminal tracer disappearance experiments Q 3 ( t )is assumed to be zero at all times. Equations ( 1 ) and (2) may be combined and substituted into Eq. (4) to yield Q d t ) = [Q 1
211
{ ( bih 1
-t b zhzehz*)
+ (k12 + k I 3 ) . ( b l e h +l f b z e A ~ c )(}5 )
Where b i is the intercept and hi the slope for each of the two exponentials in Fig. 2 (lines I1 and 111); k U and Q i are previously described. Evaluation
268
G. KIMURA AND K. R. SPRING
of Eq. (5) at time zero enables estimation of the rate constants k 1 2and k 2 3 , for ion movements from cell to lumen and cell to capillary, respectively. These rate constants are functions only of the slopes of the disappearance curves and the previously measured values of k , , and k 1 3 l : 1
k21
+ (kiz + k i 3 ) . ( A i + A 2 + k 1 2 + k 1 3 ) }
= - -{A]&
k 12
(6)
Once k z l and k 2 3 are known it is possible to calculate the membrane permeability to chloride as well as the transmembrane flux of chloride. For example, the chloride flux across the basolateral membrane, 4 2 3 , is given by
where C 2is the intracellular activity of chloride and V 2is the cell volume. Our previous data were consistent with a passive flux of chloride across the basolateral membrane that is driven by the negativity of the cell interior (7).2The basolateral chloride permeability may then be calculated from the Goldman-Hodgkin- Katz equation as p23
=
[I
-
exp(-ZFA$/RT)] ZFA$/RT
K23V2
(9)
Table I lists the rate constants, fluxes, and permeabilities across the luminal and basolateral cell membranes as determined from the tracer disappearance curves in Fig. 2. The fluxes and permeabilities in Table I may be overestimates if there is significant exchange diffusion of NaCl across the luminal membrane. Although chloride self-exchange is not apparent across the luminal membrane (5), it is possible that an unknown fraction of the Na3W flux into the tubule cell is in exchange for intracellular NaCI. It should be noted that the slopes of the tracer disappearance curves (A) enter into all terms except k I 3 and that large cumulative errors occur in the estimates of kll and kZ3. Increased accuracy in the values for k,, and kZ3is dependent on reduction of the scatter of the points in Fig. 2. * Recent measurements (Spring and Shindo, in preparation) of basolateral chloride conductance suggest that chloride movement across this membrane is electrically silent, possibly coupled to the movement of sodium.
269
PROXIMAL TUBULE CONDUCTANCE
TABLE I CELLMEMBRANECHLORIDE RATECONSTANTS, FLUXES, AND PERMEABILITIES Basolateral membrane
Parameter
k a = 0.29
k , , min-' +(,
x
M cm-2 sec-'
P$' x 10W cm sec-'
2
0.07
+23
= 309 2 70
Pa
=
3.44
2
0.78
Luminal membrane = 0.139 2 0.032 k,, = 0.044 rf: 0.01 +12 = 446 & 103 4 2 1 = 47 2 10.6 Pzl = 0.59 2 0.13 k12
IV. ESTIMATION OF BASOLATERAL MEMBRANE PERMEABILITIES AND CONDUCTANCES
The chloride permeability of the basolateral membrane calculated above and listed in Table I is in good agreement with the value obtained in Nectrrrrrs kidney slices (Y). Whittembury er crl. (Y) measured the basolateral membrane PD and the uptake of radioactive chloride into the proximal tubule cells of slices of Necrurus kidney. They calculated the membrane permeability using the Goldman- Hodgkin- Katz equation [our Eq. (9)], as 0.58 x cm sec-I, only slightly higher than our estimate cm sec-'. It was previously shown (6) that the basolateral of 0.3 x membrane sodium permeability is extremely low and that the basolateral membrane PD is primarily a KCI diffusion potential (2-4, 8, 9). The measured basolateral membrane PD and the calculated chloride permeability may be inserted into the Goldman equation for the basolateral PD and used to calculate the potasium permeability of that membrane. The potassium permeability, P&, is 1.62 5 0.37 x cm sec-I, which is in reasonable agreement with the value of 1.09 x cm sec-l obtained isotopically by Whittembury et N I . (Y) in kidney slices. The ratio of the basolateral membrane permeabilities ( P g i / P t 3 = 0.21) is also in good agreement with the ratio of 0.2 obtained with electrophysiological methods by Boulpaep (2). The partial conductance, Gh3, of the basolateral membrane for an ion, i, is (33
where
=
P,3
Z2F2 c iRT
ciis the logarithmic mean concentration
270
G. KIMURA AND K. R. SPRING
of the cell ( C , ) and capillary ( C , ) concentrations. The calculated 0 2 3 for C1 and K are 768 2 174 and 1430 k 320 pmho cm-2, respectively. The total basolateral membrane conductance is 2200 k 540 pmho cm-2, and the estimated basolateral membrane resistance, R Z 3 is , 455 2 119 n.cm2. V.
ESTIMATION OF LUMINAL MEMBRANE IONIC CONDUCTANCES
The luminal membrane conductance may be estimated in two ways. The voltage divider ratio is measured and used to calculate the ratio of the resistance of the luminal membrane to that of the basolateral. This ratio is typically 3-5 (2, 7), and the calculated luminal membrane resistance is 3 to 5 times greater than the basolateral membrane resistance or 1365- 2275 cm2. Alternatively, the passive ionic permeabilities may be converted to conductances and summed as was done for the basolateral membrane. The luminal membrane C1 conductance from P Z l in Table I is 132 pmho/cm2, luminal membrane K conductance is negligibly small, and luminal membrane Na conductance is 430 pmho/cm2 (Kimura and Spring, unpublished observations). Table I1 lists these values and the estimated total luminal membrane conductance of 562 pmho/cm2, equivalent to a membrane resistance of 1779 R-cm2. VI.
ESTIMATION OF SHUNT PERMEABILITIES AND IONIC CONDUCTANCES
Shunt permeabilities and conductances are also listed in Table 11. The shunt permeabilities to Na and C1 were measured and the K permeability was assumed to be two times the CI permeability from the data of Whittembury et a / . (9). Using the shunt permeabilities to CI (5) and to Na (6) the NaCl dilution potential can be calculated from the NernstPlanck-Henderson equation. The dilution potentials measured by Boulpaep (2) are simulated exactly using the tracer permeabilities. The partial conductances of the shunt pathway for Cl, Na, and K were also calculated 1010 x and 189 x mho cm-2, respectively. as 3090 X The ratio of transference numbers tCl/fNa = 3.1) is in good agreement with the measured value of 3.0 (2). Neglecting the conductance of ions other than C1, Na, and K, the total shunt conductance is 4290 x mho cm+, equivalent to a shunt resistance, R13, of 233 n.cm2.
TABLE I1 ION PERMEABILITIES A N D CONDUCTANCES Basolateral membrane Ion C1-
K+
Na+
G Total R n.cmz
P ( x 1W5c d s e c )
G (prnho/cmZ)
0.344 1.62 -0
768 1428 -0 2196 455
Luminal membrane (x
P 1W5c d s e c ) 0.06 -0 0.176
G (pmho/cmz) 132 -0 430 562 1779
Shunt (x
P
G (pmho/cmP)
0.834 1.60 0.266
3090 189 1010 4290 233
cdsec)
272
G. KIMURA AND K. R. SPRING
VII.
ELECTRICAL ANALOG MODEL
The values for cell membrane and shunt resistance along with the measurements of potential differences may be incorporated into the electrical analog model of the Nrcturus proximal tubule originally proposed by Windhager et d.( 8 ) .Figure 3 indicates the values calculated from the equations for the electrical equivalent circuit. The transepithelial resistance of the circuit is 215 fl*cm2, and the cellular electromotive force (emf) required to produce the observed 9.7 mV transepithelial PD is 123 mV. The cellular emf is made up of two batteries-a luminal emf of 43.4 mV and a basolateral emf of 79.9 mV-assuming the shunt emf to be negligible. The circulating electric current, calculated by dividing the transepithelial PD by the shunt resistance, is 41.6 pA/cmZ. VI II. MEMBRANE RESISTANCES
The cell membrane resistances calculated in Section VII (Fig. 3) are one-half to one-third of the resistances determined by cable analysis of the epithelium ( I , 8) and the ratio of cell membrane resistance to shunt resistance is around 12, much lower than previous estimates of a ratio of 100 (2). This discrepancy may be due either to an overestimate of the cell membrane ionic conductances calculated from the tracer data, o r to an underestimate of the conductances calculated from the cable analysis. The rate constants in Table 1 may be overestimates if significant exchange diffusion of 36Cloccurred with intracellular chloride. Our previous investigations (5, 7) indicated that exchange diffusion of chloride was not significant across the cell membranes or shunt pathway. This conclusion was based on the observations that chloride entry into the tubule cells required luminal Na and that unidirectional chemical chloride movement across the shunt pathway was equal to tracer chloride movement. However, neither of these earlier observations preclude significant exchange diffusion of NaCl across the luminal membrane of the tubule cell. A luminal membrane carrier for NaCl might rapidly exchange luminal Na3TI for intracellular NaCI, thereby causing an overestimate of the 3sCI fluxes on which the determination of k,, and k 2 3 depends. The possibility of NaCl exchange across the luminal membrane could be tested by loading the cells with tracer NaCl and measuring the tracer washout to the lumen after rapidly switching the luminal perfusate to a cold NaCl Ringer’s solution. .IIS tubule ( / ) We have reviewed the cable analysis of N ~ C . / I I I proximal
273
PROXIMAL TUBULE CONDUCTANCE
I
ECF
Cell (2)
Lumen (1)
AW21
-51.3 mV 2275 43
-I-++
Qcm2 mV '12
(3)
"23
-62.1 rnV
80 456 mV Qcm2
El2
Shunt
0 rnV
E23
'23
3 1 '
-9.7 mV "13
FIG. 3 . Electrical ar.,.Jg model of Necfiirus proximal tubule. Membrane and series resistances are lumped together and indicated by R,. Electromotive forces are shown as E,, and observed potential differences as Aeu. A circulating current of 41.6 FA/cm* is indicated.
and have not found any unreasonable assumptions o r calculations. The values obtained ( I ) are in good agreement with estimates of the cell membrane resistances of other leaky epithelia derived from the cable analysis (2). However, it has been shown (2) that the simple electrical analog in Fig. 3 does not result in correct values for the transepithelial PD if the cell membrane resistances from cable analysis are used. A more complex analog model has been proposed (2) which requires a large circulating transepithelial electrical current. It is of interest that the cell membrane resistances estimated from the tracer data presented here result in an adequate representation of the electrical properties of the Nectur'us proximal tubule by the simple analog circuit rather than the more complex model. We have shown how a limited number of measurements of tracer kinetics may be utilized to estimate the permeabilities, conductances, and electromotive forces of the entire tubular epithelium. Our results suggest that a simple electrical analog circuit may adequately depict the steady-state properties of the epithelium under control conditions.
274
G. KIMURA AND K. R. SPRING
IX. SUMMARY
An analytical method is described in which isotopic tracer and electrophysiologic observations are utilized to estimate the ionic permeabilities and electrical resistance of the cell membranes and shunt pathway of Necturus proximal tubule. The rate of disappearance of luminal 3sCl is utilized to calculate the chloride flux and permeability of the luminal and basolateral cell membranes. Membrane electrical conductances are calculated from the individual ion permeabilities and incorporated into the electrical analog model of the Nrcturus proximal tubule. REFERENCES 1. Anagnostopoulos, T., and Velu, E. (1974). Electrical resistance of cell membranes in Necturus kidney. Pfluegers Arch. 346,327-339. 2. Boulpaep, E. L. (1976). Electrical phenomena in the nephron. Kidney Inr. 9,88-102. 3. Boulpaep, E. L. (1967). Ion permeability of the peritubular and luminal membrane of the renal tubular cell. In "Transport and Funktion Intracellularer Elektrolyte" (F. Kruck, ed.), pp. 98-107. Urban & Schwarzenberg, Munich. 4. Giebisch, G. (1961). Measurements of electrical potential differences in single nephrons of the perfused Necturus kidney. J . Gen. Physiol. 44, 659-678. 5 . Kimura, G . , and Spring, K. R. (1978). Transcellular and paracellular tracer chloride fluxes in Necturus proximal tubule. A m . J . Physiol. 235, F617-625. 6 . Spring, K. R., and Giebisch, G. (1977). Tracer Na fluxes in Necturus proximal tubule. A m . J . Physiol. 232, F461-F470. 7. Spring, K. R., and Kimura, G. (1978). Chloride reabsorption by renal proximal tubules of Necturus. J . Membr. Biol. 38, 233-254. 8. Windhager, E. E., Boulpaep, E. L., and Giebisch, G. (1967). Electrophysiological studies on single nephrons. Proc. In,. Congr. Nephrol. 1, 35-47. 9. Whittembury, G., Sugino, N., and Solomon, A. K. (1961). Ionic permeability and electrical potential differences in Necturus kidney cells. J . Gen. Physiol. 44, 689-712.
13
Chapter 18 Ionic Conductance of the Cell Membranes and Shunts of Necturus Proximal Tubule GENJtRO K I M U R A A N D KENNETH R . S P R t N G Lahoraton*of Kidney & Electrolyte Metmholiswi Natiotiul Heart. Lutig. and Blood Institute National Itrstitutes of Heulth Bethrsda, Maryland
I . Introduction . . . . . . . . . . . . . . . . . . . .
265
. . . . . . . . . . . . . . . . . . . 266 H I . Estimating k 21 and h 23 . . . . . . . . . . . . . . . . . 267 11. Estimating h I 2
IV. V. VI. VII. VII1. IX.
Estimation of Basolateral Membrane Permeabilities and Conductances . . 269 Estimation of Luminal Membrane Ionic Conductances . . . . . . . 270 Estimation of Shunt Permeabilities and Ionic Conductances . . . . . 270 Electrical Analog Model . . . . . . . . . . . . . . . . 272 Membrane Resistances . . . . . . . . . . . . . . . . 272 Summary . . . . . . . . . . . . . . . . . . . . 274 274 References . . . . . . . . . . . . . . . . . . . .
1.
INTRODUCTION
Analysis of ion tracer fluxes into the cells of the proximal tubule is hampered by the presence of paracellular shunts. The unidirectional flux of most ions is largely through the extracellular route, and steady-state tracer movements often yield little information about the movement of substances across the cells. We describe an analytical method by which the rate constants of the luminal and basolateral membrane may be calculated from measurements of luminal tracer disappearance. In previous experiments (6) it was shown that the initial flux of tracer Na out of the Nec~rrrrrrsproximal tubule lumen was the sum of the fluxes into 265
266
G. KIMURA AND K. R. SPRING
the cell across the luminal membrane and into the shunt across the tight junction. A similar result was obtained for the movement of tracer chloride (5). The tracer disappearance data are analyzed with a compartment model. Necturus proximal tubule may be represented as a three-compartment, series-parallel system (6) containing (i) lumen, (ii) cell, and (iii) extracellular fluid (ECF) including the shunt arranged as shown in Fig. 1. The rate of tracer disappearance from the lumen is given by d Q i ( t ) / d t = -(kn
f ki3)
Q i < t >+ kziQz(t) + k31Q3(1)
(1)
where Q l ( t )is the quantity of tracer in compartment i at time t, and kij is the rate constant for the flux from compartment i to j. Since the tracer is diluted and washed away quickly by the capillary perfusate, Q 3 ( t )is assumed to be equal to zero. II. ESTIMATING k l z
Equation (1) can be solved in the form of the two exponentials (fast and slow components): Q l ( t ) / Q l ( O )= bIexp(Alt) ibzexP(Azt)
(2)
where b i is the intercept and At is the slope for each exponential, and Q l ( 0 )is the tracer quantity in the lumen at time zero. Since Q z ( t )is also zero for the first few moments after the tracer is introduced into the lumen, the initial rate of tracer disappearance is given by dt dele
1
= t=o
-(k12
+ k13)Q1(0)
k23 k32
k'3 ! k31
! I
Shunt (3)
267
PROXIMAL TUBULE CONDUCTANCE
FIG. 2. Tracer disappearance curves. The logarithm of the ratio of tracer "CI activity in re-collected luminal droplets to that in original perfusate, log[Ql(t)l/[Ql(0)], is plotted as a function of the time elapsed after introduction of tracer into the tubule lumen. Lines I , 11, and 111 are the initial, fast, and slow components, respectively, obtained by least-squares fit of exponentials. A droplet of equilibrium N a T I was introduced into proximal tubules, while capillaries were perfused with CI Ringer's solution. [From Kirnura and Spring (S).]
Thus the initial slope, ho, of tracer disappearance is equal to - ( k l z + kI3). When the lumen is filled with a solution containing 36Cl, the tracer disappearance curves conform to the above equations ( 5 ) . Figure 2 shows the disappearance of luminal 36Cl as a function of time after droplet injection. Line I on the figure is used to calculate the initial rate of tracer disappearance for determination of (k12 + k 1 3 )by Eq. (3). The shunt permeability is determined independently (9,and once the shunt rate constant, k13, is known, a value for k , 2 , the rate constant for movement from lumen to cell, may be obtained by subtraction. 111.
ESTIMATING k Z 1and k 2 3
The rate of change of the quantity of tracer in the proximal tubule cell is given by
d Q 2 ( t ) / d t= k l z Q l ( t ) -
WZl + k 2 d Q z ( t ) + k 3 , Q 3 ( t )
( 4)
In luminal tracer disappearance experiments Q 3 ( t )is assumed to be zero at all times. Equations ( 1 ) and (2) may be combined and substituted into Eq. (4) to yield Q d t ) = [Q 1
211
{ ( bih 1
-t b zhzehz*)
+ (k12 + k I 3 ) . ( b l e h +l f b z e A ~ c )(}5 )
Where b i is the intercept and hi the slope for each of the two exponentials in Fig. 2 (lines I1 and 111); k U and Q i are previously described. Evaluation
268
G. KIMURA AND K. R. SPRING
of Eq. (5) at time zero enables estimation of the rate constants k 1 2and k 2 3 , for ion movements from cell to lumen and cell to capillary, respectively. These rate constants are functions only of the slopes of the disappearance curves and the previously measured values of k , , and k 1 3 l : 1
k21
+ (kiz + k i 3 ) . ( A i + A 2 + k 1 2 + k 1 3 ) }
= - -{A]&
k 12
(6)
Once k z l and k 2 3 are known it is possible to calculate the membrane permeability to chloride as well as the transmembrane flux of chloride. For example, the chloride flux across the basolateral membrane, 4 2 3 , is given by
where C 2is the intracellular activity of chloride and V 2is the cell volume. Our previous data were consistent with a passive flux of chloride across the basolateral membrane that is driven by the negativity of the cell interior (7).2The basolateral chloride permeability may then be calculated from the Goldman-Hodgkin- Katz equation as p23
=
[I
-
exp(-ZFA$/RT)] ZFA$/RT
K23V2
(9)
Table I lists the rate constants, fluxes, and permeabilities across the luminal and basolateral cell membranes as determined from the tracer disappearance curves in Fig. 2. The fluxes and permeabilities in Table I may be overestimates if there is significant exchange diffusion of NaCl across the luminal membrane. Although chloride self-exchange is not apparent across the luminal membrane (5), it is possible that an unknown fraction of the Na3W flux into the tubule cell is in exchange for intracellular NaCI. It should be noted that the slopes of the tracer disappearance curves (A) enter into all terms except k I 3 and that large cumulative errors occur in the estimates of kll and kZ3. Increased accuracy in the values for k,, and kZ3is dependent on reduction of the scatter of the points in Fig. 2. * Recent measurements (Spring and Shindo, in preparation) of basolateral chloride conductance suggest that chloride movement across this membrane is electrically silent, possibly coupled to the movement of sodium.
269
PROXIMAL TUBULE CONDUCTANCE
TABLE I CELLMEMBRANECHLORIDE RATECONSTANTS, FLUXES, AND PERMEABILITIES Basolateral membrane
Parameter
k a = 0.29
k , , min-' +(,
x
M cm-2 sec-'
P$' x 10W cm sec-'
2
0.07
+23
= 309 2 70
Pa
=
3.44
2
0.78
Luminal membrane = 0.139 2 0.032 k,, = 0.044 rf: 0.01 +12 = 446 & 103 4 2 1 = 47 2 10.6 Pzl = 0.59 2 0.13 k12
IV. ESTIMATION OF BASOLATERAL MEMBRANE PERMEABILITIES AND CONDUCTANCES
The chloride permeability of the basolateral membrane calculated above and listed in Table I is in good agreement with the value obtained in Nectrrrrrs kidney slices (Y). Whittembury er crl. (Y) measured the basolateral membrane PD and the uptake of radioactive chloride into the proximal tubule cells of slices of Necrurus kidney. They calculated the membrane permeability using the Goldman- Hodgkin- Katz equation [our Eq. (9)], as 0.58 x cm sec-I, only slightly higher than our estimate cm sec-'. It was previously shown (6) that the basolateral of 0.3 x membrane sodium permeability is extremely low and that the basolateral membrane PD is primarily a KCI diffusion potential (2-4, 8, 9). The measured basolateral membrane PD and the calculated chloride permeability may be inserted into the Goldman equation for the basolateral PD and used to calculate the potasium permeability of that membrane. The potassium permeability, P&, is 1.62 5 0.37 x cm sec-I, which is in reasonable agreement with the value of 1.09 x cm sec-l obtained isotopically by Whittembury et N I . (Y) in kidney slices. The ratio of the basolateral membrane permeabilities ( P g i / P t 3 = 0.21) is also in good agreement with the ratio of 0.2 obtained with electrophysiological methods by Boulpaep (2). The partial conductance, Gh3, of the basolateral membrane for an ion, i, is (33
where
=
P,3
Z2F2 c iRT
ciis the logarithmic mean concentration
270
G. KIMURA AND K. R. SPRING
of the cell ( C , ) and capillary ( C , ) concentrations. The calculated 0 2 3 for C1 and K are 768 2 174 and 1430 k 320 pmho cm-2, respectively. The total basolateral membrane conductance is 2200 k 540 pmho cm-2, and the estimated basolateral membrane resistance, R Z 3 is , 455 2 119 n.cm2. V.
ESTIMATION OF LUMINAL MEMBRANE IONIC CONDUCTANCES
The luminal membrane conductance may be estimated in two ways. The voltage divider ratio is measured and used to calculate the ratio of the resistance of the luminal membrane to that of the basolateral. This ratio is typically 3-5 (2, 7), and the calculated luminal membrane resistance is 3 to 5 times greater than the basolateral membrane resistance or 1365- 2275 cm2. Alternatively, the passive ionic permeabilities may be converted to conductances and summed as was done for the basolateral membrane. The luminal membrane C1 conductance from P Z l in Table I is 132 pmho/cm2, luminal membrane K conductance is negligibly small, and luminal membrane Na conductance is 430 pmho/cm2 (Kimura and Spring, unpublished observations). Table I1 lists these values and the estimated total luminal membrane conductance of 562 pmho/cm2, equivalent to a membrane resistance of 1779 R-cm2. VI.
ESTIMATION OF SHUNT PERMEABILITIES AND IONIC CONDUCTANCES
Shunt permeabilities and conductances are also listed in Table 11. The shunt permeabilities to Na and C1 were measured and the K permeability was assumed to be two times the CI permeability from the data of Whittembury et a / . (9). Using the shunt permeabilities to CI (5) and to Na (6) the NaCl dilution potential can be calculated from the NernstPlanck-Henderson equation. The dilution potentials measured by Boulpaep (2) are simulated exactly using the tracer permeabilities. The partial conductances of the shunt pathway for Cl, Na, and K were also calculated 1010 x and 189 x mho cm-2, respectively. as 3090 X The ratio of transference numbers tCl/fNa = 3.1) is in good agreement with the measured value of 3.0 (2). Neglecting the conductance of ions other than C1, Na, and K, the total shunt conductance is 4290 x mho cm+, equivalent to a shunt resistance, R13, of 233 n.cm2.
TABLE I1 ION PERMEABILITIES A N D CONDUCTANCES Basolateral membrane Ion C1-
K+
Na+
G Total R n.cmz
P ( x 1W5c d s e c )
G (prnho/cmZ)
0.344 1.62 -0
768 1428 -0 2196 455
Luminal membrane (x
P 1W5c d s e c ) 0.06 -0 0.176
G (pmho/cmz) 132 -0 430 562 1779
Shunt (x
P
G (pmho/cmP)
0.834 1.60 0.266
3090 189 1010 4290 233
cdsec)
272
G. KIMURA AND K. R. SPRING
VII.
ELECTRICAL ANALOG MODEL
The values for cell membrane and shunt resistance along with the measurements of potential differences may be incorporated into the electrical analog model of the Nrcturus proximal tubule originally proposed by Windhager et d.( 8 ) .Figure 3 indicates the values calculated from the equations for the electrical equivalent circuit. The transepithelial resistance of the circuit is 215 fl*cm2, and the cellular electromotive force (emf) required to produce the observed 9.7 mV transepithelial PD is 123 mV. The cellular emf is made up of two batteries-a luminal emf of 43.4 mV and a basolateral emf of 79.9 mV-assuming the shunt emf to be negligible. The circulating electric current, calculated by dividing the transepithelial PD by the shunt resistance, is 41.6 pA/cmZ. VI II. MEMBRANE RESISTANCES
The cell membrane resistances calculated in Section VII (Fig. 3) are one-half to one-third of the resistances determined by cable analysis of the epithelium ( I , 8) and the ratio of cell membrane resistance to shunt resistance is around 12, much lower than previous estimates of a ratio of 100 (2). This discrepancy may be due either to an overestimate of the cell membrane ionic conductances calculated from the tracer data, o r to an underestimate of the conductances calculated from the cable analysis. The rate constants in Table 1 may be overestimates if significant exchange diffusion of 36Cloccurred with intracellular chloride. Our previous investigations (5, 7) indicated that exchange diffusion of chloride was not significant across the cell membranes or shunt pathway. This conclusion was based on the observations that chloride entry into the tubule cells required luminal Na and that unidirectional chemical chloride movement across the shunt pathway was equal to tracer chloride movement. However, neither of these earlier observations preclude significant exchange diffusion of NaCl across the luminal membrane of the tubule cell. A luminal membrane carrier for NaCl might rapidly exchange luminal Na3TI for intracellular NaCI, thereby causing an overestimate of the 3sCI fluxes on which the determination of k,, and k 2 3 depends. The possibility of NaCl exchange across the luminal membrane could be tested by loading the cells with tracer NaCl and measuring the tracer washout to the lumen after rapidly switching the luminal perfusate to a cold NaCl Ringer’s solution. .IIS tubule ( / ) We have reviewed the cable analysis of N ~ C . / I I I proximal
273
PROXIMAL TUBULE CONDUCTANCE
I
ECF
Cell (2)
Lumen (1)
AW21
-51.3 mV 2275 43
-I-++
Qcm2 mV '12
(3)
"23
-62.1 rnV
80 456 mV Qcm2
El2
Shunt
0 rnV
E23
'23
3 1 '
-9.7 mV "13
FIG. 3 . Electrical ar.,.Jg model of Necfiirus proximal tubule. Membrane and series resistances are lumped together and indicated by R,. Electromotive forces are shown as E,, and observed potential differences as Aeu. A circulating current of 41.6 FA/cm* is indicated.
and have not found any unreasonable assumptions o r calculations. The values obtained ( I ) are in good agreement with estimates of the cell membrane resistances of other leaky epithelia derived from the cable analysis (2). However, it has been shown (2) that the simple electrical analog in Fig. 3 does not result in correct values for the transepithelial PD if the cell membrane resistances from cable analysis are used. A more complex analog model has been proposed (2) which requires a large circulating transepithelial electrical current. It is of interest that the cell membrane resistances estimated from the tracer data presented here result in an adequate representation of the electrical properties of the Nectur'us proximal tubule by the simple analog circuit rather than the more complex model. We have shown how a limited number of measurements of tracer kinetics may be utilized to estimate the permeabilities, conductances, and electromotive forces of the entire tubular epithelium. Our results suggest that a simple electrical analog circuit may adequately depict the steady-state properties of the epithelium under control conditions.
274
G. KIMURA AND K. R. SPRING
IX. SUMMARY
An analytical method is described in which isotopic tracer and electrophysiologic observations are utilized to estimate the ionic permeabilities and electrical resistance of the cell membranes and shunt pathway of Necturus proximal tubule. The rate of disappearance of luminal 3sCl is utilized to calculate the chloride flux and permeability of the luminal and basolateral cell membranes. Membrane electrical conductances are calculated from the individual ion permeabilities and incorporated into the electrical analog model of the Nrcturus proximal tubule. REFERENCES 1. Anagnostopoulos, T., and Velu, E. (1974). Electrical resistance of cell membranes in Necturus kidney. Pfluegers Arch. 346,327-339. 2. Boulpaep, E. L. (1976). Electrical phenomena in the nephron. Kidney Inr. 9,88-102. 3. Boulpaep, E. L. (1967). Ion permeability of the peritubular and luminal membrane of the renal tubular cell. In "Transport and Funktion Intracellularer Elektrolyte" (F. Kruck, ed.), pp. 98-107. Urban & Schwarzenberg, Munich. 4. Giebisch, G. (1961). Measurements of electrical potential differences in single nephrons of the perfused Necturus kidney. J . Gen. Physiol. 44, 659-678. 5 . Kimura, G . , and Spring, K. R. (1978). Transcellular and paracellular tracer chloride fluxes in Necturus proximal tubule. A m . J . Physiol. 235, F617-625. 6 . Spring, K. R., and Giebisch, G. (1977). Tracer Na fluxes in Necturus proximal tubule. A m . J . Physiol. 232, F461-F470. 7. Spring, K. R., and Kimura, G. (1978). Chloride reabsorption by renal proximal tubules of Necturus. J . Membr. Biol. 38, 233-254. 8. Windhager, E. E., Boulpaep, E. L., and Giebisch, G. (1967). Electrophysiological studies on single nephrons. Proc. In,. Congr. Nephrol. 1, 35-47. 9. Whittembury, G., Sugino, N., and Solomon, A. K. (1961). Ionic permeability and electrical potential differences in Necturus kidney cells. J . Gen. Physiol. 44, 689-712.