Na-K pump current in the Amphiuma collecting tubule.

There is strong evidence supporting the hypothesis of an electrogenic Na-K pump in the basolateral membrane of several epithelia. Thermodynamic considerations and results in nonepithelial cells indicate that the current carried by the pump could be voltage dependent. In order to measure the pump current and to determine its voltage dependence in a tight epithelium, we have used the isolated perfused collecting tubule of Amphiuma and developed a technique for clamping the basolateral membrane potential (Vbl) through transepithelial current injection. The transcellular current was calculated by subtracting the paracellular current (calculated from the transepithelial conductance measured in the presence of luminal amiloride) from the total transepithelial current. Basolateral membrane current-voltage (I-V) curves were obtained in conditions where the ratio of the pump current to the total basolateral membrane current had been maximized by loading the cells with Na+ (exposure to low-K+ bath), and by blocking the basolateral K+ conductance with barium. The pump current was defined as the difference of the current across the basolateral membrane measured before and 10-15 s after the addition of strophanthidin (20 microM) to the bath solution. With a bath solution containing 3 mM K+, the pump current was nearly constant in the Vbl range of -20 to -80 mV (52 +/- 5 microA.cm-2 at -60 mV) but showed a marked voltage dependence at higher negative Vbl (pump current decreased to 5 +/- 9 microA.cm-2 at -180 mV). In a 1.0 mM K bath, the shape of the pump I-V curve was similar but the amplitude of the current was decreased (24 +/- 4 microA.cm-2 at -60 mV). In a 0.1 mM K bath, the pump current was not significantly different from 0. Our results indicate that the basolateral Na-K pump generates a current which depends on the extracellular potassium concentration. With physiological peritubular concentration of K+ and in the physiological range of potential, the pump activity, measured as the pump-generated current, was independent of the membrane potential.


INTRODUCTION
The electrogenic nature of the Na-K pump, a phenomenon demonstrated in several types of cells (subject reviewed in De Weer, 1985) means that one or several of the steps of the pump cycle must be carrying one or more charges across the mem-brahe. From thermodynamic considerations, such a charge-moving step may be dependent upon the potential difference across the membrane, and if this chargemoving step is rate limiting, then the pump activity will be voltage dependent (De Weer, 1984). Data supporting voltage dependence of the Na-K pump current have been obtained in the isolated cardiac cell (Gadsby et al., 1985), in the squid axon (De Weer et al., 1987;Rakowski et al., 1989) and frog oocyte (Lafaire and Horisberger et al., 1987). The current across the cell (Ic) was calculated as the difference between the measured total transepithelial current (Ire) and the "shunt" current (Is). The pump current was defined as the part of the transcellular current, measured under basolateral membrane voltage clamp conditions, that could be abolished by strophanthidin. In order to obtain optimal conditions to measure the pump current the following maneuvers were performed: (1) The pump activity was stimulated by a high intracellular Na + activity obtained by previously inhibiting the pump for 4 min by a low-K + bath. (2) The basolateral membrane conductance was reduced as a consequence of previous pump inhibition (Horisberger and Giehisch, 1988b) and by addition of 2 mM barium to the peritubular bath. (3) The paracellular conductance was decreased by potassium adaptation of the animals ; (4) this maneuver also increased the apical membrane conductance and reduced the apical-basolateral membrane resistance ratio , a condition necessary to allow for voltage clamping of the basolateral membrane potential through transepithelial current injection.
1986; Rakowski and Paxson, 1988). Several investigators have reported data supporting the electrogenic nature of the Na-K pump of "leaky" or "tight" sodiumtransporting epithelia of various origin (Sansom and O'Neil, 1986;Lewis et al., 1978;Kirk et al., 1980;Sackin and Boulpaep, 1983;Graf and Petersen, 1974;Nielsen, 1979a, b;Proverbio and Whittembury, 1975;Horisberger and Giebisch, 1988b). Na-K-ATPase, isolated from kidney medulla and reconstituted in artificial membranes, has also been shown to be electrogenic (Borlinghaus et al., 1987;Fendler et al., 1985). Although depolarization of the basolateral membrane did not affect the basolateral ouabain-sensitive Na § emux (Cox and Helman, 1986c), no direct measurements of the voltage dependence of the pump current in epithelia have so far been reported. Considering the possible physiological relevance of the voltage dependence of the pump activity in sodium-transporting epithelia, we have developed a technique that allows measurements of the current across the basolateral membrane of the cells of an isolated perfused renal tubule, under voltage clamp conditions.
The voltage dependence of the pump current corresponds phenomenologically to a "pump conductance." Under physiological conditions, this conductance amounts to only a small part of the total membrane conductance (De Weer, 1986). Therefore, for our study we have chosen conditions in which the pump conductance was maximized when compared with the total membrane conductance which was minimized. We had observed such conditions in previous experiments where membrane conductances and intracellular Na + and K + activities were measured (Horisberger and Giebisch, 1988b): after a 4-min exposure to a low-potassium bath, the principal cells of the collecting tubule of Amphiuma had a high Na + and low K + intracellular activity, and a markedly reduced basolateral membrane K + conductance. We have further reduced the basolateral membrane conductance by adding barium to the peritubular solution: barium has been shown to be an inhibitor of this conductance Horisberger et al., 1987). As stated in previous papers from this laboratory Horisberger and Giebisch, 1988b), exposing Amphiuma to a high potassium environment induces in the collecting tubule (a) an increase of the apical membrane conductance, largely a sodium-selective conductance and (b) a decrease of the paracellular conductance. Since these conditions allow for optimal measurements of the transcellular current, all the experiments reported here have been performed on potassium-adapted Araphiuma (see methods) . The strategy used to measure the pump current under optimal conditions is illustrated in Fig. 1. Under conditions described, we have measured the strophanthidin-sensitive basolateral membrane current in relation with the basolateral membrane potential. We found this pump current dependent on the peritubular bath K + concentration and we describe its dependence on the membrane potential.

METHODS
Amphiuma of both sexes were obtained from C. Sullivan (Nashville, TE) and were K + adapted by being kept for at least 4 d in aquaria containing a 10 mM NaCI + 50 mM KCI solution . The identification, preparation, and perfusion of single collecting tubules were carried out as described in previous papers from this laboratory Horisberger et al., 1987). The technique used to measure the transepithelial potential and to inject transepithelial current through the perfusion pipette has also been described in these papers. Short segments (range 182-270 /zm) were dissected and cannulated at both ends for perfusion with control of the intratubular pressure (Horisberger and Giebisch, 1988b). In these short tubules with high transepithelial resistance, current injected at the proximal end of the tubule induced a nearly constant voltage deflection along the whole length of the tubule (Horisberger and Giebisch, 1988a). Experiments were performed only when the voltage deflection measured at the distal end of the tubule was >80% of the voltage deflection measured at the proximal end. The effective transepithelial voltage (Vt*) was taken as the mean of the values measured at both ends of the tubule. Cellular impalements with conventional microelectrodes filled with 1 M KC1 allowed for measurements of the basolateral membrane potential (V~) . The mean distance of the impalement point of the intracellular electrode from the proximal end of the tubule was 35 _+ 3% of the whole tubule length.

Data Acquisition and Voltage Clamp
Except for 25-s voltage-clamp experimental periods, the tubules were maintained under open circuit conditions. The transepithelial potentials (Vt*) measured at both ends of the tubule and the basolateral membrane potential (VbO were continuously recorded on two paper chart recorders (model 220, Gould, Inc., Cleveland, Ohio).
During Vu-clamp periods, data were also recorded by means of a data acquisition system consisting of a microcomputer (IBM-XT), an analog-digital converter (RTI-815, Analog Devices, Inc., Norwood, MA) and a software package (UnkelScope, Unkel Software, Lexington, MA). Four channels sampled once every 50 ms: (a and b) Vt* recorded at both ends of the tubule, (c) Vbl, and (d) the transepithelial current (It,). These data were stored digitally on the hard disk of the computer for later analysis. The controller included in the UnkelScope system also allowed us to adjust the current injected through the lumen with regard to the basolateral membrane potential every 50 ms. Thus, we were able to voltage clamp the basolateral membrane potential.
The paraceUular conductance (G,) was estimated as the transepithelial conductance measured with 10 t~M amiloride present in the luminal fluid, using a 1-s positive luminal current injection. We have shown previously that this method yields valid estimates of the paracellular conductance Horisberger et al., 1987), and that this conductance is linear in the +_200 mV range (Horisberger and Giebisch, 1988a) and not influenced by the bath K + concentration . G, was measured immediately before and immediately after the maneuver described below and the mean of these two measurements was used to calculate the paracellular current (I,) at each transepithelial potential value: I, = Vt*.Gs. (1) The transcellular current (Ir was then calculated as the difference between the total transepithelial current (It*) in the absence of amiloride and the paracellular current: Ic = It* -I,. ( All currents and conductances are expressed per unit of luminal tubule surface area. The length and the luminal diameter of the tubule were measured optically by means of a calibrated eyepiece micrometer.

Experimental Protocol
After a stable cellular impalement had been obtained under open circuit condition, the tubule was exposed during a 4-rain period to a 0.1 mM concentration of K + in the peritubular bath solution ([K+]b). Then 2 mM barium was added to the bath and simultaneously, [K+]b was set to 3.0, 1.0, or 0.1 raM. As soon as the bath solution change had been completed (within 10 s), the control was switched to the basolateral membrane voltage clamp mode and Vb, was clamped at -60 mV for 2 s and then for four successive 0.5-s periods at -20, -100, -140, and -180 mV (15 experiments). Alternatively, Vbl was clamped at -50 mV for 2 s and then for four successive 0.5-s periods at -20, -80, -110, and -140 mV (11 experiments). The control potential was then set at -60 mV (or -50) for 18 s. During this time strophanthidin 20 aM was added to the bath solution. A second series of voltage steps at -20, -100, -140, -180, and -60 (or -20, -80, -110, -140, and -50) was carried out and then the control was switched back to the open circuit mode. Amiloride was added to the luminal solution to measure the shunt conductance and then the hath solution was changed for the control solution. A period of at least 10 min with luminal amiloride and another period of at least 5 rain with control solutions were allowed to elapse. If the potential recording from the intracellular electrode was still stable after this recovery period, a second or a third experiment using a different bath K + concentration was performed. By blocking the pump, strophanthidin may induce changes of the K + concentration in the unstirred layers along the basolateral membrane. As the basolateral membrane has been shown to be K § selective, these changes in the unstirred layers could generate an inward K + current which would be indistinguishable from the abolition of the outward pump current during simple transcellular current measurements. Thus, the "strophanthidin-sensitive" basolateral membrane current may not represent only a real pump current. However, as stated earlier, our experimental conditions were chosen to minimize the current flowing through the basolateral membrane K + conductance. To estimate the magnitude of the residual K + current flowing through the basolateral membrane under our experimental conditions, we have measured the transcellular current induced by changes of [K § under Vbrclamp conditions. Using a protocol analogous to that of the pump measurement, the pump was first blocked for 4 min by 20 #M strophanthidin, and then 2 mM barium was added to the peritubular bath solution. Then, [K+]b concentration was raised from 3.0 to 15 mM while Vu, Vte, and Ite were recorded, during a 20-s experimental period under Vu clamp conditions (Vu set to -60 mV). The transcellular current was then calculated by the same method as described for the strophanthidin experiments.

Solutions and Drugs
The composition of the "control" solution was (in millimolar) Na + 97.0, K § 3.0, Ca § 1.8, Mg 2+ 1.0, C1-89.6, HEPES/HEPES-14.4, and H2PO4/HPO~ 0.8. The "low-K" solution was similar except for the 0.1 mM K + and the 100.0 mM Na + concentration. The same control solution was used for the bath and the perfusate except that 2.0 mM glucose and 0.25 mM glycine were added to the bath solutions. The pH of all solutions was adjusted to 7.6 with NaOH. The solutions were bubbled with O2. Amiloride (gift of Merck, Sharp & Dohme, West Point, PA) was added to the luminal perfusion fluid at a concentration of 10 aM and strophanthidin (Sigma Chemical Co., St. Louis, MO) was added to the peritubular bath solution at a concentration of 20 aM.

Statistics
Results are expressed as mean + SEM (n ffi number of observations). The statistical significance of the difference between mean values was determined by Student's t test. When appropriate, Student's t test for paired data was used, as indicated in the text. P < 0.05 was chosen as the level of significance.

Electrophysiological Characteristics
Under control conditions, the transepithelial (Vte) and basolateral membrane (Vbl) potential, --38 + 3 and -61 + 2 mV (n = 39), respectively, and the apical (Ga) and basolateral (Cma) membrane conductances, 2.2 -+ 0.3 and 2.9 _+ 0.4 mS.cm -2 (n = 39), respectively, were similar to those measured previously in potassiumadapted Amphiuma by the same method Horisberger and Giebisch, 1988b). The response to exposure to the low-K + bath was also similar to that described previously, consisting of a large reduction of Ga and C,b~ to 0.64 _+ 0.22 and 0.39 +_ 0.11 mS.cm -2 (n = 39), respectively, so that we can assume that the intracellular Na + and K + activities were also similar to those measured under the same conditions (Horisberger and Giebisch, 1988b). The mean paracellular conductance-the transepithelial conductance measured with amiloride in the luminal fluid--was 2.24 + 0.25 mS.cm -2 (n = 39).

Effects of K + Concentration and Strophanthidin on the Basolateral Membrane Potential
An original recording of the basolateral membrane potential (Vbl) during a typical experiment is presented in Fig. 2. We shall first consider the part of the experiment in which Vbl was recorded under open circuit conditions; the 25-s period during which potentials and current were recorded under basolateral membrane voltage clamp conditions (hatched bar) is described in more detail in Fig. 4 and will be discussed later.
Upon exposure to a peritubular bath solution in which the potassium concentration had been decreased to 0.1 mM, Vm first rapidly hyperpolarized from -79 to -112 mV; this is due to the change of the K + equilibrium potential across the K+-selective basolateral membrane Horisberger and Giebisch, 1988b). There was then a slow depolarization of Vb~ down to -57 mV owing both to the decrease of the intracellular K + activity and the decrease of the basolateral membrane K+-selective conductance (Horisberger and Giebisch, 1988b) (Fig. 2, point A). At this point, adding 2 mM barium and raising [K+]b to 3.0 mM produced a fast hyperpolarization to -106 mV (Fig. 2, point B). The following 25-s period (hatched bar) was recorded under Vbl-Clamp conditions; this part of the recording is shown magnified in Fig. 4 and will be discussed later (however, it can be seen in Fig.  2 that Vb~ was effectively clamped at -60 mV). During this voltage clamp period, 20 #M strophanthidin was added to the peritubular bath solution; it did not modify Vb~ (which was clamped), but induced large changes of the transepithelial current and potential, as shown later in Fig. 4. When the recording mode was changed back to the open circuit conditions, Vbl had decreased to -22 mV (Fig. 2, point C). Under control conditions, raising [K+]b and addition of barium to the peritubular bath solution are two maneuvers which induce a depolarization of Vbl, because, under control conditions, V~a is mainly determined by the potassium-selective basolateral membrane conductance and the large negative equilibrium potential of potassium (EK+) across this membrane . The large hyperpolarization of Vbl produced by raising [K+]b and adding barium after the cell has been loaded with Na + indicate that, in contrast under these circumstances, Vbl is mainly dependent on another K+-dependent electrogenic process: the Na-K pump. This is confirmed by the very fast and large depolarization observed after the addition of strophanthidin. Hence, before the addition of strophanthidin, Vb~ had a much larger negative value when [K+]b was at 3.0 mM than when it was at 0.1 mM (-68 _+ 7 mV [n = 18] vs. -13 _+ 3 mV [n = 11], P < 0.001). This effect of [K+]b was opposite to the effect predicted for a conductive, K+-selective pathway. Rather than depolarizing the peritubular cell membrane, potassium activated an electrogenic hyperpolarizing process in the basolateral membrane. The fact that the K+-induced hyperpolarization could be inhibited by strophanthidin strongly suggest that this process is a Na+/K + countertransport with a higher number of Na + ions than K + ions being transported.

Effect of Strophanthidin on the Basolateral Membrane I-V Curve
We next consider the part of the experiments done under Vbrclamp mode. Original recordings of the transepithelial potential, basolateral membrane potential and  strophanthidin on the membrane current diminished towards high negative membrane potentials.
Inasmuch as the transcellular current before and after strophanthidin were measured at the same measured basolateral membrane potentials (basolateral membrane voltage clamp conditions) and in the presence of the same concentration of barium, our measurements of the strophanthidin-sensitive current did not depend on the precise nature of block of the K + conductance by barium. However, as shown in another paper (Horisberger and Giebisch, 1988a), at positive membrane potential, the basolateral membrane conductance becomes very large even in the presence of barium. Under these conditions, the pump conductance becomes only a very small part of the total basolateral membrane conductance, and the measurement of the pump current becomes inaccurate. For this reason, pump current measurements were carried out only at negative membrane potentials.
In Fig. 5, we have plotted the pump current (/pump), calculated as the difference between the current across the basolateral membrane before and after strophanthidin, as a function of the basolateral membrane potential. able, because the I-V curve may be S-shaped and cross the 0 current line at much higher potential. With a [K+]b of 1.0 raM, the shape of the I-V curve was roughly similar, with a strophanthidin-sensitive current of reduced amplitude when compared with the values obtained with [K+]b at 3.0 mM. A reversal potential around -160 mV could be observed. The data obtained with a [K+]b of 0.1 mM indicated that the strophanthidin current was abolished at low membrane potentials. With more negative membrane potentials, all the mean values of the strophanthidin-sensitive current were negative and these inward currents tended to be larger with higher negative potentials. The scatter of the data (no values significantly different from 0 under these conditions) did not allow to determine a reasonably accurate value for the reversal potential.

Potassium Current in the Presence of Barium
To estimate the K + current flowing through the basolateral membrane conductance under our experimental conditions we also measured the transcellular current induced by changes of [K+]b in another group of tubules. After the pump had been blocked for 4 min and 2 mM barium had been added to the bath solution, and under voltage clamp conditions (Vbl set to --60 mV), raising the bath K + concentration from 3 to 15 mM induced an inward-directed current of 9 _+ 3 /zA.cm -2 (n = 4), to be compared with an ouabain-sensitive current of >50 #A.cm -2 measured with a K § concentration of 3 mM. In this group of four tubules all the electrophysiological variables (Vt,, -28 _+ 6 mV; Vbl,--55-+ 7 mV; G,, 3.1 _+ 0.4 mS.cm-~; C~ after 4-min pump block, 1.0 _+ 0.3 mS.cm -~) were similar to those measured in the tubules used for the pump current measurements. Thus, a large change of [K+]b produced only minor changes of the current across the basolateral membrane after the K + conductance had been blocked by barium. We show in the Appendix that this change of the peritubular bath concentration of potassium is much larger than the change of K + concentration that can be expected in the unstirred layers from a sudden inhibition of the K § flux carried by the pump.

DISCUSSION
Our measurements of the current across the basolateral membrane under voltageclamped conditions, and our recordings of the basolateral membrane potential after potassium readmission confirm the electrogenicity of the Na-K pump of the basolateral membrane of cells of a sodium-transporting "tight" epithelium. The electrogenicity of the K+-activated, strophanthidin-sensitive process in the basolateral membrane cannot be explained by the K § conductance and K + concentration gradient in the unstirred layers along the basolateral membrane because when [K+]b is increased the voltage change occurs in a direction opposite to that predicted by the K § concentration changes in the bulk solution. Furthermore, when the basolateral membrane K § conductance was blocked by barium, the hyperpolarizing effect of external K + in the present experiment and the depolarizing effect of strophanthidin tended to be larger than what had been observed in similar studies performed in the absence of barium (Horisberger and Giebisch, 1988b). This fact strongly argues against a major role of the basolateral membrane potassium conductance in the potential changes observed when the pump was blocked or activated.
In order to consider the strophanthidin-sensitive current across the basolateral membrane as a reliable estimate of the current directly generated by the Na-K pump, we had to demonstrate that the strophanthidin-sensitive current was not significantly influenced by a potassium current flowing through the basolateral K § selective conductance. To achieve this aim, our experimental conditions were chosen to minimize the effects of basolateral K + conductance. We had previously shown that after a period of pump inhibition the basolateral K § conductance was greatly reduced (Horisberger and Giebisch, 1988b). Furthermore, we added barium to the peritubular bath solution, a maneuver known to inhibit the basolateral K § conductance Horisberger et al., 1987). To assess the magni-THE JOURNAL OF GENERAL PHYSIOLOGY. VOLUME 94 9 1989 tude of the K + current flowing across the basolateral membrane in the presence of barium and strophanthidin, we tested the effect of a large change of the bath K + concentration. For a peritubular bath concentration of potassium change from 3 to 15 mM, we observed an average current of 9 #A-cm -~. Although the changes in K + concentration were by far larger than those which might have been expected in the unstirred layers as a result of pump inhibition (see Appendix), the current change was only a modest fraction of the 50 #A.cm -2 current change measured when the pump was inhibited by strophanthidin. Thus, the largest part of the strophanthidinsensitive current is a pump-generated current.

The Pump I/V Curve
In accordance with thermodynamic considerations indicating a possible voltage dependence of an electrogenic process driven by a finite energy source (De Weer, 1984), the present results indicate that the Na-K pump current is related to the membrane potential. With a 3.0 mM concentration of K + in the peritubular bath, the voltage dependence is small in the physiological membrane potential range (below-100 mV), but is marked between -100 and -180 mV. In this range, the voltage dependence of the pump current is roughly equivalent to a conductance of 0.5 mS.cm -2 of tubular surface, a value of similar magnitude as the residual basolateral membrane conductance under these specific experimental conditions (basolateral conductance decreased by previously blocking the pump and by barium). It should be noticed that under normal conditions, the conductance of the pump amounts to a much smaller part of the total membrane conductance than under the conditions in which the present measurements were done, since under control conditions (a) the pump activity is probably lower because of the lower intracellular Na + activity (Horisberger and Giebisch, 1988b), (b) the basolateral membrane conductance is about 10 times larger , and (c) the slope of the pump I-V curve is negligible in the physiological range of the basolateral membrane potential.
The dependence of the pump current on the membrane potential was roughly similar to that observed by Gadsby et al. (1985) in cardiac myocyte, De Weer et al. (1987) in squid giant axon (1987, and Rakowski and Paxson (1988) in Xenopus oocyte. Since we could not explore the positive membrane voltage range, we cannot compare our data with those of Lafaire and Schwartz (1986), who observed a biphasic I-V curve with a negative slope conductance in the positive membrane voltage range.
An apparent voltage dependence can be due to the effect of the potential on one or several charge translocating steps of the pump cycle (Chapman et al., 1983;De Weer, 1986), and thus on the pump turnover rate. However, the possibility of a change of the Na+/K + coupling ratio towards unity (electroneutral Na+/K + exchange) with high negative membrane potential cannot be excluded. The constancy of the coupling ratio of the Na-K pump is still a controversial matter: in nerve and cardiac cells, parallel changes of the pump-generated current and Na + transport rate indicate a constant coupling ratio (Abercrombie and De Weer, 1978;Eisner and Lederer, 1980;Rakowski et al., 1989); similarly in rabbit proximal tubules (Avison et al., 1987), the 3 Na + to 2 K + ratio appears to be constant over a wide range of transport rate. However, a coupling ratio changing with the transport rate has been reported in frog skin (Cox and Helman, 1986a, b), amphibian proximal tubule (Sackin and Boulpaep, 1983), and rabbit cortical collecting tubule (Sansom and O'Neil, 1986). In the collecting tubule of Amphiuma, estimates of the pump coupling ratio, by comparison of the pump current to the transceUular sodium current under steady-state conditions, are compatible with a 3 Na + to 2 K + ratio (Horisberger, 1989). However, the measurements of the present study were made under transient conditions, far from a steady state, and give no information about the pump coupling ratio.
Assuming a constant stoichiometry, we can tentatively apply our data to a very simplified pump model described by De Weer (1986). The small slope conductance of the pump at physiological membrane potentials indicates that the pump rate is limited by a voltage-insensitive step (pump of the "rheogenic type"). Goldshlegger et al. (1987) have provided evidence that this rate-limiting, voltage-insensitive step is the potassium translocation step (conformational change Fa(2K)--* EI(2K), in accordance with the data by Nakao and Gadsby (1986) indicating that the sodium translocating step is charged.

Voltage Dependence of the Pump: Physiological Relevance
From the observed I-V relation of the pump current, variations of the basolateral membrane potential of the same magnitude as those observed under hormonal stimulation (in the range of -50 to -80 mV ) would entail only minor changes of the pump activity. These findings are in accordance with the results of Na + flux measurements by Cox and Helman (1986c). Thus, in the physiological range of the basolateral membrane potential, the assumption that the Na-K pump is electrically equivalent to a pure current source is appropriate (Boulpaep and Sackin, 1979). This property of the Na-K pump contrasts with that of the H + pump in acid secreting cells which is markedly voltage dependent in the physiological range of membrane potential and H + concentrations (Andersen et al., 1985;Ehrenfeld et al., 1985;Harvey and Ehrenfeld, 1986).

Dependence on Peritubular K + Concentration
The dependence of the pump current on [K § could theoretically be due either to a change of the stoichiometry of the pump or to a change of the activity of the pump with a constant stoichiometry. The current dependence on external potassium appears to be similar to the well-known K + dependence of the enzymatic (ATPase) activity of the Na-K pump (Jorgensen, 1986). This parallel dependence of the pump current and enzymatic activity on external [K +] suggests a constant pump stoichiometry.

Reversal Potential and Reverse Pump Current
By choosing appropriate experimental conditions, De Weer and Rakowski (1984) have been able, in the squid giant axon, to record current generated by the backward-running electrogenic Na + pump. With low peritubular K + concentrations we have also recorded negative (inwardly directed) strophanthidin-sensitive currents, which tended to be larger with higher negative potentials. In a peritubular bath containing 1.0 mM K + the pump reversal potential was about -160 mV. Assuming a constant pump stoichiometry (3 Na+/2 K+/1 ATP) and using the values of intracellular Na § (45 mM) and K § (16 mM) activities measured previously under similar conditions--after inhibition of the Na-K pump for 4 min-- (Horisberger and Giebisch, 1988b), an excess of free energy of ATP hydrolysis (AGATP) can be calculated according to the equations given by De Weer (1986). This yields a AGAT P of 360 mV. This value is lower than those reported in amphibian nonepithelial tissues (muscle), 480 mV (Kushmerik, 1969) and 560 mV . The lower AGAxp observed in the present study and the finding that all the strophanthidin-sensitive currents measured at membrane potentials lower than -50 mV at 0.1 mM [K § were negative suggest the possibility of a systematic bias in pump current estimates. For instance, if the basolateral membrane conductance were to decrease between the I-V curves established before and after strophanthidin, this could lead to an overestimate of the pump conductance and to larger apparent negative pump currents at high negative membrane potentials. This possibility must be considered, but we believe that such conductance changes must be small in view of the short intervals (20 s) between the time of the two I-V curves taken before and after strophanthidin exposure. We cannot, at present, evaluate to what extent other factors, such as the uncertainty concerning the precise intracellular ionic activities, the intrinsic difference of the tissues and the experimental conditions (isolated perfused tubule, at room temperature) may have contributed to our finding lower AGAT P values than those reported in nonepithelial tissues.
In summary, our data confirm that the cardiac steroid-sensitive Na-K pump of the basolateral membrane of "tight" epithelia is electrogenic and transports an asymmetrical number of charges. In agreement with thermodynamic considerations, the activity of this pump is voltage sensitive, with the largest voltage dependence in the range of -100 to -200 mV of the membrane potential. This voltage dependence is similar to that reported in nonepithelial cells. As expected from measurements of its enzymatic activity, the electrical activity of the pump is also dependent on the external K + concentration.

APPENDIX
We try below to estimate the magnitude of the possible change of the concentration of K § produced by sudden blocking of the Na-K pump in the unstirred layers along the basolateral membrane. The basolateral membrane of the principal cells of the collecting tubule of Amphiuma has a very complicated geometry; numerous infoldings of the basolateral membrane amplify its surface by a factor larger than 10 (in K § animals) (Stanton et al., 1984). Thus, to analyze the unstirred layers effect within the lateral spaces and the basolateral membrane invaginations, we use a very simplified, "worst case" model: all the active transport sites, pumps and K § channels, are assumed to be located at the deep end of the membrane infoldings and therefore separated from the well stirred peritubular solution by the whole length of the basolateral membrane infoldings (Fig. 6). We use also the simplifying assumptions of a linear gradient of K § along the membrane infoldings.
Starting from a steady-state situation, where the inward K § flux carried by the pump (JK pump) is equal to the outward "leak" flux through the conductance, sudden blocking of the [K.] FIGURE 6. Simplified cellular model used to estimate the effect of inhibition of the basolateral Na-K pump on the K + concentration in the unstirred layers along the basolateral membrane.
Na-K pump produces the appearance of a net outward K § flux equal to -Jx pump. We now use the Fick equation (Davson, 1970): where ds/dt expresses the rate of transport, D the diffusion coefficient, and dc/dx the K + concentration gradient. A is the mean cross-sectional area of the extracellular spaces between the cells and within the basolateral membrane infoldings. From inspection of histologic pic-THE JOLrRNAL OF GENERAL PHYSIOLOGY. VOLUME 94. 1989 tures of the Amphiuma collecting tubule (Stanton et al., 1984), we can see that the width of the lateral spaces and of the basolateral membrane invaginations is not negligible and that these spaces contain a sizeable amount of extracellular fluid; we assume that this crosssectional area of the extracellular spaces (A) amounts at least to 1/100 of the peritubular surface area. Let us take, for example, a K + concentration gradient of 1 mM between the well-stirred bath and the deep end of the infoldings and a depth of the infoldings of 20 #m. For 1 cm 2 of tubular surface, (A equal to 0.01 cm~), with aJK pump equivalent to twice the pump current (2.60 #A/F = 1.3 nmol. s -l) and for a K + concentration gradient of 1 raM/20 #M (0.5 mol.liter-l.cm-l), the Fick equation yields a value of D amounting to 2.6-10 -7 cm2.s -1. This value is two orders of magnitude lower than the diffusion coefficient of K + in free solution (1.99.10 -s cmLs -x [Robinson and Stokes, 1959]). It is also about 10 times lower than estimates of the diffusion coefficient of K + in kidney slices (2.3.10 -6 cm2.s -a [Proverbio and Whittembury, 1975]). Thus, the assumed 1 mM K + concentration gradient in the unstirred layers when the pump is blocked was greatly overestimated. As we have shown that an increase of the concentration of K + in the bath of 12 mM (from 3 to 15 mM) produced an inward K + current amounting to only a modest fraction (<20%) of the measured strophanthidin sensitive current, we may safely conclude that, under our experimental conditions, the potassium current flowing through the K + conductance and produced by the effect of strophanthidin on the K + concentration in the unstirred layers is negligible.
We are very grateful to G. Whittembury and L. G. Palmer for critical reading of the manuscript and useful suggestions.