Effects of pH, Ca, ADH, and theophylline kinetics of Na entry in frog skin LAZARO J. MANDEL Department of Physiology, Durham, North Carolina

Duke 27710

University

Medical

MANDEL, LAZAR~ J. Effects ofpH, Ca, ADH, and theophylline on kinetics of Na entry in frog skin. Am. J. Physiol. 235(l): C35-C48, 1978 or Am. J. Physiol.: Cell Physiol. 4(l): C35-C48, 1978. -The short circuit current as a function of Na concentration in both solutions was found to obey Michaelis-Menten kinetics under a variety of experimental conditions. Values of maximal transport rate (J,J and half-maximal Na concentrations (K,) were determined from these experiments. Thr&e type of results were obtained: I) Im and K, both decreased by approximately the same fraction when the pH of both solutions was reduced by increasing PCQ, 2) Im decreased and K, increased when the external pH was decreased, and 3) &,, increased with ADH and theophylline, decreased with external Ca, and K, remained unchanged. Various criteria were utilized to determine that these were properties of the entry barrier for Na into the “transport pool.” The results are explained in terms of a model that separates three different types of actions on the entry barrier: I) competition of Na with other ions in the external solution for entry, 2) modulation of the number of sites available for Na translocation by changing the cytoplasmic pH, and 3) alterations in the rate of Na translocation caused by changes in the Na permeability or the electrochemical gradient across the entry barrier. Michaelis-Menten sues; Rana pipiens

kinetics;

applied

potential;

epithelial

tis-

NA TRANSPORT through frog skin has been visualized by numerous investigators as a process that consists of two main barriers: Na entry into a cellular compartment and Na exit from this compartment into the serosal extracellular space. The postulated anatomical localization of these barriers has changed over the years, originally involving only the innermost epithelial layer stratum germinativum (26) and, thereafter, being localized predominantly at the outermost living cell layer, stratum granulosum (50). Recently, evidence has been accumulating from various laboratories indicating that all living epithelial layers in frog skin act as a functional syncytium (7, 37, 40), localizing the entry barrier at the outer membrane of the stratum granulosum and the exit barrier at the basolateral membranes. Sodium entry appears to be normally rate determining for active transepithelial Na transport in frog skin as judged by the following criteria: 1) The resistance of the outer barrier represents 80-90% of the total transepithelial resistance (22, 23); 2) The rate of rapid Na ACTIVE

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Copyright

0 1978 the American

Physiological

on

Center,

entry is identical to the rate of transepithelial active Na transport, indicating that little Na efflux occurs through the entry step (38, 40); 3) The intracellular Na concentration of frog skin measured by electron microprobe analysis is 9 mM when the skin is bathed in regular Ringer (40). This Na concentration is well below saturation for the Na-K-ATPase (24); 4) The functional dependence of active transepithelial Na transport on applied potential is relatively independent of external Na concentration, indicating that the applied potential affects mainly the entry step, which would be rate determining (36). This latter criterion was utilized in the present study to ascertain whether Na entry remained rate determining under the experimental conditions tested. Specialized sites located at the external membrane surface appear to be responsible for the properties displayed by the Na entry process: that is, saturation as a function of external Na concentration (5, 13, 16, 38, 41, 42), competition of Na entry elicited by lithium (5) and potassium (36) from the external solution, and specific inhibition by amiloride of the saturable portion of the Na influx (3) with high affinity and specificity (2, 14). These sites have been modeled as parts of a Naselective carrier (6) or, more recently, a pore (31) traversing the external membrane of the frog skin. The aforementioned properties of the Na entry process suggest that the initial interaction of Na with the entry sites might be describable by Michaelis-Menten kinetics and, with some modifications of this treatment, could describe the whole process of Na entry. Because Na entry appears to be rate determining, its properties are reflected in those of active transepithelial transport as demonstrated by the hyperbolic relationship between active Na transport and Na concentration (9, 25, 36). Although this hyperbolic relationship may be described by the Michaelis-Menten kinetic equations, this is clearly not a unique treatment because other model systems may behave kinetically in a similar manner. Michaelis-Menten kinetics are used because of their simplicity; they allow the calculation of a maximum transport rate &) and of the external Na concentration [Na], producing one-half the maximal rate of transport (K,). In the present study, the hyperbolic relationship between active Na transport and [Na] 0 was maintained at various values of internal or external pH, external Ca and, on addition of ADH or theophylline, allowing Society

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c35

C36

L. J. MANDEL

the calculation ofl, and& under all these experimental conditions. Measurement of the functional dependence of active transepithelial Na transport on applied potential under these same experimental conditions indicated that the entry step remained rate determining and, therefore, the calculated kinetic parameters could be attributed to properties of Na entry. The various experimental conditions elicited three types of results: 1) 1m andK, decreased in about the same proportion when the pH was reduced with C02, 2) & decreased and & increased when the external pH was decreased, or 3) 1m changed and J& remained unchanged with ADH, theophylline, and external Ca. These observations are explained with the aid of a model based on the known behavior of enzymes as a function of pH. METHODS

General The experimental methods used were identical to those previously described (35). Briefly, the skin of Rana pipiens was mounted as a flat sheet (3.14 cm”) between Lucite chambers equipped with solution reservoirs (12 ml each), which were stirred and oxygenated with the appropriate gas mixture. The potential difference (PD) across the skin (expressed with reference to the outside solution) was measured with calomel electrodes and current was passed through the skin via AgAgCl electrodes. Both pairs of electrodes were connect&d to the solution reservoirs with agar bridges that have a composition identical to that of the bathing solution in the chamber. An automatic voltage clamp that compensated for the resistance of the solution between the PD bridges was used to pass the appropriate current through the skin to maintain a preset PD value. During most experiments the PD was maintained at zero to obtain short circui .t conditions. It is well known that the magnitude of the short circuit current . Vertical bars are 2 SE. gles). Average Isc = 56.7 PA/cm”

difference in half-maximal pH of about 3 units between the first, two and the latter experiment is similar to that observed by Schoffeniels (43) by titrating either the outside or the inside solutions, respectively, in the presence of a phosphate buffer. This intriguing result prompted an investigation described below into the effects of external and internal pH on Na transport kinetics. The kinetics of the active Na transport system as a function of Na concentration in both solutions were measured in two groups of experiments. In one group, the pH of both solutions was varied simultaneously by adjusting the CO2 concentration whereas, in the other, the external pH was varied with the internal solution pH held constant at 8.5. The results from these experiments show that under all experimental conditions tested a hyperbolic relationship existed between Isc and the Na concentration of the bathing *solutions [Na]. From the derivation of Eadie and Hofstee (see, for example, Ref. 33) they are expressed as single reciprocal plots of Isc versus I,, /[Na] from which the maximal transport rate (&J and half-maximal concentration ( Kt > are easily obtained as the intercept on the ordinate and the slope of the line, respectively. Figure 2 shows the results of a typical experiment from the first group performed at two CO, concentrations, The filled circles were obtained under control conditions with the bathing solutions bubbled with 100% 0, to obtain a pH of 8.5 in regular Ringer (containing HCOJ. The Na concentration was rapidly changed on both sides and the experimental points were obtained at [Na] of 110, 55, 20, 6, and 3 mM. The open circles were obtained on the same skin when the bubbling gas was changed to a mixture of 95% 02, 5% CO, to obtain a solution pH of 6.5. Each solution was equilibrated at this pH prior to contacting the skin and the same Na concentrations were utilized as above. This experiment showed that reducing the pH to 6.5 in both bathing solutions caused a decrease in both & and Kt. The results of seven such experiments (all with regression line correlation coefficients larger

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C38

L. J. MANDEL 1, = 79.8

80

pA/cm=

k 60

+ slope

= Kt= 25.3 mM

\

(PA/cm’-mM)

I=#/[NO] FIG.

circles) bathing on both TABLE

2. Single reciprocal plots of Isc vs. Isc /[Na] at pH 8.5 (filled and 6.5 (open circles). Lower pH was obtained by bubbling solutions with 95% OP, 5% CO,. Na concentrations utilized sides were 110,55, 20, 6, and 3 mM.

1. Effects Solution

of solution pH

pH on II11and K, I m, /&cm’

JL, mM

n

External

Internal

A

8.5 6.5

8.5 6.5

51 + 9 14 2 2.4

16.2 -r- 2.6 6,4 2 1.0

7 7

B

6.0 4.5

8.5 8.5

41 -+ 4.5 33 2 3.1

8.7 k 0.8 16.9 2 0.9

10 10

In group A, the pH of both bathing solutions was simultaneously decreased by changing bubbling gas from 100% 0, to 95% Or, 5% CO, in the presence of bicarbonate buffer (2.5 mM), In group B, the internal solution pH was maintained constant while the external solution pH was decreased by addition of HCl to a tartrate-phosphate buffer solution (2.5 mM),

than 0.95) are summarized in Table 1A. At pH 6.5, Zm decreased by a factor (paired) of 3.6 t 1.0 and Kt decreased by a factor of 2.5 -t- 1.0; these two numbers are not significantly different from each other (P > 0.4), indicating that Zm and K, decreased by approximately the same fraction. Measuring these kinetic parameters as a function of external pH while the internal pH is maintained constant causes an asymmetry across the epithelium and the possibility that the I,, may not be a good measure of active Na transport arises. Therefore, a series of five experiments was performed in which active Na transport andI,, were simultaneously measured at the lowest Na concentration utilized in the next series of experiments, namely, 6 mM at external pH values of 6 and 4.5. The measurement of fluxes when both sides contained 6 mM Na Ringer was attempted, but failed, because the skins showed continual long-range deterioration in the presence of low Na Ringer on the serosal side. This same behavior has been previously reported by Mandel and Curran (36); these results prompted the experiments to be performed with regular Ringer on the serosal side. They were initiated with 110 mM NaCl Ringer on both sides with phthalate buffer (pH 6.0) in the external solution and bicarbonate buffer in the

serosal solution (pH 8.5). Thereafter, the external solution was changed to 6 mM NaCl Ringer at pH 6.0, followed by titration with 1 M HCl to pH 4.5, and terminated by adding 10B4 M ouabain to the serosal solution while maintaining the previous external solution unchanged. Simultaneous influxes of Na and urea were measured under each of these experimental conditions. The active portion of the Na flux was calculated as described in METHODS. The results, shown in Table 2, demonstrate that ISc is a good measure of active Na transport at an external pH of 6 and Na concentrations of 6 and 110 mM. At an external pH of 4.5 and [Na], of 6 mM, Zscexceeds active Na transport by 30%, a value that is probably exaggerated by the asymmetry in Na concentrations present in these experiments. This figure represents the maximal error in a measurement of active transport versus Na concentration performed by utilizing I,, as the magnitude of active transport, because 6 mM was the lowest Na concentration tested. The effect of this error on a single reciprocal plot (Fig. 3) would be to give the appearance of nonlinearity at low Na concentrations, which tends to reduce the calculated value of K,. This error tended to be small, as seen in the next series of experiments, because the large majority of skins demonstrated good linearity down to 6 mM Na, as ascertained by the value of the correlation coefficient (larger than 0.95) In the next group of experiments the -I,, was measured at Na concentrations of 110, 55, 20, 10, and 6 mM, initially at an external pH of 6.0 and, thereafter, at an external pH of 4.5 on the same skins (the external solution contained phthalate buffer). The internal solul

TABLE 2. Comparison between active Na influx and IScat two external Na concentrations and pH values

WI, 110 6 6

PH,

J’!$;), peq/h - cm’

I,, peqlh - cm?

6.0 6.0 4.5

0.51 f 0.04 0.28 2 0.1 0.07 1 O*Ol

0.53 A 0.05 0.32 4 0.09 0.10 + 0.01

Values are means 2 SE; IZ = 5. J;S$ = active external Na concentrations. 60

Na influx;

P

>0.7 >0.7 >0.05 [Nal,

=

t~~“=54~A/cm’

w

(PA/cm’-mM)

Iv ENoI

FIG. 3. Single reciprocal plots of Is, vs. I,, /[Na] at external pH values of 6.0 (filled circles) and 4.5 (open circles with dot). pH of serosal solution was 8.5 throughout these experiments, Na concentrations were changed on both sides of skin; those utilized were 110, 55,20,10, and 6 mM.

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PH,

CA,

ADH,

AND

THEOPHYLLINE

ON

NA ENTRY

IN

FROG

SKIN

c39

tions had the same Na concentration as the external solutions throughout these experiments, but they contained a bicarbonate buffer that maintained the internal pH constant at 8.5 when both sides were bubbled with 100% 0,. The Na concentrations were changed rapidly to prevent the deterioration of I,, mentioned earlier. A typical result is shown in Fig. 3, in which the lines were calculated, as before, by linear regression analysis. It may be seen that the result of decreasing the external pH is strikingly different from that shown in Fig 2: while & decreases as before, Kt significantly 0 I increases, The results of IO such experiments are aver2 3 0 I aged in Table IB , showing a 20% decrease in &-, at pH (pA/cm’-mM) %C/ 4.5 (paired data P < 0.01) and a doubling of the& value t NaI (P < 0.001). This relatively large change in Kt in the FIG. 4. Single reciprocal plots of Is, vs. Is, /[Na] at external Ca concentrations of zero (filled circles) aid 1 rnM (open circles). Serosal presence of a small accompanying change in &-, could solution contained regular Ringer with 1 mM Ca throughout these result from competition between protons and Na in the experiments. Na concentrations utilized were 110, 55, 20, 6, and 3 external solution for entry into the active transport mM; they were changed on both sides of skin. system. The next series of experiments was devised to test this possibility. TABLE 4. Effects of external Ca, ADH, and Active Na transport and the I,, were simultaneously theophyllirte oIz I and K m t measured when the external solution contained 3 mM NaCl Ringer at either pH 6 or 4 and the internal Experimental Condition I m, pNcm2 K, mM solution was regular Ringer (pH 8.5). Influxes of Na 34 k 2 6.4 k 0.6 No external Ca 1 mM Ca (external) 27 2 3 5,5 2 0.4 8 and urea, as well as the I,,, were measured at external pH values of 6 and 4; thereafter, fluxes continued to be Regular Ringer 23 k 2 6.0 iz 0.6 measured after addition of 10B4 M ouabain to the interADH, 20 rim/ml 40 k 10 5.6 k 0.7 5 nal solutions (external solution was at pH 4). The active flux was determined as described in METHODS and the Regular Ringer 42 4 5 13.0 -+ 10.5 k 3.0 3.4 8 mM 73 k 5 results are shown in Table 3. The&, appears to be equal Theophylline, 5 to the active Na transport at pH 6 but not at pH 4. It is Values are means 2 SE. noteworthy that the ZSc is significantly larger than the active Na influx at pH 4; in the presence of this extreme hibit active transport by acting on the same or different asymmetry, a ouabain-sensitive flux of approximately barriers in the process. The effects of 1 mM external Ca 0.1 peq/h*cm2 is present that is not due to active Na were tested in regular Ringer under conditions in which transport. It is, therefore, possible that this flux is due active Na transport was already inhibited by about 40% to the movement of protons through the active Na through a reduction in the pH bf both bathing solutions transport system in competition with Na. to 6.9 with an appropriate partial pressure of CO,. The Effects of external Ca. The effects of external Ca on Zm results were as follows: with no external Ca the average and Kt were tested by initially measuring the I,, as a 1 was 26 -+ 2 pA/cm2; when 1 mM Ca was added to the function of Na concentration in an external solution &ternal solution, the average current decreased to 20 containing no Ca and 0.25 mM EDTA, followed by t 2 pA/cm2. This ability to inhibit the ISc with external similar measurements on the same skins in 1 mM Ca. Ca even while the ISc was being inhibited by decreased The results from a typical experiment are shown in Fig. pH suggests that these two conditions act within the 4. It may be observed that the effects of Ca are in sharp same barrier (see DISCUSSION). The reasoning behind contrast to those of pH: external Ca causes a decrease in this conclusion may be summarized as follows: if the Jm but leaves Kt largely unchanged. The results of eight 40% inhibition of I,, by decreased pH occurred at the experiments with Ca are summarized in Table 4, showserosal barrier, no additional inhibition would be exing a 21% decrease in 1m (paired data P < 0.01) and a pected from an action at the external barrier. Therefore, slight but not significant decrease in Kt (paired data P both of these actions probably occur on the same barrier, > OJ). namely, the entry barrier that is the known site of A series of IO experiments was performed to try to action of external Ca (12, 13). determine whether external Ca and decreased pH inEffects of ADH and theophylline. The effects of ADH on &,* &nd Kt were determined by measuring the JSc as a function of Na concentration on both sides first in TABLE 3. Comparison between active Nu influx regular Ringer and, thereafter, after the addition of and short circuit current ADH to the same skins. The latter portion of these External pH $4:’, peqlh*cm2 P experiments was performed rapidly during the plateau phase of the ADH response* The results, shown in Table 6.0 0.46 + 0.07 0.44 2 0.10 >O.l 4.0 0.08 2 0.02 0.19 2 0.04 co.01 4, indicate that ADH produced the expected increase in 1m but caused no significant change in the Kt of the Values are means 2 SE; n = 6. Comparison made when external solution is 3 mM NaCl Ringer at pH 6 and 4, J$)= active Na influx. transport system; the same result was obtained by Downloaded from www.physiology.org/journal/ajpcell at Lunds Univ Medicinska Fak Biblio (130.235.066.010) on February 18, 2019.

c40

L. J. MANDEL

tials when the external Na concentration was decreased. This type of behavior was interpreted as being elicited by a single rate-determining barrier, probably located at the site of Na entry from the external solution In the present investigation, a series of experiments was performed to compare the active transport versus applied potential characteristics at pH 6-9 of paired skins in external solutions which contained either 110 or 3 mM NaCl Ringer. The internal solutions of all skins contained 110 mM NaCl Ringer; both solutions were bubbled with CO, to decrease the pH to 6.9. Influxes of Na and urea were measured at the same voltages as above, and active transport was calculated in the same manner. The active Na fluxes as a function of an applied potential obtained at pH 6.9 and 110 mM NaCl Ringer in these experiments were almost identical to those already shown in Fig. 5 (open circles). Therefore, the open circles served as control conditions and the fluxes obtained at pH 6.9 and 3 mM NaCl Ringer (open triangles) were normalized to these control points. When a fractional decrease in active Na flux is calculated for these experiments (not shown in Fig. 5) it becomes apparent that lowering the external Na concentration causes a constant fractional inhibition in transport rate at all potentials. In this response, the behavior of the active transport system is very similar at pH 6.9 to what it is at pH 8.5, indicating that the locus of the rate-determining step is not changed by reducing the pH. Effects of theophylline. Paired experiments were performed to measure the effects of theophylline on the active transport versus applied potential characteristics. All experiments were performed with regular Ringer. After pairing of skins under short circuit conditions, 1 mM theophylline was added to one-half of each skin. Simultaneous influxes of Na and urea were measured at 80, 40, 0, and -50 mV; active Na fluxes were calculated as above. The results obtained from nine experiments are shown in Fig. 6; these were normalized in each pair to the active transport measured in regular Ringer at -50 mV. Theophylline is seen to cause an increase in active transport of about 65%; this increase appears to be voltage independent. Effects of external Ca. The effects of external Ca on the active transport versus applied potential characteristics proved difficult to measure in paired experiments because of differences in responsiveness to Ca even between paired halves from the same animal. Instead, fluxes were measured with and without external Ca in the same skin at just two potentials and the complete curve was constructed bY sequential fitting. The experimental procedure was as follows: in one group of seven experiments, Na and urea influxes were measured at 40 and 0 mV, initially, in an external Ringer solution containing no Ca (rinsed in regular Ringer containing 0.5 mM EDTA for 2 min at the beginning of the experiment) and, thereafter, at the same two potentials in the presence of 0.5 mM Ca added to the external solution. The average active Na influx at short circuit without external Ca was 1.21. t 0.12 peq/h 9cmp; with Ca it was 0.93 t 0.11 ,ueq/h*cm:!, or 79 -+ 10% of the flux without Ca. In another series of seven experiments, Na l

pH 8.5

IlOmM

No

6.9

0 VhW

-50

FIG. 5. Plots of normalized active Na influx as a function of applied potential when pH of both bathing solutions was either 8.5 or 6.9. Results with filled circles were obtained at pH 8.5 and Na concentrations of 110 mM on both sides. Open circles represent experiments performed at pH 6,9 and 110 mM Na (both sides). Experiment with open triangles was obtained at pH 6.9, external solution was 3mM NaCl Ringer and serosal solution was 110 mM NaCl Ringer. Upper portion of figure shows fractional inhibition of active influx at each potential when pH is reduced to 6.9, while Na concentration is constant. Vertical bars are SE (n = 8).

Frazier et al. (19) in toad urinary bladder. A corresponding series of experiments with theophylline gave similar results (Table 4), showing an increase in 1m but no significant change in Kt l

Active Na Transport Applied Potential

as a Function

of

Effects ofpH. The effects of decreased pH (both sides of the skin) on the active transport versus applied potential characteristics were studied in paired skins. Simultaneous influxes of Na and urea were measured at applied potentials (with reference to the external solution) of 80, 40, 0, -50, and - 100 mV; one half of each pair was bathed in regular Ringer (pH 8.5), whereas the other half was in 110 mM NaCl Ringer bubbled with sufficient CO, to reduce the pH in both solutions to 6.9. Skins were initially paired under short circuit conditions in regular Ringer at pH 8.5. The active Na flux was calculated from the total Na influx as described in METHODS. The results, normalized to the active transport rate observed in regular Ringer at -50 mV, are shown in Fig. 5. The main effect of decreased pH appears to be a downward shift of the curve, to obtain an almost constant fractional rate of transport at all applied potentials. The percent inhibition appears to be independent of potential. The next series of experiments (also shown in Fig. 5) was performed to determine which step in transport was affected by the decreased pH. Mandel and Curran (36) found that at pH 8.5 the functional dependence of active Na transport on applied potential was similar at all external Na concentrations; that is, there was a proportional decrease in transport at all applied poten-

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PH, CA, ADH,

AND

THEOPHYLLINE

ON

NA ENTRY

IN

FROG

c41

SKIN DISCUSSION

01

I 100

L

1

0

-100

v hw 6. Action of 1 mM theophylline influx vs. applied potential characteristics. shows active influx ratio of theophylline Vertical bars are * SE; n =9. FIG.

on normalized active Na Upper portion of figure to control at each potential.

and urea influxes were measured at 0 and -50 mV initially in Ringer with no external Ca (rinsed in Ringer with EDTA as above) and, thereafter, at the same potentials in an external solution containing 0.5 mM Ca. In these experiments, the average Na active influx at short circuit without external Ca was 1.88 t 0.17 peg/h cm2; with 0.5 mM Ca it was 1.02 t 0.15 peq/ h 9cm2, or 54 t 6% of the flux without external Ca. The results of both of these series of experiments were fitted together and are shown in Fig. 7. The fluxes at 40 and -50 mV in the zero Ca solution are normalized to those at short circuit in the same external solution The fluxes under short circuit conditions in the 0.5 mM Ca solution are also normalized to the respective fluxes in the zero Ca solution at this potential; thus, the average flux at short circuit in 0.5 mM Ca is 66 t 8% of what it is at short circuit without external Ca. The fluxes in 0.5 mM Ca at 40 and -50 mV are each normalized (to 0.66, not to 1.0) to the flux measured in each skin in 0.5 mM Ca under short circuit conditions. By this procedure of triple normalization, it is possible to plot a composite graph of the effects of external Ca on the active transport versus applied potential characteristics, as shown in Fig. 7. This figure demonstrates that the main action of external Ca is to proportionately decrease active transport at all potentials. Thus, its action appears to be on the same barrier as that of decreasing the pH of both solutions.

The results shown in Fig. 1 demonstrate that the I,, has a differential sensitivity to bathing solution pH depending on whether: 1) either the pH of the external solution or that of both solutions was altered by incremental additions of CO:!, or 2) the external solution pH was changed by acid titration in the presence of an impermeant buffer. Schoffeniels (43) demonstrated that changes in the pH of the internal solution by itself produced identical results to those of the simultaneous pH changes in both solutions shown in Fig. 1; on the other hand, changes in external pH in the presence of phosphate buffer were identical to those obtained in the present communication with phthalate buffer (open triangles). The differential sensitivity of the I,, to pH from each of the bathing solutions prompted Schoffeniels (44) to postulate the existence of two series barriers for active Na transport. A competition between Na and protons was thought to be present at each of the barriers and the differential sensitivity to pH was explained by the different inhibitory pH values for protons at each of the barriers. The need for a postulated effect on two separate barriers was questioned by Funder et al. (Zl), who suggested that the site of action of either the external or internal pH on I,, was probably through the changes exerted on cytoplasmic pH. This conclusion was reached on the basis of experiments with CO, addition in conjunction with various buffer combinations. The present results are consistent with this conclusion because they suggest that the effects of external pH on Jsc in 110 mM NaCl Ringer may be largely determined by the permeability of the buffer through the outer barrier of frog skin. In the presence of a highly permeable buffer, such as the HCO,,--CO, 0.8 , the value of K, decreased somewhat, suggesting that a similarity may exist between the saturation of Na translocation as a function of potential and the inhibition of ISc produced by decreasing cytosol pH. In both cases, Na translocation may be inhibited by a limitation in the number of sites available for transport, possibly by affecting the number or distribution of anionic charges on the transport sites. In summary, the variety of experimental results presented in this study has been brought together with the aid of a rather simple model. Calculation of two kinetic parameters under various conditions has allowed for the separation of three different actions of the entry barrier: 1) competition for Na entry, 2) modulation of the number of sites available for Na translocation, and 3) alterations in the rate of Na translocation caused by changes in Na permeability or electrochemical gradient across the entry barrier. Even in this oversimplified form, the model describes adequately the complex response to pH by assuming a modulation of the number of sites available for Na translocation as a function of cytoplasmic pH, a prediction that remains to be tested. Various types of experiments are presently being planned to test this possibility. APPENDIX Kinetic Effects

Model of Na Entry into Frog Skin: of External and Cytoplasmic pH

General properties. Consider a transport system for Na entry into the frog skin consisting of two steps: 1) association of external Na with a transport site (pore or carrier) and 2) translocation of Na through the outer barrier into the cell interior (through either a pore or carrier). Under the assumption that a finite total number of Na transport sites X0 exists, these two steps may be expressed by the following equations

Nql+ + X- +f NaX

$

Nai+

+ X-

(14

4

X = [X] + [NaXJ

(24

where Na, and Naj represent Na concentration in the external solution and intracellular transport pool, respectively, X is a free site, not associated with Na (valence omitted), and NaX is a site associated with Na.

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C46

L. J. MANDEL

In equation la, k, and k, are the rates of formation and dissociation of Na with the site X, llzx is the translocation rate of Na to the cytoplasmic transport pool, and k, is the backward translocation rate across the outer barrier. Measurements of rapid Na entry through frog skin show that the inward flux is identical to the IsC, indicating that the backward flux is negligible under short circuit conditions (38, 41); therefore, k, may be neglected as compared to k3. Under these conditions, the kinetics of Na flux from the external solution to the cytosol may be expressed as a chemical reaction under steady-state conditions passing through a chemical intermediate form NaX; this type of reaction obeys Michaelis-Menten kinetics, as we see below. Under steady state conditions a* Substituting

= k,[Na],[Xj

- k$NaX1

= 0

(3a)

- k,[NaX)

= 0

(44

= k,[NaXJ[HJ - k,[NaXHJ

(X0 - [Nail)

- kJNaX1

UW

equations 12a and 13a, we obtain

Adding

h[WoKl Introducing

- UNaXl

- MNaXl

= 0

(144

equations 1 Oa and lla into 14a, we obtain (154

- k,[NaXJ - k,[ NaX] = 0 Rearranging

[NaX] = [Nalt&(l/(l

+ [q/Kd)

for [NaX]

J' I [Nax]

=

[Na]O%

K, = (ke +

and the maximum

kJ/k 1. Because

flux 1m would

the Na influx

be obtained

&a is

Lll'[wo

(174

Na Kt’ + [Na],

(54

K + [Wo where

= 0

equation 2a into 3a, we obtain k,[Na],

Solving

- kg[NaXI

v

given by

(194

if all X0 was in the form

NaX I, = k,X, combining

(7 a

where

ImO and

KtO are the values

of these

variables

obtained

in the

equations 5a, 6a, and 7a we obtain

Ji = rdNalCJ Na

(8a

K, + [Na],

This is, of course, the classical form of the Michaelis-Menten equation. It is important to note certain features of equation 8a at this point and how they relate to experimental observations on this system. 1m is directly proportional to k3, the translocation rate and, therefore, anything that affects &,, can be conceived as affecting the translocation rate (assuming that X0 is constant). On the other hand, ks also enters into Kt, but its effect is determined by its relative magnitude in comparison with k,. In order to reconcile the present model with the experimental data, which show that certain experimental conditions change &,, but leave K, unaltered (Table 4), it must be assumed that k, >> k,, and, therefore, Kt is relatively independent of k,. Under these conditions, K, = ke/kI, which is the dissociation constant for the reaction of Na with the transport site, and the translocation step is rate determining. Effect of cytoplasmic PH. To account for the effects of cytoplasmic pH on 1m and K,, the model presented above is modified to include a reaction of NaX with cytoplasmic protons to produce NaXH+, which is a form of the complex that cannot translocate Na. The model now may be expressed as Na,+

+ X- 2 NaX 2 kz k5 1 t k6 NaXH+

Nai+

+ X-

w

where

maximal &,, and, equal- to KXH . At pH 8.5, we are in the region-of therefore, its value in Table 1 may be equated with ImO. At pH 6.5 KXH = 1.2 2 0.5 x 1W7 M with the use of and &, = 14 PA/cm’, equation 18a; with equation 19a and the values for Kt given in Table 1, KxH = 2.1 ? 0.8 X lo-’ M+ Effect of external PH. To account for the effects of external pH on 1m a’nd Kt, the initial model is modified to include a reaction of X with protons from the external solution to form a complex that is not avail .able for association with external Na. The equations are Na,+

+ X- sNaX2

Nai+

+ XWd

H’lfKH XH

In this model, the effect of external protons is to compete with external Na for association with the transport site. Once a proton associates with a site it may translocate to the cytosol, thereby contributing to the IsC and also decreasing the cytosol pH; however, this translocation will not contribute to the Na influx. Assuming that the cytosol pH does not change, we have under steady state (omitting valences)

(1W

qT From

= k,[Na],[Xj

-

k,[NaX]

- kJNaX1 = 0

(234

equations 21 a and 22a

The effect of protons in this model is to decrease the available number of Na transport sites by either blocking channels (preventing translocation of Na) or by combining with carrier sites to immobilize them. The kinetic equations are modified as follows (valence omitted)

- k,[NaX-j - k3[ NaX’J = 0

(244

Rearranging v

= k,[Na],[w

-

k,[NaI - h[NaX] + kJNaXH]

(124 - kJNaXJ[HJ

= 0

[NaXl =

Xorw* K,U

+ CWIKd

+ [W,

Downloaded from www.physiology.org/journal/ajpcell at Lunds Univ Medicinska Fak Biblio (130.235.066.010) on February 18, 2019.

(254

PH,

CA,

ADH,

The Na influx

AND

THEOPHYLLINE

ON

NA ENTRY

IN

FROG

is

J' _ LnoCwo Na - K,” + [Na],

(264

= &,(1.

(27a)

where K”

+ [ W/&d

Thus, assuming that the cytosol pH remains unchanged, the effect of external pH is totally on K,, increasing its value as the pH decreases. Because protons appear to permeate through the entry barrier, the cytosol pH must decrease somewhat as the external pH decreases. This would be a complicating factor in the calculation of the K, value. Combining equations 19a and 27a, it is possible to obtain a composite equation that describes the effects of external and cytosol pH on K,

(28d where

[HI,

and

[HI,

are the external

and cytosol

proton

concentra-

c47

SKIN

tions, respectively. The value of K,, may be calculated from the results shown in Fig. 1 and Table 1 by making one assumption: namely, that the effect of external pH on&, (Fig. 1) istotally due to the corresponding changes produced in the cytosol pH. Thus, the 20% decrease in Isc obtained when the external pH is decreased to 4.5 may be attributed to a corresponding decrease in cytosol pH given by the filled circles in Fig. 1, that is, pH 7.0. With this value for [HL, the average calculated value of K,,, = 1.6 x 10v7 M and, with the values for the other variables given in Table 1, we obtain KH = 1.5 x lo+ M.

I thank Ms. Terry Riddle and Ms. Teresa Rummans for their valuable technical assistance. I am also indebted to Dr. Dale Benos for the helpful criticism of this manuscript. This work was supported by Public Health Service Grant 16024 from the National Institute of Arthritis, Metabolism, and Digestive Diseases. Received

6 June

1977; accepted

in final

form

23 January

1978.

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