Coupling between the sodium and proton gradients in respiring Escherichia coli cells measured by 23Na and 31P nuclear magnetic resonance.

The relationship between the steady-state sodium gradient (delta pNa) and the protonmotive force developed by endogenously respiring Escherichia coli cells has been studied quantitatively, using 23Na NMR for measurement of intracellular and extracellular sodium concentrations, 31P NMR for measurement of intracellular and extracellular pH, and tetraphenylphosphonium distribution for measurement of membrane potential. At constant protonmotive force, the sodium concentration gradient was independent of extracellular concentrations over the measured range of 4-285 mM, indicating that intracellular sodium concentration is not regulated. The magnitude of delta pNa was measured as a function of the composition and magnitude of the protonmotive force. At external pH values below 7.2, delta pNa was parallel to delta pH but showed no simple relationship to the membrane potential; above pH 7.2 the parallel relationship began to diverge, with delta pH continuing to decrease but delta pNa starting to level off or increase. Although plots of delta pNa versus delta pH had slopes of close to 1, the value of delta pNa consistently exceeded that of delta pH by approximately 0.4 units, indicating a partially electrogenic character to the putative H+/Na+ antiport. The apparent stoichiometry was 1.13 +/- 0.01 at external pH below 7.2. The possible significance of this nonintegral stoichiometry is discussed according to a model in which two distinct integral stoichiometries (possibly 1H+/1Na+ and 2H+/1Na+) are available with some relative probability; the model predicts futile cycling of sodium ions and a dissipative proton current. In the course of this study, we discovered that the magnitude of the pH gradient developed by the cells was osmolarity-dependent, yielding steady-state intracellular pH values that varied from 7.1 at 100 mosm to 7.7 at 800 mosm.

The relationship between the steady-state sodium gradient (ApNa) and the protonmotive force developed by endogenously respiring Escherichia coli cells has been studied quantitatively, using 23Na NMR for measurement of intracellular and extracellular sodium concentrations, 31P NMR for measurement of intracellular and extracellular pH, and tetraphenylphosphonium distribution for measurement of membrane potential. At constant protonmotive force, the sodium concentration gradient was independent of extracellular concentrations over the measured range of 4-285 mM, indicating that intracellular sodium concentration is not regulated. The magnitude of ApNa was measured as a function of the composition and magnitude of the protonmotive force. At external pH values below 7.2, ApNa was parallel to ApH but showed no simple relationship to the membrane potential; above pH 7.2 the parallel relationship began to diverge, with ApH continuing to decrease but ApNa starting to level off or increase. Although plots of ApNa versus ApH had slopes of close to 1, the value of ApNa consistently exceeded that of ApH by -0.4 units, indicating a partially electrogenic character to the putative H+/Na+ antiport. The apparent stoichiometry was 1.13 f 0.01 at external pH below 7.2. The possible significance of this nonintegral stoichiometry is discussed according to a model in which two distinct integral stoichiometries (possibly lH+/lNa+ and 2H+/lNa+) are available with some relative probability; the model predicts futile cycling of sodium ions and a dissipative proton current. In the course of this study, we discovered that the magnitude of the pH gradient developed by the cells was osmolarity-dependent, yielding steady-state intracellular pH values that varied from 7.1 at 100 mosm to 7.7 at 800 mosm.
In bacteria, as in many other cells, the intracellular concentrations of the major cations, H+, K+, and Na+, are in general quite different from the extracellular concentrations. There is a high intracellular K'/Na+ ratio and a closely regulated intracellular pH (pHin'), while in the extracellular medium *This work was supported by Public Health Service Grant AI 12202 (to R. M. M.) and National Science Foundation Grant PCM-8402670 (to R. G. S.). The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
the K+/Na+ ratio is often quite low and the pH can range from acidic to alkaline values. The framework for understanding how the differential composition of intracellular and extracellular compartments is developed and maintained is Mitchell's chemiosmotic hypothesis, which postulates that the energy of chemical bonds is transduced into the transmembrane electrochemical potential of a particular ionic species, and this potential then provides for the generation and maintenance of gradients of other ions and molecules (1). In most bacteria, protons extruded by coupling to oxidationreduction reactions or hydrolysis of ATP are the primary source of transmembrane electrochemical energy.
In Escherichia coli, the first experimental evidence for H'/ Na+ antiport came from a study by West and Mitchell (18), who observed proton extrusion following addition of Na+ to an anaerobic cell suspension. Since membrane-permeant ions had no effect on the Na+-dependent acidification of the medium, the authors concluded that the antiport was electroneutral. Later studies, primarily carried out in membrane vesicles from E. coli, have provided more direct evidence for the coupling between Na+ and H+ movements and have further characterized the properties of the antiport. It was demonstrated that addition of Na+ partially collapsed a pre-existing outwardly directed pH gradient in inverted vesicles (12,19) and could drive the formation of a pH gradient in right-sideout vesicles (12). Because Na+ movements via H+/Na+ antiport could be driven by either A+ or ApH (20), it was concluded, contrary to the original proposal, that the antiport could operate in an electrogenic manner. Schuldiner and Fishkes (12) have suggested that the stoichiometry of the antiport may be dependent on the external pH, behaving electroneutrally at acidic pH values and electrogenically at alkaline pH values. However, more recent studies (21) have demonstrated that, even at pH,, values as low as 5.5, A+ enhances Na' efflux mediated by H+/Na+ antiport, a result that suggests an electrogenic process. Additional information 7797 on the properties of the H+/Na+ antiport process came from kinetic analyses of the effects of a n imposed ApH or A$ on the rate'of Na+ efflux (22). An important conclusion was that the device responsible for the H+/Na+ antiport is regulated by intraiesicular pH, low pHi, (C6.6) being inhibitory.
Although the kinetics of the H+/Na+ antiport process have been extensively studied, information on the magnitude of  Preparation of Cell Suspensions for NMR Measurements-The procedures for growing, harvesting, and preparing strain MRE 600 for NMR measurements were as described (24), except that cells were maintained aerobically throughout the experiment, unless otherwise indicated in the text. Strain CS 71 was grown in me&.m M9 containing 0.4% glucose or 0.5% glycerol and 1 pg ml" thiamine, and strain RA 11 was grown in medium 63 supplementedwith 1% tryptone (Difco) and 1 pg ml" thiamine. The procedures for harvesting these cells for NMR were the same as for strain MRE 601). The buffer used depended on the particular experiment, and is given in the text or the appropriate figure legend. For studies of [Naf] as a function of pH,, at constant [ N L ] and osmolarity, the composition of the resuspension buffer was chosen according to the desired value of pH.,: for pH., values below 6.8, it contained 30 mM Pipes, 30 mM Mes, 5 mM KH2P04, 80 mM NaC1, with KOH and NaOH added to adjust the pH to the desired value and KC1 added to bring the osmolarity to 370 mosm. For higher pH,, values, the resuspension buffer was modified by replacing 30 mM Mes with 60 mM Tes and adjusting the pH to approximately 0.3 units higher than the desired final value of pKx. To attain pH.. values above 7.1, small aliquots of 310 mM Bicine, pH 12.5, were introduced into the cell suspension after it had been warmed up and oxygenated in the spectrometer. We found that the additional base and buffering capacity was necessary to maintain the higher pH.. values, probably because under these conditions the cells generate and excrete acidic metabolites. Shift reagent was prepared by combining DyCl, and tripolyphosphate in a 1:3 molar ratio and added to the cell suspension at -6 mM with respect to dysprosium, as described (24). In most experiments the shift reagent contained potassium tripolyphosphate; sodium tripolyphosphate was used as indicated in the text.
NMR Measurements of Nu' Concentration and PH-'~N~ and 31P NMR spectroscopy were used to measure [NaL] and [Nd.] (based on the areas of the corresponding Na+ resonances) and pHi. and pH,. (based on the corresponding chemical shifts of Pi) as described previously (24,30). In the case of a UNa NMR experiment, pH.. was measured with a pH electrode immediately after the experiment. Values of pH,. measured by 31P NMR (from the chemical shift of Pi) and by pH electrode agreed within 0.1 units. All measurements were made at 25 "C.
Calculation of the Na+ Gradient-The Na+ gradient, ApNa, refers to pNai, -pNa, = log[N~\]/[Nag], where the ratio [Ndx]/[NafJ was obtained from the areas of the two resonances, the volumes of the two aqueous compartments, and the NMR visibilities of Na+ in the two compartments; the methods used have been described (24). The measured intracellular volume was found to decrease with increasing osmolarity (Fig. l), as has been reported by Stock et al. (31) and was unaffected by pH, or pHin. For calculation of [Nag], the value of intracellular volume was made by interpolation at the appropriate osmolarity.
Measurement of Membrane Potential-Steady-state values of A+ were determined from uptake of [,H]TPP+ by filtration assay as described (24, 32). In the presence of sucrose, measurement of A+ was more difficult because sucrose interfered with the elution of [,HI TPP+ from the filters. Improved elution was achieved by placing the filters in 0.5 ml of water for 2 h before scintillation fluid was added.

RESULTS
Effect of External Na+ Concentration on ApNa-In a typical experiment, the cell suspension was initially anaerobic and then oxygenated; [Na;] and [Naf] were monitored throughout. Oxygenation led to rapid extrusion of Na+ followed by stabilization of [Naf], as we have described (24). The same final value of [Nqz] was attained using either the above protocol, or one where the cells were pre-loaded with Na+ to an initial concentration 2-fold higher than usual, or one where the cells were maintained aerobically throughout the experiment. Since the final value of [Na;] was independent of the protocol, we consider it to be a true steady-state value for respiring E. coli cells. We also examined the kinetics by which ApNa readjusted to a new steady state. Fig. 3 shows the changes in ApNa and the components of A; , upon a sudden increase in [NdJ from 1 to 100 mM. The initially large ApNa dropped within 2 min to slightly below the prestimulus value and subsequently (within 6 min) rose to a stable level comparable to that obtained in steady-state measurements. The magnitude and composition of A; H changed little: A+ decreased slightly throughout the period, while ApH increased (as a result of a rise in pHi,*) by 0.12 units immediately following the fNa&] jump and then remained constant.
Effect of pHez on ApNu-Several studies with membrane vesicles and intact cells have indicated that gradienlts formed by secondary H+-driven transport systems can be aKected not only by the magnitude of A; , but also by the relative contributions of ApH and A$ (33-35). We wished to examine how ApNa was affected in this regard. To do so, we chose several different ways of manipulating A~H , the first being a simple variation of pH,,.  The value of pHin in well-energized cells is almost independent of pH,, over a large range (5.5-8.5), and therefore, ApH is essentially a linear function of pH,, alone (30,36, 37), with the contribution of ApH to A , i i~ being considerable at acidic values of pH,, and reaching zero at pH., -7.5. A+ compensates for the decreasing ApH, but only partially (by -60%), and therefore A; , decreases slightly over this range (36, 37).
The steady-state value of [Naf] and the corresponding ApNa was measured at pH, values between 6.25 and 7.6 at two different [Nd,] values (80 and 180 mM) and constant osmolarity (375 mosm). The results are presented in Fig. 4A along with the corresponding values of ApH, A+, and Ai,. It is evident that at both [Nd,] values, ApNa parallels ApH closely up to pH,, -7.2. A plot of ApNa uersus ApH (Fig. 4B) shows that, in the pH,, range 6.25-7.2, the relationship is linear with a slope of 1.01 f 0.09 ( n = 11). Throughout this pH,, range, all values of ApNa were slightly greater (by -0.38 units) than the corresponding values of ApH. Above pH,, 7.2, the correlation appeared to break down, with ApNa either levelling off or beginning to increase while ApH continued to decline, reaching zero at pH,, 7.5 (Fig. 44).
We also measured steady-state values of ApNa and ApH in two other strains of E. coli (RA 11 and CS 71), at a single pH,, value of 6.9 (Fig. 4B). As with strain MRE 600, ApNa was found to exceed ApH. However, the magnitude of the discrepancy differed considerably among the three strains: When ApH was suddenly increased by shifting pH,, to a more acidic value, it stabilized after undergoing a slight transient, as has been noted previously (38); AI ) decreased more slowly, providing a partial compensation for the ApH increase. Also with slower kinetics (rise time -2 min), ApNa responded to the ApH shift by readjusting to a new stable value which corresponded within experimental error to that predicted from steady-state measurements at the same ApH. Fig. 5 illustrates such an experiment in which pH,, was lowered from 6.8 to 6.1.
Effect of Benzoate on ApNa-A different type of manipulation of ApH was achieved by lowering pHin at constant pH,, by addition of the membrane-permeant weak acid benzoate. With respiring cells at pH,, 6.1, [Naf] = 140 mM, and constant osmolarity (410 mosm), pHin decreased from 7.5 in the absence of benzoate to 6.8 at 40 m M benzoate, whereas pH,, rose slightly3 (to 6.3), giving a net change in ApH of 0.9 units ( Fig. 6A; cf. similar results in Fig. 5 of Ref. 38). As has been observed previously in E. coli (39), A$ only partially compensated (by 50%) for the decrease in ApH, so that there was a net decrease of A,& in the presence of benzoate. The parallel changes of ApNa and ApH (Fig. 6A) were strikingly similar to those shown above when ApH was manipulated by varying pH,,; there was a linear relationship (Fig. 6B) between ApNa and ApH with a slope of 1.00 f 0.09 ( n = 12) and a displacement of ApNa from the corresponding values of ApH, in this case by -0.33 units.
As in the case when ApH was perturbed by altering pH,,, a sudden change in ApH by shifting pHin resulted in a somewhat slower readjustment of ApNa to a new value which corresponded well to that obtained from steady-state measurements (Fig. 7).
Effect of Osmolarity on pHi,--In the course of this study, it became apparent that the osmotic strength of the external The rise in pH, can be attributed to a combination of benzoatemediated transfer of protons into cells and excretion of basic metabolites associated with respiration on endogenous carbon sources (24). 80 mM NaC1, 10 mM KH2P0, adjusted to pH 7.0 with NaOH and KOH such that [NE&] was 100 mM. Upon resuspension pH, dropped to 6.8. The arrow indicates the point at which 2 N HCl was introduced (within 10 s) to lower pH., from 6.8 to 6.1. ApNa (01, ApH (01, and A$ (X) were measured as described in Fig. 3, except that ApH values corresponded to 1-min spectra before the pH jump, 10-s spectra immediately following it, and 4-min spectra beginning at 3.5 min. medium was affecting the pHi, achieved by endogenously respiring cells.
We first observed the effect in an experiment where 200 mM KC1 was added (final concentration 210 mM) to respiring cells in a buffer of low osmolarity (90 mosm). Following the addition, pHin rose from 7.15 to 7.6 within 2 min, then dropped to 7.5 and remained at that value for at least 15 min (Fig. 8).
Because the pK of the buffer (Pipes) is lower at high ionic strengths, there was also a decrease in pH,,, comparable to  Fig. 3, that seen in a control experiment in the absence of cells.
We believe the change in pHin reported by intracellular Pi to be real. For example, it was not an artifact caused by a change in magnetic susceptibility, since there were no substantial changes in the chemical shifts of other major intracellular metabolites: the chemical shift of the cy resonance of ATP was unaltered and only a small upfield shift (0.1 ppm) was observed for the ,#and yATP resonances. Nor was the effect a consequence of the suddenness of the addition of KC1, since cells washed with and resuspended in a buffer containing 210 mM KC1 also achieved a pH, value of 7.5.
The effect was not ion-specific: KC1, NaC1, choline chloride, and sodium tripolyphosphate all caused pHin to increase, as did a nonionic compound, sucrose. There was only one parameter common to the addition of the above compounds, an increase in the osmolarity of the medium. Indeed, when values of pHi, measured in buffers of different composition were plotted as a function of their osmolarity, the points fell on a single curve (Fig. 9). There was no correlation between pHi, and the ionic strength of the buffer, provided the osmolarity was the same. The osmolarity of the extracellular medium is known to affect the size of the cytoplasmic compartment (Ref. 31 and Fig. 1) and the intracellular K' concentration (23), and therefore might also affect the ionic strength of the cytoplasm, and hence the chemical shift of Pi, whose pK is ionic-strength dependent (40). However, an ionic-strength independent pH probe, methylphosphonate (30,40), reported a similar dependence of pHin upon osmolarity (Fig. 9). Because strain MRE 600 did not take up methylphosphonate, these experiments had to be carried out with a different strain of E. coli, CS 71; interestingly the steady-state value of pHi, in strain

Effect of Osmolarity on the Composition of AbH and on
ApNa-At constant pH,,, the changes of pHin due to variation in external osmolarity were of course reflected in ApH (Fig.  1OA). The steady-state value of A+ declined gradually as extracellular osmolarity was increased from 120 to 750 mosm, producing a partial compensation (-50%) for the rise in ApH (Fig. 1OA). We next examined the effect of extracellular osmolarity on ApNa. Sucrose was added at various concentrations, at [Nd,] = 50 mM and pH,, = 6.75 (Fig. 1OA). As with the other two methods of varying AbH, ApNa exhibited a linear correlation with ApH (Fig. lOB), with a slope of 0.89 4 0.09 ( n = 11). Once again, the line did not pass through the origin but gave an intercept corresponding to a ApNa of 0.49 units when ApH was zero.
Generality of the Relationship between ApNa and ApH-

DISCUSSION
In this study we have described the quantitative relationship between the Na+ gradient generated by respiring E. coli cells and the protonmotive force that is generally believed to be the driving force for Na+ extrusion. Further, we have examined the contributions of the proton electrical and chemical potentials to that gradient. Although a number of studies of Na+ fluxes have been reported (12, 21, 22, 41), we believe that the present study, together with our recently published description of Na+ levels during the process of energization (24), provides the first reliable measurements of cytoplasmic Na+ concentration in E. coli. The NMR approach we have used permits continuous measurement of extracellular and intracellular Na' concentration in well-energized cells.

Osmolarity (rnOsrn)
FIG. 10. Effect of osmolarity on ApNa, ApH, A$, and ASH. E. coli MRE 600 were resuspended in a buffer containing 30 mM Pipes, 10 mM KC1,5 mM KH2P04 and adjusted to p&. of 6.8 with NaOH thus giving [NdJ of 50 mM. Except for some of the A+ measurements, sucrose was used to achieve osmolarity values above 115 mosm. A , each value of ApNa (0) represents an average of at least five 4-min accumulations. ApH (0) was measured by 31P NMR. A+ was measured as described in Fig. 4, using either sucrose (X) or KC1 (B) to vary osmolarity. B, ApNa values were replotted as a function of the corresponding ApH shown in A . Also included are data from experiments in which pH.. was 6.7.  (23), whose measurements by flame photometry indicated a variable ApNa; as we have discussed (24), the latter results are likely to be in error.
The absence of any regulation of pNain is in striking contrast to the situation observed with pHi,, which remains essentially constant over several units variation in pH,. Thus ApNa remains constant regardless of pN%,, whereas ApH varies directly with pH, (30,36,37).
Since many biomolecules (including all proteins and nucleic acids) are acid-base species, whose conformations are pHdependent, the regulation of pHi, serves a centrally important physiological function by providing a suitable environment for maintenance of stable structure and enzymatic activity. By the inverse argument, we conclude from our results that normal functioning of the cell does not depend on keeping the cytoplasmic Na' concentration constant.
The Magnitude of ApNa Is Determined by the Magnitude of ApH-We have shown previously (24) that as cells become energized, whether by introduction of oxygen to permit respiration on endogenous energy sources or by introduction of glucose to permit glycolysis, the time course of development of ApNa follows that of ApH. In the present study, it has become evident that the steady-state ApNa that is achieved is also closely related to the steady-state ApH. Similar relationships were observed when ApH was manipulated by variation of either pH,, or pHin, suggesting that it is the magnitude of ApH rather than pH, or pH.;, alone that determines ApNa.
In order to interpret these relationships between ApNa and ApH it is important to consider the probable nature of the Na+-transporting devices that are responsible for bringing about the steady state. All of the available evidence regarding Na+ transport in E. coli is consistent with H'-driven extrusion mediated by H+/Na' antiport (12, 13,21,24,41,42). We shall assume that such an antiport is the major process responsible for generating and maintaining the observed ApNa.
The kinetics that we observed following the imposition of sudden changes support this assumption of H+-driven Na' extrusion. A sudden change in ApH accomplishedby changing either pH,, (Fig. 5) or pHin (Fig. 7) produced a more gradual but substantial change in ApNa. In contrast, a sudden change in ApNa accomplished by changing [Na;,] ( Fig. 3) had little effect on ApH or A$, and the change in ApNa was itself cancelled within a few minutes. These results are what would be expected if a high-capacity proton pump (the respiratory electron transport chain) was responsible for developing a H' potential that in turn was responsible for developing Na+ extrusion.
The fact that at moderately acidic pH values (pH, < 7.2) ApNa closely followed ApH but not A$ during various manipulations (Figs. 4, 6, and 10) suggested to us at first that the process might be electroneutral, i.e. occurring as a 1:l antiport. This idea was supported by linear regressions of ApNa versus ApH which, for data obtained by three distinct types of manipulations, gave slopes of close to 1.
However, in each case we encountered a nonzero intercept of 0.3-0.5 units, so that ApNa consistently exceeded ApH; this result is, of course, thermodynamically forbidden if ApNa is being developed by 1:l antiport.
We have considered possible artifactual causes of the discrepancy. Of the parameters which enter the determination of ApNa (24), the most likely source of error was overestimation of intracellular volume. The error would have to be by a factor of at least 2.5 in order to account for a discrepancy of 0.4 units between ApNa and ApH. This could be the case if the extracellular space marker (taurine) was excluded from the periplasm and the measured volume actually represented cytoplasm plus periplasm, but two observations argue against this possibility. First, measurements of cytopIasmic volume (31, 43) using a marker (sucrose) known to cross the outer membrane have yielded values similar to ours. Second, since the percentage of total volume representing the cytoplasm decreases from 70% to approximately 40% as the osmolarity of the medium is raised from 100 to 800 mosm (31), the discrepancy between ApH and ApNa would be expected to increase from 0.15 to 0.4 units in this osmolarity range. Our measurements show that this is not the case (Fig. 10).
Another possible source of error in estimating ApNa involves the NMR visibility of Na+ in the cytoplasm versus buffer. We have reported previously our conclusions on this subject (24); briefly, they are that the cytoplasmic Na+ is -40% visible, a result that is expected where quadrupolar interactions yield transitions with different T, values, and where the shorter T2 broadens the signal beyond detection.
To account for the nonzero intercept, the visibility would have to be below 20%. This we consider to be outside the error limits of the measuremenk it is also inconsistent with theoretical considerations (see, e.g. Ref. 44).
The NMR measurements indicate the amount of visible Na' but not its chemical activity. Measurements (not shown) of the activity of Na+ in the external medium showed it to be unaffected by the presence of cells or of the shift reagent, indicating that this was not a likely source of systematic error. If the activity of cytoplasmic Na+ were low, the thermodynamic gradient of Na+ would have been underestimated, making the discrepancy between it and the H' gradient still greater.
A systematic error in ApH would most likely reside in the estimation of pHi,, which in this work was obtained from the chemical shift of intracellular Pi in 31P NMR spectra of E. coli suspensions. It has been claimed (45) that intracellular Pi cannot give pHk values with greater certainty than 0.2-0.5 units, primarily because of effects of ionic strength and Mg2+ on its pK. However, in E. coli the pHi, values obtained from Proton Gradients in E. coli Pi have been confirmed with an ionic-strength independent probe, methylphosphonate (30,40). The effect of M$+ was not controlled for but, since M$+ lowers the pK and thus the true pHi, corresponding to any given chemical shift, this would imply that, if anything, we were overestimating ApH, and hence the discrepancy between ApNa and ApH would be even greater than indicated on the figures.
The above considerations suggest that systematic errors cannot explain the observed relationship between ApNa and ApH. The finding that the relationship varies from strain to strain of E. coli supports this contention, since a systematic error would not be expected to be strain-dependent; in the case of strain RA 11, ApNa was much higher (-1 unit) than ApH. We therefore conclude that the non-zero intercept is not artifactual in origin, but reflects the true relationship between ApNa and ApH. In other words, we conclude that devices with a H+/Na+ stoichiometry of greater than unity participate in the generation and maintenance of ApNa.
What is the ,+/Nu+ Stoichiometry?-Thermodynamic considerations dictate that if a H+/Na+ device has a stoichiometry n, and operates in the direction of H+-driven Na+ extrusion, then A~N , 5 nAiiH (potentials expressed in p units, and A~H positive). We may then define an apparent stoichiometry napp by the equality A,ii~, = nappAiiH (Equation 1). If we assume that the same stoichiometry applies throughout the range of our measured gradients (excepting those at pH,, > 7.21, napp may be estimated from a linear regression of AbNa uersw Aji, constrained to pass through the origin. For E. coli MRE 600 below pH,, 7.2, this yields nap, = 1.13 2 0.01, suggesting that the antiport is slightly electrogenic. A similar calculation using the data above pH,, 7.2 yields nap, = 1.26 2 0.03, indicating that the antiport is gaining greater electrogenic character. Equation 1 may be rewritten as ApNa = ApH + (n,,, -1) A,& and so the observed slope of close to 1 in plots of ApNa versus ApH (Figs. 4B, 6B, and 10B) is to be expected, provided either that A& remains relatively constant as ApH is varied, or that (napp -1) is small; both of these conditions are in fact met, since cells compensate to a considerable degree for changes in ApH by changes in A#, and nap, is close to 1. This version of the equation may be used as another means of estimating napp; with the observed intercept of -0.4 units and a A i H of -3 units, nap, is estimated to be 1.13, in good agreement with the value obtained by linear regression of AjiNa versus AbH.
The Significance of the Observed H+/Nu+ Stoichiometry-Since the apparent stoichiometry nap, is slightly greater than 1, the development of ApNa cannot simply result from operation of an electroneutral 1:1 antiport device.
The data are consistent with the operation of an antiporter with an integral stoichiometry greater than 1 (say n = 2). With nap, = 1.1, however, such a device would be operating far from equilibrium, implying a very large Na+ leakage current, either through the bulk membrane or through specific devices. It is unlikely that the bulk membrane conductance for Na+ is high, and the buffers used in our experiments preclude Na+-driven uptake of organic metabolites. For both reasons, the explanation of a 21 antiporter operating in the face of a large leakage current unrelated to H+/Na+ antiport seemed unsatisfactory.
We have therefore been led to consider another type of explanation, whereby two integral stoichiometries (probably 1:I and 21) for H+/Na+ antiport are in use simultaneously. This could arise either because there are two classes of device, or because a single class of device can operate with different stoichiometries such that the observed apparent stoichiometry napp is a statistical average of the actual (mechanistic) integral stoichiometries n used per elementary cycle. We shall refer in either case to stoichiometric modes. The idea of variable stoichiometry is not a new one. However, discussion in the literature of such variable stoichiometry is usually restricted to the situation where only one stoichiometric mode is employed under any given set of conditions, whereas we explicitly invoke the simultaneous use of different stoichiometric modes. A full discussion of the consequences of this idea will be published separately, and therefore only brief review will be given here.
Since the driving forces for the two modes are by definition different, it is not possible for the ApNa developed by the cell to be at or close t o equilibrium with both of these driving forces. The system will therefore come to a steady state which is intermediate between the equilibrium positions that either mode would ideaIIy have reached if it could have operated in the absence of the other; the actual value of the steady state will be determined by the relative conductances of the two modes. As a result, the modes will operate in opposite directions and thus establish a futile cycle for Na+,4 with a net inward flux of H+ that is presumably balanced by efflux driven by the respiratory electron transport chain. Fig. 12 depicts schematically two possible examples of pairs of modes: cme A involves a 1:l H+/Na+ antiporter and a 2:l H+/Na+ antiporter, and case B involves a Na+ uniporter (which may be thought of as a 0 1 H+/Na+ antiporter) and a 2:1 H+/Na* antiporter.
To define the steady state more precisely, the fluxes need to be described. Phenomenological rate equations which relate fluxes to their thermodynamic driving forces (flux-force relations) provide a useful approach for describing membrane transport processes, especially when the equations are linear (46). Linearity is always valid near equilibrium (47) and frequently remains valid even far from equilibrium (46, 48); we therefore felt justified in using these equations as a first approximation. Fig. 12 gives the flux-force relations for the pairs of modes shown. At steady state the Na+ fluxes throagh Modes 1 and 2 are equal in magnitude and opposite in direction so that, setting J~, N~ = -J2,Na and rearranging, napp as defined in Equation 1 is seen to be (ml + 2mz)/(m, + mz) for case A and 2m2/(ml + m,) for case B, where ml and mz are the conductances of Modes 1 and 2. It is evident that as long as both conductances are nonzero, nap, will in general be nonintegral. In case A the observed apparent stoichiometry of 1.1 would be obtained when the conductance of the 1:l antiporter dominated over that of the 2:l antiporter (ie. ml = 9 m2), and in case B when the Conductances for the uniporter and the 2:l antiporter were almost equal (i.e. ml = 0.8 mz).
At higher pH,, values, napp increases, presumably because of an increase in the conductance of the electrogenic antiporter relative to either the electroneutral antiporter (case A) or the uniporter (case B).
The relationship between ApNa and ApH observed in other strains of E. coli (cf. Fig. 4B) can be accommodated within the model by postulating different relative conductances of the two modes. In strain RA 11, in which ApNa exceeded ApN by 1 unit, the relative conductance of the electrogenic antiport would be larger than in strain MRE 600 while in The futile cycling of Na+ that we propose here is a concept distinct from the Na" recycling described in, for example, Ref. 51. Futile cycJing is an ongoing process. RecycIing is a process that, because of the finite reservoir of intracellular Na+, is required to achieve substantial acidification of the cytoplasm at alkaline pH.,; it is a process that, at least in an idealized system, does not need to continue operating once the acidification has been achieved.
FIG. 12. Schematic illustration of pairwise use of different stoichiometric modes of Na+ transport. Case A represents the use of a H+/Na+ antiport mode and a 2H+/Na+ antiport mode; case B represents the use of a uniport mode and a 2H+/Na+ antiport mode. Modes may represent different devices or the same device in different states. The Na+ fluxes, J~,N* and Jz,N~, through the two modes are expressed in terms of their conductances, ml and m2, and the relevant thermodynamic driving forces. Steady-state Na+ levels are attained when the sum of the fluxes is zero. Under these conditions, Na+ cycles through the two modes as shown by the dashed lines; the apparent stoichiometry, nap,, deriving from use of the two modes is simply AENJAGH. The net H+ flux through the two modes is compensated for by the primary H+ pump, the respiratory electron transport chain. <.Na ml * zNa strain CS 71, in which the difference between ApNa and ApH was only 0.1 units, its relative conductance would be smaller. This interpretation of the data for strain RA 11 is consistent with the results of Bassilana et al. (21) who have demonstrated that, in RA 11 vesicles, unidirectional flux of 22Na can be driven by either ApH alone or AI) alone at pH,, values above 6.6, thus implying the presence of an electrogenic antiport.
In case A (Fig. 12A), the steady state is between an electrogenic and an electroneutral antiport, with the former operating (in the direction of H+-driven Na+ extrusion) far from equilibrium but with a low conductance and the latter operating in the reverse direction (Na+-driven H+ extrusion) rather close to equilibrium (since n is close to nap,) but with a high conductance. Variable stoichiometry of H+/Na+ antiport in E. coli has been suggested by Schuldiner and Fishkes (12), who reported electroneutral behavior at pHex = 6.6 and electrogenic behavior at pH,, = 7.5. Behavior at intermediate pH values, or the consequences of simultaneous use of different stoichiometries, was not discussed.
In case B (Fig. 12B), if the uniporter is a different device from the electrogenic antiporter, the situation is formally equivalent to a pump loaded down by leakage pathways for its substrate. If, on the other hand, it is the antiporter itself that has the capacity to operate as a uniporter, the situation is equivalent to what has been described by Eddy (49) as "carrier operation with slip,".In either event, both modes are operating far from equilibrium since napp is far from both mechanistic stoichiometries. Although both cases depicted in Fig. 12 are consistent with our data, we favor the interpretation of a 1:l antiport and a 2:1 antiport (case A, Fig. 12A), since it (i) explains why values of napp of less than unity were never seen, (ii) makes the closeness of napp to unity understandable in terms of a lower bound rather than a coincidental value, and (iii) is in accord with the conclusions of other workers (12,13,21,41,42) that H+/Na+ antiport is responsible for the development of ApNa. There is also no evidence that Na+ can be accumulated by E.
coli, even at low pH,,, whereas a uniport might be expected to dominate over a 2:1 antiport under these conditions and cause such accumulation. However, we should emphasize that our data do not rule out the interpretation of a uniport plus a 2:l antiport (case B, Fig. 12s). A rigorous choice must await further measurements, especially ones that could indicate the extent of the cycling.
It has been postulated that Na+ transport is involved in pH homeostasis and that the mechanism involves a shift from electroneutral to electrogenic H+/Na+ antiport at alkaline pH (50). The change in the relationship between ApNa and ApH that we observed above pH,, 7.2 is preliminary evidence in support of this postulate, but further investigation is needed. Measurements of the apparent stoichiometry over a wider pH range could yield valuable clues as to which types of devices are responsible for developing and maintaining the Na+ gradient and might help clarify the mechanism of pH homeostasis in bacteria.
pHi, in E. coli Is Affected by Osmolarity of Extracellular Medium-Two observations made in the course of these studies have indicated that, in spite of the well-established phenomenon of pH homeostasis in E. coli (30,36,51), there appears to be no unique value of pHi, that is achieved under all conditions, at least by endogenously respiring cells. First, we have noted significant strain-to-strain variation: pHin values in E. coli CS 71 were always higher by 0.2-0.3 units than those in strain MRE 600. Second, pHi, was dependent on the in E. coli osmolarity of the extracellular medium, probably reflecting in some way the cellular response to osmotic stress. The mechanisms of sensing osmotic stress are not understood in detail but are thought to involve K+ transport (52), regulation of porin biosynthesis (53), and uptake of osmoprotectants such as glycine, betaine, or proline (54, 55). The latter two mechanisms are unlikely to be responsible for the changes in pHi, that we observed, since both require protein synthesis, which would not be occurring to any appreciable extent in buffer. Furthermore the timescale required for such synthesis would be at least 30 min, while pHi, was found to change within 2 min following a change in osmolarity of the extracellular medium. K+ transport, on the other hand, can respond rapidly to osmotic changes, K+ being taken up following an osmotic increase and released following an osmotic decrease (23). In K+-depleted cells of E. coli, it has been found that K+ uptake correlates with an increase of pHi, (and thus ApH) with a concomitant decrease in A+ (56). Therefore the rise in pHi, and drop in A$ observed by us as the osmolarity of the extracellular medium was increased might be attributable to osmolarity-stimulated K+ uptake.
It should be remembered that our observations were made in endogenously respiring cells. It might be that growing cells can, in the face of osmolarity changes, achieve a higher degree of pH homeostasis.
Concluding Remarks-The present study of the bioenergetics of Na" in E. coli has confirmed that, as has been strongly predicted by other studies, the Na+ gradient is closely linked to that of the proton. Based on the quantitative relationship, we suggest that ApNa in E. coli represents a steady state between Na+ extrusion and Na+ influx using different H+/ Na' stoichiometries. The futile cycling that would occur as a result of the presence of two devices with differing driving forces would of course represent an ongoing expenditure of energy. However, we are inclined to view such an expenditure as functionally important and not as an unfortunate lack of efficiency. If it were to contribute to the regulation of an important cellular parameter such as cytoplasmic pH, it would presumably convey net advantage to the cell.