Proc. Natl Acad. Sci. USAVol. 78, No. 7, pp. 4324-4328, July 1981Biophysics

Proton and hydroxide ion permeability of phospholipid vesicles(membrane permeability/phospholipid bilayers/proton transport/liposomes)

YASUHIKO NOZAKI AND CHARLES TANFORDWhitehead Medical Research Institute and Department of Physiology, Duke University Medical Center, Durham, North Carolina 27710

Contributed by Charles Tanford, April 20, 1981

ABSTRACT The apparent permeability of H' through phos-pholipid bilayers was determined by measuring H' efflux fromlarge unilamellar phospholipid vesicles with internal space buf-fered at pH 4. The value obtained is about 10-9 cm/sec at roomtemperature, five orders of magnitude lower than was recentlyreported for the combined permeability forH' and OH- [Nichols,J. W. & Deamer, D. W. (1980) Proa NatL Acad& Sci USA, 77,2038-2042]. The apparent permeability measured in this way isthe sum of contributions from the movement of H' and of un-charged species (HCI or HNO3) in equilibrium with anions in thesolution. There is evidence that the uncharged species make thedominant contribution and that the permeability coefficient forH+ per se is no larger than 5 x 10-12 cm/sec. An attempt to mea-sure OH- permeability by use of vesicles buffered at pH 10 didnot give a conclusive result because the vesicle walls appeared tobe damaged by exposure to this pH. An apparent permeabilitycoefficient of about 10-7 cm/sec was estimated for undamagedmembranes.

The work described in this paper was prompted by a report (1,2) that large unilamellar phospholipid vesicles prepared by anether injection method have a remarkably high permeability(>10-4 cm/sec) for H', OH-, or both ions. We have recentlydescribed a method for preparing large phospholipid vesiclesby removal of detergent from solutions of mixed micelles ofphospholipid and octyl glucoside (3). These vesicles were shownto have very low permeabilities for both cations and anions,comparable to permeabilities measured in the much smallervesicles obtained by sonication (4, 5) or by removal of cholatefrom cholate/lipid mixed micelles (6). Because of the seriousphysiological implications of a high H+/OH- permeability, ifit were a general property of all phospholipid bilayers, wedeemed it important to measure this property in vesicles pre-pared by the octyl glucoside method. The results obtained arequite different from those reported for vesicles prepared by theether injection method: the permeabilities to H+ and OH- werefound to be comparable to those for other small cations andanions.

While this work was in progress, it came to our attention thatGutknecht and Walter (7) have come to a similar conclusionfrom studies using decane-containing planar phospholipid bi-layers. By using both electrical conductance and ion flux mea-surements, Gutknecht and Walter were also able to demon-strate that the net proton fluxes observed by them arose fromdiffusion of neutral acid molecules (e.g., HCl) across the mem-brane, and not from diffusion of H+ per se. The results of thispaper support that conclusion even though conductivity mea-surements are not possible when vesicles are used for transportsutdies.

') 60 10~~~~

75~~~~P

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EXEIMNA PRCEUR

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FIG. 1. Titration curve of aspartic acid, based on successive pKvalues of 1.9, 3.65, and 9.65. The curve in the Inset is a greatly ex-panded portion of this curve, translated into the molarity of added H'(positive sign) or OH- (negative sign) that is theoretically required tobring a solution of 0.04M aspartic acid to a given pH. The experimentalpoints represent the actual titration of an aliquot of the vesicle prep-aration used for the data of Fig. 2.

EXPERIMENTAL PROCEDURE

Aspartic acid solutions were used to generate gradients in Heand Hr activity. Aspartic acid is a tribasic acid with reportedpK values of 1.9, 3.65, and 9.7 under the conditions used here(8). We confirmed these values by titration of the sample usedin this work, but the data indicated that 9.65 is a better valuefor pK3 than 9.7. As Fig. 1 shows, aspartic acid has a high buffercapacity at pH 4 and pH 10, but almost none at pH 7.

Egg yolk phosphotidylcholine vesicles containing 0.04 M as-partic acid solutions were prepared at pH 4 or pH 10, using theprocedure previously described (3), with minor modifications.The vesicle suspension was placed into a cell for pH measure-ment (see below), and permeability measurements were initi-ated by addingHCe or NaOH to bring the measured pH closeto 7. The pH adjustment could be made sufficiently quickly toavoid escape ofH+ or OHe from the vesicle during adjustment,so that an initial gradient of 10-4 M in H' or O oactivity be-tween intravesicular and external solutions could be assumedto have been established. Measurement of pH as a function oftime was then used to determine the rate of H+ or OHW dif-fusion across the membrane. Because the intravesicular volumein these experiments is usually only 1% or 2% of the total vol-ume, H' or OHW escaping from the vesicles become greatlydiluted, but the low buffer capacity ofthe external solution com-

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pensates for this, so that pH values change at a measurable rate.We did not rely on the theoretical titration curve of aspartic acidto determine rates of H' and OH- efflux from measured pHvalues, but experimentally determined the relationship be-tween pH and changes in H' or OH- concentration by a sep-arate titration, as shown in the Inset of Fig. 1. This titration wasperformed either on the sample actually used for the effluxmeasurement, by back-titration to pH 7, or by use of a separatealiquotrof the same solution.

Additional experiments were done using vesicles containingprotein solutions as intravesicular buffer. The protein was re-moved form the extravesicular solution by gel chromatographybefore the adjustment to pH 7. This procedure has the advan-tage of decreasing the buffer capacity of the solution to evenlower values than for a neutral aspartic acid solution, but hasthe disadvantage of delaying the start of efflux measurements.The titration vessel and electrode assembly used for pH mea-

surement have been described (figure 7 of ref. 9). A stream ofargon was passed over the surface of the solution (or bubbledthrough it) to prevent contamination by CO2 and also to avoidlipid oxidation by 02 Standard HC1 or NaOH was added bymeans of a Hamilton syringe to adjust the pH at the beginningof each experiment and to obtain titration data such as those inthe Inset of Fig. 1. It is difficult to avoid pH drift in poorly buf-fered solutions near neutrality, and the overall accuracy of ourmeasurement ofdpH/dt is estimated to be not much better than+0.01 per hr, which corresponds to an uncertainty of order 5X 10-1° cm/sec in the determination of permeability coeffi-cients. When different vesicle preparations were used undersimilar conditions, results were generally reproducible towithin a factor of 2.

All measurements were made at room temperature (23-240C).All solutions contained 0.22 M NaCl, NaNO3, or NaCl04, andthis ensured that H' and OH- fluxes would not be the limitingfactors in maintaining neutrality in the intra- and extravesicularsolutions. Because salt concentrations were equal on the twosides, no significant potential difference across the membranceshould have been established.

Total phospholipid in each sample (generally between 1 and5mM) was determined in terms of the organic phosphate con-tent by the method of Bartlett (10). Internal vesicular volumewas determined for a few samples by use of Cl- efflux, as de-scribed (3), or by a similar procedure using Na+ efflux. In mostcases a less accurate procedure was employed, based on mea-surement of pH after lysis of the vesicles by detergent. Mea-sured internal volumes were sufficiently close to the valuesexpected on the basis of phospholipid content (table I of ref. 3)to permit the assumption that most or all of the phospholipidin each preparation was present in vesicular form. (The maximalerror in permeability measurements resulting from this as-sumption is less than a factor of 2, which is of the same orderof magnitude as the overall reproducibility of the results.)

Vesicles used in this work are sufficiently large to permitneglect of the difference between internal and external radii.The total surface area of the membrane separating internal andexternal solutions is then independent of actual size, beingequal to one halfthe surface area of-the total vesicular lipid con-tent in the suspension. Using an average surface area of 70 A2per lipid molecule (3), and assuming that all of the analyticallydetermined lipid is present in vesicular form, the membranearea per liter of solution can be calculated as 70N[PL]/2A2, inwhich N is Avogadro's number and [PL] is the phospholipidconcentration in moles per liter. The apparent flux ofions acrossthe vesicle walls is then given by the measured rate of changeof H' or OH- concentration (moles per liter per second), di-vided by the membrane area per liter.

RESULTS

Experimental Results. Vesicles prepared at pH 4, examinedby negative-staining electron microscopy, had an appearancesimilar to that of vesicles prepared at neutral pH (3). Most ofthe vesicles had a diameter close to 2000 A, but there was some-what greater heterogeneity in size and in some preparations alarger proportion of vesicles with a diameter near 1000 A thanwas observed at neutral pH. Internal volume measurementsranged between 3000 and 9000 cm3/mol of phospholipid, com-pared to the range of 5000-7000 cm3/mol for vesicles preparedat neutral pH (3).

Vesicles prepared at pH 4 also resembled previous prepa-rations in their permeability for Na'. Two samples gave PNa+= 5 x 10-13 and 1.5 x 10-12 cm/sec, respectively, comparedto the value of 1.0 x 10-2 cm/sec obtained for one vesicle prep-aration at neutral pH (3). The kinetic curves were nonlinear,indicating that a small proportion of the vesicles (less than 10%)had a higher permeability than the rest. Permeability for Cl-was measured for one sample prepared in NaCl, with extra-vesicular Cl- replaced by N03-. We obtained Pcl- = 4 X 10 10cm/sec, about 5 times larger than the value.obtained by thesame procedure at neutral pH (3). This is the expected result,because studies using sonicated vesicles have demonstrated thatlowering the pH accelerates Cl- diffusion (4, 5).

Vesicles prepared at pH 10 differed significantly from vesi-cles prepared at neutral pH or at pH 4. Electron microscopyshowed that the vesicles were heterogeneous in size and oftenirregular in shape. Many large vesicles with diameters of3000-5000 A were seen. Internal volume measurements fell inthe range of14,000-24,000 cm3/mol ofphospholipid. Assumingthat all of the analytically determined phospholipid is in vesic-ular form, this corresponds (by an extension of table I of ref. 3)to vesicle diameters between 3400 and 7000 A. If some of thelipid was not in vesicular form, the calculated diameters wouldbecome even larger. These vesicles were also considerablymore permeable to Na+ and Cl-. For the preparation used toobtain the OH- efflux data of Fig. 3, PNa+ was found to be 5X 10-12 cm/sec-i.e., about 5 times larger than at neutral pHor at pH 4. Two other vesicle preparations yielded even highervalues for PNa+. Pcj- was measured for one sample, and a valueof 5 x 10-10 cm/sec was obtained. Because studies using son-icated vesicles have shown that an increase in pH tends to re-duce Pcl- (4, 5), this result cannot be explained on the same basisas the relatively high Pcl- measured at pH 4. It has to be con-cluded that vesicles prepared at pH 10 have an intrinsicallyhigher permeability for both Na+ and Cl- (and presumably forall small ions) than vesicles prepared at neutral pH or pH 4. Themost likely explanation is that the long exposure to alkaline pHduring the preparative procedure (several days) leads to partialhydrolysis of the phospholipid, with retention of the hydrolysisproducts in the membrane.

Fig. 2 shows a typical H+ efflux experiment, using vesiclesprepared at pH 4 in the presence of 0.22 M NaNO3. The time-dependent pH values were converted to increments in the con-centration ofH+ by use ofthe titration curve in the Inset of Fig.1. The slope d[H+]/dt divided by the membrance area per litergives the flux JH+ per unit membrane area, and this was con-verted to an apparent permeability PappH+ by the relationship

JH+ = Papp,H- AaH+, [1]in which AaH+ is the difference in hydrogen ion activity acrossthe membrane. (Activity units must be referred to concentra-tion units of moVcm3 to obtain P in units of cm/sec.) For theinitial slope, AaH+ is based on the initial internal pH of 4. Forlater times, the accumulation ofprotons in the external solution

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2: ~~~~~~~~~~~~~~~.07.3-/ ~

x

0 10 20 30 40Time, hours

FIG. 2. Typical efflux experiment for vesicles prepared at pH 4.The concentration of H' that must have entered' the extravesicularsolution to attain each measured pH was calculated from.the Inset ofFig. 1. A pH of 6.85mwas measured after lysis of the vesicles with de-tergent, and is taken to represent the final pH that would have beenreached in the experiment.

was equated with the loss ofprotons from the internal solution.Assuming that the vesicles are homogeneous, the internal pHat any time can then be calculated from knowledge of the ratioof internal to external volume and the titration curve of Fig. 1.For the data of Fig. 2, Pa H+Was found to be 4.5 x 10-9 cm/see, essentially independent of time, which may be taken as aconfirmation of the assumption of vesicle homogeneity. Some-what lower values for Papp,H+ were obtained from other exper-iments of this kind. One preparation led to a biphasic effluxcurve, d[H+]/dt being about 6 times larger in the first hour thanat subsequent times. Considering the experimental result as asuperposition of a fast and a slower efflux curve, the data in-dicated the presence ofabout 10% ofvesicles with anomalouslyhigh permeability, with PappH' = 2 x 10-9 cm/sec for the re-mainder. Given the inherent error ofmeasurement in P, whichis close to 1 X i0' cm/sec, and the possible error arising fromthe presence of lipid in nonvesicular form, all the results areconsistent with PappH+ = (3 ± 1.5) x 10-9 cm/sec.When these experiments were repeated for vesicles prepared

at pH 4 in the presence of 0.22 M NaCl instead of NaNO3, pHchanges were found to be much slower, close to the limit of themethod. Observed changes were of the same order of magni-tude as the rate ofpH fluctuations, and periods of pH increaseas well as pH decrease were seen. The net change over a longperiod was, however unambiguously in the downward direc-tion. Similar estimates of PappH+ 5 X 10-'0 cm/sec wereobtained for two separate preparations. It is clear that the ap-parent proton permeability in the presence of Cl- is significantlyless than in the presence ofN03 .

Vesicles containing ribonuclease at pH 4 instead of asparticacid were studied, using NaClO4 as electrolyte. Values ofPapp,H+ = 2.0 x 10- and 2.5 x 109cm/sec were obtained fortwo preparations.

Vesicles prepared at pH 10 (in NaCl) were used to measurethe apparent permeability for OH-. Fig. 3 shows data for onepreparation, and it is clear from the time scale that the per-meability is much higher than for H'. By using an equationanalogous to Eq. 1, Pap OH- was calculated to be 1.0 X 10-6cm/sec, independent oltime to within 10% over the entire ef-flux curve. A similar result was obtained for another prepara-tion, and even faster efflux was observed for a third sample. Onthe other hand, smaller values ofPappOH+ were obtained for two

I

I100

Time, minutes

o0

x

I

FIG. 3. Typical efflux experiment for vesicles prepared at pH 10.The incremental concentration of OH- at each pH was determinedfrom data similar to those of the Inset of Fig. 1, measured by back-ti-tration of the vesicle suspension at the end of the experiment. A finalpH of 8.25 was attained at the end of about 4 hr, after which no furtherchange took place.

vesicle preparations containing cytochrome c buffered atpH 9.4and pH 10, respectively. In view of the evidence presentedearlier to indicate that vesicles prepared at pH 10 have damagedmembranes, and permeabilities for Na' and Cl- that are 5- to10-fold higher than expected, the result obtained cannot betaken to reflect OH- permeability of uncontaminated phos-pholipid bilayers. On the basis of the Na' and Cl- permeabilitymeasurements, OH- permeability in uncontaminated bilayersmight be expected to be about an order of magnitude less thanthe observed value, so that aPpOH-H 1 X 10-7 cm/sec' rep-resents a reasonable estimate for uncontaminated vesiclemembranes.

Interpretation ofResults. Because pH measurements cannotdistinguish between gain of protons and loss of hydroxide ions,measured fluxes formally represent the sum ofboth processes-i.e., the right hand side of Eq. 1 should formally be written asPappH+AaH+ + PappOH- AaOH-, in which AaH+ and AaOH- rep-resent gradients in opposite directions. However, AaH+ =103AaOH- in the experiments at pH 4, and the values ofPappOH- obtained from the experiments at pH 10 (PappOH-maximally about 200 times Papp,H+) preclude the possibfity ofa significant contribution of OHW flux to the measurements atpH 4. The impossibility ofa contribution ofH+ flux to the mea-surements at-pH 10 is self-evident.

Another possibility that has to be recognized in the inter-pretation of the experimental data is that H+ does not neces-sarily cross the membrane as an ion, but may do so as a neutralspecies, the possible species in the present context being un-dissociated HCl, HNO3, and HCl04 and the neutral zwitter-ionic form of aspartic acid. We measured the permeability coef-ficient for aspartic acid, using the radioactive label influxmethod, and obtained a value of P = 5 x 10-13 cm/sec, whichis an order of magnitude too small to account for the fluxesmeasured at pH 4. The undissociated acid molecules cannot,however, be excluded. In fact, because PaP,H+ in solutions con-taining NaNO3 was observed to be higher than in-solutions con-taining NaCl, a major contribution from HNO3 is certainly;in-dicated. Where X is the anion of the supporting electrolyte,the general expression for H+ flux thus becomes

JH+ = PH+ AaH+ + PHX A[HXI, [2a

in which A[HX] is the difference between HX concentrations

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across the membrane. If KHX is the equilibrium constant forformation of the undissociated species,

KHX = [HX]/aH+[X7, [3]

combination with Eqs. 1 and 2 leads to

Papp,H+ = PH+ + PHxKHX[X7. [4]Because PH+ must be the same in NaCl and NaNO3 solutions,we can (within the experimental error of measurement) assignall the flux observed at pH 4 in NaNO3 to the second term.Nitric acid is a relatively weak acid, and the value of KHNO3 iswell established to be 10'4 in dilute solution (11, 12). With[NO3-] = 0.22 M, this leads to PHNO3 = 4 X 10-7 cm/sec.

Although HC1 is a much stronger acid than HNO3, withKHC1 = 10-6.1 (12), it is likely that the data obtained at pH 4 inNaCl may also reflect membrane permeation by the undisso-ciated acid rather than by H' per se. Gutknecht and Walter(7) studied H+ permeability by using decane-containing planarphospholipid bilayers, with a gradient of 0.3 M HC1 across themembrane. Using both ion flux and conductivity measure-ments, they were able to show that less than 1% ofthe measuredflux reflected the movement of H' across the membrane. Interms of Eq. 4, this means that PHcIKHCI > 300PH+ for decane-containing bilayers. Because decane-containing bilayers havemuch higher apparent permeabilities for H' than do the mem-branes of the vesicles used here (see Discussion), the ratiosPHCI/PH+ will not necessarily be the same for both, but if weassume that the same ratio applies, the second term on the right-hand side of Eq. 4 would be dominant under our conditions aswell. With the experimental value of PappH+ = 5 X 10-1' cm/sec, this leads to PHC1 = 3 X 10-3 cm/sec and PH+ < 5 X10-12 cm/sec. Support for this interpretation of the results isprovided by the fact that the ratio PHCI/PHNO3 obtained in thisway is nearly the same as that reported by Gutknecht and Wal-ter (7) on the basis of preliminary experiments with HNO3.

In view ofthe experimental evidence suggesting that vesiclesprepared at pH 10 have damaged membranes, the observedvalues Of PappOH- 1 X 10-7 cm/sec does not warrant furtheranalysis. Using lecithin/cholesterol films containing tetradec-ane, Gutknecht and Walter (7) estimated POH- from conduc-tance measurements to be about4x 10-9 cm/sec. This suggeststhat our measured value may reflect movement of unchargedNaOH across the membrane.

DISCUSSIONTable 1 summarizes the direct experimental data of this paperin terms of the sum'of allifluxes that-contribute to pH equal-

Table 1. Apparent permeability coefficients

Papp, cm/secStudy H+ OH-

This work, in NaNO3 3 x 10-9This work, in NaClO4 2 x 10-9This work, in NaCl 5 x 10-10 (1 x 1j-7)*Gutknecht and Walter (bilayers)t 3 x 10-7 (4 x 10-9)Nichols et al. (Vesicles)* 1 x 10-4

Ppp represents the sum of contributions from charged and un-charged species. Data from the present study have an uncertainty ofabout a factor of 2.* Estimated value.tRf 7. The value for OH- is based on conductance measurements withlecithin/cholesterol/tetradecane bilayers and excludes possible con-tributions from uncharged species.

* Refs. 1 and 2. The measured value represents a net permeability fromthe combined diffusion of H' and OH-.

ization. The values are much smaller than values recently re-ported from other laboratories. The discrepancy between ourdata and those of Gutknecht and Walter (7) has a plausible ex-planation, because the bilayer membranes used by them con-tain decane and are also subject to a possible edge effect wherethe bilayer is attached to its solid support. The membranes usedin the present study are composed of essentially pure egg yolkphosphatidylcholine and, being vesicular, constitute a uniforminterface between internal and external solutions. The magni-tude of the permeability difference between the two systemsis perhaps surprisingly large, because many previous studieshave indicated that decane-containing bilayers have permeabil-ities for nonelectrolytes that are less than an order ofmagnitudehigher than permeabilities measured with vesicles. However,Brunner et aL (13) observed differences in ionic permeabilitiessimilar to those reported here, and they showed that anoma-lously high fluxes across planar bilayers can also be obtained fornonelectrolytes when the intrinsic rate of diffusion is slow. Weare not able to explain the difference between our results andthose of Nichols et aL (1, 2), because their studies were alsocarried out in phospholipid vesicles. Nichols et aL observedhigher permeabilities for Na+ than have been reported for smallsonicated vesicles, and they suggested difference in vesicle sizeas a possible reason. This explanation cannot be used here, be-cause our vesicles have about the same diameter as the vesiclesused by them, and our value for PNa+ is only slightly larger thanthat for small vesicles (13). Nichols et aL used a different prep-arative procedure (ether injection rather than detergent di-alysis), and their membranes contained a small percentage ofphosphatidic acid in addition to egg yolk phosphatidylcholine.It is difficult to see why either of these factors should have alarge effect.

Our data support the conclusion of Gutknecht and Walter(7) that net proton fluxes result from transfer of undissociatedacid molecules and that the permeability of phospholipid bi-layers for H+ per se is very low. A value of PH+< 5 X 10- cm/sec was estimated by using Gutknecht and Walter's estimateof PHCI/PH+, and this is comparable to the value of 1 x 10-12cm/sec obtained for PNa*. The permeability coefficients for theuncharged acids that are required to account for the observedfluxes are shown in Table 2. They are smaller than the valuesreported by Gutknecht and Walter because our measuredfluxes are smaller (Table 1), and it should be noted that PNa+is also smaller for the vesicle membranes. Relative values arein reasonable agreement.The high value that has been assigned to PHC1 merits some

comment. High values are in fact consistent with the generalanalysis of polar nonelectrolyte permeability by Finkelstein(14). Finkelstein showed that permeabilities are proportionalto the diffusion coefficient (D) ofthe permeant in a hydrocarbonmedium and to the molar distribution constant (kI) of the per-

Table 2. Permeabilities for individual species

Permeability, cm/secGutknecht and

Species This work Walter (7)HNO3 4 x 10-7 1 x 10-3HCl04 1 x 10-6 _HOl 3 x 10-3 2.9H+

4328 Biophysics: Nozaki and Tanford

meant between liquid hydrocarbon and aqueous media. HClhas been shown to have a very high solubility in hydrocarbonsolvents (15). Bytcombining the measured solubility in hexadec-ane with vapor pressure and activity coefficient data for aqueous-HC1 solutions (16) one can calculate the product KdKHC1 (KHCIdefined by Eq. 3), and this leads to Yd = 0.06, which is con-siderably higher than the value of YKd for water and other polarnonelectrolytes listed by Finkelstein for distribution betweenthe same solvents. With this value of Kd, PHC1 = 2.9 cm/sec isconsistent with Finkelstein's data for other nonelectrolytepermeabilities of decane-containing bilayers (14). Our value ofPHC1 = 3 X 10-3 cm/sec is below the expected value for sphin-gomyelin/cholesterol/decane bilayers, which were found to bethe tightest of three planar membrane preparations studied byFinkelstein.We are grateful to Dr. J. Gutknecht for providing us with a copy of

his paper in advance of publication. This work has been supported byResearch Grant PCM-7920676 from the National Science Foundationand by Research Grant AM-04576 and a Research Career Award (toC.T.) from the National Institutes of Health.

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2. Nichols, J. W., Hill, M. W., Bangham, A. D. & Deamer, D. W.(1980) Biochim. Biophys. Acta 596, 393-403.

3. Mimms, L. T., Zampighi, G., Nozali, Y., Tanford, C. & Rey-nolds, J. A. (1981) Biochemistry 20, 833-840.

4. Hauser, H., Oldani, D. & Phillips, M. C. (1973) Biochemistry 12,4507-4516.

5. Toyoshima, Y. & Thompson, T. E. (1975) Biochemistry 14, 1525-1531.

6. Brunner, J., Skrabal, P. & Hauser, H. (1976) Biochim. Biophys.Acta 455, 322-331.

7. Gutknecht, J. & Walter, A. (1981) Biochim. Biophys. Acta 641,183-188.

8. Cohn, E. J. & Edsall, J. T. (1943) Proteins, Amino Acids and Pep-tides (Reinhold, New York).

9. Nozaki, Y. & Tanford, C. (1967) Methods Enzymot 11, 715-734.10. Bartlett, G. SR. (1959) J. Biol Chem. 234, 466-468.11. Hogfeldt, E. (1963) Acta Chem. Scand. 17, 785-796.12. Perrin, D. D. (1969) Pure Appli Chem. 20, 133-236.13. Brunner, J., Graham, D. E., Hauser, H. & Semenza, G. (1980)

1. Membr. Biol 57, 133-141.14. Finkelstein, A. (1976) J. Gen. Physiol. 68, 127-135.15. Linke, W. F. (1958) Solubilities (Am. Chem. Soc., Washington,

D.C.), 4th Ed.16. Lewis, G. N. & Randall, M. (1923) Thermodynamics (McGraw-

Hill, New York).

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