ELSEVIER Bioelectrochemistry and Bioenergetics 39 (1996) 101-108

Activity coefficients of CaC12 and MgC12 in the presence of dipalmitoylphosphatidylcholine-phosphatidylinositol vesicles

in aqueous media

M.D. Reboiras Departamento de Qufmica, Facultad de Ciencias, Unioersidad Autdnoma de Madrid, 28049 Madrid, Spain

Received 14 March 1995; in revised form 10 April 1995

Abstract

Mean activity coefficients of CaCl 2 and MgC12 salts have been measured in the presence of phospholipid vesicles, by use of the EMF method with ion-exchange membrane electrodes, as a novel procedure for studying the direct interactions between electrolytes and phospholipid vesicles. Mixed lipid sonicated vesicles have been prepared from dipalmitoylphosphatidylcholine (DPPC)-phosphati- dylinositol (PI) mixtures, covering a range of composition. The CaCI 2 and MgCI 2 concentration range studied was 0.01-0.001 mol 1-1. For both salts studied, the activity coefficients decrease linearly as the vesicle concentration in the suspension increases while the concentration of salt was kept constant. Maintaining a constant vesicle concentration, the decrease in the activity coefficients is more pronounced the more dilute the concentration of the salts. Quantitative differences were observed in the behaviour of both salts which are explained on the basis of a higher affinity of the Ca 2+, compared with that of Mg 2+ ions, to the vesicle surface. Using a simple model for the vesicle-salt systems, the number of cations specifically bound to the vesicles has been calculated. In view of the results it can be concluded that estimation of the activity coefficients of the salts is a useful method for the study of the interactions taking place in vesicle-salt systems.

Keywords: Activity coefficients; Calcium chloride; Magnesium chloride; Phospholipid vesicles; Ion binding; Liposomes

1. Introduct ion

Because of the increasing number of potential applica- tions in colloid science, electrochemistry and biological problems, systems with charged surfaces in contact with electrolyte solutions are subjects of growing interest. In particular, phospholipid vesicles or liposomes have come into widespread use in many different areas of science as simplified models for cell membranes and their fusion and as a tool for drug delivery. Liposome suspensions can be stable for several weeks, although amphiphilic surfaces such as lipid bilayers are thermodynamically unstable in nature. The temporary stability should be regarded as the interplay of interaction forces such as van der Waals, solvation, electrostatic or steric forces; although their spon- taneous aggregation may lead to vesicle destruction by the process of fusion. An understanding of the different inter- action forces responsible for the stability of the liposome suspensions is, therefore, essential not only in colloid

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chemistry but also in the practical application of lipid vesicles as tools for drug delivery.

Much of our current knowledge regarding membrane interactions has been derived from investigations of fusion in artificial phospholipid vesicles systems, which have the advantage of being structurally simple and experimentally amenable. Moreover, since phospholipids form a major part of biological membranes, fundamental similarities be- tween synthetic phospholipid bilayers and their natural counterparts could be anticipated. At the present time theoretical predictions regarding the interactions between phospholipid bilayers and electrolytes far exceed experi- mental verification.

Experimental studies to date can be conveniently di- vided into two categories: (i) those in which the aggrega- tion and /or fusion of phospholipid bodies are examined in aqueous media [1-4]; and (ii) those which approach the ideal of determining the distances between interacting planar bilayers, their forces of interaction, and their

102 M.D. Reboiras / Bioelectrochemistry and Bioenergetics 39 (1996) 101-108

structures [5-7]. Studies of type (i) have generally concen- trated on systems comprising negatively charged lipo- somes, dosed with suitable concentrations of electrolyte to initiate aggregation. The process of ion-induced aggrega- tion in such systems is conveniently followed by monitor- ing the increase in turbidity or light scattering with time at a given wavelength [3,8,9]. Fusion processes are by com- parison more complicated to monitor, and a variety of more or less satisfactory criteria have been introduced to assess ion-mediated fusion of liposomes, which include mixing of vesicle contents, mixing of membrane compo- nents, increase in vesicle size, and alteration in vesicle morphology [10-13].

Information regarding the mechanism of these processes is still fairly limited and, for this reason, a number of investigations have been carded out on the interactions between ions and membrane surfaces, which are essential for a full understanding of both aggregation and fusion events. Most of the techniques employed to study the binding of ions to liposomes do not measure directly the amount of bound ion but rather they inferred this quantity indirectly from measurements of other parameters such as the electrostatic interbilayer repulsive force, or elec- trophoretic mobility [14-16]. A direct measurement of the amount of bound ion can be obtained, however, by using differential scanning calorimetry, or atomic absorption spectroscopy [ 17-19].

In this paper a novel method for studying the direct interactions between phospholipid systems and electrolyte solutions, namely the measurement of the activity coeffi- cients of CaC12 and MgCI 2 salts in the presence of negatively charged liposomes is presented. The determina-

tion of the activity coefficients of the salts was carried out by measuring the electromotive force of a concentration electrochemical cell using ion-exchange membrane elec- trodes. This procedure has been used succesfully for the investigation of the interactions of salts in protein solutions [20-24], and the main objective of the present work is to explore the possible application of this technique to the study of the interactions between electrolyte solutions and phospholipid vesicles. Sonicated liposomes, prepared from mixtures of different compositions of dipalmitoylphos- phatidylcholine (DPPC) and phosphatidylinositol (PI), have been used for the study of their interactions exerted on the salts CaC12 and MgCI 2 at various concentrations between 10 -2 and 10 -3 molal.

2. Materials and methods

2.1. Reference solutions

The pure CaC12 and MgCI 2 used as reference solutions were prepared from reagent grade salts (Carlo Erba) and bidestilled deionized water. The molalities (10 - 2 - 10 -3 mol kg - i water) were adjusted to an accuracy of < +0.1%.

2.2. Lipids

L-a-Dipalmitoylphosphatidylcholine (DPPC), molecular weight 734, approximately 99% pure, was obtained from Sigma London Chemical Company Ltd. Phosphatidylinosi- tol (PI) from wheat germ, molecular weight 846, Grade 1,

E l

S b

St

/ 1 \ ~ J k J . J

C M AM ~ I =1

C

S b

M I

El

R

Fig. 1. Schematic representation of the equipment used for the determination of the mean activity of MCl2-salts in MCl2-vesicle suspensions: (C) three-compartment cell made of lucite material, with silicon rubber gaskets; (CM) cation exchange membrane; (AM) anion exchange membrane; (St) stirrers; (Sb) salt bridges (sat. KCI agar-agar); (El) reference electrodes; (M) multimeter;, (R) potentiome~c recorder.

M.D. Reboiras / Bioelectrochemistry and Bioenergetics 39 (1996) 101-108 103

was obtained from Lipid Products, South Nutfield, UK. Both phospholipids gave a single spot when analysed by thin-layer-chromatography (TLC) and were used without further purification.

2.3. Vesicle preparation

mV

10 O 5 x l O ' 3 m CaCI 2 • .. ÷

5 0 mg DP PC/PI ( 5 0 / 5 0 ) / m L v

Sonicated phospholipid vesicles were prepared by addi- tion of the desired amounts of stock solutions (5 mg cm -3 in chloroform) of DPPC and PI together with 50 cm 3 of chloroform/methanol solution (4:1 v / v ) to a 1-1itre round-bottom flask. The solvent was removed by rotary evaporation at a temperature of 50-55°C. The resulting lipid film was flushed with nitrogen for at least 30 min to eliminate trace solvent and dispersed by shaking with 5 - 7 cm 3 of nitrogen-saturated distilled water added at 50°C. The resulting dispersions were saturated with nitrogen, sealed and sonicated above the chain-melting temperature of DPPC (41°C) for 2.5 h in a bath sonicator.

The size and size distributions of the vesicles were determined by photon correlation spectroscopy using a Malvern Autosizer model 2c. Prior to the determination of the activity coefficients, the desired amounts of salts from a concentrated stock solution were added to the vesicle suspension.

2.4. Determination of activity coefficients

The following three-compartment electrochemical cell

solution(, ) solution(. ) solution(, )

CM A M

was used:

reference saturated electrode KCI saturatedKCi I electrodereference

It consists of the vesicle suspension, solution C) contain- ing e.g. mM~+ moles M 2+ ions per kg water and 2m o - moles C1- ions per kg water, separated from two pure MCI 2 solutions ( ') of identical concentration mMC h by a cation exchange membrane CM and an anion exchange membrane AM, respectively. The outer solutions ( ' ) are connected to two identical Cl--reversible electrodes through salt bridges (KCI saturated). Under conditions of equal and constant pressure and temperature in all phases, and of zero current between the two electrodes, the electro- motive force (EMF), E, of the electrochemical cell can be measured.

The EMF can be related to the chemical potential, and consequently to the activity, of MC12 in the liposome suspension and in the reference solution by considering the following reversible isothermal work process (constant pressure in all phases).

Let pass reversibly 1 Faraday, F, of positive electrical charge through the electrochemical cell from left to right. If the cation- and anion-exchange membranes are com- pletely charged with M 2+ and Cl- ions, respectively, and

-5

I l I I I I "~ 0 .004 0 .005 0 .006 0 .007

a~aCl2/mol .kg- t

Fig. 2. Electrochemical titration of a vesicle-salt suspension in compart- ment (") of the cell shown in Fig. 1, containing 5.00× 10 -3 tool CaCI 2 and 5.00 g DPPC/PI (50/50) per kg water. Electromotive force E in mV vs. the activity d of CaCI 2 in mol kg - i water in the compartments (') of the cell is shown, d = 5 . 9 8 × 1 0 -3 mol kg - I at E = 0 and m=5.00×10 -3 mol kg-S; 7±=0.753, according to Eq. (4). For comparison the titration line for the pure salt solution of identical concentration is shown (0); a value of y°± = 0.788 is obtained which deviates by 0.13% from the tabulated one.

are totally impassable for the respective coions (CI- in CM, M 2÷ in AM) - - that means "ideal membranes" - - and the phospholipid vesicles; this results in a reversible transfer of 1 mole of MC12 from the outer reference solutions into the liposome suspension in the middle com- partment, and the transfer of a definite amount of KCI from the salt bridge solution to the reference solution at the left and of the same amount MC12 from the reference solution to the salt bridge solution at the right. The work delivered by the electrochemical cell is then simply given by the difference of the chemical potential of MC12 in the vesicle suspension and reference solution, since the contri- butions at the salt bridges and the electrodes cancel each other out. This work must be equal to the work done in the external part of the elecirical circuit which is - F E . Thus we arrive at the relation (see e.g. Refs. [25,26])

- F E =/Z'~c]2 -/Z'MC h = 6RT ln(d'~/d±) (1)

where /~'MCh and /Z'~c h are the chemical potentials of MC12 in the reference solution ( ') and in the presence of the vesicles ("), T the absolute temperature, R the univer- sal gas constant and a the activity of the salt MC12. The derivation of this simple relation between the EMF of the electrochemical cell and the activities of MC12 neglects the effects of the not vanishing coion transference across the

104 M.D. Reboiras / Bioelectrochemistry and Bioenergetics 39 (1996) 101 - 108

membranes, of the chemical potential gradients within the liquid films adherent on the membrane surfaces, of the conventional transport of water across the membranes and of the contribution of the transference of the H + and OH- ions always present in aqueous solutions.

It may be shown [27] that the two former effects diminish the number of moles of MC12 reversibly trans- ferred across the membrane phases per Faraday by an amount equal to the sum of the means of the respective coion transference numbers tin2÷ and to- , taken over the membrane phase and the adjacent liquid films, whereas the two latter effects may be disregarded under the experimen- tal conditions in question. Eq. (1) now becomes

E = ( 6 R T / F ) X (1 - t c ~ - tA~+) In( d'±/d+ ) (2)

If E -- O, one obtains:

(a'+)E_o = d~: (3)

In the experiments reported here, the determination of the mean activity coefficients of MCI 2 salts in vesicle suspen-

sions was based on Eqs. (2) and (3) by means of electro- motive force (EMF) measurements, applying the "zero titration" method [28].

A schematic representation of the complete equipment used is shown in Fig. 1. The commercially available ion exchange membranes (Nepton AR-111 an Cr-61, Ionics, Watertown, MA, USA) had been charged with the respec- tive species and equilibrated in 1.00 x 10 -3, 5.00 × 10 -3 and 1.00 X 10 -2 molal MC12 solutions before measure- ment. All compartments were equipped with electrome- chanical stirring devices in order to achieve rapid equilib- rium at the membrane interfaces and reduction of the film potentials. The cell and the electrodes were kept at a temperature of 25°C with the aid of a water bath thermo- stat.

The reference solutions were conected to the terminals of a 1 G~2 input resistance multimeter (Keithley Instru- ments, Inc., Cleveland, OH, USA), so approximating the necessary condition of zero current, through salt bridges (KC1 saturated in agar-agar) and calomel reference

0.901

(a) (b)

l "'~,~I,,10" ' I . g g "+

0.8001- \ 0.800

5x10" In Mg a"

0.75G -3 Z + 5x10 m Ca

Mg z+

lx10 "2 m Ca z÷

\ I 0"700 I" lx lO"m Ca'* 0.7001-

0.6501 I I I 0.650 I I ! 1 2 3 1 2 3

mpi/mmol.kg -t mpl/mmol.kg -1

Fig. 3. Stoichiometric mean activity coefficients of (a) CaCl 2 and (b) MgCI 2 in DPPC/PI (50/50) vesicle suspensions depending on the PI molality, for the salt concentrations shown. Only mean values of at least four experimental values of 7 are shown. The data points on the ordinate show the mean activity coefficients 3, 0 of the pure MCI 2 solutions taken from the literature [29].

M.D. Reboiras/Bioelectrochemistry and Bioenergetics 39 (1996) 101-108 105

electrodes (Beckman Instruments, Inc., Irvine, CA, USA). The EMF values were recorded to an accuracy of +0.15 mV with a potentiometric recorder (Philips, Eindhoven, Netherlands). The electrochemical cell was installed in a Faraday cage. The EMF values were taken from the mean value of the two measurements obtained by interchanging the salt bridges in order to eliminate the asymmetry of the electrodes.

By changing the concentration and, as a consequence, the activity of the outer reference solutions and keeping the vesicle salt suspension unchanged, one obtains EMF values linearly related to the logarithm of the salt activity of the reference solution as long as the variation of the salt concentration is not too large to result in a considerable change of the coion transference numbers in the mem- branes.

By linear interpolation of E = 0, (d±)e: o is obtained. According to Eq. (3) this equals the mean activity d~ in the vesicle salt suspension. High accuracy is necessary for detecting small influences of the vesicles on the activity of

the salt. The error in EMF being + 0.2 mV, the relative error in (d±)e= o was -t-0.5%.

Fig. 2 shows, as an example, the titration curve for a liposome-CaC12 suspension in the middle compartment whose composition is given. From the intercept of the straight line, which can be drawn through the experimental EMF values, with the line E = 0, a mean activity of 5.98 X 10 -3 for the CaC12 in the liposome suspension is obtained. From Eq. (3), and using the fundamental rela- tions between activity and molal concentration, m, Ref. [25], the stoichiometric mean ionic activity coefficient of CaC12 in the liposome suspension is obtained:

(d±)~=o 3/±= 4]/3 m (4)

For comparison, the intercept for a pure CaCI 2 solution of equal mean ionic concentration, m = 5.00 × l0 -3, is also given in the figure. As can be seen, in the presence of the liposomes the value of (d±)e: o is shifted to the left,

0.950

1.00

0.950

0.9001- \ 0 .900

(a)

0.850F \ 0~50

0.8001- \ 0.80q

(b)

0.750[ I I I 0.75( I I I 1 2 3 1 2 3

mpt/rn mol .kg -Z mp0/m m ol .kg -1

Fig. 4. Relative stoichiometric mean activity coefficients 7 / 7 ° of (a) CaCI 2 and (b) MgCI 2 in DPPC/PI (50/50) vesicle suspensions in relation to the PI molality. Symbols and salt concentrations are as in Fig. 3. The bars at the regression lines correspond to the standard deviations of the data points.

106 M.D. Reboiras / Bioelectrocheraistry and Bioenergetics 39 (1996) 101-108

indicating a lower mean activity of CaC12 as a result of the influence of the liposomes.

In practice, at each composition of DPPC/PI liposome suspensions a linear relationship between E and In a'± could be observed within the experimental limits of error. The a'± values have been calculated from the molalities and interpolated values for the activity coefficients in pure salt solutions given in the literature [29]. The accuracy of the method is + 0.2%.

3. Results

In Fig. 3, the mean stoichiometric activity coefficients, y ±, of CaC12 and MgC12 are shown with respect to their dependence on the PI molality for three sets of experi- ments in which the concentrations of the salts were kept constant at 1.00 × 10 -3, 5.00 × 10 -3 and 1.00 × 10 -2 mol kg -] water. The DPPC/PI composition of the pholpholipid vesicles was 50 /50 (w /w) in all cases. (For the sake of simplicity, the subscript + of the convention-

ally used symbol 3' ± is omitted in the following, since no confusion with symbols for other activity coefficients is possible.)

The stoichiometric mean activity coefficients, calcu- lated from (d±)E_ 0 by means of the total ion concentra- tions according to Eq. (4), reflects the influence of all mutual interactions between the components of the solu- tion and the salt. To arrive at a more direct measure of the interactions which are caused by the addition of increasing amounts of liposomes, the normalized ratio 3'/3'0 is plotted versus the PI molality in Fig. 4, were 3'0 represents the mean activity coefficient of the respective salt in pure salt solution [29]. Thus, 3'/3'0 describes the net effect of the liposomes on the salt.

It is evident from these results that the presence of liposomes causes a linear decrease of 3' in relation to y °, being more pronounced for the more diluted salt solutions for both CaC12 and MgC12 salts. The amount of the negatively charged lipid PI in the composition of the liposomes, also has its influence on the activity coeffi- cients of the salt, as can be seen from the results shown in Fig. 5. The higher the PI content of the liposomes added to the salt, the more pronounced the decrease of 3'.

Y

0.75(:

0.70C

DPPCIPI : 25175 (i;]) $0/5010)

75/2S (zx)

0.6001 I I I 2 4 6

mllpl¢l/m m o I .kg ' l

Fig, 5. Stoichiometric mean activity of CaCl 2 in DPPC/PI vesicle suspensions of the compositions shown in relation to the PI molality. Salt concentration: 5 .00× 10 -3 CaCi 2 tool k g - 1 water.

4. Discussion

The influence of the vesicles on the chemical potential of the salts is described by the change in their activity coefficients when adding vesicles to the pure salt solutions. The interpretation of the stoichiometric activity coeffi- cients in terms of interactions between the solution compo- nents requires the assumptions below, considering the appreciable amounts of water bound on the vesicle surface, and that the ions are tighly bound distinct from those concentrated in the double layer region and the bulk of the suspension.

The term molal activity coefficient only has real mean- ing if the estimation of the ion concentrations in the vesicle suspension takes into account the ions which are actually free in solution, i.e. those that exist in the solution as kinetically independent units and, at the same time, only if the amount of solvent which really is available to them is considered. The term y, as defined by Eq. (4), includes the real influence of the vesicles on the free M 2+ and C1- ions in addition to all effects caused by the free ions whose concentrations deviate from those measured by the weight of the salt added to the vesicle suspensions.

The results presented in the previous section shown that the activity coefficients vary differently for each MCI 2 salt. The fact that both salts bear a common anion leads us to suppose that a considerable difference exists between the effects of Ca 2+ and Mg 2÷ ions on the vesicles. A similar behaviour has been detected in the numerous ag- gregation kinetics studies carried out between divalent cations and phospholipid vesicles [9,13,30,31]. The spe-

M.D. Reboiras / B ioelectrochemistry and Bioenergetics 39 (1996) 101-108 107

cific binding of divalent cations on the vesicular surface has been ascribed as the driving force for the vesicle aggregation; frequently reported with a special emphasis on the evidence that Ca 2+ binds more strongly than Mg 2+ [2,32,33].

Therefore, a first approach to the interpretation of our results is to assume that the decrease in the activity of the salts in the presence of liposomes is caused by the de- crease in the concentration of " f r e e " cations owing to the binding of cations to the phospholipid vesicles.

In view of this assumption, the concentration of M 2+ ions in the MCI 2 vesicle suspension will be lower than that added and, according to Eq. (4), a decrease in the mean activity of the salt is expected. The average number of bound M 2+ ions per vesicle, VM2+, depends both on the concentration of M 2+ ions in the vesicle suspension and the vesicle molality. This may be described by the relation:

me+=m+--VM2+×mv=[1--VM2+(mv/m+)] (5)

where me+ represents the concentration of free M 2+ ions

per kg water and m+, mv, the concentration of the total

M 2+ ions and vesicles, respectively, per kg water.

Assuming that no binding of Cl--ions occurs, it follows

that m f_ = m_. Further, taking into account that m+-- (m+

• m2_) I/3 and mMCl~ = raM2+= 2m_, and combining Eqs.

(4) and (5), we obtain:

y = y°% (6)

with

% = [1 - ~,M2+X(mv/m+)] '/3 (7)

% describes the contribution to the stoichiometric activ- ity coefficients through the binding of the cations to the vesicles. Rearranging Eqs. (6) and (7), an equation for //M2+ C a n be obtained

VM2+=(m+/mv)[l--('y/T°) 3] (8)

from which the number of cations M 2+ specifically hound to the vesicles can be calculated,

The results obtained, which are given in Table 1, clearly indicate that the binding of Ca 2+ ions is always greater than that of Mg 2+, in accordance with other experimental and theoretical results in many colloidal systems [4,17,34,35]. The affinity of the two ions to vesicles is sensitive to the concentrations of both lipid and salt. The number of ions bound to the vesicles decreases slightly as the concentration of lipid increases, at constant salt con- centration and when the vesicle concentration is mantained constant Vu2+ increases as the salt concentration rises• The constancy of the UM2+ values at the higher MgCl 2 concentrations may be an indication that this ion reaches saturation of its binding capability at concentrations above 10 -3 molal in the DPPC/PI compositions studied.

The treatment presented here is susceptible to further refinement if we consider two additional factors so far ignored which influence the activity coefficients of the salts, namely, the portion of suspension water bound to the vesicles and the electrostatic influence of the charge of the vesicles.

It is well known from experiences with independent methods [2,13] that a certain amount of the suspension water around the vesicles is altered in its structure and presumably is not available as solvent to ions. Taking this amount of bound water into account, with respect to our model, the charge of the vesicles is the same while the concentration of the ions in the remaining " f r ee " water becomes higher than that under the assumptions in our treatment. The electrostatic component arises from the existence of electrical charges on the surface of the vesi- cles and measures the influence of the presence of the vesicles on the activity coefficients of the salts.

These two contributions to the real value of Y:Yw, taking into consideration the influence of the water bound and YcL, accounting for the electrostatic influence caused by the vesicles, inserted into Eq. (6) as independent param- eters allows a more realistic interpretation of the mecha- nism by which the presence of vesicles affect the activity coefficients of the salts, provided y, Yw and YcL are known from independent measurements. Unfortunately, as this is not the case at present, many more systematic investiga-

Table 1 Average number of Ca 2+ and Mg 2+ ions bound to DPPC/PI (50/50) vesicles, ~,, in relation to the PI concentration, calculated from the stoicbiometric mean activity coefficients using Eq. (8)

Concen t ra t ion a CaCI 2 b CaCI 2 c CaCI 2 d M g C I 2 b MgC12 c M g C I 2 d

"y/3, ° v "y/'),° v '),/'y° v ~'/'y° v 3,/'y ° v 3,/3, ° v

0.369 0.973 0.43 0.993 0.57 0.996 0.65 0.991 0.15 0.998 0.16 0.999 0.16 0.739 0.946 0.42 0.987 0.52 0.993 0.60 0.982 0.14 0.996 0.16 0.998 0.16 1.48 0.893 0.39 0.976 0.48 0.986 0.56 0.965 0.14 0.992 0.16 0.996 0.16 2.22 0.839 0.37 0.965 0.46 0.981 0.50 0.949 0.13 0.988 0.16 0.994 0.16 2.96 0.787 0.35 0.956 0.43 0.978 0.44 0.934 0.13 0.984 0.16 0.992 0.16

a (Moles PI/kg H20) X 10 3. b 1 X 10 -3 molal. c 5 X 10 -3 molal. d I × 10 -2 molal.

108 M.D. Reboiras / Bioelectrochemistry and Bioenergetics 39 (1996) 101-108

tions are needed before all these parameters are known quantitatively in detail. It is hoped that future studies will elucidate the importance of the additional refinements.

So far we can conclude that the experimentally obtained mean activity coefficients of salts as a function of both vesicle and salt concentrations by means of the EMF method with ion-exchange membrane electrodes is an ade- quate procedure for showing the real interactions present in vesicle-salt systems, the prevailing ones being those due to the specific binding of cations on vesicles, at least in the concentration ranges described in this paper. The data obtained on the specific binding of ions can be relevant to physical studies of this type of system where the quantification of the interactions between the vesicles and ions is significant to other parameters under investiga- tion. Finally, this method is not limited to the specific lipids and ions studied here since the ion-exchange mem- branes can behave as specific reversible electrodes for many ions.

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