interaction of ionic compounds with multilamellar liposomes. an electrokinetic model

Colloids and SurfacesA: Physicochemical and Engineering Aspects 140 (1998) 91–101

Interaction of ionic compounds with multilamellarliposomes. An electrokinetic model

F. Molina *, C. Llacer, A.O. Vila, A. Puchol, J. FiguerueloDpt. de Quımica Fısica, Facultad de Farmacia, Universidad de Valencia, Avda. Vicent Andres Estelles s/n,

46100 Burjassot, Valencia, Spain

Received 10 February 1997; accepted 21 April 1997

Abstract

We have proposed a theoretical model of interaction of ionic compounds (ionic adsorbate or ionic drugs), withmultilamellar-liposomes, by means of their electrokinetic property variation with the ionic compound concentration.In this work, we show the complete development of the model proposed. Its theoretical results have been analysed tostudy the influence on the zeta-potential value of the following: number of membranes, size, shear-plane situation,critical concentration of formation (ccf ), and the ionic compound concentration which annuls the zeta-potential valueof the multilamellar-liposomes formed. © 1998 Elsevier Science B.V. All rights reserved.

Keywords: Biomembrane-ionic compounds interaction; Liposomes; Zeta-potential

Nomenclature n+1

adsorbate cations per unit volume bind-ing to the external surface sites of lipo-

r1 external equivalent radius of the inner-some

most bilayer of multilamellar liposomen+2

adsorbate cations per unit volume in thern

external equivalent radius of the nthaqueous mediumbilayer of multilamellar liposome

nT0

number of binding sites per unit volumeN adsorbate concentrationon the internal surfacesN+, N− cation and anion adsorbate concen-

nT1

number of binding sites per unit volumetrationson the external surfacez+, z− cation and anion adsorbate valences

nT total number of binding sites per unita ratio z−/z+volume. (nT=nT

0+nT

1)z+

i, z−

ication and anion valences of the phos-

b degree of multilamellarity. b=nT0/nTpholipidic molecules

a radius of Hemholtz’s external surfacen number of bilayers of the multilamellarh distance between Hemholtz’s externalliposome

surface and shear planen+0

adsorbate cations per unit volume bind-f ratio h/aing to the internal surface sites of thesa surface density of charge on externalliposome

surface of liposomes0a surface density of charge on external

* Corresponding author. surface of liposome without adsorbate

0927-7757/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved.PII S0927-7757 ( 97 ) 00269-0

92 F. Molina et al. / Colloids Surfaces A: Physicochem. Eng. Aspects 140 (1998) 91–101

s1 surface density of charge on external double layer (screening effect) [10,11]. If the bind-ing force is fairly strong, the surface charges aresurface of liposome due to adsorbate

cations compensated for and sometimes a net charge ofthe opposite sign appears on the surface. This hassT total surface density of charge on exter-

nal surface of liposome due to adsorbate also been observed in the interaction of the lipo-somes with some antibiotics [12–14], anestheticscations, when all binding sites of external

surface are occupied [15,16 ] and calcium channel antagonists [17],among others.N0 adsorbate concentration which annuls

zeta-potential value In general, the theoretical bases of studying theinteraction of ionic compounds with biomem-IA ionic strength due to adsorbate ions

Ii ionic strength due to free phospholipidic branes are well enough established when we beginwith the electrokinetic properties of liposomesmolecules

I total ionic strength (Ii+IA) [18]. Therefore, in drug encapsulation in liposomesother factors appear, which may contribute to the

1. Introduction systematization of a more specific drug-encapsula-tion model, appear. All these considerations havebeen taken into account in the model proposedThe discovery and development of preparation

methods of phospholipidic vesicles or liposomes in this work, which starts from the Gouy–Chapman–Stern–Grahame model and the Healyhave led to an important advance in cellular bio-

membrane simulation. These ‘‘sui generis’’ colloi- and White [19] and Matsumura and Furusawa[18] works.dal particles are the object of research in several

scientific fields such as biology, biochemistry, In this work, we show the complete developmentof the model proposed. Its theoretical results havemedicine and pharmacology. In this context this

use of liposomes as drug carriers [1] may be been analyzed to study the influence on the zeta-potential value of the following: number of mem-applied in the future, as therapeutic agents

targeting of the sick organ [2,3] and as retard branes, size, shear-plane situation, critical concen-tration of formation (ccf ), and the ionic compounddrug delivery systems [4,5].

The electrical properties of these lipidic vesicles concentration which annuls the zeta-potentialvalue of the multilamellar-liposomes formed.merits special attention. These may participate in

ion-transportation through the membrane, the bio-logical activity of the membrane proteins [6 ], andin the adhesion of vesicles or cells to each other, 2. Theoretical modeland so on [7,8]. Both the interaction of cellularmembranes with liposomes and the substance- The drug encapsulation process in liposomes

implies, in general, the phospholipid dispersion intransportation mechanism, from the liposomes tothe cellules and their intracellular structures, pro- the drug solution. It leads the drug to interact not

only with the external surfaces of the liposomes,vide the possibility of studying the general laws ofintercellular phenomena [9]. but also with all their internal surfaces. The devel-

opment of the model starts from the so calledIn this work, our main objective has been cen-tered on the interaction of ionic compounds with ‘‘partition hypothesis’’. This hypothesis assumes

that the drug-ions (adsorbate-ions) are distributedbiomembranes by means of their electrical proper-ties. This is a theme which has produced many among all the internal surfaces of the multilam-

ellar-liposome, the external surface of the multi-outstanding results in the past decade. The metalcations can reduce the negative surface potential lamellar-liposome and the aqueous medium —

proportionally to the free binding-sites of themembrane formed from phospholipids by bindingwith ionizable groups of these lipids. Monovalent internal surfaces, the free binding-sites of the outer-

most surface and the number of occupied sites,metal cations can reduce the membrane surfacepotential by decreasing the thickness of the diffuse respectively. In this hypothesis the character of the

93F. Molina et al. / Colloids Surfaces A: Physicochem. Eng. Aspects 140 (1998) 91–101

ion-site binding is not considered, and the aqueous Similarly, integration of the equation formed bythe second and the last member yieldsmedium is assumed to be the same inside and

outside the liposomes.n+1=nT

1(1−e−N/nT) (4)We suppose that the suspension is formed by a

determined number of liposomes with a homogen- and n+2

is finally given byeous size and that the total volume of the suspen-

n+2=N−nT(1−e−N/nT). (5)sion, V, can be divided in equal cells with a v

volume. We also suppose that every cell containsThe surface density of charge in the Hemholtz’sone liposome and that the theoretical development

external plane, sa, will be modified when theis equal for each cell.binding-sites of the external surface are occupiedIf N is the number of drug molecules per unitby adsorbate ions and it can be written as:volume in the aqueous medium, they will yield

N+ positive species and N− anions, related by: sa=s0a+s1, (6)

N=N+=aN− where s0a is the surface density of charge of theliposome without binded ions and s1 is the surfacewhere a is defined according to the electricaldensity of charge due to ions adsorbed on thisneutrality condition, so-called (N+z+=N−z−), asexternal surface. sa will depend on the adsorbate

a¬z−/z+ concentration as:

with z+ and z− standing for the mean valence of sa=s0a+sT(1−e−N/nT), (7)the cationic species and for the valence of the

where sT should be the surface density of chargeanions, respectively.due to adsorbate ions if all the binding-sites ofOn the other hand, if nT

0is the total number of

external surface were occupied, with a value:binding-sites on all the surfaces of the liposomeexcept for the external one (which contains nT

1binding sites), at any moment they will be partially sT=nT

1z+e

a

3, (8)

occupied by n+0

and n+1

positive ions, related withN+ through: where e is the quantum of electric charge and a

the external radius of the spherical vesicle.N+=n+0+n+

1+n+

2(1)

The theoretical results of this model providewhere n+

2is the number of non-adsorbed drug more information when the ionic compounds

cations, free ions in the aqueous medium. Further employed are able to invert the electrical chargeaddition to the system of dN drug molecules, will sign of liposomes, because in this case, a greaterresult on the addition of dN+ positive ions, which simplification in the mathematical development ofwill distribute among the internal surfaces dn+

0, the model is possible. Then, when the adsorbate is

the outermost surface, dn+1

, and the aqueous able to reverse the sign of the electric charge ofmedium, dn+

2, about the following proportion: the liposome surface, it should occur at a drug

concentration of N=N0, at which sa=0.dn+0

nT0−n+

0

=dn+

1nT1−n+

1

=dn+

2n+1+n+

0

=dN+

nT, (2) The ‘‘1/D’’ parameter is defined by the following

equation:where nT is the total number of sites.

1/D=(sT+s0a )/sT, (9)Integration between N=0 and N=N of the

differential equation formed by the first and the which represents the relative variation of sT. Bothlast members of the above multiple equality yields: the electrical characteristics of the vesicle when the

adsorbate is absent, as well as those which then+0=nT

0(1−e−N/nT) (3)

adsorbate ions provide when all sites are occupied,influence the 1/D parameter. Thus, the totaltaking into account that n+

0=0 when N=0.


number of binding-sites is given by:

nT=N0/lnD, (10)

in these conditions, recalling Eq. (7), it holds that:

sas0a

=1−D1−N/N

0

1−D. (11)

From Eq. (7) and Eq. (11) the surface-densityof charge can be deduced:

sa=z+ea

3N0(1−b) C1−D1−N/N

0

D ln D D, (12)

where b=nT0

/nT.

3. b determination Fig. 1. Transversal section of a multilamellar liposome. Theexternal radius of the innermost bilayer is a1 and a

nis that of

nth bilayer. The shaded zones represent lipidic bilayers of thick-Assuming that the sites are homogeneously dis-ness e0 separated by aqueous interlayers of thickness e∞

0.tributed on the liposome surfaces, it can be consid-

ered that the number of sites is proportional tothe area of the surfaces over which they are

and rn, in turn, is given by:

distributed. Therefore, the total number of sites,nT will be proportional to the total area of all the

rn=r

1+(n−1)+

1

e0

∑1

n−1e∞0i

, (15)surfaces of the liposome (SSn) and the number of

internal sites nT0

will be proportional to the differ-where r1 is the external equivalent radius of theence between the total area and the area of theinnermost bilayer and e∞0i the thickness of the ithoutermost surfaces Sext. b is then given by:aqueous layer between lipidic bilayers. Assumingthat all aqueous inter-bilayer thicknesses are equal,b=1−

SextSS

n

, (13)with a value e0∞ , the above equation may be writtenas:

where the sum extends from n=1 to n=n, with nstanding for the number of bilayers.

rn=r

1+A1+

e∞0

e0B(n−1). (16)Fig. 1 shows the transversal section of a multi-

lamellar liposome. The shaded zones representIn Fig. 2 the b dependence on the number n oflipidic bilayers with thickness e0 separated by

bilayers is illustrated for a system with alike thick-aqueous interlayers with thicknesses e0∞ . The exter-nesses of lipidic bilayers and of aqueous layers,nal radius of the innermost bilayer is a1, and a

nis

e∞0=e0. Observe the fast variation of b for a smallthat of the nth bilayer.number of bilayers. When n is approximately 25The above areas may be defined in terms of theor more, the variation is very slow.external equivalent radii of liposome, r

n, defined

as the ratios between the radius of the nth bilayer,an, and the bilayer thickness, e0, namely,

4. f-Potential determinationrn=a

n/e0. Thus:

To determine zeta-potential values, we beginb=1−r2n

∑1

n(2r2

n−2r

n+1)

(14)with the Gouy–Chapman–Stern–Grahame modeltaking into account the solution of the Poisson–


due to drug free ions in the aqueous medium,recalling Eq. (5), it is given by:

IA=1

2(1+a)z+2N

0CN

N0

−DN/N

0−1

DN/N01nDD. (19)

5. Theoretical results

From Eq. (17), Eq. (18) and Eq. (19), we haveobtained the zeta-potential variation in functionof the drug (or ionic adsorbate) concentration,where liposomes have been formed. The values of

Fig. 2. b,(nT0

, nT) dependence on number of bilayers, n, for ccf, N0, and vesicle sizes are experimentally accessi-r1=1 and e∞

0=e

0. ble. b, is in turn determined by the external radius

of the vesicle, the lipidic bilayer thicknesses, andthe aqueous interlayer thicknesses, with r1=1Boitzman equation for a sphere with the(Eq. (15)). In the analysis of the model, we sup-Debye–Huckel approximation for low potential.pose two aqueous inter-bilayer distributions andThus, from Eq. (11) and Eq. (12) f-potential maywe have obtained results for both, e∞0#e0 andbe expressed as a function of drug (or ionic adsor-e0∞#0. For quantitative calculations e0=4.23 nmbate) concentration by:corresponding to egg lecitine [21]. To study theinfluence of the different parameters on the zeta-f=

z+e

e

a2

3(1−f )(1−b)N

0

e−faV(Ii+IA)1/2

1+aV(Ii+lA

)1/2 potential values, we have given them the followingvalues for ‘‘f ’’, which is related to the shear-planesituation, 10−5, 10−4, 10−3, and 10−2, for ‘‘1/D’’,0.3, 0.5, 0.7 and 0.9 and finally for z+=1 (a:1,2,3),C1−D

1−NN0

D ln D D, (17)for z+=2 (a:0.5,1,1.5) and for z+=3 (a:0.3,0.7,1).In optimal conditions, both the fitting of experi-mental data of zeta-potential versus diverse adsor-

where f is the ratio between the position of the bate concentrations and the experimental valuesshear plane and the external radius of the liposome of ccfs allow the determination of the aforemen-( f=h/a). V is a constant at temperature 298 K, tioned parameters that can characterize thewith a value V=3.288 when k is in nm−1 and the system studied.ionic strength is in mol l−1. Ii is the ionic strengthdue to free phospholipid molecules in the aqueousmedium, with a concentration equal to the critical 6. Influence of critical concentration of formationconcentration of formation, ccf. The definition of of liposomes (ccf ).ccf is similar to that of the critical micellar concen-tration, cmc, for tensioactive materials. This ccf, The ccf is an important parameter for the char-about 10−6 M [20], influences the electrical proper- acterization of this type of system, since on theties of liposomes, at least in the screening effect, one hand it is closely connected with the thermo-mainly when there is low drug. Therefore, dynamic of lipidic vesicle formation [9], and on

the other it provides the system with an aditionalIi=

ccf

2 Cz+2i +z−2i D, (18) ionic strength. To calculate this additional ionicstrengh, we have employed z+

i=z−

i=1 in Eq. (18).

Figs. 3 and 4 illustrate the zeta-potential depen-where z+i

and z−i

are the valences of the ionicspecies of phospholipid. IA is the ionic strength dence with the adsorbate concentration for diverse


Fig. 3. Variation of zeta-potential of liposomes with the adsorbate concentration in mol/l, for the following ccf values: (a) 10−5 M;(b) 10−6 M; and (c) 10−7 M calculated from Eq. (17) with the parameter values indicated. The aqueous interlayer thickness consideredis e∞

0#e

0.

Fig. 4. Variation of zeta-potential of liposomes with the adsorbate concentration in mol/l, for the following ccf values: (a) 10−5 M;(b) 10−6 M; and (c) 10−7 M calculated from Eq. (7) with the parameter values indicated. The aqueous interlayer thickness consideredis e∞

0#0.

ccf values, with the parameter values indicated. In 7. Influence of N0

valueeach figure, the aqueous interlayer distributionsare also indicated. Observe the great influence of The adsorbate concentration which annuls the

zeta-potential value (N0) is probably the mostccf values on the results obtained for N<N0.Therefore, for N>N0, the influence of ccf values outstanding parameter for the characterization of

the system studied, as it this is connected with theis practically negligible.


electrical characteristics of the vesicles and this enclosed solely to illustrate the great influence ofN0 on zeta-potential values.N0 concentration is analogous to the isoelectrical

point.Figs. 5 and 6 show the zeta-potential dependence

with adsorbate concentration for diverse N0 values 8. Influence of liposome radius (a)with the other parameter values indicated. Notethat N0 values: 2×l0−4 M (in Fig. 5) and For a fixed distribution of the internal bilayer

of a model multilamellar liposome, the size is2.5×l0−4 M (in Fig. 6), lead to excessively highpotential values for the application limits of the determined by the number of bilayers.

Consequently, the distribution of the internalmodel (Debye Huckel’s approximation). They are

Fig. 5. Variation of zeta-potential of liposomes with the adsorbate concentration in mol/l, for the following N0 values: (a)5×10−5 M; (b) 7.5×10−5 M; (c) 10−4 M; and (d) 2×10−4 M calculated from Eq. (17) with the parameter values indicated. Theaqueous interlayer thickness considered is e∞

0#e

0.

Fig. 6. Variation of zeta-potential of liposomes with the adsorbate concentration in mol/l, for the following N0 values: (a)5×10−5 M; (b) 10−4 M; (c) 2×10−4 M; and (d) 2.5×10−4 M calculated from Eq. (17) with the parameter values indicated. Theaqueous interlayer thickness considered is e∞

0#0.


bilayers is closely related to b and to a greater or for two adsorbate concentrations, 10−7 and10−3 M, which give negative and positive zeta-lesser capacity to the hydrosoluble substance

encapsulation. Fig. 7 shows the zeta-potential potential values respectively. The distributionse0∞#e0 and e0∞#0. have been considered. Note thatdependence with the adsorbate concentration for

diverse values of liposome vesicle radius, with the for N>N0 the size influence on zeta-potentialvalues is practically negligible.parameter values indicated there. In this case, the

distribution employed is e0∞#e0. In order to The liposome radius is accessible experimentally.Nonetheless the fitting of experimental values toillustrate in detail these results, Fig. 8 shows the

zeta-potential variation with the lipidic vesicle radii the theoretical results obtained in the model,

Fig. 7. Variation of zeta-potential of liposomes with the adsorbate concentration in mol/l, for the following liposome radius values:(a) 250 nm; (b) 500 nm; (c) 1000 nm; and (d) 2000 nm, calculated from Eq. (17) with the parameter values indicated.

Fig. 8. Variation of zeta-potential of liposomes with the liposome radius values for two adsorbate concentrations, 10−3 mol/l for (a)e∞0#e

0and (d) e∞

0#0 and 10−7 mol/l for (b) e∞

0#e

0and (c) e∞

0#0, calculated from Eq. (17) with the parameter values indicated.


together with experimental determinations of ccf zeta-potential variation in a function of 1/D isillustrated for two adsorbate concentrations,and N0, can provide an estimation of the ‘‘model

liposome’’ size. Moreover, the model allows an 10−7 and 10−3 M, which provide negative andpositive values of the zeta-potential, respectively.estimation of the ‘‘model aqueous interlayer thick-

ness’’ of multilamellar liposomes to be obatined. The distributions e0∞#e0 and e0∞#0 have beenconsidered.Consequently an estimation of the encapsulation

capacity of hydrosoluble substances as possible,when the other parameters (ccf, N0 and a) aredetermined experimentally.

10. Influence of f

As was thought to be the case, the variation of9. Influence of 1/Dthe shear-plane situation ( f ) between 10−5 and10−2 does not provide a significant variation inAs has been previously described, the 1/D

parameter is related to the ratio between total the zeta-potential for the adsorbate concentrationand particle size employed in this work. Fornumber of binding-sites and the adsorbate concen-

tration which annuls the zeta-potential value example, a vesicle with a=1000 nm andf=10−5 (N0=2.5×10−4 M, 1/D=0.9, a=1,(N0). This is a characteristic parameter of the

vesicle-adsorbate system studied and may be of z+=1 and ccf=10−6 M) provides a zeta-potentialof −21.63 mV for a 5×10−5 M adsorbate concen-great use in its characterization. The values tested

of ‘‘1/D’’ correspond to nT>N0 values (Eq. (10)). tration. Another vesicle with the same radius andf=10−2, in the same conditions as the precedingFig. 9 shows the zeta-potential dependence with

the adsorbate concentration for diverse 1/D values case gives a zeta-potential of −21.42 mV. In bothcases the distribution employed is e0∞#e0. Thiswith the conditions indicated. As the figure shows,

1/D significantly influences the zeta-potential happens in all adsorbate concentrations studied:N>N0 and N<N0.results for both N<N0 and N>N0. In Fig. 10, the

Fig. 9. Variation of zeta-potential of liposomes with the adsorbate concentration in mol/l, for the following 1/D values, (a) 0.3, (b)0.5, (c) 0.7 and (d) 0.9, calculated from Eq. (17) with the parameter values indicated. The aqueous interlayer thickness consideredis e∞

0~0.


Fig. 10. Variation of zeta-potential of liposomes with 1/D values for two adsorbate concentrations, 10−3 M for (a) e0∞#e0 and (d)e0∞#0 and 10−7 mol/l for (b) e0∞#e0 and (c) e0∞#0, calculated from Eq. (17) with the parameter values indicated.

11. Influence of z+ and a N0 with the indicated parameter values. For eachz+ value, a variation provides only light differencesin zeta-potential values obtained for N<N0 adsor-The cationic valence of adsorbate, z+, and the

ratio between the mean valences of the anionic bate concentrations. For example, vesicles with thesize and other conditions indicated in Fig. 11, forand cationic species (a) are closely connected to

the disociation degree of adsorbate molecules 5×10−6 M adsorbate concentration, give a zeta-potential of −15.97 mV for z+=1, a=1 and awhere the pH has a notable influence. Fig. 11

shows the variation of zeta-potential with adsor- zeta-potential of −15.93 mV for z+=1, a=3.Moreover, at the same conditions, zeta-potential=bate concentration for diverse z+ values and fixed

Fig. 11. Variation of zeta-potential of liposomes with the adsorbate concentration in mol/l, for the following z+ values, (a) z+=1,(b) z+=2 and (c) z+=3 calculated from Eq. (17) with the parameter values indicated. The aqueous interlayer thickness consideredis e0∞#0.


−44.90 mV for z+=3 and a=0.3, and zeta- Referencespotential=−43.90 mV for z+=3 and a=1N=10−5 M. [1] G. Gregoriadis (Ed.), Liposomes as Drug Carriers, Recent

Trends and Progress, Wiley and Sons Ltd, Chichester,Analogously, the a variation provides only small1988.differences in zeta-potential values obtained for

[2] G. Gregoriadis, B. McCormack, G. Poste (Eds.), TargetingN>N0 adsorbate concentrations. For example, forof Drugs 4. NATO ASI Series, Plenum Press, New York,an adsorbate concentration of 10−3 M, vesicles1993.

with size and other parameters equal to those of [3] A. Bejan, G. Turcu, Rom. J. Intern. Med. 33 (1995) 141.the preceding case, give a zeta-potential of 3.59 mV [4] D.D. Lasic, B. Ceh, M.C. Stuart, L. Guo, P.M. Frederik,when z+=1 and a=1 and a zeta-potential of Y. Barenholz, Biochim. Biophys. Acta 1239 (1995) 145.

[5] M. Diaz, M.J. Martos, E. Espana, M. Cervera, A.O. Vila,2.51 mV when z+=1 and a=3. Moreover, forA. Navea, F. Molina, F.J. Romero, Documentaz+=3 and a=0.3, zeta-potential=4.24 mV, andOphthalmologica 82 (1992) 297.when z+=3 and a=1, zeta-potential=3.34 mV.

[6 ] L. Wojtczak, M. Nalecz, in: G. Benga (Ed.), Structure andProperties of Cell Membrane, Vol. II, CRC Press, BocaRaton, Florida, 1985, p. 215.

12. Model optimization [7] J.N. Israelachvili, Intermolecular and Surface Force,Academic Press, New York, 1985.

[8] G. Gregoriadis, Interaction of liposomes with the biologi-For an accurate application of the model, it iscal milieu, in: G. Gregoriadis (Ed.), Liposomes as Drugadvisable to obtain experimental values of at leastCarriers, Wiley and Sons, New York, 1988, pp. 3–114.ccf and N0 with the maximum precision possible

[9] E.D. Schuckin, A.V. Pertsov, A.V. Amelina, Quimicabecause they exert an important influence on theColoidal, Ed Mir, Moscow, 1988.

results. Moreover, the experimental determination [10] S. Ohki, R. Sauve, Biochim. Biophis. Acta 298 (1978) 377.of the liposome radius allows us to extract more [11] S.G.A. McLaughiin, G. Szabo, G. Eisenman, J. Gen.information from the model in order to enhance Physiol. 58 (1971) 667.

[12] L. Chung, G. Kaloyanides, R. McDaniel, A. McLaughlin,the characterization of the adsorbate–liposomeS. McLaughlin, Biochemistry 24 (1985) 442.system. For greater refinement in the application

[13] C. Colome, M.A. Alsina, M.A. Busquets, I. Haro, F. Reig,of the model, it is necessary to take into accountInt. J. Pharm. 90 (1993) 59.that the liposome characteristics (size, aqueous

[14] C. Mestres, M.A. Alsina, M.A. Busquets, I. Haro, F. Reig,interlayer thickness, etc) are different when they Langmuir 10 (1994) 767.are formed in different adsorbate concentrations. [15] P. Schlieper, Biochem. Pharmacol. 34 (1985) 708.Probably the greatest differences in the characteris- [16 ] J. Seelig, P. Ganz, Biochemistry 30 (1991) 9354.

[17] H.D. Bauerle, J. Seelig, Biochemistry 30 (1991) 7203.tics of liposomes formed will appear in those[18] H. Matsumura, K. Furusawa, Adv. Colloid Interface Sci.formed in the absence of adsorbate. These differ-

30 (1989) 71.ences can be negligible or significant depending on[19] T.W. Healy, L.R. White, Adv. Colloid Interface Sci. 9the adsorbate–liposome system. Consequently, we

(1978) 303.must to determine the sizes and ccfs of liposomes [20] A.O. Vila, J. Almerich, C. Llacer, M.J. Martos, F.J.formed in each adsorbate concentration. This will Molina, An. Quim. 87 (1991) 332.be important when the discrepancy between theo- [21] J. De Gier, J.G. Mandersloot, L.L.M. Van Deenen,

Biochim. Biophys. Acta 150 (1968) 666.retical and experimental values are analyzed.

interaction of ionic compounds with multilamellar liposomes. an electrokinetic model

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