6252
J . Phys. Chem. 1987, 91, 6252-6251
Ionotroplc Lateral Phase Separatlon in Mixed Lipid Membranes. A Theoretical Study Antonio Raudino,* Felice Zuccarello, and Giuseppe Buemi Dipartimento di Scienze Chimiche, Universitii di Catania, Male A . Doria 8-951 25, Catania, Italy (Received: May 7, 1987)
A statistical model has been developed in order to investigate the role of small ions ( H', Ca2+,etc.) in triggering lateral phase separation of lipid membrane components. The studied systems are equimolar mixtures of charged and neutral lipids. The total energy of the system has been partitioned into different contributions: (a) mixing entropy; (b) van der Waals interactions between the lipid hydrocarbon tails; (c) solvent-screened electrostatic repulsion between the lipid charged head groups; (d) adsorbed ions-membrane binding energy; (e) electrostatic repulsion between the adsorbed ions. Other energy contributions which do not depend upon the lipid distribution have been disregarded. The total energy has been expressed as a function of a set of variational parameters: size (D), composition ( H ) of lipid microdomains, and mole fraction (e) of adsorbed ions. The total energy has been minimized with respect to these parameters and a set of coupled nonlinear algebraic equations was obtained, from which the variational parameters have been calculated in a self-consistent way. Main results are (1) the size of lipid microdomains increases with concentration of adsorbed ions, the divalent ions being more effective with respect to the monovalent ones; (2) microdomains formation leads to an increasing of the adsorbed ions concentration with respect to a random mixture of charged and neutral lipid molecules; (3) the ionic strength lowers the number of specifically adsorbed ions, consequently reducing also the size of lipid aggregates; (4) rising temperature reduces the extent of the lipid lateral phase separation. A comparison between these predictions and the available experimental findings confirms most of the present results. Possible improvements of the model are also discussed.
Introduction The possibility of lateral segregation of specific lipid components of a membrane is a new interesting field of investigation which allows a better understanding of membrane-modulated phenomena. In fact, several properties such as membrane fluidity, permeability, tendency to undergo fusion, and reactivity of membrane proteins are markedly affected by "local" lipid composition. Particularly dramatic are the segregation effects in mixed lipid systems containing charged phospholipids ( e g , phosphatidylserine, phosphatidic acid) which usually are triggered by protons,"*5 divalent cations (Ca2+, Mg2+),6-13and protein^.'^-'^ Several experimental techniques (NMR,9J7 pin^.^ and fluorescencelC-1Z,16.18,19 probes, Raman spectroscopy,z0 differential
scanning calorimetry,'0J'J~22 and freeze electron m i c r o ~ c o p y ~ ~ - ~ ~ ) have been proposed to study such segregation phenomena in lipid membranes. Little attention has been paid in developing theoretical models in order to gain a better picture of the leading forces involved in the process. In a previous paperz6one of us developed a variational approach which relates the size and composition of lipid microdomains to the molecular properties of the membrane and of the surrounding electrolyte solution. In this paper we will extend such an analysis taking into account the effect of specifically adsorbed ions in inducing lateral phase separation in mixed lipid membranes. Moreover, we will try to rationalize the markedly different effects of mono- and divalent cations; finally, the role of lipid segregation upon the concentration of adsorbed charged species will be discussed.
Theory In a previous paper26the space variation of the charged lipid concentration over the membrane plane has been described by the simple variational function
(1) Karnovsky, M. J.; Kleinfeld, A. M.; Hoover, R. L.; Klausner, R. D. J . Cell Biol. 1982, 94, 1. (2) Grant, C. W. M. In Membrane Fluidity in Biology; Aloia, R. C., Ed.; Academic: New York, 1983. (3) Klausner, R. D.; Kleinfeld, A. M. Recept. Ligands Intercell. Commun. 1984, 3, 23. (4) Tokutomi, S.; Eguchi, G.; Ohnishi, S. I. Biochim. Biophys. Acta 1979, 551, 78. (5) Tokutomi, S.; Ohki, K.; Ohnishi, S. I. Biochim. Biophys. Acta 1980, 596, 192. (6) Papahadjopoulos, D.; Vail, W. J.; Pangborn, W. A.; Poste, G. Biochim. Biophys. Acta 1976, 448, 265. (7) Tokutomi, S.; Lew, R.; Ohnishi, S. I. Biochim. Biophys. Acta 1981,
CB(x,Y) = TB
+ (H/2)(cos kx + cos hu)
(1)
where XBis the mean concentration (mole fraction) of the charged lipid, X and Yare the spatial coordinates over the membrane plane, while H a n d h are parameters to be determined. They contain the essential information about the extent of lipid segregation. In fact, h is related to the mean size D of lipid microdomains size (1 = 27r/D), while H measures the excess of one kind of lipid molecule inside a microdomain. The free energy of the membrane has been partitioned into three contributions: (a) electrostatic interactions between the lipid polar head groups; (b) short-range
643, 276. (8) Berclaz, T.; McConnell, H.M. Biochemistry 1981, 20, 6635. (9) Duzgunes, N.; Paiement, J.; Freeman, K.; Lopez, L.; Wilschut, J.; Papahadjopoulos, D. Biophys. J . 1983,41, 30. Tilcock, C. P. S.; Bally, M. B.; Farren, S. B.; Cullis, P. R.; Gruner, S. M. Biochemistry 1984, 23, 2696. (10) Graham, I.; Gagne, J.; Silvius, J. R. Biochemistry 1985, 24, 7123. (11) Leventis, R.; Gagne, J.; Fuller, N.; Rand, R. P.; Silvius, J. R. Biochemistry 1986, 25, 6978. (12) Parsassassi, T.; DeFelip, E.; Lepore, F.; Conti, F. Cell. Mol. Biol. 1986, 32, 261. (1 3) Tamura-Lis, W.; Rebex, E. J.; Cunningham, B. A,; Collins, J. M.; Lis, L. J . Chem. Phys. Lipids 1986, 39, 119. (14) Bernard, E.; Fancon, J. F.; Duforcq, J. Biochim. Biophys. Acta 1982, 688, 152. (15) Abrey, J. R.; Owicki, J. C. Prog. Protein-Lipid Interact. 1985, I , 1. (16) Jones, M. E.; Lentz, B. R. Biochemistry 1986, 25, 567. (17) Tilcock, C. P. S.; Cullis, P. R. Biochim. Biophys. Acta 1981,641, 189. (18) Galla, H. J.; Hartman, W. Chem. Phys. Lipids 1980, 27, 199.
(19) Hresko, R. C.; Barenholz, Y.; Thompson, T. E. Biophys. J. 1985.47, 116. (20) Hark, S. K.; Ho, J. T. Biochim. Biophys. Acta 1980, 601, 54. (21) Barenholz, Y.; Freire, E.; Thompson, T. E.; Correa-Freire, M. C.; Bach, D.; Miller, I. R. Biochemistry 1983, 22, 3497. (22) Lee, A. G. In Membrane Fluidity in Biology; Aloia, R. C . , Ed.; Academic: New York, 1983. (23) Van Dijck, P. W. M.; De Kruijff, B.; VerMeij, A. J.; Van Deenen, L. L. M.; De Gier, J. Biochim. Biophys. Acta 1978, 512, 84. (24) Sakmann, E. Ber. Bunsen-Ges. Phys. Chem. 1978, 82, 891. (25) Sakmann, E.; Ruppel, D.; Gebhan, C. In Liquid Crystals in One- and
Two-Dimensional Order; Helfrich, W., Heppke, G., Eds.; Springer: Berlin, 1980. (26) Raudino, A,, submitted for publication.
0022-3654187 12091-6252S01.5OlO 1
0 1987 American Chemical Society
The Journal of Physical Chemistry, Vol. 91, No. 24, 1987
Phase Separation in Mixed Lipid Membranes interactions between the hydrocarbon chains; (c) entropy effects. Each of them has been expressed as a function of H and X variational parameters and, eventually, the total free energy has been minimized with respect to these parameters. Since the total free energy shows a minimum only for particular values of some external parameters (charge density, salt concentration, short-range interactions, etc.), it is possible to determine the physical conditions leading to clusters formation. Let us extend this model to a lipid membrane interacting with an electrolyte solution containing two different kinds of charged species: (i) ions (e.g., H+, Ca2+)which can be tightly bound to the ionic heads of charged phospholipids (usually the PO4- group), and (ii) ions (e.g., Na', ) 'K which experience only the solventscreened electrostatic potential of the charged lipids. In physiological conditions the concentration of the first kind of ions is much lower (- 10" M) than that of the second one (-10-1).z7 The total partition function of the system can be expressed as the product of the membrane and electrolyte solution partition functions:
ZTOT= Z M Z S The Z s can be written as
energy of the membrane AUeI(H,X)is the sum of lipid-lipid and lipid-adsorbed ion interaction
AUeI(H,X) = (1 - v8)AUe,*(H,X)
considered later. Consequently, the free energy of the lipic membrane can be written as FM = (1 - v6')AUe1*(H,h) AHsR(H,X) - TAS(H,X) (9)
+
The explicit expressions for AUeI*(H,X),AUsR(H,X),and AS(H,X) have been obtained in a previous paper;z6 they are
+
AUeI*(H,X)= UeI(0)
(2)
=Nk(
where the term in brackets refers only to ions which can be tightly bound on the membrane surface. In particular, ni is the number of bound ions whose binding energy is eBi, (ZB)iis their partition function, and gi is the degeneracy factor. A4 is the number of binding sites having different energy (if all the sites are equivalent M = l), Z Fis the partition function of free ion, and N is the total. (bound and unbound) ions. ZREM refers to the other solvent molecules (water and alkaline ions which are not tightly bound to the lipid molecules) whose energy can be considered constant during the segregation process. Neglecting the constant term ZREM, we can approximate eq 3 by
H
M
ZS = ngj(zB)?2FN-Tnf i
(gB)(ZB)nZFN-n
(4)
where n = Cf"ni. In eq 4 we replaced the local electrostatic potential acting on a generic site by its mean value. This is a good approximation. In fact, the main contribution to the ion-membrane interaction comes from specific binding forces between the adsorbed cation and the phosphate (or carboxylic) group of the lipid end, the solvent-screened electrostatic potential of the surrounding lipid molecules having a smaller effect. The evaluation of the total partition function allows us to calculate the free energy of the system through the well-known relationship2*
FTOT = -kBT log ZTOT (5) where kBis the Boltzmann constant. Inserting eq 2, 3, and 4 into eq 5 we obtain FToT = FM - kBT (log (gB) n log ( Z B ) ( N - n) log z ) (6) where FM is the free energy of the lipid membrane perturbed by the bound ions. In a previous paper26we shown that FM can be expressed as a sum of electrostatic (AUel),short-range (AUSR) and entropic (-TAS)contributions. Other energies (e.g., hydrophobic) which do not depend upon the lipid distribution over the membrane surface are unessential to the present analysis. While short-range forces and mixing entropy are not directly affected on the number of adsorbed ions, the electrostatic energy does. Defining B as 6 = n/NB (7) n being the number of adsorbed ions and NB that of charged lipids ( N B= NXB) and letting AUeI*(H,X)the electrostatic repulsion energy between the lipid polar head groups, the total Coulomb
+
(8)
v being the ion charge. The ion-membrane and ion-ion energies are accounted for in the (2,) partition function and will be
(3)
M
6253
+
2(iOg 2)3 7r(2 log 2)
+
)
KB
H>>O
(1OC)
where Uel(0),USR(O), and AS(0) are the electrostatic, short-range, and entropy contributions calculated for a random distribution of charged and neutral lipids over the membrane surface, while the remaining terms describe the effect of microdomains formation on the energy contributions. Q is the net charge of the ionic heads, K is the Debye kappa, e is the dielectric constant of the lipid membrane-water interface region, and a is the mean interlipid distance. The short-range energy parameter W is defined as W = '/2(WAA WBB - 2 WAB) where W,, WBB, and WAB are the van der Waals energies between the hydrocarbon chains of different lipid molecules. The calculation of the other terms appearing in the right-hand side of eq 6 can be done in a quite simple way. In fact, in our mean-field approximation, (gB) is simply the number of ways to arrange n ions into NB equivalent sites; that is (gB) = N B ! / ( N B- n)!n! Making use of eq 7 and Stirling's approximation, we obtain after simple algebraz9 log (gB) = -NB[e log 8 + (1 - 8) log (1 - e)] (11)
+
The other term we need to calculate the total free energy is the partition function ( Z B )of adsorbed ion. In the present mean-field approximation, it is simply connected to the mean energy of ion-membrane interaction by the relationship: (2,) = exp(-( UB) /kB r ) * ( U B )can be partitioned into two contributions: the first one, say eB, represents the binding energy of the ion with a lipid charged end (or with two charged ends, when a bridge is formed between divalent cation and lipids); the second term describes the solvent-screened electrostatic interactions with the other more distant ionic heads. This latter electrostatic energy in turn can be written as a sum of ion-membrane electrostatic energy, -v AU,I*(H,X)/NB, and ion-ion repulsion, +vzO AUeI*(H,X)/NB.On the basis of eq loa, AUeI*(H,X)/NBis the electrostatic energy per unity charge. The implicit approximation in the previous formulas is the assumption that the electrostatic repulsion between the charged lipid head groups and that between the adsorbed ions can be described by means of the same functional relationship. In other words, the model describes the lipid ionic heads as point charges embedded in a dielectric medium which can be neutralized by the adsorbed ions. This approximation can be easily removed by considering different screening effects between the lipid charged ends and between the adsorbed ions. Both these approximations will be discussed in the Results section. Within the former simplest
~~
(27) Lehninger, A. L. Biochemistry; Worth: New York, 1975.
(28) Landau, L. D.; Lifsits, E. M. Siatisiicnl Physics: Pergamon: New
York, 1975.
(29) Prigogine, I. The Molecular Theory of Soluiions; North Holland: Amsterdam, 1957. (30) Debye, P.; Hiickel, E. Phys. Z . 1923, 24, 305.
6254 The J o w n a l of Physical Chemistry, Vol. 91, No. 24, 1987
Raudino et al. differentiate eq 6 only with respect to n (n is related to 0 through eq 7) and the nondimensional parameter Xu. Putting H = we obtain after simple manipulations
I ~FTOT -(11 N axa NB
Figure 1. Total free energy (arbitrary units) vs Hand Xu nondimensional parameters. Full line refers to a lipid membrane without adsorbed ions (0 = 0) and the discontinuous line to the same membrane with an arbitrary amount of tight bound ions (1 > 0 > 0).
approximation, the partition function of the adsorbed ion, (ZB), can be written as
In the case of monovalent adsorbed ions, the binding energy tB is a constant. However, when we consider divalent cations, cB may be a function of the surrounding concentration of lipid molecules and/or adsorbed ions. The explicit form of such a function will be given later (eq 19). Now we simply assume that it depends upon 6, H , and A. The last term we need to calculate the total free energy (eq 6) is the partition function ZFof the ion in the bulk of solution. Standard thermodynamics gives
-kBT log ZF = + kBT log y c (13) where po is the chemical potential of the ion in the bulk extrapolated at zero ionic strength. C is the ion concentration in the bulk and y is its activity coefficient. In the Debye-Hiickel theory y is given by I
(14)
It must be pointed out that both K~ and eo appearing in the right-hand side of eq 14 refer to the bulk of solution, while K and e appearing in the previous formulas indicate the Debye kappa and dielectric constant evaluated in the lipid polar head groups region. These latter values strongly depend upon the adsorption site and will be discussed in more detail in the following section. Inserting eq 10 through 13 into eq 9, we obtain a relationship between the total free energy of the system (membrane + ions) and the variational parameters 0, H , and A. In Figure 1 we report FTOT/Nas a function of H and A calculated for two different values of 0. The curves are qualitative and have been drawn according to the analytical form of the different energy contributions. Full lines refer to a mixed lipid membrane without adsorbed ions (0 = 0), discontinuous lines refer to the same membrane with adsorbed ions (1 1 0 > 0). As we can see, stable configurations can be attained only when the parameter H i s 0 or H,,,. When H = 0 we have a random lipid mixture, while for a equimolar mixture of charged when H = H,,, (H,,,,, is and neutral lipidsz6) the system shows a lateral phase separation. Moreover, the ion adsorption shifts the absolute minimum toward smaller X values (larger domains: X = 27~/D). In order to obtain the size of microdomains and the number of adsorbed ions, we must differentiate the total free energy (eq 6) with respect to the variational parameters 0, H , and X and equate these derivatives to zero. Since stable configurations are we may defined only by two H values ( H = 0 and H =
- V O ) 2 aAuel*(k) + - 1 ~ A U S R (-~ ) axa T NB a l a
ahso)
NB
axa
acB(o,x) o-----= axa
0 (15b)
where AU,,*(X), AUsR(X), and AS@) are defined by eq 10. The last task is the evaluation of tB(O,A), Le., the binding energy of the adsorbed ion with the charged lipid heads. When we consider a monovalent ion such as H', the binding energy is independent of the surrounding lipids distribution, apart from the solventscreened electrostatic potential described by AUe1(HJ)(see eq 8). However, when we are dealing with divalent cations (e.g., Ca2+) the situation is different because these ions can form bridges between two adjacent lipid heads. A simple way to calculate eB(O,X) is the folowing. Let -aAUB (a being a normalization constant) be the binding energy of a divalent ion with two lipid molecules, averaged over all the membrane plane binding energy; it can be written as
BRIDGE
- ~ A U B'/z
CI CJ P , " " P ~
(16)
where plmc is the probability of having the ith site occupied by a divalent cation and p y is the probability of having in the j t h adjacent site a charged lipid molecule on the head of which no other cations are standing. Without loss of generality, we can assume that pioccand p y follow the distribution of charged lipids. In particular, the probability ploccwill be directly proportional to the mean concentration of adsorbed ions 0 and to the concentration of charged lipids in the ith site:
pimc ocB(xt,K) (17a) In a similar way, the probability p y will be directly proportional to 1 - 0 and directly proportional to the concentration of charged lipids in the j t h site
p? 0: (1 - O)CB(XJ,Y,) (17b) the proportionality coefficients in eq 17 can be englobed in the normalization constant a. Inserting eq 1 and 17 into eq 16, replacing the sums by integrals and following the same procedure adopted in a previous paper26 to calculate the short-range energy in a mixed membrane with a inhomogeneous lipid distribution, we find
+
Jo(ha) being a Bessel function3' (Jo(Xa) 1 - X2a2/4) 0(X4d)). The normalization constant a can be determined by calculating UBRiDGE for a membrane built up only by charged lipids = 1, H = 0) fully neutralized by adsorbed divalent cations (0 = From eq 18 we have UBRIDG~B=18=~/2 = -(+)A&. If we identify AUB with the binding energy at 0 = 'Iz and = 1, it follows that CY = 8. The bridge energy given by eq 18 shows a correct trend. In fact, when 0 = 0 the bridge energy is zero, then it grows with 0, reaching a maximum at 0 = (fully neutralized membrane charges) and after decreasing for 0 > ' I 2because the number of bridges must decrease in order to accommodate more ions (with single bonds when 0 > on the membrane surface. The mean bridge energy per adsorbed ion can be simply calculated by dividing the total bridge energy by the number of adsorbed ions n ( n = OXBN);then
(xB
xB
tg
p'o
( ' 6 )+
= 4(1 - O)AUaB 1 + -Jo(Xa)
p'o
(19)
contains all those energy contributions, such as the solvation
The Journal of Physical Chemistry, Vol. 91, No. 24, 1987 6255
Phase Separation in Mixed Lipid Membranes energy of adsorbed ions, which do not depend appreciably on the lipid distribution within the membrane. Inserting now eq 19 into = H = ’Iz and rearranging, we obtain the eq 15 and putting searched set of equations for 0 and Xu. In the case of monovalent ions they are
xB
- 01-0
- yCk(T)
exp[ ~ Xu =
2
1
( - O)(A(K) 1 - B ( K ) X ~ U ~ ) (20a)
2AST B( W) - (1 - e)’B(K)
@Ob)
where y has been defined by eq 14, C is the bulk concentration of monovalent ion, k( T ) the binding constant defined as k( T ) = exp((eB - h)/kBT) while the terms A ( K )and B(K),which describe the solvent-screened electrostatic interactions between the charged lipid head groups, are defined as
The short-range forces parameter B( W) and the mixing entropy variation As are B(W) (?r/l6)Wand hs kB(2 log 2)3/2(r(2 log 2)):’/2. The corresponding equations for divalent ions are
+
Xu =
2AST B(W) - (1 - 20)’B(K) + Xe(1
- 0)AUB
Results and Discussion The set of nonlinear algebraic equations (20) and (22) has been solved numericallly in a self-consistent procedure by a computer program. Two different approximations were considered: the “solvated heads” model assumes the charged lipid ends embedded into the electrolyte solution, while the “compact layer” model assumes the electrolyte solution in contact with the membrane surface but no water molecules are allowed to stay between the ionic lipid ends. Input parameters were as follows: interlipid distance 10 A,35 temperature 25 “C (same calculations with different temperatures were also carried out), and dielectric constant of the lipid membrane-water interface region 30.36-38 The binding constant of H+ with the ionic head of phosphatidylserine (one of the most important cellular lipids), obtained by averaging the values reported in the l i t e r a t ~ r e ,was ~ , ~ set ~ equal to 400 M-’. Other parameters such as ionic strength and concentration of charged species which can tightly bind to the lipid ends were considered as variables. The bridge energy AUB of divalent cations with the membrane was assumed to be an adjustable parameters because the experimental values of binding constant span over a too large ( 1-105 M-l). Moreover, the experimental binding constants have been obtained assuming a mass-action model which is a drastic approximation in such cooperative systems. Also the short-range forces parameter W = 1/2( W, + WBB - 2w.B) was considered as an adjustable coefficient. It mainly depends on the lengths of the hydrocarbon chains and on the number of C-C double bonds, as confirmed by some experimental evidence^.^'-^^ The term po - wfo appearing in eq 22a takes into account the variation of the solvation energy of the adsorbed ion on going from the bulk to the membrane-water interface. It may be calculated by the Born equations1
(22b)
Equations 20 and 22 are two coupled nonlinear algebraic equations which can be solved numerically yielding 0 and X. All the previous formulas have been obtained from a model based on the assumption that the lipid charged ends are embedded in the electrolyte solution in contact with the lipid membrane. This is a good model for ionic glycolipids, such as ganglioside^,^^ where the charged and hydrophilic moiety deeply protrudes into the surrounding aqueous medium. The model fails in describing close-packed molecules, such as phospholipids, where the bulky polar head groups are in contact, preventing water or salt molecules to accommodate themselves between the lipid ends. In this case a better model should take into account the presence of a local ionic strength at the membrane-water interface region, different from the bulk one, as suggested by some a ~ t h o r s . ~Mathe~,~~ matically speaking, this latter model does not require dramatic changes in the previous formulas, the only modification taking ) ( u = 1 or 2) appearing in the place in the (1 - u O ) ~ B ( Kterm right-hand side of eq 20b and 22b. It must be replaced by B ( K , ~ ) - 2dB(K) U % ~ B ( KThe ) . physical meaning of this equation is a different description of the electrostatic interactions between ) ) respect to that between the adsorbed the lipid ends ( B ( K , ~with ions and the membrane ( B ( K ) ) .The B ( K ~term ~ ) can be formally added to B( W) (see eq 20b and 22b) yielding B( W? = E( W) B(K,,). The new parameter W’has the same analytical form of u? ‘ / Z ( W ~4-A W’BB- 2wLB); the only difference is that WIij contains both the electrostatic and short-range energies of the ij couple. Both these models will be investigated in the following section.
+
+
(31) Gradshteyn, I. S.;Ryzhik, I. M. Tables of Integrals, Series and Products; Academic: New York, 1965. (32) Rapport, M. M.; Gorio, A. Gangliosides in Neurological and Neuromuscular Function, Deuelopment and Repair; Raven: New York, 198 1. (33) Manning, G. S.Q.Rev. Biophys. 1978, 11, 179. (34) Zimm, B. H.; Le Bret, M. J . Biomol. Struct. Dyn. 1983, I , 461.
b being the adsorbed ion radius and elm the dielectric constant of the interface region where the ion is bound. The numerical values of po - p’o crucially depend on the region of binding. If the ion can penetrate in the polar head groups region, the local dielectric constant will be different from the water’s one (eloc N 3036-38),while if the ions are in the aqueous phase over the cw and membrane plane (compact layer model) we have clot then po - pfo N 0. Within this set of parameters, we were able to calculate 0 (number of adsorbed ions/number of charged lipids) and D (mean size of lipid microdomains). These results are shown in Figures 2a,b and 3, where we report 0 and D as a function of the concentration logarithm of added ions. The curves were calculated at different ionic strengths: 0.05, 0.10, and 0.50 M. The curves (35) Mason, J. T.; Huang, C. Ann. N.Y. Acad. Sci. 1978, 308, 29. (36) Thomas, J. K. Chem. Rev. 1980, 80, 283. (37) Mukerjee, P.; Ramachandran, C.; Pyter, R. A. J . Phys. Chem. 1982, 86, 3189. (38) Lessard, J. G.;Fragata, M. J . Phys. Chem. 1986, 90, 811. (39) Neuhaus, F. C.; Korkes, S. Biochem. Prep. 1958, 6, 75. (40) Newton, C.; Pangborn, W.; Nir, S.; Papahadjopoulos, D. Biochim. Biophys. Acta 1978, 506, 281. (41) Nir, S.; Newton, C.; Papahadjopoulos, D. Bioelectrochem. Bioenerg. 1978, 5, 116. (42) Portis, A,; Newton, C.; Pangborn, W.; Papahadjopoulos, D. Biochemistry 1979, 18, 780. (43) McLaughlin, S.; Mulrine, N.; Gresalfi, T.; Vaio, G.; McLaughlin, A. J . Gen. Physiol. 1981, 77, 445. (44) Ohki, S.; Kurland, R. Biochim. Biophys. Acta 1981,645, 170. (45) Ohki, S.;Duzgunes, N.; Leonards, K. Biochemistry 1982,21, 2127. (46) Nir, S.J . Colloid Interface Sci. 1984, 102, 313. (47) VanDijck, P. W. M.; Kaper, A. J.; Oonk, H. J.; DeGier, J. Biochim. Biophys. Acta 1977, 470, 58. (48) Luna, E. J.; McConnel, H. M. Biochim. Biophys. Acta 1978, 509, 462. (49) Chidichimo, G.; Golemme, A,; Doane, J. W.; Westerman, P. W. J . Chem. Phys. 1985,82, 536. (50) Chidichimo, G.; Golemme, A.; Doane, J. W. J . Chem. Phys. 1985, 82, 4369. (51) Warshel, A.; Russel, S. T. Q.Reu. Biophys. 1984, 17, 283.
The Journal of Physical Chemistry, Vol. 91, No. 24, 1987
6256
B
100
1
b
I 3
2
5
4
s
'
Lrl%
1
2
3
'
4
Figure 2. (a,b) Monovalent ions. Number of adsorbed ions/number of charged lipids 0 (left) and size D (A) of lipid microaggregates (right) vs logarithm of the bulk ion concentration (M). Curves 1, 2, and 3 have been calculated at 0.50, 0.10, and 0.05 M ionic strengths, respectively. Figure 2a has been calculated assuming the lipid charged heads fully embedded onto the electrolyte solution and Figure 2b assuming a compact lipid membrane model (no solvent molecules between the lipid ends).
d 3
4
5
6
i s , y
