The hydrophobic acyl-chain effect in the lipid domains appearancethrough phospholipid bilayers

Liviu Movileanua,* , Dumitru Popescub, Maria Luiza Flontac

aUniversity of Missouri-Kansas City, Division of Cell Biology and Biophysics, School of Biological Sciences, 405 Biological Sciences Building,5100 Rockhill Road, Kansas City, Missouri 64110-2499, USA.

bMembrane Biophysics Laboratory, Institute of Biology, Splaiul Independentei 296, P.O. Box 56-53, Bucharest R-79651, Romania.cBiophysical Laboratory, University of Bucharest, Faculty of Biology, Splaiul Independentei 91-95, Bucharest R-76201, Romania.

Received 2 July 1997; accepted 3 February 1998

Abstract

An intermolecular interaction model for selective association processes of double-chain phospholipids in bilayer lipidmembranes has been proposed, analysed and solved numerically. A large variety of binary mixtures of asymmetrical dou-ble-chain phospholipids with the cross-sectional areas of the polar headgroupsa1� 40 A2 (the first component) anda2� 60 A2

(the second component) have been investigated. Changing the hydrophobic acyl-chain lengths of both mixture components, wefound in all cases that the self-association probability (the association of like-pairs of phospholipids) of the first component inparallel alignment of the electric dipole moments of the polar headgroups is higher than the cross-association probability (theassociation of cross-pairs of phospholipids) and the self-association probability of the second component. This result is in goodagreement with the experimental evidence that where the cross-sectional area of the polar headgroups matches the hydrocarbonchain-packing cross-sectional area (a ù 2S ù 40 A2), lipids possess a high tendency to aggregate into well packed bilayerstructures with the acyl-chains oriented perpendicularly to the bilayer plane. Our theoretical data confirm that the double-chainphospholipids may associate themselves into anti-parallel alignment of the polar headgroups (P

022) as well. The hydrophobic

acyl-chain effect of phospholipids may modulate the distribution of lipid domains within bilayers that have a large variety offunctional roles in cellular metabolism.q 1998 Elsevier Science B.V. All rights reserved.

Keywords:Bilayer lipid membrane; Lipid domains; Phospholipid; Hydrophobic acyl-chain effect; Computer simulation

1. Introduction

Phospholipids are of fundamental importance sincethey are the main constituents of biological mem-branes. The phospholipid molecules have an amphi-philic character and, when hydrated, self-assembleinto a diversity of structural phases [1, 2]. Recently,the typical sequence of ordered phases for binary

amphiphilic systems has been modelled using a Ginz-burg–Landau model describing the concentration andorientation of the amphiphilic molecules [3]. Studiesregarding the structural polymorphism observed inlipid–water systems help us to understand the majorrole played by intermolecular forces in the phospho-lipid bilayers that modulates the structure and func-tion of integral proteins [4–6].

Aggregation of membrane proteins and aggregationof gel-phase lipids during lateral phase separation hasbeen modelled as cluster–cluster association on a

Journal of Molecular Structure (Theochem) 434 (1998) 213–227

0166-1280/98/$19.00q 1998 Elsevier Science B.V. All rights reserved.PII S0166-1280(98)00112-2

* Corresponding author. Tel.: 001 816-235-2500; fax: 001 816-235-1503; e-mail: mliviu@cctr.umkc.edu

squared lattice [7]. Since natural membranes aremulti-component systems containing a variety oflipid species, especially double-chain phospholipids,an understanding of the mixing behaviour of lipidcomponents is important for the explanation of differ-ent molecular processes in biomembranes. Forinstance, the surface charge of micelles and mem-branes might be strongly influenced by the lipid pack-ing density as well as the mixing state of the lipidspecies from biomembranes [8].

For the above reasons, it is natural to think aboutthe usefulness of theoretical studies regarding lipid–lipid interactions and their consequences for aggrega-tion phenomena in bilayer lipid membranes. Huangand Feigenson (1993) and Huang et al. (1993) haveinvestigated the non-ideal mixing of binary mixturescontaining phosphatidylcholine (PC) and phosphati-dylserine (PS) [9, 10]. In this computer simulationmodel, the excess energy of mixture contains oneadjustable term that includes all non-ideal interactions.They found that electrostatic interactions greatly influ-ence the cluster size and phase composition in the two-phase region. The hydrophobic effects of the phospho-lipid acyl-chains on the phase equilibria and the localstructure in binary lipid bilayers have been investi-gated using a molecular interaction model [11–14].Jorgensen et al. (1993) have shown that mismatch inthe hydrophobic lengths leads to an increasingly localordering while the chain length difference is increased[12]. These theoretical data, together with the experi-mental evidence for the formation of microclustersseparated by microinterfaces in binary mixtures ofsynthetic lipids [15], might be explained by the pre-sence of selective association processes between themixture phospholipids. Many years ago (1980), Chengshowed that in a binary mixture the compounds may bein a single completely mixed phase or in two separatecoexisting phases [16]. These phases depend on theacyl-chain lengths, the headgroup composition andthe mixing ratio of the two components [16].

We reported previously that the distribution of thelipid components in the supermolecular aggregate isnot random, but is the result of a selective associationprocess of lipid molecules from the binary mixtures[17–23]. It is well-known that the phase transitiontemperatures depend on the nature of the mixturecomponents, especially on the length of hydrophobicacyl-chains [24–26].

Therefore, in this paper we were strongly motivatedto study the hydrophobic effects of the acyl-chains onselective association processes of double-chain phos-pholipids in binary mixtures organised as bilayermembranes. The molecular interaction model for dou-ble-chain phospholipids has been imagined by extend-ing the previous one intended for the evaluation of theassociation probabilities of lysophospholipids intobinary mixtures organised as planar monolayers [17].

2. The association probabilities of double-chainphospholipids

Our simulation system represents a lipid bilayer inhydrated conditions that possesses a binary mixture ofnon-symmetrical saturated phospholipids. We consid-ered that the lipid bilayer is in the gel phase, so thatphospholipid molecules are close enough and all theC–C covalent bonds from the hydrophobic tails are inthe trans conformation. The polar headgroups areneutral, but possess an important electric dipolemoment. The major phospholipids in biomembranes,phosphatidylcholine and phosphatidylethanolaminehave neutral polar headgroups at pH 7. Coupling thetwo electric dipole moments can occur in both possi-ble orientations: parallel and anti-parallel alignments.In saturated hydrophobic chains, the electronic chargeis self-organised into independent distributions ofatomic dimensions that are localised in atoms andbonds. As far as the electron correlation is concerned,this is negligible between distant points of the acyl-chains. The covalent bonds in the hydrophobic chainhave such an arrangement so that a methylene groupcan be considered as an attractive centre. For thesereasons, within the limits of the second order pertur-bation theory, the assumption that the dispersionforces are locally additive is acceptable. Accordingly,the attraction energy between two neighbouringhydrophobic acyl-chains can be calculated by addingall the attraction energies between pairs of attractivecentres from both acyl-chains involved in interaction(see below). On the other hand, the distance betweenthe nearest attractive centres is about 7.14 A˚ (equal tothe distance between the axes of two neighbouringsaturated phospholipids), which is large comparedwith the sizes of the attractive units (atoms, bonds).

The model has been designed to give the

L. Movileanu et al. / Journal of Molecular Structure (Theochem) 434 (1998) 213–227214

association probabilities for a binary mixture ofdouble-chain phospholipids. Pascher et al. (1992)showed that double-chain amphiphilic moleculesmight associate themselves in both alignments paral-lel (the association probabilities are denoted byP) andanti-parallel (denoted byP 0) [27]. In the presentmodel, the binary mixtures of double-chain phospho-lipids are characterised by the following parameters:

1. the cross-sectional areas for the two mixture com-ponents,a1 anda2. Popescu and Victor (1991) ima-gined a method for the evaluation of the cross-sectional area of the polar headgroups for the con-crete physical conditions [28];

2. the electric dipole moments of the polar head-groups for the first and second mixture component,p1 andp2, respectively;

3. the acyl-chain lengths of the shorter and longerchains for the first mixture component,NS1 andNL1, respectively. The hydrophobic acyl-chainlength is given by the number of carbon atomsfrom the chain;

4. the acyl-chain lengths of the shorter and longerchains for the second mixture component,NS2

andNL2, respectively;5. the molar fraction of the first mixture componentx1

(x2 � 1 2 x1).

There are two types of interactions between the dou-ble-chain phospholipids [22]: (a) dipole–dipole inter-action between the polar headgroups; (b) van derWaals–London dispersion interaction between thehydrophobic chains inside the hydrophobic core.This mathematical version of the double-chain binarymixture model provides us with the association prob-abilities for the pair formation between the two neigh-bouring phospholipid molecules of the same type withthe electric dipole moments in parallel alignment (P11,P22 called the self-association probability as well), orthe same type in anti-parallel alignment (P

011, P

022, the

two electric dipole moments are in anti-parallel orien-tation), or different type (cross-pair) for the two pos-sible alignments (P12, P

012, called the cross-association

probabilities). The association probabilities will beexpressed with functions depending on the mixingratio (f) between the two mixture components:

f � x1

x2(1)

For the calculation of the dispersion energy, we con-sider that the electronic charge distribution is loca-lised in bonds and atoms and a methylene groupbehaves as an attractive centre. The van der Waals–London dispersion energy obeys the inverse-sixthpower distance law [29]:

W � 2A

d6 (2)

whereA is equal to 5.6× 103 A6 J mol 2 1 [30].The double-chain binary mixture model might pro-

vide the association probabilities for the above-men-tioned six distinct classes of association processes.

(a) The self-association probabilities of the firstmixture component in parallel alignment.

Let us consider a couple formed by the same phos-pholipid molecules belonging to the first mixturecomponent. In this case, the van der Waals–Londondispersion term of the pair-interaction energy (W11) isthe sum of the dispersion energies for the three hydro-phobic interactions: (i) between the shorter acyl-chains of the first component (WS1S1); (ii) betweenthe longer acyl-chains of the first component (WL1L1)and (iii) between the shorter acyl-chain and the longeracyl-chain of the first component (WS1L1). These termsare given by the following expressions:

W11 �WS1S11 WL1L1 1 2WS1L1 (3)

WS1S1�XNS1

k�1

XNS1

i�1

2A

�4r21 1 �k 2 i�2l2��3 (4)

WL1L1 �XNL1

k�1

XNL1

i�1

2A

�4r21 1 �k 2 i�2l2��3 (5)

WS1L1�WL1S1�XNS1

k�1

XNL1

i�1

2A

�d211 1 �k 2 i 2 4�2l2��3 (6)

with

d11 �����������4r2

1 1 l2q

(7)

r1 ����a1

p

r(8)

wherer1, d11, l andl are the radius of the headgroupcross-sectional area for the first mixture component,the distance between the hydrophobic acyl-chains

L. Movileanu et al. / Journal of Molecular Structure (Theochem) 434 (1998) 213–227 215

located in diagonal position (from two different phos-pholipid molecules), the average distance between thetwo hydrophobic acyl-chains of the same phospholi-pid molecule (l � 5.6 A) and the length of the C–Ccovalent bond (l � 1.27 A) normally projected to thebilayer, respectively (see Fig. 1). 4l is the distance bywhich the two acyl-chains are displaced by each otherwithin a phospholipidic conformation due to the factthat the glycerol bridge is in continuation of the ester-ified fatty acid by an opposite OH (see Fig. 1).

The dipole–dipole interaction energy has the fol-lowing expression:

E11 � p21

4p1�2r1�3(9)

where1 is the dielectric constant of water. Although1is a function depending on the distance between thesaturated phospholipids, we used the dielectric con-stant of water. The results are not affected qualita-tively whether we calculate the associationprobabilities with1 � 20. We considered that thepolar headgroups are hydrated, since the lipid bilayeris in a hydrated condition. This approximationdecreases the electrostatic forces between the polarheadgroups. In a previous paper [22], we evaluatedthe accuracy of eqn (9) for the dipole moments ofthe polar headgroups by estimating the mean associa-tion probabilities across a distance domain betweentwo adjacent phospholipids. As the effective charges(of the polar headgroups) and the distance betweenthem are not constant (they are strongly dependenton the external medium parameters including theionic composition and pH), we were motivated toevaluate the mean association probabilities over therange 5–45 D. The conclusions reached in the presentpaper are not affected as the mean association prob-abilities have the same behaviour by applying eqn (9).In other words, qualitatively, the mean associationprobability over the range 5–45 D (1 D� 1 Debye�3.335× 10 2 30 Cm) has the same monotony as theabsolute association probability (9).

We decided to use the dimensionless pair-interac-tion energy:

U11 �W11 1 E11

RT(10)

Here,R and T are the gas constant and the absolutetemperature, respectively.

(b) The self-association probabilities of the firstmixture component in anti-parallel alignment. Thevan der Waals–London dispersion energy of theself-association processes of the first mixture compo-nent in anti-parallel alignment (W

011) is given by the

sum of the dispersion energies in all the above-men-tioned hydrophobic interactions, but in anti-parallelalignment:

W0

S1L1�XNS1

k�1

XNL1

i�1

2A

�4r21 1 �k 2 i 2 4�2l2�3 (11)

W0

S1S1�XNS1

k�1

XNS1

i�1

2A

�d211 1 �k 2 i�2l2�3 (12)

L. Movileanu et al. / Journal of Molecular Structure (Theochem) 434 (1998) 213–227216

Fig. 1. A scheme showing two different phospholipids with the twoelectric dipole moments in parallel orientation. For notation seetext.

W0

L1L1 �XNL1

k�1

XNL1

i�1

2A

�d211 1 �k 2 i�2l2�3 (13)

W0

11 �W0S1S11 W

0L1L1 1 2W

0S1L1 (14)

whereas the dipole–dipole interaction energy in anti-parallel alignment is:

E011 � 2E11 (15)

and the dimensionless pair-interaction energy (U011)

is:

U011 �W

011 1 E

011

RT(16)

(c) The self-association probabilities of the secondmixture component in parallel alignment and (d) theself-association probabilities of the second mixturecomponent in anti-parallel alignment are approachedsimilarly to cases (a) and (b), respectively.

(e) The cross-association probabilities of binarymixture components in parallel alignment. The vander Waals–London dispersion energy for these pro-cesses (W12) will contain the hydrophobic interactionsbetween: (i) the shorter acyl-chain of the first andsecond mixture phospholipids (WS1S2); (ii) the longeracyl-chain of the first and second mixture phospholi-pids (WL1L2); (iii) the shorter acyl-chain of the firstmixture phospholipid and the longer acyl-chain ofthe second mixture phospholipid (WS1L2); (iv) theshorter acyl-chain of the second mixture phospholipidand the longer acyl-chain of the first mixture phos-pholipid (WL1S2). The expressions for these interac-tions are as follows:

W12 �WS1S21 WL1L2 1 WS1L2 1 WL1S2 (17)

WS1S2�XNS1

k�1

XNS2

i�1

2A

��r1 1 r2�2 1 �k 2 i�2l2�3 (18)

with

r2 ����a2

p

r(19)

WL1L2 �XNL1

k�1

XNL2

i�1

2A

��r1 1 r2�2 1 �k 2 i�2l2�3 (20)

W0

S1L2�XNS1

k�1

XNL2

i�1

2A

�d212 1 �k 2 i 2 4�2l2�3 (21)

with

d12 ��������������������r1 1 r2�2 1 l2

q(22)

W0

S2L1�XNS2

k�1

XNL1

i�1

2A

�d212 1 �k 2 i 2 4�2l2�3 (23)

and the dipole–dipole interaction energy, in this case,is:

E12 � p1p2

4p1�r1 1 r2�3(24)

Thus, the dimensionless cross-pair interaction energyis:

U12 �W12 1 E12

RT(25)

(f) The cross-association probabilities in the anti-parallel alignment. The notations are the same as in(e):

W0

12 �W0

S1L2 1 W0L1S2 1 W

0S1S21 W

0L1L2 (26)

W0

S1L2�XNS1

k�1

XNL2

i�1

2A

��r1 1 r2�2 1 �k 2 i 2 4�2l2�3 (27)

W0

L1S2�XNL1

k�1

XNS2

i�1

2A

��r1 1 r2�2 1 �k 2 i 2 4�2l2�3 (28)

W0

S1S2�XNS1

k�1

XNS2

i�1

2A

�d212 1 �k 2 i�2l2�3 (29)

W0

L1L2 �XNL1

k�1

XNL2

i�1

2A

�d212 1 �k 2 i�2l2�3 (30)

E012 � 2E12 (31)

U012 �W

012 1 E

012

RT(32)

Finally, we can evaluate the association probabilitiesof the non-symmetrical double-chain phospholipids

L. Movileanu et al. / Journal of Molecular Structure (Theochem) 434 (1998) 213–227 217

from binary mixtures:

P11 � f eU122U11

1 1 E(33)

P22 � eU122U22

f �1 1 E� (34)

P12 � eU122U012

1 1 E(35)

P011 � f eU122U

011

1 1 E(36)

P022 � eU122U

022

f �1 1 E� (37)

P012 � 1

1 1 E(38)

where:

E � f �eU122U11 1 eU122U011�1

1f�eU122U22 1 eU122U

022�

1 eU122U012 (39)

3. Results

All computer simulations were carried out for equaldistributions of phospholipids in bilayer lipid mem-branes (x1� x2, so thatf � 1). The acyl-chain lengths(NS1, NL1, NS2, NL2) of the double-chain phospholipidscan be changed depending on a concrete bilayer situa-tion. Pascher et al. (1992) reported the structural para-meters of membrane lipids [27]. IfS represents thehydrocarbon chain cross-section, the majority ofmembrane lipids haveS in a range 18–20 A˚ 2. Themolecular area (S) coincides with the cross-sectionalarea of the two mixture headgroups.S ranges in adomain 20–70 A˚ 2, but usually reaches 2S ù 36–40 A2 [27, 31, 32]. In our simulations, we have chosenthe cross-sectional areas of the two mixture head-groups in such a manner that one of them is compar-able with 2S(a1� 40 A2) and the other is higher than2S(a2� 60 A2). If the cross-sectional area of the polarheadgroups matches the hydrocarbon chain-packing

cross-section, then these lipids possess a high ten-dency to aggregate into well packed bilayer structureswith the acyl-chains oriented perpendicularly to thebilayer plane [27]. This is one of the viewpoints toverify the validity of the present computer model andits consistency with the experimental results.

To pursue the influence of the acyl-chain lengths onthe association probabilities, we investigated the setsof the homologous binary mixtures:NS1–C24:C16–C20, C12–NL1:C16–C20, C16–C20:NS2–C24 andC16–C20:C12–NL2. As can be seen, in these binarymixtures one mixture component has two chains withfixed values of a medium acyl-chain length (C16–C20) and the other has one of the acyl-chain lengthsas a variable (NS1, NL1, NS2 andNL2, respectively). Thephospholipid C16–C20 as the second mixture compo-nent in the binary mixturesNS1–C24:C16–C20 andC12–NL1:C16–C20 has been permuted for the othertwo binary mixtures in order to draw suitable conclu-sions regarding the cross-sectional area influence ofthe polar headgroups (a1 or a2). Popescu and Victor(1990) reported that the electric dipole moment of thepolar headgroups of phospholipids lies in the range 5–45 D [17]. To test the modulation of the selectiveassociation processes by the magnitude of the electricdipole moment of the polar headgroups, we computedthe association probabilities (P11, P12, P22, P

011, P

012

andP022) for the extreme values of the electric dipole

moment, namelypi � 5 D orpi � 45 D (i � 1,2) in allthe possible combinations (p1, p2): ((5,5); (5,45);(45,5) and (45,45)).

In Fig. 2(a), the dependence of the self-associationprobabilitiesP11 and P

011 on the shorter acyl-chain

length of the first mixture component (NS1) can beseen. The highest self-association probabilityP11 isreached when the electric dipole moment of the firstcomponent isp1 � 45 D and the electric dipolemoment of the second component isp2 � 5 D. Inother words, the self-association processes of thefirst mixture component are favoured when its electricdipole momentp1 has high values, while the othercomponent has a very lowp2 (0.58 # P11(45,5) #0.8, P11(45,5) is P11 computed forp1 � 45 D andp2 � 5 D). It is well known that the hydrophobicchains of the most natural phospholipids are unequal,having 14–22 carbon atoms [33] and the electricdipole momentp $ 35 D [34]. Because the self-asso-ciation probability P11(45,45) is still high (0.48#

L. Movileanu et al. / Journal of Molecular Structure (Theochem) 434 (1998) 213–227218

P11(45,45)# 0.65), then it is reasonable to think thatthe majority of the natural phospholipids with thecross-sectional area equal to about 2S tends to associ-ate in parallel alignment and the acyl-chains areoriented perpendicularly to the bilayer plane, whichis in good agreement with experimental studies [27].For instance, DLPE (2,3-dilauroyl-dl-glycero-1-phsphatidylethanolamine acetic acid) lies in this cate-gory of double-chain phospholipids [35, 36].

In the case that the first electric dipole moment issmall (p1� 5 D), then the self-association probabilityof the first mixture component in parallel alignment ofthe electric dipole moments of the polar headgroups isstrongly diminished (P11(5,45) ranges between 0.22and 0.35, Fig. 2(a)). Since the self-association prob-abilities in anti-parallel alignment are negligibleregardless of the magnitude of the electric dipolemoments (P

011(45,45) andP

011(45,5) are less than

0.05), then we conclude that these association phe-nomena are less likely when the cross-section areais a1 ù 2S � 40 A2. From the analysis of Fig. 2(a),we have seen that the electric dipole moment of thesecond mixture phospholipid might modulate the self-association process of the first mixture phospholipid.This finding suggests that the aggregation of a class ofphospholipids from a binary mixture is stronglydependent on the dipole–dipole interaction betweenthe same phospholipids. The aggregation is alsomodulated by the magnitude of the electric dipolemoment of the other mixture phospholipid from thatbinary mixture. As can be seen in Fig. 2(a), the largerthe short-acyl chain of the first double chain lipid(NS1), the higher the self-association probability ofthe same phospholipid (P11).

The pair formation resulting in a drop in the occu-pied volume decreases the packing pressure in therespective monolayer and directly triggers a flip-floptranslocation in the other direction, since the packingpressure in the other monolayer has not dropped. Inother words, the decrease in the packing pressure thatresults from the enhancement in the packing densitystimulates the passive entry of more phospholipids.Therefore, we deal with the dynamics of the unoccu-pied volume distributions or so-called free-volumedistribution. Concerning the free-volume distributionin a bilayer lipid membrane, Xiang (1993) proposedan interesting combined method of moleculardynamics and Monte Carlo simulation for evaluation

of the free-volume distributions as a function of posi-tion [37]. In binary mixtures with largerNS1, the prob-abilitiesP11 andP

011 indicate a higher capability of the

association for double-chain lipids of the first class.Therefore, in some cases, the selective associationprocesses can induce the non-bilayer structures dueto a high lipid accumulation or even a breakdown ofthe lipid bilayer [38] followed by a brutal flip-flopmovement according to Norris’s model [39].

In Fig. 2(b), we presented the cross-associationprobability (P12 andP

012) as a function depending on

the shorter acyl-chain length of the first mixture com-ponent (NS1). For all the possible values of the electricdipole moments, the cross-association probabilitiesare monotonously decreasing with the shorter acyl-chain length of the first mixture component. Thus,by increasingNS1 from 12 to 22 methylene groupswe had a large reduction of the cross-association prob-ability in parallel alignmentP12(5,45). The highestcross-association probability was computed for thebinary mixture C12–C24:C16–C20.

Surprisingly, the self-association of the secondmixture phospholipid is largely dependent on theshorter acyl-chain length of the first mixture phospho-lipid. However, for our set of parameters (f � 1, a1�40 A2, a2 � 60 A2) and the binary mixtureNS1–C24:C16–C20, the self-association process of thefirst mixture component is predominant (P11 q P22)and this finding explains the accumulation of the firstmixture component into larger lipid domains. Weassumed in this study that the relative area of thephospholipid domains (within the bilayer) in differentphases is given by the relative association probabil-ities of the respective phases.

Fig. 2(c) shows the dependence of the self-associa-tion probability (P22 or P

022) on the shorter acyl-chain

length. We are interested in those probabilities com-puted for higher electric dipole moments. SinceP22(45,45) , 0.05, it is unlikely a self-associationprocess of the second mixture component witha2 ù3S, when mixed with a double-chain phospholipidwith a1 ù 2S. On the other hand, the self-associationprocesses of the second mixture phospholipid in anti-parallel alignment attain the highest magnitude whenboth headgroups are very polarised (p1� p2� 45 D).

Naturally, when both components of mixtures havehigh values for the electric dipole moments, there is acertain tendency to increasing the associated couples

L. Movileanu et al. / Journal of Molecular Structure (Theochem) 434 (1998) 213–227 219

L. Movileanu et al. / Journal of Molecular Structure (Theochem) 434 (1998) 213–227220

with lipid molecules of the same type in parallel orien-tation (P11, see Fig. 2(a)) or in anti-parallel alignment(P

022, see Fig. 2(c)). To comment on the biological

significance of the value ofP022 from Fig. 2(c), we

should remind the reader of the mechanism for theflip-flop diffusion proposed by Kornberg and McCon-nell [40]. Two identical mixture components (indi-cated here by index ‘2’) with high electric dipolemoments, located in different monolayers andoriented in anti-parallel alignment to each other tendto have an extremely high capability to associatethemselves mainly by the means of a specific polarinteraction. A flip-flop process might be possibleimmediately, when this association phenomenontakes place adjacent to a permeant site. Therefore,an inversion of phospholipids occurs according tothe mechanism of Kornberg and McConnell [40]. Atshorter values ofNS1, this mechanism for the flip-flop

transition is more probable for two reasons: (i) theself-association probability of phospholipids in anti-parallel alignment is increased (P

022 is increased, see

Fig. 2c); (ii) the inversion of coupled phospholipidswith shorter acyl-chain lengths would be faster andeasier, because this requires a smaller permeant site.According to this mechanism for the flip-flop diffu-sion and taking into account the results of Fig. 2(c), itis concluded that the passive flip-flop transition rate isdecreased by increasing the acyl-chain length of phos-pholipids. Our finding is consistent with the experi-mental evidence of Homan and Pownall [41], whofound for phosphatidylcholine analogues an approxi-mate two-fold decrease in the flip-flop rate for everytwo methylene groups added to the acyl-chain length.

Looking at Fig. 2(a) and 2(c), we can see that, ifp1 � 5 D andp2 � 45 D, then for the binary mixturesC12–C24:C16–C20 and C22–C24:C16–C20 the self-association probabilities in anti-parallel orientationare P

011 � 0.18 andP

011 � 0.37, P

022 � 0.17 and

P022 � 0.11, respectively. This finding suggests the

idea that for a binary mixture witha1 ù 2S anda2 ù3S and the electric dipole momentsp1� 5 D andp2�45 D, the self-association processes in anti-parallelalignment of the polar headgroups are probable.Therefore, lipids from the same class, regardless ofwhether they are the first or the second mixture com-ponent, also have a tendency to couple themselves inanti-parallel alignment. From the results presented inFig. 2, the following conclusion was drawn. Theincrease of the shorter acyl-chain length of the firstmixture phospholipid promotes the self-associationprocess of the first component (P11 andP

011 increase),

but opposes the cross-association process and the self-association process of the second mixture component.We can expect that the actual distribution in thebilayer lipid membrane is approximately aroundP11(45,45):P12(45,45):P

022(45,45), since the sum of

these probabilities is always equal to about 0.9. Forinstance, in Table 1, in the case of the binary mixtureC12–C24:C16–C20,P11(45,45)� 0.49,P12(45,45)�

L. Movileanu et al. / Journal of Molecular Structure (Theochem) 434 (1998) 213–227 221

Table 1The magnitudes of the association probabilities, which, combinedmake the major contribution toward the aggregation phenomena inthe case of the highest dipole momentsp1 � p2 � 45 D

Binary mixture P11 P12 P022 P111 P121 P

022

C12–C14:C16–C20 0.402 0.249 0.248 0.899C12–C16:C16–C20 0.416 0.220 0.265 0.901C12–C18:C16–C20 0.428 0.196 0.279 0.893C12–C20:C16–C20 0.443 0.177 0.285 0.905C12–C22:C16–C20 0.464 0.161 0.281 0.906C12–C24:C16–C20 0.490 0.149 0.269 0.908C16–C20:C12–C14 0.672 0.064 0.175 0.911C16–C20:C12–C16 0.652 0.068 0.190 0.910C16–C20:C12–C18 0.634 0.073 0.204 0.911C16–C20:C12–C20 0.619 0.077 0.293 0.909C16–C20:C12–C22 0.608 0.083 0.219 0.910C16–C20:C12–C24 0.600 0.089 0.220 0.909C16–C20:C14–C24 0.559 0.106 0.242 0.907C16–C20:C16–C24 0.522 0.126 0.257 0.905C16–C20:C18–C24 0.491 0.151 0.262 0.904C16–C20:C20–C24 0.464 0.182 0.256 0.902C16–C20:C22–C24 0.437 0.218 0.245 0.900

Fig. 2. Dependence of the association probabilities on the shorter hydrophobic chain of the first mixture phospholipid (NS1) for the binarymixtures of double-chain amphiphiles:NS1–C24:C16–C20. The parameters used in this simulation test system are: the cross-section area of themixture phospholipidsa1� 40 A2 anda2� 60 A2, the molar ratio of the mixture phospholipidsf � 1, the Hamacker constant of the dispersionforcesA� 5.6× 103 A6 J mol2 1, the length of the C–C covalent bondsl � 1.27 Aand the average distance between two phospholipids,l �5.6 A2. (a) The self-association probabilities of the first mixture phospholipid; (b) The cross-association probabilities; (c) the self-associationprobabilities of the second mixture phospholipid.

0.15,P022(45,45)� 0.27, so thatP11 1 P12 1 P

022 �

0.91.By increasing the longer acyl-chain length of the

first mixture component (NL1), we obtained the sameresult as in the case ofNS1. The enlargement ofNL1

promotes the self-association of the first mixture com-ponent, but opposes the cross-association processes(Fig. 3(a) and 3(b)). From Fig. 3(a) it can be seenthat the higher probabilities areP11(45,5) andP11(45,45), while the other probabilities are lowerthan 0.3. BecauseP

011(45,5) and P

011(45,45) are

lower than 0.05, these processes are considered neg-ligible, although they are able to promote the clusterformation and local regular defects.

We also investigated the influence of the acyl-chainlength of the second mixture component (NS2) to theassociation processes (Fig. 4(a)–4(c)). Here, we haveagain high values of the self-association probabilitiesP11(45,45) andP11(45,5). Therefore, variation of the

hydrophobic acyl-chain length does not stronglyaffect the high tendency of the first mixture compo-nent to associate in parallel alignment. However, theincrease of the longer acyl-chain length of the secondcomponent (NL2) produces a monotonous increase ofthe probabilitiesP12, P

012, P22 andP

022 and a monoto-

nous decrease of the self-association probabilitiesP11

andP011 (results not shown). The same result was also

obtained by variation ofNS2. This finding, togetherwith that drawn from Figs 2 and 3 suggest that selec-tive association processes can be modulated by thehydrophobic acyl-chain effect, but the sense of thismodulation is given by the magnitude of the cross-sectional area of the polar headgroups. We found thatincrease of the acyl-chain lengths of the first compo-nent (NS1, NL1) increases monotonouslyP11 and P

011,

while increase of the acyl-chain lengths of the secondcomponent decreases monotonously the probabilitiesP11 and P

011. This fact is largely related to the

L. Movileanu et al. / Journal of Molecular Structure (Theochem) 434 (1998) 213–227222

Fig. 3. Dependence of the association probabilities on the longer hydrophobic chain of the first mixture phospholipid (NL1) for the binarymixtures of double-chain amphiphiles: C12–NL1:C16–C20. The other parameters are the same as in Fig. 2. (a) The self-association probability ofthe first mixture component. (b) The cross-association probability.

transition temperature behaviour with the acyl-chainlengths in pure bilayers and is discussed in Section 4.In Fig. 4(c) it can be seen thatP

022(45,45) is the highest

probability and the ruleP11:P12:P022 is the composition

for the major lipid domains of a two-componentbilayer with a1 � 40 A2 and a2 � 60 A2. As welearned from these investigations, the selective asso-ciation processes of double-chain phospholipids arestrongly dependent on the acyl-chain lengths of themixture components.

4. Discussion

We have seen that the selective association pro-cesses of double-chain phospholipids from binarymixtures in bilayer lipid membranes cannot bedoubted. These membrane phenomena have potentialconsequences for the physical state of biomembranesas well as the modulation of the functional and struc-tural properties of other membrane components likethe integral membrane proteins [42]. In this paper, wereferred to the hydrophobic acyl-chain effect of dou-ble-chain phospholipids on the selective associationprocesses. Cheng [16] reported that in a binary mix-ture the components might be in a single completelymixed phase or in two separate coexisting phasesdepending on the acyl-chain lengths, the headgrouptype and the mixing ratio of the components.

The composition of the bilayer expressed throughstable couples isP11:P12:P

022, since the sum of these

probabilities is constantly high (around 0.9, see Table1) regardless of the binary mixture case. Therefore, ina binary mixture of double chain phospholipids withcross-sectional areasa1 ù 2S� 40 A2 anda2 ù 3S�60 A2, we have three possible major lipid domainscorresponding to: (a) the cross-association process(P12); (b) the self-association process of the first mix-ture phospholipid in parallel alignment (P11) and (c)the self-association process of the second mixturephospholipid in anti-parallel alignment (P

022). In

other words, the coexistence of the three ‘phases’, inthis case, is consistent with the phase rule.

On the other hand, the hydrophobic acyl-chaineffect should be taken into account for the flip-flopdiffusion of phospholipids through bilayer lipid mem-branes. According to our results, the flip-flop diffusionrate may be reduced by increasing the acyl-chain

length of the phospholipid molecules, when thecross-sectional area of the polar headgroups lies inthe range 25–50 A˚ 2 [43]. This finding is also consis-tent with the experimental evidence of Homan andPownall [41]. They found for phosphatidylcholineanalogues an approximate two-fold decrease in theflip-flop rate for every two methylene groups addedto the acyl-chain length.

Recently, Nibu et al. [44] devoted a paper to theheadgroup type effect on the miscibility of homolo-gous phospholipids in hydrated bilayers. It was shownthat the non-ideality parameterr0 is positive and thismeans that the mixed-pair formation is energeticallyless favourable than the like-pair formation. Thus, ourresults (for instance, see Fig. 2(a)–2(c)) strongly con-firm the fact that cross-association processes are lessprobable than self-association processes of at leastone of the mixture phospholipids (P12 , P

022 , P11).

We have seen that the headgroup composition of thephospholipid (cross-sectional area, electric dipolemoment) makes a greater contribution to the changesin magnitude of the association probabilities than doeshydrophobic acyl-chain length. This finding is alsoconsistent with the results of Nibu et al. [44]. Forbinary mixtures of homologous phospholipids havingdifferent acyl-chains the coupling energies for like-pairs and cross-pairs are strongly dominated by thelarge inter-headgroup interaction. Therefore, theselective association processes of double chain phos-pholipids are largely determined by the relative con-tribution of the headgroup interaction to the overallintermolecular lipid–lipid interaction.

By increasing the acyl-chain lengths of the firstmixture component, we found that this promotes theself-association phenomenon of the first component,but decreases the cross-association probabilities andthe self-association probabilities of the second com-ponent. Therefore, the hydrophobic effect increasesthe stability of like-pairs of phospholipids, whosecross-section area of polar headgroups matches thehydrocarbon chain-packing cross-section (Fig. 2).On the other hand, the increase of the acyl-chainlengths of the second mixture component promotesthe association phenomenon of cross-pairs of phos-pholipids for both parallel and anti-parallel orienta-tions of the electric dipole moments of the polarheadgroups (Fig. 4(b)).

The hydrophobic acyl-chain effect of phospholipids

L. Movileanu et al. / Journal of Molecular Structure (Theochem) 434 (1998) 213–227 223

L. Movileanu et al. / Journal of Molecular Structure (Theochem) 434 (1998) 213–227224

can promote phase separation in binary mixtures.Thus, binary mixtures of phospholipids having thesame polar headgroups, but different acyl-chainlengths (for instance, mixtures of dimyristoyl- (C14:0)and distearyoyl- (C18:0) phosphatidylcholine) mayobey phase separation. These phase separations arecaused by solidification of the higher melting pointcomponent in a gel phase domain while the dispersionis cooled [9, 24, 45].

The hydrophobic acyl-chain effect can modulatethe interactions of phospholipids with other mem-brane components. In particular, the interactionbetween cholesterol molecules and phosphatidylcho-lines with different acyl-chain lengths has been per-formed by Mattjus et al. [46]. They showed that thecholesterol molecule is less readily soluble in mix-tures with long chain phosphatidylcholines than inthose with intermediate chain phosphatidylcholines.The mismatch of longer phosphatidylcholine acyl-chain length with cholesterol length strongly influ-ences the interaction between cholesterol and adjacentacyl-chain segments and this induces the thermodyna-mically more favourable lateral domains of choles-terol [46].

The selective association processes of phospholi-pids may induce different lipid domains that have agreat variety of functional roles in cell metabolism.Studies regarding the size and structure of lipiddomains containing cholesterol have also been carriedout by Snyder and Freire [47]. They found that lipiddomains are very small at concentrations of less than15% cholesterol, whereas the cholesterol clusterdomain covers the entire bilayer when its concentra-tion exceeds 30%. The formation of lipid domains isthe result of both specific lipid–lipid interactions andlipid–protein interactions, regardless of whether theproteins are integral or peripheral to the lipid bilayers[48, 49]. The lipid domains include lipids selected dueto phase separations. Because the phase separationsand the transition temperatures are strongly related tothe selective association processes of lipids, it is nat-ural to think that these processes modulate the size

and composition of lipid domains into biomembranes.The distribution of components within the lipiddomains is not made randomly and is strongly deter-mined by the selective association processes. Manystudies regarding nearest neighbour lipids haveshown that phospholipids of different classes are notrandomly mixed. For instance, phosphatidylethanola-mine and phosphatidylserine do not randomly formdimers in erythrocyte membranes [50]. However,the non-random mixing of biomembrane componentshas important consequences in molecular biology[51–54].

In particular, phospholipid distribution of a domainattracts certain proteins modulating their activity. Inthis respect, Norris [55] imagined a ‘membrane tec-tonics model’ in order to point out that phospholipiddomains control the spatial organisation of theEscherichia coli cell cycle. This model includesthree domains in the cytoplasmic membrane ofE.coli: chromosomal, septal (for cell division) andpolar (see fig. 1 in this reference). Norris showedthat the chromosomal domain is enriched in phospho-lipids with shorter acyl-chain lengths and with phos-phatidylethanolamine, whereas the septal domain isenriched in phospholipids with longer acyl-chainlengths and in phosphatidylglycerol and diphosphati-dylglycerol [55]. Interactions between the chromo-some and protein creates a membrane domain thatcontributes to the formation and positioning of septaldomains between the nucleoids. The development ofseptal domains leads to division. This example illus-trates the hydrophobic effect of the acyl-chains onsome phospholipid domain appearances, which con-trol the spatial organisation of theE. coli cell cycle.

For calculation of the coupling energies, the phos-pholipid acyl-chains are assumed to be in extendedall-trans conformation. This conformation is closerto the gel phase case. However, the calculations arenot affected if some of the chains are not inall-transconformation. This situation might be a feasibleexplanation for the coexistence of gel phase domainsand liquid crystalline phase domains within the

L. Movileanu et al. / Journal of Molecular Structure (Theochem) 434 (1998) 213–227 225

Fig. 4. Dependence of association probabilities on the longer acyl-chain of the second mixture phospholipid (NL2) for the binary mixtures ofdouble-chain phospholipids: C16–C20:C12–NL2. The other parameters are the same as in Fig. 2. (a) The self-association probabilities of the firstmixture phospholipid in parallel and anti-parallel orientationP11 andP

011, respectively. (b) The cross-association probabilitiesP12 andP

012; the

self-association probabilities of the second mixture phospholipid in parallel and anti-parallel orientationP22 andP022, respectively.

biological membranes [56]. Certainly, the greater partof biological membranes are in the liquid crystallinephase, but explanations for selective association pro-cesses should be regarded dynamically. The life timesof phospholipid domains (for both situations) arestrongly dependent on temperature, but there aresome similarities in both the gel phase phases andcrystalline phases.

When both acyl-chain lengths of the first mixturecomponent are increased, its self-association prob-abilities (P11 and P

011 in Fig. 2(a) and Fig. 3(a)) are

increased as well. This finding is in good agreementwith the macroscopic experimental evidence for purelipid bilayers. We have to keep in mind that the tran-sition temperature of the pure lipid bilayer increaseswith the acyl-chain length [24, 56, 57]. This depen-dence may be perturbed when the large polar head-groups interact (a . 50 A2). However, in this studywe have shown that the dipole–dipole component ofthe pair formation energy has a more important con-tribution to the association probabilities than the vander Waals dispersion component. This observation isconsistent with the experimental results of Rodgersand Glaser [58] regarding the distribution of thelipid domains within the erythrocyte membrane.They demonstrated that the phospholipid headgroupmay play a more dominant role than the hydrophobicacyl-chain effect in the formation of lipid domains.The hydrophobic acyl-chain effect largely influencesthe selective association processes of phospholipidswithin biomembranes. These processes might causethe formation of lipid domains that have a large vari-ety of functional roles in biological membranes [50–54].

The intermolecular interaction model presentedhere confirmed an optimal cross-section area permolecule of about 40 A˚ 2 as found by others [27, 31,32]. Surprisingly, changes in both acyl-chains of thesame molecular species have the same effect on thechanges in association probabilities. To explain thisfact, we can say that regardless of whether the shorteror the longer acyl-chain length of the first mixturephospholipid is increased,P11 andP

011 will increase,

P12 andP012 will decrease.P22 andP

022 demonstrate a

special behaviour (a biphasic one), caused by theinfluence of the large polar headgroup (a2 ù 60 A2).Thus, our intermolecular interaction model provedthat the phospholipids tend to couple each other in

parallel alignment of the electric dipole moments ofthe polar headgroups as reviewed by Pascher et al.[27]. On the other hand, there is still a high tendencyof phospholipids with large cross-section areas to self-associate in anti-parallel alignment (Fig. 2(c) and Fig.4(c)).

The hydrophobic acyl-chain effect in two-compo-nent phospholipid mixtures is an important factor forthe immiscibility degree of the components in thehydrated systems. In hydrated systems, the interactionbetween the polar headgroups is considerably wea-kened because of intervening water molecules. There-fore, compared with non-hydrated systems, thehydrophobic chain–chain interaction has a larger rela-tive contribution to the overall intermolecular interac-tion. To conclude, in hydrated lipid mixtures the acyl-chain length difference between the two mixture com-ponents plays a prominent role in determining thecoupling energies.

Acknowledgements

We would like to express our thanks to Drs. J.M.Seddon, M. Wortis, M. Glaser, G.J. Gompper, J.B.Sorenssen, P. Mattjus and G. Victor for many fruitfuldiscussions. We also convey thanks to the SOROSFoundation for financial support. We are veryindebted to Dr. Gordon Reid for his expertise inchecking the English and also to an anonymousreferee for helpful suggestions to the manuscript.

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