EUROPHYSICS LETTERS

15 July 2004

Europhys. Lett., 67 (2), pp. 321–327 (2004)
DOI: 10.1209/epl/i2004-10057-1

Lateral phase separation in mixtures of lipids
and cholesterol
S. Komura 1 (∗ ), H. Shirotori 1 , P. D. Olmsted 2 and D. Andelman 3
1
Department of Chemistry, Faculty of Science, Tokyo Metropolitan University
Tokyo 192-0397, Japan
2
School of Physics and Astronomy, University of Leeds - Leeds LS2 9JT, UK
3
School of Physics and Astronomy, Raymond and Beverly Sackler Facultyof Exact Sciences, Tel Aviv University - Ramat Aviv 69978, Tel Aviv, Israel(received 10 February 2004; accepted in ﬁnal form 5 May 2004)
PACS. 87.16.Dg – Membranes, bilayers, and vesicles.
PACS. 64.70.Ja – Liquid-liquid transitions.
PACS. 64.75.+g – Solubility, segregation, and mixing; phase separation.
Abstract. – In an eﬀort to understand “rafts” in biological membranes, we propose phenomenological models for saturated and unsaturated lipid mixtures, and lipid-cholesterol mixtures. We consider simple couplings between the local composition and internal membrane
structure, and their inﬂuence on transitions between liquid and gel membrane phases. Assuming that the gel transition temperature of the saturated lipid is shifted by the presenceof the unsaturated lipid, and that cholesterol acts as an external ﬁeld on the chain melting
transition, a variety of phase diagrams are obtained. The phase diagrams for binary mixtures of saturated/unsaturated lipids and lipid/cholesterol are in semi-quantitative agreementwith the experiments. Our results also apply to regions in the ternary phase diagram oflipid/lipid/cholesterol systems.

Introduction. – Biological membranes typically contain various components such as lipid
mixtures, sterols, and proteins that are indispensable to cell functions [1]. Rather than being
uniformly distributed in the membrane, there is growing evidence that some intra-membranecomponents are incorporated in domains arising from lateral lipid segregation in membranes.
This phenomenon has attracted great interest in the context of “rafts” [2], i.e., liquid domains rich in cholesterol, saturated lipids (typically sphingomyelin lipids), and in some cases
particular proteins [3]. Moreover, cholesterol-rich domains have been directly observed inmodel membranes composed of lipid mixtures and cholesterol, using advanced ﬂuorescencemicroscopy [4–10].
Prior to the notion of “rafts” in biological membranes, the role of cholesterol was investigated in binary lipid-cholesterol membranes [11–13], where phase separation was observed
using NMR and calorimetry [14,15]. Lipid membranes undergo a freezing or gel-like transition,in which the hydrocarbon tails order. Addition of cholesterol has several eﬀects. It suppresses
the gel transition below physiologically relevant temperatures, and can lead to coexistenceof two liquid phases with very diﬀerent orientational order. It is now believed that model(∗ ) E-mail: komura@comp.metro-u.ac.jp
c EDP Sciences
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membranes containing two phospholipids (saturated and unsaturated) and cholesterol [4–10]
exhibit “rafts” which are liquid-ordered (Lo ) domains, coexisting with a surrounding background in a liquid-disordered (Ld ) state [3].
From a physical viewpoint, a strategy for understanding the basic structure of “rafts” inbiological membranes is as follows [16]. First, it is necessary to have a simple model for binary
mixtures of saturated and unsaturated lipids. Second, a minimal model describing binary lipidcholesterol systems is required in order to understand the eﬀects of cholesterol on membranephase behavior. Finally, these two viewpoints could be combined to fully investigate threecomponent systems. Here we focus on the ﬁrst two steps, and propose simple phenomenological models for lipid-lipid and lipid-cholesterol binary mixtures. Such an approach is quite
useful since we can predict, at least qualitatively, the complex phase behavior (shown, e.g., inﬁg. 2(a) below) of the ternary lipid-lipid-cholesterol system from the three binary sub-systems.
It is generally believed that the gel phase transition is driven by the freezing of lateralmotion as well as conformational ordering of lipids. However, because these two degrees of
freedom are strongly coupled, the gel phase transition occurs at a single temperature forpure lipid systems. One of our major assumptions is that the membrane state, even for lipid
mixtures, can be described by one internal degree of freedom, coupled to the lateral phaseseparation. Our main result is phase diagrams for two-component systems, which reproduce
experimental ones, without specifying the detailed microscopic state of the lipids. Moreover,
we shed light on recent phase diagrams obtained for ternary mixture [8, 9].
Model for saturated-unsaturated lipids systems. – If diﬀerent lipids exhibit only a small
diﬀerence in their gel transition temperature, their phase diagram in terms of temperaturecomposition parameters will include a “cigar-like” shape of liquid-gel coexistence (as inﬁg. 1(a)). As the gel transition temperature diﬀerence between the two lipids is increased, agel-gel coexistence region appears below the liquid-gel coexistence. At even larger diﬀerence,the phase diagram becomes more complex as the two coexistence regions partially overlap [17].
320

(b)

(a)
D

320

D2

D1

T [K]

T [K]

D1+D2
D+O

300

Tr

D1+O2

300

Tr
280

O1

O2

280

O1

O2

O1+O2

O1+O2
0

0.2

0.4

x

0.6

0.8

1

0

0.2

0.4

x

0.6

0.8

1

Fig. 1 – Calculated phase diagrams of binary mixtures of saturated and unsaturated lipids as a functionof mole fraction of the saturated lipid x and temperature T for (a) J = 4.0 kB Ts∗ , and (b) J = 5.0 kB Ts∗ .
The other parameters are a2 = 174 kB , a3 = −307 kB Ts∗ , a4 = 613 kB Ts∗ , Tu∗ = 240 K, Ts∗ = 260 K
as estimated in [18]. The gel transition temperature is Tg = 291 K and 311 K for x = 0 (fully
unsaturated) and 1 (fully saturated), respectively. The ordered (large ψ) and disordered (ψ = 0)phases are, respectively, denoted by O and D. The critical point is indicated by a ﬁlled circle, and thetriple point by Tr. The critical points are located at (a) xc = 0.498, Tc = 280 K, and (b) xc = 0.5,
Tc = 326 K, respectively.

S. Komura et al.: lipid-cholesterol323

We consider a single bilayer membrane composed of x mole fraction of saturated lipidand (1 − x) of unsaturated lipid. The two lipids are taken to have diﬀerent gel transition
temperatures originating from diﬀerent chain length, degree of saturation, or hydrophilic headgroup. We assume the same area per molecule for both species, and ignore lipid exchange withthe surrounding solvent. The total free energy f  = f1 + f2 comprises i) the free energy f1of mixing and binary interactions, and ii) the “stretching” energy f2 , which controls changes
in bilayer thickness.
The free energy per site f1 is the sum of the entropy of mixing and enthalpy. It can be
written within a Bragg-Williams (mean-ﬁeld) theory as1f1 (x) = kB T [x log x + (1 − x) log(1 − x)] − Jx2 ,2(1)where kB is the Boltzmann constant, T is the temperature, J > 0 is an attractive interaction
parameter that enhances demixing. Linear terms in x can be disregarded because they merely
shift the origin of the chemical potential.
To describe the gel transition, which involves chain ordering and stiﬀening, we introduce
a rescaled membrane thickness ψ ≡ (δ − δ0 )/δ0 as an order parameter, where δ is the actual membrane thickness and δ0 is the constant membrane thickness in the disordered phasecorresponding to the liquid phase [18]. Note that ψ summarizes changes in various degrees
of freedom, including the conformations of the hydrocarbon chains and their inter-chain correlations. Since the gel transition is ﬁrst order, an appropriate phenomenological Landau
expansion of the “stretching” free energy per site in powers of ψ is [18]f2 (x, ψ) =


1 
1
1
a2 T − T ∗ (x) ψ 2 + a3 ψ 3 + a4 ψ 4 ,
2
3
4

(2)

where a2 > 0, a3 < 0, and a4 > 0. For a single component membrane (i.e., x = 0 or1), T ∗ is a reference temperature, and the ﬁrst-order gel transition temperature is given
by Tg = T ∗ + 2a23 /(9a2 a4 ). For a binary mixture, the transition temperature depends onthe composition x; for convenience, we describe the reference temperature T ∗ (x) as a linear
interpolation between the two pure limits:T ∗ (x) = xTs∗ + (1 − x)Tu∗ ,(3)

where Ts∗ and Tu∗ are the reference temperatures of the pure saturated and unsaturated lipids,
respectively. With all else the same (head group size, interactions, and chain length, etc.),
we expect Ts∗ > Tu∗ , because unsaturated lipids break up the crystallizing tendencies. Notethat eq. (3) leads to a coupling term xψ 2 [19]. We have neglected a lower-order bilinear termxψ, which induces a small temperature and composition dependence in δ0 . Another possible
coupling term x2 ψ simply renormalizes the interaction parameter J.
Combining eqs. (1)-(3), we obtain the total free energy f  . After minimizing with respectto ψ, the two-phase region is obtained by the Maxwell construction. In ﬁg. 1, we show two
typical phase diagrams of binary lipid mixtures. For small J (ﬁg. 1(a)), which corresponds
experimentally to mixtures with weak segregation tendency, a cigar-like coexistence region
is obtained between a disordered phase (D) where ψ = 0 (liquid) and an ordered phase (O)where ψ > 0 (gel). At temperatures below the cigar-shape region, there is another coexistence
region between two ordered phases, O1 + O2, with ψ1  ψ2 . This type of phase diagram was
experimentally observed for DEPC-DPPC binary lipid systems [20]. When J is increased, theO1 + O2 coexistence region extends into and beyond the D + O coexistence region (ﬁg. 1(b)).
In this more complex phase diagram, there are two triple points (denoted as Tr) at which the324

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(a)

(b)
L
C L

T
C

U
S

Fig. 2 – (a) Schematic phase prism of a ternary system consisting of saturated lipid (S), unsaturated
lipid (U), and cholesterol (C). The gray and black regions on the constant-temperature triangle plane
are two-phase and three-phase coexisting regions, respectively. (b) Lattice model for a lipid-cholesterol
mixture. Each cholesterol molecule (•) forms a dimer with a neighboring lipid molecule (◦).

two disordered phases and ordered phase (D1 + D2 + O2), or the disordered phase and twoordered phases (D1 + O1 + O2) coexist. Many features of this phase diagram can be seen for
DEPC-DPPE lipid mixtures which have a stronger segregation tendency because both head
and tail moieties are diﬀerent [20].
Model for lipid-cholesterol systems. – Next we discuss the role of sterols, such as cholesterol and lanosterol, on the phase behavior. On the one hand, a small amount of cholesterol
destabilizes the gel phase in favor of a liquid-disordered (Ld ) phase [14, 15]. Substantial
amount of cholesterol, on the other hand, stabilizes a liquid-ordered (Lo ) phase in which thelipid hydrocarbon tails are extended, but maintain high lateral mobility. This reﬂects the dual
molecular mechanism of a cholesterol molecule: it can act i) as an “impurity” and weakens
the inter-lipid interactions for ordering, or ii) as a “chain rigidiﬁer” and induces conformational order in neighboring lipid chains [13]. Moreover, recent experiments using atomic force
microscopy showed that the cholesterol-rich domains are thicker than the cholesterol-poor regions [21, 22], supporting the assumption that the local membrane thickness can be taken as
the order parameter.
Based on these observations, we propose a model for lipid-cholesterol binary mixtures.
Consider a membrane with cholesterol mole fraction c and lipid mole fraction (1 − c). There
are three contributions to the total free energy f c = f1c + f2c + f3c : i) the entropy of mixing
f1c (c) between lipid and cholesterol; ii) the “stretching” energy f2c (ψ) of lipid molecules; andiii) direct coupling terms between lipid and cholesterol, f3c (c, ψ), which take into account theeﬀect of cholesterol on the bilayer thickness.
We note that the coexistence region in the lipid-cholesterol system is typically found only
for c ≤ 0.5 [8, 14, 15]. For cholesterol concentration above roughly 0.5, the entire bilayer becomes unstable. To account for such observations we assume that each cholesterol molecule
irreversibly dimerizes with a single lipid molecule forming a “condensed complex”, as has previously been inferred from experiments [23] and simulation [24]. Since all cholesterol molecules
are assumed to form dimers, as shown in ﬁg. 2(b), the entropy of mixing is taken between lipidcholesterol dimers and the remaining monomeric lipids, and is given by a Flory-Huggins form:
f1c (c) = kB T [c log 2c + (1 − 2c) log(1 − 2c)].

(4)

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340

(a)

320

(b)
D

320

T [K]

T [K]

D
D+O2
300

Tr

O1

O2

300

O+D
280

O1+O2
280
0

0.1

0.2

c

0.3

O
0.4

0.5

260
0

0.1

0.2

c

0.3

0.4

0.5

Fig. 3 – Phase diagrams of binary lipid-sterol mixtures as a function of mole fraction c of sterol andtemperature T for (a) cholesterol, Γ1 = 11 kB T ∗ , Γ2 = 47 kB T ∗ ; and (b) lanosterol, Γ1 = 28 kB T ∗ ,Γ2 = 20 kB T ∗ . The other parameters are the same as in ﬁg. 1, except T ∗ = 260 K. The gel transition
temperature at c = 0 is Tg = 311 K. The ordered (large ψ) and disordered (non-zero small ψ) phases
are, respectively, denoted by O and D. The critical point indicated by a ﬁlled circle in (a) is locatedat cc = 0.492, Tc = 338 K.

This free energy is valid only for 0 ≤ c ≤ 0.5, since each cholesterol molecule is paired witha neighboring lipid, and the monolayer loses its stability above about c = 0.5. The ﬁrst termis the entropy of dimers having an area fraction of 2c, while the second term accounts forthe entropy of lipid monomers of area fraction (1 − 2c). Although extensions of the model toinclude excess free cholesterol and/or formation of trimers, etc. is possible [25], the present
situation is enough to describe the qualitative phase behavior.
The Landau free energy describing the structural phase transition of the membrane isgiven by f2c (ψ), and is the same as f2 of eq. (2):f2c (ψ) =1 
11a2 (T − T ∗ )ψ 2 + a3 ψ 3 + a4 ψ 4 ,
2
3
4

(5)

where the order parameter ψ is again the relative bilayer thickness, and T ∗ is the reference
temperature of the pure lipid system.
The simplest free energy to account for the previously mentioned dual eﬀects of cholesterol
can be expressed by the following phenomenological coupling terms:
f3c (c, ψ) =11
Γ1 cψ − Γ2 c2 ψ,
2
2

(6)

where Γ1 > 0 and Γ2 > 0 are the coupling constants. The ﬁrst term expresses the fact thata small amount of cholesterol (c > 0) acts as an “impurity”. It interferes with the crystalline
ordering, and enhances disordered chains (smaller ψ). This term is necessary because, as
shown in the experimental phase diagram [14,15], the gel-Ld coexistence temperature decreases
upon adding cholesterol to the pure lipid system. The second term corresponds to the “chain
rigidifying” eﬀect reﬂecting the fact that a larger amount of cholesterol favors ordered tailstates and hence larger ψ. Meanwhile, this coupling induces lipid-cholesterol phase separation
since it is proportional to c2 with a negative coeﬃcient. In other words, the eﬀective lipidcholesterol interaction depends on the conformational states of the lipid chains.
Adding eqs. (4)-(6), we ﬁrst minimize f c with respect to ψ and then construct the phase
diagrams, as shown in ﬁg. 3. The topology of the phase diagram depends on the relative

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values of the two parameters, Γ1 and Γ2 . This can be seen in ﬁg. 3, where two diﬀerent
sets of values are taken to model (a) lipid-cholesterol and (b) lipid-lanosterol interactions. In
ﬁg. 3(a), there are three diﬀerent coexisting regions. Due to the Γ1 coupling term in eq. (6),the region of the disordered (D) phase, characterized by a non-zero small value of ψ, widens
at the expense of the ordered (O1) phase, characterized by a large value of ψ, upon the
addition of a small amount of cholesterol (c < 0.1). Note that D- and O1-phases, respectively,
correspond to Ld and gel phases in the experiments. For larger c, however, the Γ2 coupling
term overcomes the ﬁrst term, and the region of the D-phase narrows in favor of O2-phase(c > 0.1), which corresponds to the Lo phase where the order parameter ψ takes a value muchlarger than that in the D-phase. The obtained phase diagram for lipid-cholesterol systems
agrees semiquantitatively with the experimental one [14, 15]. The D- and O2-phases have thesame symmetry and are continuously connected, with a critical point at cc = 0.492 < 0.5.
The appearance of the critical point can be understood by noticing that the coupling terms
in eq. (6) are linear in ψ, and act as an external ﬁeld coupled to ψ. In general, the ﬁrst-ordertransition becomes continuous when the applied external ﬁeld is strong enough.
For larger Γ1 and smaller Γ2 we obtain the phase diagram shown in ﬁg. 3(b). In thiscase, the eﬀective external ﬁeld is too weak to eliminate the ﬁrst-order transition, and thecritical point does not exist. This phase diagram resembles that of binary lipid-lanosterol
mixtures [26]. Compared to cholesterol, lanosterol has three additional methyl groups andhas a structurally rougher hydrophobic part, leading to a weaker enhancement of lipid tailstretching (smaller Γ2 ). Moreover, an extra double bond in the lanosterol hydrocarbon tailcan be expected to inhibit crystallinity (larger Γ1 ). In fact, lanosterol is considered to be a
precursor to cholesterol in the evolutionary pathway [26]. Although cholesterol can stabilize
the region of coexistence between the D- and O2-phases (i.e., Ld + Lo ) as shown in ﬁg. 3(a),such a coexistence has not been identiﬁed for the lipid-lanosterol mixtures [26]. The fact thatthe coexistence region ends at c = 0.5 is due only to the artiﬁcial truncation of the model at
c = 0.5. If free excess lanosterol were allowed, the phase boundaries would continue until themembrane loses its integrity. However, such a break-up of the membrane is not consideredhere. We note that although the values of the coupling constants are chosen in an attempt
to reproduce the experimental phase diagrams, their order of magnitude is in agreement withthat obtained from molecular level theory [27].
Discussion. – Within a few simplifying assumptions we have obtained phase diagrams
that successfully mimic the experimental ones. A few points merit further discussion. We used
only one order parameter ψ (related to local membrane thickness) to describe the membraneinternal degrees of freedom of chain ordering and crystallinity. This assumption is well motivated for pure lipid membrane where both ordering and crystallization occur simultaneously.
Although addition of cholesterol may separate the chain ordering and freezing transitions andstabilize the Lo phase, the thickness ψ is suﬃcient here to distinguish between the gel (O1), Lo(O2), and Ld (D) phases. Note that the symmetry of the D- and O2-phases is the same (hence
the critical point), and diﬀers from the solid-like and local crystalline order of the O1-phase. As
an extension to the present model, it may be of interest to use two distinct order parameters.
Finally, we discuss the qualitative behavior of the full ternary phase diagram for saturated(S) and unsaturated (U) lipids in the presence of cholesterol (C). The phase diagrams inﬁgs. 1(a) and 3(a) correspond to the two side views of the schematic compositions-temperaturephase prism in ﬁg. 2(a), namely the US-T and the SC-T planes, respectively. A topologicallysimilar phase diagram to ﬁg. 3(a) is expected for the UC-T plane [26].
Consider a cut of the phase prism at a ﬁxed temperature as shown in ﬁg. 2(a). Boththe D + O coexistence region on the US-T plane and the O1 + O2 coexistence region on the327

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SC-T plane extend onto this triangle plane, and may form a three-phase coexisting region(D + O1 + O2, i.e., Ld + gel + Lo ) when they meet each other. If the phase separation does notoccur between U and C for this temperature, a critical point between D and O2 is expected toappear. As the temperature is increased, the line of critical points may end when the threephase region disappears. These arguments are consistent with recent experimental studies ofthe phase morphology inside the phase prism [6–9]. Further calculations of the full ternary
phase diagrams are in progress. “Rafts”, reported to be in the Lo (O2) phase, may correspondto nm-µm sized domains similar to the macroscopic phase separation seen in ternary mixturesat biologically relevant temperatures and compositions [3]. The small length scales associatedwith “rafts” in vivo remain unexplained.
∗∗∗
We thank T. Kato for useful discussions, and the Isaac Newton Institute, University ofCambridge, for its hospitality. This work is supported by the Japan Society for the Promotion of Science, the Royal Society, the Ministry of Education, Culture, Sports, Science andTechnology, Japan under grant No. 15540395, the Israel Science Foundation (ISF) under grantNo. 210/02, and the US-Israel Binational Foundation (BSF) under grant No. 287/02.
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