24
Biochimica et Biophysica Acta, 557 (1979) 24--31
© Elsevier/North-Holland Biomedical Press
BBA 78523
PROPERTIES OF BILAYER MEMBRANES IN THE PHASE TRANSITION
OR PHASE SEPARATION REGION
S. MARCELJA and J. WOLFE
Department o f Applied Mathemetics, Research School o f Physical Sciences, Institute o f
Advanced Studies, The Australian National University, Canberra, A.C.T. 2600 (Australia)
(Received February 28th, 1979)
Key words: Phase separation; Bilayer compressibility; Lipid domain; (Bilayer mem brahe)
Summary
The increase in passive permeability of bilayer membranes near the phase
transition temperature is usually explained as caused by either the increase in
the a m o u n t of 'boundary lipid' present in the membrane, or by the increase in
lateral compressibility of the membrane. Since both the a m o u n t of 'boundary
lipid' and the lateral compressibility show a similar anomaly near the transition
temperature, it is difficult to distinguish experimentally between the two
proposed mechanisms.
We have examined some details of both of the proposed pictures. The fluidsolid b o u n d a r y energy, neglected in previous work, has been computed as a
function of the domain size. For a single component uncharged lipid bilayer,
the results rule out the existence of even loosely defined solid domains in a
fluid phase, or vice versa. T h e r m o d y n a m i c fluctuations, which are responsible
for anomalous behaviour near the phase transition temperature, are not intense
enough to approximate the formation of a domain of the opposite phase.
Turning next to lateral compressibility of bilayer membranes we have considered t w o - c o m p o n e n t mixtures in the phase separation region. We present the
first calculation of lateral compressibility for such systems. The behaviour
shows interesting anomalies, which should correlate with existing and future
data on transport across membranes.
Introduction
In 1973, Papahadjopoulos et al. [1] observed that the passive permeability
of bilayer membranes has a pronounced m a x i m u m at the phase transition
temperature of bilayer lipid chains. This observation has aroused considerable
experimental and theoretical interest, and after a few years the proposed
Abbreviations: DPPC, d i p a l m i t o y l p h o s p h a t i d y l c h o l i n e ; DMPC, d i m i r i s t o y l p h o s p h a t i d y l c h o l i n e .
25
explanations for this effect have settled for one or the other of the following
two hypotheses: (1) The increase in permeability is associated with 'boundary
lipid', i.e. it arises because of the mismatch in packing of lipid chains at the
boundary between solid and fluid domains [1--5], or (2) the increase in permeability is correlated with the increase in lateral compressibility of the bilayer,
i.e. the increase in permeability is associated with the increase in fluctuations of
the cross-sectional area of lipid chains near the phase transition temperature
[6--8].
The two mechanisms are not entirely different if a 'boundary lipid' picture is
extended by adopting a very loose concept of a frozen domain in an otherwise
fluid bilayer or vice versa. However, the picture then becomes ambiguous, and
a poorly defined domain should rather be referred to as a local fluctuation in
the order of the lipid environment.
The conceptual clarification of the physical principles involved in the permeability anomaly at the lipid phase transition is very important as a part of a
broader range of problems where lipid environment controls membrane function [10]. We have therefore examined some details of both of the proposed
mechanisms. In the following sections we discuss in turn the concept of
domains near the phase transition, and lateral compressibility of membranes
formed from binary mixtures of lipids. We conclude by rejecting the domain
picture for neutral, single-lipid bilayers and suggesting a few relevant experiments.
Domain boundary energy
The formation of a stable domain state near the phase transition temperatures of dispersions of pure, single-component lipids is opposed b y the Gibbs
phase rule [8]. However, when lipid head groups are charged, strong surface
effects are introduced. The balance between the electrostatic and the phase
boundary energy then favours a gradual phase transition via the domain state
[9].
While no direct evidence supports the idea of formation of stable domains
near the phase transition of single-component neutral bilayer, it is possible to
imagine [ 5] a dynamic equilibrium with rapid formation and decay of 'domain'
structures. Such a concept would be appropriate and useful if most of the
thermodynamic fluctuations near the phase transition temperature, reflected
e.g. in the specific heat anomaly [5], lead to the formation of a well<tefined
domain of the opposite phase. This question is examined here by the computation of the free energy change associated with the formation of a solid domain
in a fluid bilayer just before the phase transition temperature is reached.
The computation has been performed using the model of lipid chain ordering
in bilayer membranes described previously [11]. Lipid molecules are arranged
on the sites of a two-dimensional hexagonal lattice, and various thermodynamic
quantities are c o m p u t e d separately for each site. A domain of frozen lipids is
simulated by setting the molecules occupying a selected number of sites into
the frozen state, and allowing the remainder of the system to equilibrate.
In Fig. 1 the change in the Gibbs free energy AG associated with the formation of a solid domain in the fluid phase is shown as a function of the domain
26
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F i g . 1. T h e c h a n g e in free e n e r g y , A G , a s s o c i a t e d w i t h t h e f o r m a t i o n o f a d o m a i n o f N m o l e c u l e s o f s o l i d
i n t h e b u l k f l u i d p h a s e , le B is B o l t z m a n n ' s c o n s t a n t a n d T t h e a b s o l u t e t e m p e r a t u r e .
size. The results are c o m p u t e d at the phase transition t e m p e r a t u r e of the model
system, T = 24.12°C. The free energies o f the bulk fluid and the bulk solid lipid
molecules are th er ef or e equal, and AG is the free energy of the fluid-solid
b o u n d ar y . F o r the roughly cbcular domain shapes which were selected, AG
should scale with N 1'2 where N is the n u m b e r of molecules forming the domain.
Since change of lipid order between the fluid and the solid phase is gradual
[9,11], N is d eter m i ne d by taking the dividing line approxi m at el y half-way
between the fluid and the solid phase.
The c o m p u t a t i o n shown in Fig. 1 uses lipid chain length of 12 carbon atoms.
The AG corresponding to the chains of 16 carbon atoms should be roughly
twice as large as the values shown in Fig. 1. If the domain is formed in both
halves of a bilayer, the values should be doubled again. Reading from Fig. 1, we
estimate e.g. that for a dipalmitoyl phosphatidylcholine bilayer the free energy
o f f o r m a t i o n of a frozen domain is 9kBT (domain size 25 molecules) or 12 kBT
(domain size 50 molecules).
T he free energy difference associated with t h e r m o d y n a m i c fluctuations in an
equilibrium system is typically of the order of the thermal energy, kBT. In
statistical mechanics, fluctuations where the free energy difference is an order
of magnitude higher, say 10 kBT are certainly exceedingly rare. For most
practical purposes t he r ef or e such fluctuations may be safely ignored.
F r o m the above argument, we conclude that t h e r m o d y n a m i c fluctuations
near the phase transition of single-component, uncharged lipid bilayers are n o t
intense enough to create welDdefined domains of the opposite phase. The
'domains' f o u n d from the general statistical mechanics argument by Freire and
Biltonen [51 are not frozen patches: rather they could be t h o u g h t of as correlated regions of the bilayer where local order deviates slightly from the equilibrium value. 'Domains' obtained f r om the Ising model considerations by Tsong et
al. [4] are only a consequence of applying the Ising model, which allows for
just two different states at each site. T h e y cannot be taken to mean frozen or
fluid domains in a lipid bilayer *
* T h i s c o n c l u s i o n is i n a g r e e m e n t w i t h t h e s m a l l a v e r a g e c l u s t e r size c a l c u l a t e d b y K a n e h i s h a a n d T s o n g
( ( 1 9 7 8 ) J. A m . C h e m . S o c . 1 0 0 , 4 2 4 - - 4 3 2 ) . We t h a n k Dr. T s o n g f o r a c o r r e s p o n d e n c e r e g a r d i n g t h i s a n d
related points.
27
Lateral compressibility of bflayers formed from binary mixtures
Several research groups have reported an increase in transport across the
membrane at temperatures corresponding to the coexistence of both solid and
fluid phases of lipids in the membrane. Linden et al. [6] have proposed that
the increase is due to the large lateral compressibility of bilayers in the phase
separation region. Similarly [12], the compressibility of single-component
bilayers is enhanced near the phase transition temperature, and this should be
reflected in higher transport rates over a small temperature range. This latter
case was examined in more detail by Doniach [7] and by Nagle and Scott [8].
H o w large is the increase in lateral compressibility in the phase coexistence
region? What is the shape of the anomaly? For bilayer membranes, these questions cannot be answered experimentally. We have therefore combined the
information available from related studies on both monolayers and bilayers to
obtain an insight into the problem.
Lateral phase separation in bilayer membranes is normally studied as a function of temperature, and the coexistence region shown in temperature-composition (T-x) phase diagrams. To consider lateral compressibility, the formalism
should include the lateral pressure (II) as a second thermodynamic variable.
Lipid chains in bilayers are subject to an intrinsic lateral pressure [13] which
depends strongly on the interactions at the polar head-water interface and cannot be conveniently controlled *. However, monolayer studies provide complementary data, where T is held constant and [I is continuously varied.
As an illustration of the general principles involved, we have constructed the
II-T-x phase diagrams assuming ideal mixing between the two components of
the binary mixture. The formalism used in e.g. a review article by Lee [16] is
easily extended to accommodate lateral pressure as another independent variable. In that case, the chemical potential difference between the solid and the
fluid phase of the c o m p o n e n t A is (cf. Eqn. 24 of Ref. 16)
P(As ) ° - - p(AL)° = ---(z:kHA)T, I I ( 1 - -
T / T A ) + ( A a n ) T , rl([I - - H A )
(1)
with a similar expression for the c o m p o n e n t B. Aan is the change in the molecular cross-sectional area at the phase transition of the pure c o m p o n e n t A, and
the second term on the right-hand side of the Eqn. 1 describes [13] the change
in chemical potential associated with the change in the lateral pressure acting
on lipid chains. AH A is the melting enthalpy of c o m p o n e n t A. With the assumption that (AC/)T,His unchanged by small changes in II (analogous to the assumption [16] that ( A H ) T , H is independent of T) Eqn. 1 is essentially symmetric in
its dependence on T and II. The solidus and the fluidus curves in the Fl-x plane
thus form a shape similar to the 'cigar' formed in the T-x plane.
An example of the II-T-x phase diagram corresponding to ideal mixing in
binary lipid systems is shown in Fig. 2. The diagram, corresponding to mixtures
of dipalmitoyl phosphatidylcholine (DPPC) and dimiristoyl phosphatidylcholine (DMPC), has been calculated using the monolayer data [17] on the
* To s o m e extent, intrinsic lateral pressure can be controlled by varying the pH of the a q u e o u s phase
[14,151.
28
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!
15
20
25
30
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(km.N-~)
.2!
,1
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1 /,/!
!
J
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,
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lot
~-~--~-?-~:
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•7
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r "1
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'
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1
15
20
T(°C)
25
30
Fig. 2. T h e p h a s e d i a g r a m for a m i x t u r e of DMPC a n d DPPC. T h e i n t e r s e c t i o n s of several isobaric p l a n e s
w i t h the fluidus s u r f a c e ( - ) a n d solidus s u r f a c e s ( . . . . . .
) are s h o w n . T h e plane T = 20~C is also
d r a w n to s h o w the ' c i g a r ' - s h a p e d figure in the I]-x p h a s e d i a g r a m . If a s y s t e m is specified by a p o i n t X ' ,
If', T ' w h i c h lies a b o v e the fluidus s u r f a c e , it is an h o m o g e n e o u s fluid, if X ' , II', T' lies b e l o w the solidus
s u r f a c e , it is an h o m o g e n e o u s solid. If it lies b e t w e e n t h e t w o it s e p a r a t e s into fluid a n d solid p h a s e s
w h o s e c o m p o s i t i o n s are specified b y t h e i n t e r s e c t i o n w i t h , r e s p e c t i v e l y , t h e fluidus a n d solidus s u r f a c e s o f
a line t h r o u g h X ' , 11', T' parallel to the x-axis. I d e a l m i x i n g is a s s u m e d a n d t h e d a t a are f r o m Ref. 17.
t,'ig. 3. I s o t h e r m a l c o m p r e s s i b i l i t y as a f u n c t i o n of t e m p e r a t u r e for d i f f e r e n t m i x t u r e s of DMPC a n d
DPPC. T h e f r a c t i o n s p r i n t e d on each c u r v e are t h o s e of DMPC. T h e s e curves are strictly a p p l i c a b l e to a
m o n o l a y e r at [| = 20 m N • m - l , w h i c h lateral p r e s s u r e a p p r o x i m a t e s t h a t in a b i l a y e r , a n d '£A a n d T B are,
r e s p e c t i v e l y , the m e l t i n g t e m p e r a t u r e s of DMPC a n d DPPC in such a m o n o l a y e r . Since ('£B - - T A ) is n e a r l y
i n d e p e n d e n t o f [l (see Fig. 2) a n d is a h n o s t the s a m e for m o n o l a y e r s a n d bilayers, the c u r v e s c a n be
a p p l i e d to d i f f e r e n t s y s t e m s s i m p l y b y displacing t h e m to m a t c h the n e w values of T A a n d "I'B,
melting enthalpies and the dependence of melting temperatures on pressure *
The isothermal compressibility ~ = - - ( 1 / a ) a a / a I ] is now easily evaluated
using the average area/molecule.
F + x F ~ B ) + ( 1 - - 9 C F ) ( X S a S A + xSBaSB)
a = X F ( X AFa A
(2)
(where x~ is the total fluid fraction) and standard expressions from Ref. 16. In
Fig. 3 we have plotted the compressibility as a function of temperature of a
monolayer comprising different mixtures of DMPC and DPPC. The pure fluid
phase of the II-a isotherm was fitted to the monolayer data [17] using the van
der Waals form equation and the pure solid phase was fitted assuming a small
constant compressibility. The fluid above the phase separation temperature is
twice or three times more compressible than the solid below the phase separation. In the separation region however, the compressibility is higher by an order
* Since t h e e q u i v a l e n c e b e t w e e n m o n o - a n d b i l a y e r s is only a p p r o x i m a t e (see e.g. Discussion in Refs. 17
a n d 18) t h e p h a s e d i a g r a m s of Fig. 2 s h o u l d be a p p l i e d to b i l a y e r s cure g r a n o salis.
29
38
.1,00
98
II20 9~890
(raN, r5~)
.70
10
4
.5O
-6
.8
1.0
a (nm 2)
Fig. 4. C a l c u l a t e d [l-a i s o t h c r m u s at 1 6 ° C f o r m o n o l a y e r m i x t u r e s o f D M P C a n d D P P C a t t h e a i r - w a t e r
i n t e r f a c e . T h e f r a c t i o n o f D M P C is i n d i c a t e d f o r e a c h c u r v e . T h e d a t a f r o m R e f . 17 h a v e b e e n u s e d
a s s u m i n g a v a n d e r Waals e q u a t i o n of s t a t e f o r t h e fluid a n d a s m a l l c o n s t a n t c o m p r e s s i b i l i t y f o r t h e solid.
of magnitude. The peaks in the compressibility are particularly pronounced
when the fluidus or the solidus line on the phase diagram is close to horizontal.
For example, an equimolar mixture whose components had a closer melting
temperature, or a larger melting enthalpy than DMPC and DPPC, would
produce a compressibility curve with two peaks and a marked trough between
them.
Theoretical H-a isotherms for binary mixtures of DMPC and DPPC calculated
with identical assumptions are shown in Fig. 4. Such diagrams have an advantage in allowing for easy comparison between theory and experiment. For
example, data on binary mixture monolayers at an oil-water interface [19] are
qualitatively similar to the isotherms of Fig. 4. The similarity between typical
experimental II-a isotherms for single-component monolayers and isotherms of
Fig. 4 for binary mixtures with a small concentration of one c o m p o n e n t suggests that the non-zero slope in the coexistence region may in some cases be
due to contamination b y a different species.
Discussion
The basic question which we have addressed is identification of the mechanism responsible~for an increase in transport across the membrane in the phase
separation or phase transition region. We have found that the lipid chain
interior of single-component bilayers would not lead to the formation of
domains near the phase transition temperature. Domains can then only be
formed as a result of interactions at the polar head-water interface. We know
[9] that bilayers made up of charged lipids do break up into domains in the
phase transition region. In this view, comparison of ionic permeability anomalies
exhibited by neutral and charged bilayers would be indicative of the role
played by the domain formation.
Our most interesting results are the lateral compressibility anomalies shown
in Fig. 3. In real systems, the shapes of the anomalies would be rounded, and
30
therefore closely resemble the specific heat anomalies measured for binary
mixtures of lipids [20]. It should be noted that the values of ~ obtained here
are typically an order of magnitude higher than the corresponding values for
single-component bilayers *. Anomalies shown in Fig. 3 should be compared to
the anomalies in transport determined experimentally. In some cases (e.g.
Fig. 1 of Ref. 6 or Fig. 3 of Ref. 12) the similarity is striking.
The present calculation could easily be extended to various models of nonideal mixing [16]. In some cases, it may be easier to test various non-ideal
mixing theories against ll-a isotherms or II-x phase diagrams rather than T-x
phase diagrams.
A more speculative application of our results is to enzyme activity over the
phase separation region. Many authors have discussed the temperature dependence of enzyme-catalysed reactions in terms of the fluidity of the enzyme's
lipid environment [10,21]. Where activity is presumed limited to a certain
range of membrane lipid fluidity (Raison, J.K., Berry, J.A., Armond, P.A. and
Pike, C.S., unpublished results), it is possible (and rather easier to model) that
the limitation is a certain minimum compressibility.
The importance of a change in order of magnitude in the compressibility to
the mechanical properties of a membrane is also worthy of consideration. In
the phase separation region, bending a membrane ueed create only a small
change in lateral pressures in the inner or outer monolayer since the moleculm"
area can more easily change to fit the new geometry. An organelle which is
already spherical may even swell a little at the expense of relatively little energy
in response to, say, an osmotic stress.
We have implicated physical properties, chiefly the compressibility, in two
physiological processes c o m m o n l y associated with low temperature damage in
organisms: enzyme inactivation [22] and electrolyte leakage [23]. This relationship is reported in more detail elsewhere [ 24].
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