Sterol Content

14 Pages·2005·3.04 MB·English

2616 Biophysical Journal Volume 72 June 1997 2616-2629
Bending Elasticities of Model Membranes: Influences of Temperature and
Sterol Content
Philippe Meleard,* Claire Gerbeaud,* Tanja Pott,* Laurent Fernandez-Puente,* Isak Bivas,# Marin D. Mitov,#
Jean Dufourcq,* and Pierre Bothorel*
*Centrede Recherche Paul Pascal, Centre National de la Recherche Scientifique, F-33600 Pessac, France, and #Institute ofSolid State
Physics, Bulgarian Academy ofScience, Sofia 1784, Bulgaria
ABSTRACT Giant liposomes obtained by electroformation and observed by phase-contrast video microscopy show
spontaneousdeformationsoriginatingfrom Brownian motionthatarecharacterized, inthecaseofquasisphericalvesicles, by
two parameters only, the membranetension c5 andthe bendingelasticitykc. Forliposomescontaining dimyristoyl phosphati-
dylcholine (DMPC) or a 10 mol% cholesterol/DMPC mixture, the mechanical property ofthe membrane, kc, is shown to be
temperature dependent on approaching the main (thermotropic) phase transition temperature Tm. In the case of DMPC/
cholesterol bilayers, we also obtained evidence for a relation between the bending elasticity and the corresponding
temperature/cholesterol molecular ratio phase diagram. Comparison of DMPC/cholesterol with DMPC/cholesterol sulfate
bilayers at300Ccontaining 30% sterol ratioshowsthatkc is independent ofthesurfacechargedensityofthebilayer. Finally,
bending elasticities of red blood cell (RBC) total lipid extracts lead to a very lowkc at 370C ifwe referto DMPC/cholesterol
bilayers. At 25°C, the very low bending elasticity of a cholesterol-free RBC lipid extract seems to be related to a phase
coexistence, as it can be observed by solid-state 31P-NMR. At the same temperature, the cholesterol-containing RBC lipid
extract membraneshowsan increase inthe bending constantcomparabletothe one observed forahigh cholesterol ratio in
DMPC membranes.
INTRODUCTION
Biological membranes are highly dynamic systems. They Sterols are widespread membrane molecules found in
are able to deform themselves following external stresses most ofthe plasma membranes. In mammals, cholesterol is
(erythrocytes in blood capillary) or cytoskeleton solicita- known to act as aregulator ofmembrane fluidity and many
tions (mitosis). In a general way, such geometric transfor- other different bilayer properties. One point to notice is a
mations cannot be considered without involving at least modulationofthephysical stateofasterol-containing mem-
some physical properties of the membrane such as lipid brane as afunction ofits sterol enrichment. This is the case
fluidity, shear, stretching, and bending elasticities (Sack- for water permeability (Milon et al., 1986), chain order
mann et al., 1986; Bloom et al., 1991; Sackmann, 1994). parameters of phospholipids (Davis, 1983; Leonard and
Giant unilamellar vesicles were shown to deform similarly Dufourc, 1991), polymorphism (Epand and Bottega, 1987;
(Berndl et al., 1990; Kas and Sackmann, 1991), proving Vist and Davis, 1990; Tampe et al., 1991; McKay and
such behavior to be quite independent of the membrane Robert, 1994; Slotte, 1995), self-diffusion coefficients
nature. (Almeida et al., 1992), viscoelasticity (Chabanel et al.,
Shape changes can be understood by using reduced pa- 1983; Elise Gabriel and Roberts, 1986), and membrane
rameters. This means that shape transition lines are found mechanical properties (Evans and Needham, 1986; Need-
independently ofliposomecharacteristics suchasgeometric ham et al., 1988; Duwe et al., 1990; Needham and Nunn,
(volume, area) ormechanical (elasticity) ones (Seifertetal., 1990; Bloom et al., 1991). To reinvestigate the last point,
1991; Heinrich et al., 1992). Nevertheless, the energy cost webegan asystematic studyto comparebendingelasticities
ofany deformation can be evaluated according to effective as a function of sterol content and temperature, for model
parameters and compared to a reference state. To study the and natural membranes. We will briefly give some theoret-
connection between membrane composition and deform- ical background forthe understanding ofthe bending mod-
ability of sterol-containing bilayers, we can thus vary the ulus measurement method using thermal fluctuations of
former and measure the response ofthe system.
giantquasispherical vesicles. The influences oftemperature
and sterol content were investigated for dimyristoyl phos-
phatidylcholine (DMPC)/cholesterol (Chol) bilayers. To
Receivedforpublication 18 October 1996 and infinalform 14 March checkwhetherthesteroleffectismodifiedbyachangeinits
1997. polarheadregion, cholesterol was substitutedby ananionic
Address reprint requests to Dr. Philippe M6l1ard, Centre de Recherche derivative, the cholesterol sulfate (CholS), found mainly in
PaulPascal,CentreNationaldelaRechercheScientifique,F-33600Pessac, the stratum corneum, a specialized outer layer of the skin.
France. Tel.: [phone]; Fax: [phone]; E-mail:
[email protected]. Finally, these complex lipid mixtures were related to mem-
C 1997 bythe Biophysical Society branes obtained from total lipid extracts of red blood cells
0006-3495/97/06/2616/14 $2.00 (RBCs), in the presence and absence ofphysiological cho-
Meleard et al. Bending Elasticities of Membranes 2617
lesterol concentration. The macroscopic behavior of the ulus, kc, ofmodel membranes (Bo andWaugh, 1989; Evans
obtained liposomes using RBC lipid extracts is shown to be and Rawicz, 1990; Kummrow and Helfrich, 1991). Histor-
related to microscopic and macroscopic information ob- ically, the first one was the analysis ofthermal fluctuations
tained by solid-state 31P-NMR measurements. of giant liposomes as seen by phase-contrast microscopy
(Servuss et al., 1976; Schneider et al., 1984; Bivas et al.,
1987; Faucon et al., 1989; Duweetal., 1990; Niggemann et
al., 1995); this is used herein to study kc variation as a
THEORETICAL BACKGROUND
function of the model membrane composition. Conse-
Mechanical properties of membranes quently, a theoretical description of this phenomenon will
be given first, before going into details ofthe experimental
In 1973, Helfrichintroducedthreeelasticities characterizing
requirements.
the membrane mechanical responses to a stress (Helfrich,
1973), in the limit ofa thin surface slightly deformed from
its equilibrium shape. The firstone, i.e., shearelasticity, has Theoretical description of the thermal
to play a role for biological membranes because of the fluctuation phenomenon
cytoskeleton but seems tobe ineffective forbilayers in their
fluid state (Evans and Needham, 1987). In this description, only quasispherical liposomes will be
Stretching elasticity is important only if an expansion or considered, i.e., vesicles characterized, for a given inner
a compression ofthe area is expected. The energy per unit volume %0, by a surface 9f0 in excess compared to the area
area,fs required to increase a surface element S0 by AS is of the sphere with the same volume. Defining R as the
equal to radius of the sphere:
4qrTR
(2)
JS 2 So to = 3
Atypical valueforks, the stretchingmodulus, is intherange -=4rR2(1 +s) (3)
100-300 mJ/m2 (Evans and Needham, 1987). Thus any
deformation involving k, needs a large amount of energy, where s ' 0 isthe excess area. Looking at such avesicleby
comparable with that required when increasing an oil/water a two-dimensional technique (Fig. 1), we observe the exis-
interface. tence ofmembrane undulations originating from Brownian
The third mechanical property of importance for mem- motion, as in the case ofred blood cell flickering phenom-
branes is bending elasticity. Considering So deformed ac- ena (Brochard and Lennon, 1975). These thermal fluctua-
cording to the twoprincipal curvatures cl and c2 atconstant tions induce permanent oscillations of the vesicle shape
area, the bending energy per unit areaf, is around aspherical form. Thenwecandefine r(O, (,, t) asthe
function locating the bilayer center in the direction (0, cp)
(spherical coordinate system) at a time t:
fc = 2 (c + c2-co)2 + kCIc2 (1)
r(0, (p, t) =R[I + u(0, p, t)] (4)
In this expression, kc,, the splay modulus, is always positive,
a typical value for a lipid bilayer being 10-19 J (Faucon et u(0, (p, t) is the relative deformation assumed to be small
al., 1989; Duwe et al., 1990; Evans and Rawicz, 1990; comparedto 1 (Jul << 1 andhence, s << 1). Inthatcase, we
Niggemann et al., 1995). On the other side, kc, the saddle- can write all ofthe characteristic quantities ofaliposome as
splaymodulus, canbeeitherpositiveornegative, depending a power series ofu(0, 'p, t) (and its derivatives u0, up, . . . )
on the molecular characteristics of the membrane. Up to keeping only the terms up to the second order. This can be
now there has been no experimentally determined value for done for the volume, the surface, and the elastic energy
the saddle-splay modulus; simulations give absolute values functionals, respectively /{u}, Y{u}, and i;u{u} (Mitov et
al., 1992):
from kBT (where kB is the Boltzmann constant and T the
temperature) to kc, i.e., -25 X kBT (Szleifer et al., 1990).
Moreover, when a closed object like a perfect or a slightly
deformed sphere is considered, the integration ofthe Gaus- V{u} = V(u) dOdqp, V(u) = R + u + u2)sin 0 (5)
siancurvature overthetotal surface, fiC1C2dS, isequalto4ir
(Gauss-Bonnet theorem; Darboux, 1972). As a result, there
is no contribution from the kc term to the deformation free
Y{u} = S(u, u0, uq,) dOdqp,
energy when we consider only continuous perturbations of
(6)
a given shape.
Significant work has been done to invent experimental
S(u, Uo, U,) = R2(1 + 2u + u2±+ 2)sin 0
methods that make itpossible to measure the bending mod-
2618 Biophysical Journal Volume72 June 1997
A B C
-N,~ ~~~~~~~~~
V~~~~~~~~~~~
hi~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~t
FIGURE 1 Twovideoimagesofaquasisphericalvesicle,asseenthroughaphase-contrastmicroscopeatdifferenttimes(AandB).Afterimageanalysis,
thecontourfluctuationsfunction,p(~p,t),canbedrawnandsuperimposedforthetwovideoimages(C)andrelatedtotheamplitudesofthethree-dimensional
shape through the autocorrelation function ofthe contourdeformations. The barat the lowercorer inA corresponds to 10 p!m.
or, equivalently, by minimization ofthe functional (Arfken,
9;,{u} = FC(u, u0, uqp, u0o, ue) dOd*p, 1985):
f{u} = 9iAu} + f{u}- Ap *V{u} (10)
F,u0,uq,P, Uoo, U~K) (7)
o and Ap are the Lagrange multipliers associated with the
constant area and volume constraints (physically, crcan be
= 2 [4 - 4V2u + 4uV2u + (V2u)2 + 2(Vu)2]sin 0 considered as a membrane tension and Ap as the pressure
difference between the inside and the outside of the mem-
with brane).
After calculation (Mitov et al., 1992), we obtain the
__2 Cos 0 expression for the fluctuation amplitudes u(O, sp, t):
(Vu)2 = (2+0ssini2no} Vu = (ka+ ssiinn00Ue+ ssin2 0,
AO nlnax
where we can omittheGaussian term in Eq. 7 as aconstant u(0, cp, t) = + > Unm(t)Yn(0 9P) (11)
when the sphere topology is maintained (Darboux, 1972). #7IT n=2,lml|n
We consider now the volume and the area of our lipo-
Y' being the spherical harmonics (Arfken, 1985). nma, is a
some.Wehaveshownpreviouslythatitisveryexpensiveto
cutoffintroduced inthe summation tolimitthedeformation
increase the overall area ofthe vesicle. On the other hand,
to wavelengths larger than molecular size. Using the re-
our experiences last no more than 10 min, the hydrostatic
duced membrane tension -a = O-R2/kc and the reduced pres-
pressure difference between the interior and the exterior of
theliposomebeingvery small (otherwise, wecannotexpect suredifference = APR3lkc, wewritefortheconstantfactor
AO (the static deformation compared to the sphere with a
large thermal fluctuations). We can thus assume that both
radius R):
the areaandthe volume areconstantduring the observation
of the thermal fluctuation phenomenon. Consequently we
Ag __P-__
can write (12)
2(;
H7r - 0 > - 2
f{u} = 0O (8)
which is somehow an equivalent expression for the well-
Y{u} = YO (9) known Laplace relation (Mitov et al., 1992). The dynamic
part itself, Un'(t), is not directly related to a theoretical
where ro and YO are the constants representing, respec- quantity, but the time average of its square modulus,
tively, the total volume and area ofthe liposome. (IU,(t)I2), can be obtained using the equipartition theorem:
Thequasisphericalvesicle, limitedbyasinglebilayerand
fully characterized by ('O, '0), is immersed in a thermal n22, Iml|n
bath atatemperature T. The shapes minimizingthebending (13)
energy, Eq. 7, andkeeping both the volume V{u} and area (IUm(t)|2) = kBT 1
9'{u} constantareobtainedbysolvingavariationalproblem n kc X"(n-1)(n+2)[V"+n(n+1)
Meleard et al. Bending Elasticities ofMembranes 2619
Measurable quantities Using spherical harmonics decomposition, thetime average
of the autocorrelation function, ~(y), can be written equiv-
Equations and 13 show that the dynamic part of the
11 alently (Faucon et al., 1989):
deformation (or equivalently the thermal fluctuations) is
definedusing sphericalharmonics, Ym(0, cp). Unfortunately,
nn
we cannot observe the liposome in three-dimensional space ((y) = E (Bn(t))Pn(cos Y)
(using, forexample, aconfocal microscope) atasufficiently n=2 (17)
high resolution intime. As aresultofthe spherical symme-
_kTPgo(cos .Y)
try of the static shape, one can demonstrate that a two- >
dimensional section of a quasispherical vesicle (Fig. 1) is kc °( =)2 (n + 2)(n- 1)[r+ n(n + 1)]
enough to obtain the information we are interested in, i.e.,
the fluctuation amplitudes (IUmJ2).
kBT (2n + 1)
conTthoeurimoafgteheaneaqluyastiosrioaflFsiegc.ti1onBolfeatdhsetloiptohseoimnes,tap(netpa,net)ou=s Bnt) 4(rkc(X (n + 2)(n -1)[ + n(n + 1)]
(18)
R[1 + u(fl/2, sp, t)] (Fig. 1 C). Two different methods have (2n + 1)
been proposed in the literature to link this experimental (I[(Um(t)|1)
information to thebending modulus kc. One was introduced
by Engelhardt et al. (1985). Calling Vq(t) the q mode am- from which kc and a can be determined using a least-
plitude obtained using a Fourier analysis of the relative squares method (Mitov et al., 1992).
contour deformation u(Q/2, Sp, t) = (p(cp, t) - R)IR at t, we It is important to note that the autocorrelation function,
can write Eq. 16, and its decomposition into Legendre polynomials,
Eq. 17, give directly a proportionality relation, Eq. 18,
27r
betweenthetheoretical amplitudes ofthe sphericalharmon-
ics, (IUnm(t)12), and the experimentally measurable quanti-
q 2 2, Vq(t) C2 i; u(QI2, Sp, t)exp(,,eqcp) dep ties, (Bn(t)). Comparing to Eq. 15, one observes that
(IVq(t)12) is unfortunately a complex sum over many
P=o (IUq(t)12), depending on kc and &r. This complicates the
nmax parameter-fitting procedure and makes this approach very
E Uq(t)0Er(r7T/2) (14) tedious at least, ifnot unsuitable.
=
n=nql
nfma
> (IVq(t)12) = > (Ium(t)2)[E{q(O2)]2 (15) MATERIALS AND METHODS
n=max(2,jqj) LipidswereobtainedfromFluka(Buchs,Switzerland).Cholesterolsulfate
was kindly provided by Christian Dior Laboratory (St Jean de Braye,
where enm(O) is defined through the Legendre polynomials, France).Redbloodcellmembranelipidswereextractedbyhexane/isopro-
Pm, using the relation (Arfken, 1985) panol according to the method ofRadin (1981). In thecase ofredblood
cells this solvent mixture is preferable to commonly used chloroform/
nm(o)- (_1)m 2+ I (n m)! X Pm(cos 0) mBreitehfalyn,olwitmhixctounrsetsa,ntasstiirtridnig,ss2o0lvmesloaflmpoasctkendocepllisgmaerentasdd(eRdaddirno,pw1i9s8e1)t.o
500mlofhexane/isopropanol(3:2,v:v),followedbyfiltering.Thesolvent
isevaporatedunderreducedpressure. Theresulting lipidic filmis imme-
The second method was introduced by Bivas et al. diatelydispersedincyclohexane,lyophilized, andstoredundervacuumat
(1987). It is based on the analysis of the autocorrelation -20°C.ForfurtherpurificationofRBClipidsfromnonlipidcontaminants,
function ofthe contour fluctuations, ~(y, t): Sephadex(G-25,coarse,beaded;PharmaciaFineChemicals)columnchro-
matography isperformed asdescribed by Rouser etal. (1967) and Kates
(1972). The integrity of the lipid extract was qualitatively checked by
two-dimensional thin-layer chromatography (elution solvents: 1) chloro-
form/methanol/water (65:25:4 v:v:v); 2) butanol/acetic acid/water (6:2:2
O(7 t)= [ pjrp(q + y, t)p(c, t) dp-p2(e)] (16) v:v:v)).Onlytracesoflysolipidsweredetected.Therelativeamountsofthe
R2 main phospholipid classes in the lipid extract were determined by high-
resolution31P-NMRandfoundtobeinaccordancewithknownratios(34%
phosphatidylcholine,27%phosphatidylethanolamine, 24%sphingomyelin,
and 15% phosphatidylserine). The sterol content ofthe RBC lipids was
where -y is the correlation angle, is the p complex conju- determinedwithapathologylaboratory system(BM/Hitachi911;Hitachi,
gate function, and p(t) is the angle average of the contour Tokyo, Japan) by a standard kit (Boehringer Mannheim Meylan, France
radius function p(Sp, t): SA) using cholesterol esterase and cholesterol oxydase reactions. Sterol
extractionfromthetotalRBClipidswasachievedbytheso-calledacetone
precipation (Kates, 1972). Separation was verified by thin-layer chroma-
tography. Thechromatography oftheacetone-insoluble fraction showsall
p(t) = 2 4p(9p, t) dp phospholipids initially present, as well as the absence offree fatty acids,
cholesterol, anddiacylglycerides.
2620 Biophysical Journal Volume72 June 1997
Solid-state31P-NMRmeasurementsonlipiddispersionsinexcesswater lipid
werecarriedoutonaBrukerARX300implemented forhigh-powersolid-
state spectroscopy and operating at 121.49 MHz. A phase-cycled Hahn-
echopulsesequence(RanceandByrd, 1983)withquadraturedetectionand
gatedprotondecouplingwasused.Sampleswereallowedtoequilibratefor
atleast30minatagiventemperaturebeforetheNMRsignalwasacquired;
the temperature was regulated to ±1°C. Typical acquisition parameters
wereaspectralwindowof50kHz,a-n/2pulsewidthof8p.s,delaybetween
thetwopulsesformingtheechoequalto40p.s,arecycledelayof6s(50 ITOelectrodes
s forhigh-resolution spectra), and 2200 scans. Spectral simulations were
performed on an Alpha computer (Dec 4000, Digital, Nashua, NH) as
described by Pott and Dufourc (1995), assuming either a spherical or a
slightly ellipsoidal distribution of the bilayer normal. The amount of
isotropic lines superimposed on a powder pattern was determined by
simulation of a Gaussian or Lorentzian line and subsequent subtraction
fromtheexperimental spectrum. Percentages areexpressedrelative tothe needle
total spectral area. I.
The samples used for NMR studies were observed under a phase-
contrast microscope for direct visualization of the consequences of a r l - o I
-L -
temperature changeforliposome dispersions. Deionized waterwasadded
(I
to obtain a lipid concentration close to 0.2 mg/ml. The vesicles were
injectedinacellsimilartotheonedescribedbyFauconetal.(1989).Then / /~ a\
the cell was sealed and maintained at different temperatures (room tem-
L L- I
perature, 37°Cand50°C)for 1 daytoallowequilibrium. Theevolutionof
theliposomeshapewasfollowedfromtheirequilibriumtemperature(37°C I
and 50°C) toroomtemperature. lipid Ptelectrodes
FIGURE 2 Sketches ofthe electroformation cells used (A) when tem-
Electroformation of giant
peratureregulationisneededand(B)whenobservationsaremadeatroom
quasispherical liposomes
temperature.
According to the model introduced in the previous paragraph, bending
elasticity ofmembranes can be measured usingquasispherical and unila- immersion x100/1.25objective;Zeiss,Oberkochen,Germany)andaCCD
mellarliposomes. GUVs(giantunilamellarvesicles) with atypical radius
video camera (C2400-77; Hamamatsu, Hamamatsu City, Japan). Video
of 10 p.m are used to obtain an accurate measurement of the thermal images are recorded on a U-matic recorder (VO 7630; Sony, Tokyo,
fluctuationdeformationsbyvideomicroscopy(seebelow).Theymustalso
Japan),digitizedonaPericolor 1500(Matra,Paris,France), andanalyzed
be isolated andhaveno (visible) surface defects. onan AlphaComputer (Dec 4000; Digital) (Mitovetal., 1992).
Suchvesiclesarepreparedusingelectricfieldstoincreasetheirforma- Thecontourextractionprocedure(Fig. 1,BandC)isverysimplewhen
tionrateandyield(Angelovaetal., 1992b).Lipidsarefirstsolubilizedinto aphase-contrastmicroscopeisused.ThepicturesinFig. 1,AandB,were
an organic solvent (chloroform/methanol 9:1, lipid concentration -0.2 obtained afterabackground substraction. The equatorial cross section of
mg/ml). Twodifferentexperimental chambersareprepared, dependingon the vesicle is a slightly deformed black circle. Looking at a defined
theworkingdistanceofthemicroscopeobjective.Thefirstoneisusedwith direction pfrom thecenter0, theintensity resembles thatofaninverted
anoilimmersionsetupwhenatemperaturecontrolisneeded(thisthermal Gaussiancurve, whichisclosetothemeanimageintensityIeverywhere,
regulation device is presented by Fernandez-Puente et al., 1994, and
except in the contour region, where it decreases abruptly (within 5-10
detailed by Fernandez-Puente, 1994). It is built from two Indium Tin
pixels) through aminimum Im, the value (but not the position) ofwhich
Oxyde (ITO) covered glass slides separated by a 0.3-mm-thick silicon usuallydependsontheprecisepositionoftheobjectivewithrespecttothe
spacer(Fig.2A)(innervolume -100,ul).Thesecondchamberisusedfor liposome bilayer. Fitting this intensity profile with a Gaussian function
roomtemperatureobservationwithawaterimmersionobjective(Angelova leads to the location of that minimum, assumed to be the membrane
etal., 1992b). Itismade ofa 1-mm-thick glass cell (similarto afluores- positioninthecpdirection.Usingthatprocedureonceforevery9pdirection,
cence cell) where two parallel platinum wires of0.8 mm diameter have weobtainbetween500and900pointsforeachcontour,dependingonthe
been introduced (Fig. 2B) (innervolume -300 p.l).
liposome size (Fig. 1 C).
The lipid solution is deposited on the electroformation cell conductor Adetailed descriptionoftheexperimental limitations inherentinsuch
(-2 p.l ofthechloroform/methanol lipidsolutioninasingle spotforITO a method can be found in Mitov et al. (1992). To summarize, the noise
slides or in four to six different locations along the platinum wires). introduced by the video system (essentially the video recorder) and the
Organic solvents are removed by evaporation undervacuumfor 1 h, and digitization procedure leads to a white noise in the Fourier spectrum (an
deionized water(Millipore mQ, Bedford, MA)isaddedslowly toprevent unknown constant value added to all (IVq(t)12)) and a Dirac 6-function
lipiddispersion.Thentheelectricfieldisappliedat10Hzfromlowvoltage
addedtotheautocorrelationfunction6(y).Becauseofanicemathematical
(30 mV/mm) to "high" voltage (400 mV/mm) in 10 min. After atypical propertyofthe8-functionandtheLegendrepolynomials,thisnoisehasno
periodof2h,quasisphericalvesicles areformed. Usuallyliposomes stick influence on the experimental (Bn(t)), thus leading to a higher precision
(probablythroughfilaments)totheconductor.Dispersionisthenpromoted
thantheFouriermethod(Engelhardtetal., 1985).Usingalargenumberof
by alow-frequency (4-Hz) field, sometimes followedby "afew taps" on analyzed images (N 400) leads to aprecision ofthemean value (Bn(t))
the cell bottom. During the whole process, electroformation can be con- N-1/2 due to the intrinsically stochastic nature ofthe thermal fluctua-
trolled by microscopy.
tions.Moreover,itisknownthatvideoimagesareessentiallytheresultof
lightsignalaccumulationonthecameratarget,eachpixeloftheCCDplate
Data treatment being illuminated for 40 ms. Each movement characterized by a speed
greaterthanonepixel (tobeexact,thedistanceseparatingtwopixels)per
Fluctuating vesicles are observed with a phase-contrast microscope (Ax- 40 ms is blurred. Another important improvement in ourtreatmentis the
iovert 135withawaterimmersion X40/0.75objectiveorIM35withanoil introduction of a correction factor to take into account this integration
Meleard et al. Bending Elasticities of Membranes 2621
effect ofthe video camera (Faucon et al., 1989). We also note that the that can be obtained from their analysis. In the case of
integration effect becomes negligible when a stroboscopic lamp replaces DMPC in excess water (we are close to the infinite dilution
theusualincandescentlightasamicroscope source(Meleardetal., 1992) condition, the lipid to water mass ratio being smaller than
oriTfhaeheixgphe-rsipmeeendtaclamaeurtaociosrruesleadtiionnstfeuandctoifonasncoarnditnhaerynTbeVcCalCcuDlactaemdearan.d 0.1%), we know the phase diagramtobe characterizedby a
theirLegendrepolynomialamplitudesestimated.FromEqs. 17and 18,we thermotropic behavior. Whereas we already know that the
deduce these amplitudes tobe independent quantities thatcanbe directly vesicle reacts to a temperature change by a modification of
corrected for the integration effect of the video camera (Faucon et al., its membrane tension (Kas and Sackmann, 1991), it has
1989).Thisisthemainadvantageoftheapproachusingtheautocorrelation beenreportedrecentlythatthebendingrigidityalsodepends
fmuantcitoinon(Ecnogmeplaharreddtteotaal.m,o1r9e85d)i.reWcittFhoutrhieesreacnoarlryescitsedofdatthaeacnodntfoourradseeftoro-f on the temperature (Fernandez-Puente et al., 1994; Honger
p different experimental amplitudes Ber'P, 2 ' n ' p + 1, we must et al., 1994; Niggemann et al., 1995).
minimize the following sumusing aniterative procedure: The results for kc measurements obtained with pure
DMPC liposomes are reported in Table 1. We should recall
P+l(Bexp-(B (0) 2 thatforall oftheresults shown (as otherwise indicated), the
n- cell temperature was held constant at the required temper-
n=2\ ex
ature during the electroformation swelling and the thermal
Inthisexpression, Be,XPandDeXPare,respectively, then-orderexperimen- fluctuation video recording procedures. For a temperature
taly estimated average amplitude andthecorresponding dispersion ofthe range from 15°C to 50°C, the cell temperature is controlled
PoLegendrepolynomialamplitudes(Bn(t))beingthetheoreticalexpression with a precision ofabout ±0.250C. The error bars in Table
l1i8.poAsolmeeas(tF-isgq.ua3)r.esItmceatnhobednloetaedsdtthoatthfeoresltoiwmaetnioonugohfm(kecm,b&r)anfoertaengsiivoenn, 1 are the usual standard deviations for kc values only. It is
kc is obtained independently from &f when n2 is large compared to cr possible to detect three different regions for kc dependence
(Faucon etal., 1989). as a function ofthe temperature. For T> Tm + 6°C (Tm =
Finally, thisprocedure isrepeatedondifferent liposomes toreachakc 23.9°C is the gel-to-liquid phase transition temperature for
dispersion equal to afew percent (typically, a setof 10different vesicles DMPC; Lewis et al., 1987), kc seems to be independent of
tisharteqsuuicrhedantoaovbetraaigneaesdtiismpaetrisoinonfofrorkckcreoqfui-r5e%s)a.boIuttshaomuoldntbhe'smewnotrikonfeodr the temperature, the increase being too small to be mean-
eachparticularexperimental condition, including apreliminary periodfor ingful compared to the error bars. This behavior does not
theelectroformation procedure adjustment. seem to be general for unsaturated lipids far from their
phase transition temperature (Niggemann et al., 1995),
whereas it has also been found for other saturated phos-
RESULTS
phatidylcholine bilayers (Fernandez-Puente et al., 1994).
DMPC bilayers Furthermore, kc increases slowly when Tis decreasing from
The general requirements already introduced were taken Tm + 6°C to Tm + 3°C. This effect is not very important
(-20%) but is statistically significant. This behavior is
intoconsideration forboththechoiceoffluctuating vesicles
inside the electroformation cell and the experimental data followed by a relatively sharp drop in the range Tm + 3°C
to Tm + 1°C. Unfortunately, we were unable to measure kc
very close to Tm for technical reasons.
6 However, wenotice thatitis possible topass through the
phase transition region without destroying the vesicle dis-
persion (results not shown). Independently ofthe liposome
5 considered when reducing Tto Tm, we observe first a rapid
disappearance ofthe thermal fluctuations at the microscope
41 resolution. This phenomenon is notrelatedto avery precise
(b temperature, because other liposomes still fluctuate. At a
-x 3 temperature closer to Tm, one can distinguish between two
X1-
2
TABLE I Bending moduli for DMPC/Chol membranes
T kcl 0/0 kc90l kr03 coS
1 (OC) (X10-19J) (xio-19J) (xO-1'9J) (xO-1'9J)
20 6.1 ± 0.2
O_ 24.8 0.9 ± 0.1
5 10 15 20
25 0.8±0.13
25.2 1.45 ± 0.06
Order
26 1.1 ± 0.1 1.63 ± 0.07
27 1.52 +0.06 2.23 ± 0.07
FIGURE 3 Results ofthethermal fluctuations analysis ofthe liposome
30 1.30 + 0.08 2.00 ± 0.1 4.1 ± 0.25 6.1 ± 0.3
shown in Fig. 1. Result of the fitting procedure obtained without
, 40 1.27±0.09 1.84±0.09 3.07±0.13 3.7±0.3
introducingthecorrectionfactor(seetext). Fittingprocedurewhere
-,
thethermalfluctuationamplitudesarecorrectedfromthevideointegration T is the cell temperature. The superscript on the bending modulus kc
effect. indicates the DMPC/Chol molarratio.
2622 Biophysical Journal Volume 72 June 1997
different behaviors. Depending on the liposome followed blood cells. The data are reported in Table 2. DMPC/Chol
during the cooling process, either an "explosion" process is andDMPC/CholS systems containing both 30% sterol con-
observed (the liposome being destroyed), or the liposome tents at 30°C are characterized by the same kc (within the
assumes a spherical shape that stays stable at T < Tm. The experimental error).
latter restores its fluctuating shape afterincreasing the tem- Using the RBC lipid extraction procedure (see Materials
perature to T > Tm. All of the liposomes remaining now and Methods), we also succeeded in measuring bending
show very large thermal fluctuation amplitudes, and the rigidity ofnatural protein-free membranes. The analysis of
mean shape resembles an ellipsoid. the RBC lipid extract yield acholesterol to lipid mass ratio
of 18.4%, as expected in the case ofhuman redbloodcells
(Devaux and Seigneuret, 1985), leading to a molar ratio
close to 40%. The measurements ofkc for the lipid extract
Sterol-containing membranes
give very interesting results (Fig. 4). At room temperature
An importantfeatureofthe additionofcholesterol toapure (taken to be 25°C), bending elasticity of RBC lipid mem-
saturatedphospholipid seemstobetheappearance ofdipha- branes is better represented by three distinct values in the
sic equilibria (coexistence of two lamellar phases within a range (2.68-4.7) X 10-19 J, whereas the analysis ofsterol-
bilayer) as afunction ofthetemperature andthe cholesterol free RBC lipidmembranes leads to a singlekcestimation of
content (Vist and Davis, 1990; Almeida et al., 1992; Mc- -1.0 X 10-19 J. The electroformation method was also
MullenandMcElhaney, 1995). Withreferencetotheabove, used with lipid extracts to produce giant vesicles at physi-
we suspect that such phase transitions influence the bilayer ological temperature. This procedure did not create any
mechanical properties. Thus we firstmeasured kc as afunc- technical problems, except for sterol-free RBC lipid ex-
tionofthetemperatureforDMPC/cholesterol mixtureswith tracts. In that case, all ofthe vesicles obtained were spher-
variable mole fractions of sterol. ical (no thermal fluctuations), explaining the absence ofkc
According to thephase diagrampublishedbyAlmeidaet values at 37°C. Toimprovetheyield offluctuating vesicles
al. (1992), we choose three different cholesterol molar ra- and in that case only, the liposomes were swollen at room
tios: 10%, 30%, and 50%. A 10% cholesterol-containing temperature first, then T was slowly increased to 37°C.
membrane should be a bilayer in which phase separation Unfortunately, no improvement was noticeable. However,
occurs at T < 30%. Thirty percent cholesterol membranes comparing the results presented in Tables 1 and 2, we see
are close to the limit of the liquid order phase in the that the bending rigidity for cholesterol containing RBC
temperature range studied here. A 50% cholesterol ratio is lipid extract at 37°C is quite identical to that of DMPC
roughly the upper limit content for mammalian lipid sys- membranes at high temperature.
tems. It is also important for a comparison with the mea- To understand the results obtained for kc measurements
surements for RBC lipids (see below). on lipid extracts by microscopic observations and, particu-
The bending elasticity obtained as a function oftemper- larly, the strange behavior of cholesterol-free RBC lipid
ature andcholesterol ratioforDMPC/cholesterol bilayers is extract liposomes, samples can be studied by solid-state
summarized in Table 1. We notice that kc changes versus 31P-NMR experiments (Bloom et al., 1991). Thermal vari-
temperature are qualitatively identical forboth pure DMPC ations have been accomplished by firstheating the samples
and DMPC systems containing 10% cholesterol. However, from 25° to 60°C, followed by adecrease in temperature to
this is not the case for larger sterol contents, at 30% and 25°C (temperature steps: 5°). Lipid extracts with and with-
50%, wherekcincreases continuously withadecreaseinthe out cholesterol are both characterized by a superposition of
temperature T. At a given high temperature (30°C and an isotropic line on a powderpattern (datanot shown). The
40°C), kc also increases as a function of the cholesterol phospholipid fraction characterized by a fast isotropic re-
fraction. orientation was found to vary strongly, depending on the
Qualitatively, a 10% cholesterol ratio in DMPC leads to method used for the dispersion preparation. However, for
aliposome behavior very similar to the one ofpure DMPC
bilayers when T is lowered to Tm. All of the fluctuating
liposomes change their shape from a Brownian spheroid to TABLE 2 Bending moduli for DMPC/CholS and RBC lipid
extract bilayers
a nonfluctuating sphere. Some ofthem disappear at a tem-
perature close to Tm, whereas others cross Tm without any RBC RBC Sterol-free
apparentdamage. Athighercholesterolcontent, itis always DMPC/CholS extract extract RBC extract
T= 30°C T= 250C T= 37°C T= 25°C
possibleto cross Tm (definedforpure PC) withoutdramatic
changes in the stability and morphology of the GUVs, 2.68 + 0.19
leading to kc measurements at temperatures below Tm for kc 3.8 ± 0.2 3.56 ± 0.14 1.46 ± 0.16 1.0± 0.15
(Xl'o9J) 4.7 ±0.2
30% cholesterol molar ratio bilayers.
We also measured the bending rigidity of other choles- Tis the temperature and kc is the bending rigidity. The concentration of
cholesterol sulfate (CholS) inDMPC bilayers is 30 mol%. In the caseof
terol-containing model systems, to compare theirbehaviors
red blood cell lipid extracts, two kinds ofbilayers were studied: with a
to thatofDMPC/cholesterol bilayers. This was the case for natural cholesterol amount (RBC extract) and after the elimination of
DMPC/CholS bilayers or for a total lipid extract from red uncharged lipids (sterol-free RBCextract).
MelXard et al. Bending Elasticities ofMembranes 2623
7 I I I . I I I . . I I I 14
6 S12
5
° 0
4 ug66
(b *
-X cr.
3
u
2
4-
-0 :
I 25 35 45 55 25 35 45 55
Temperature [°C]
un- . . . . . .. . . . . I .---I-.I ..
20 24 28 32 36 40
FIGURE 5 Secondmoments of31P-NMRspectraofRBClipidextracts
T (°C)
without (A) andwith (B) cholesterol, as afunctionoftemperature. Filled
symbolscorrespondtoanincreaseinthetemperatureandopensymbolsto
FIGURE 4 kcdependenceontemperature,asafunctionofthemembrane adecrease. Lines aredrawnto helpthereader.
composition. For DMPC/Chol mixtures: 0, pure DMPC; E, 10 mol%
Chol; O, 30 mol% Chol; A, 50 mol% Chol. 0, Bending rigidity of 30
mol%cholesterolsulfate/DMPCbilayersat30°Conly.Thebehaviorofred fication inFig. 6A). By spectral simulationitwas estimated
bloodcelllipidextractisshownwith(X)andwithoutsterol (U)for25°C
that -10% ofthe phospholipids contribute to this subspec-
and37°C.Linesareusedtohelpthereader;thearrowpointstothebending
modulus ofsterol-free RBC lipidextracts. trum, with achemical shiftanisotropy, Aor, of-90ppm. In
the case ofthe cholesterol-containing lipid extract, spectra
acquired under the same conditions are characterized by a
both systems (with and without cholesterol) and whatever single axially symmetrical powder pattern component with
the sample preparation, the amount of isotropic line in- a Aorof -42 ppm (Fig. 6 B).
creases with increasing temperature. In the case of the Finally, one can correlate NMR and kc measurements in
cholesterol-free RBC extract, the amount of isotropic line a qualitative manner by following the behavior of giant
increases significantly for T 40°C. This behavior is vesicles when changing the temperature usingdirectmicro-
irreversible, i.e., a decrease in temperature leads to un- scope visualization of NMR sample preparations. Qualita-
changed percentages ofthe isotropic line. In the case ofthe tively, RBC lipid extract GUVs (with cholesterol) never
cholesterol-containing RBC lipids, the amount ofisotropic show fluctuations when maintained for along time atroom
line rises quasicontinuously with increasing temperature, temperature. Some liposomes stick to others, indicating a
butincontrasttothe sterol-free RBC lipids, this behavioris lowering oflong-range repulsions. Raising the temperature
reversible. Furthermore, one remarks an important differ- to -50°C leads to the appearance of fluctuating vesicles.
encebetweenthetwobilayersystems intheevolutionofthe Whileobserving suchliposomes duringtheloweringofTto
second spectral moment, M2, withtemperature (Fig. 5). The room temperature, a rapid decrease in the thermal fluctua-
polar RBC lipids exhibit a substantial hysteresis in the tion amplitudes is detected. Finally, their shapes transform
thermal variation. The firstincrease in temperature leads to into spherical objects. The cholesterol-free lipid extract
an important decrease in M2 centered on 40°C. Once 60°C behaves differently when GUVs are observed at 25°C after
is reached, cooling results in a remarkable increase in M2, the incubation at 50°C. In the first seconds afterthe begin-
leadingtoavalueof 12.5 X 103ppm2 at25°C, incontrast
to -8 X 103 ppm2 observed before the thermal treatment
(Fig. 5 A). In contrast, in the case of the cholesterol- A B
containing RBC lipids, M2 decreases only slightly and al-
most linearly with increasing temperature, and reversibility
is observed (Fig. 5 B), a typical behavior for lipid disper-
sions containing high amounts ofcholesterol ('30 mol%).
Yet the thermal evolution ofM2 for the dispersion without
cholesterol isquitesurprising; thehighvaluesofM2at25°C
-60 -40 -20 0 20 40 60 -60 -40 -20 0 20 40 60
in particular are remarkable. In this context it is interesting ppm ppM
to further analyze the shape ofthe 31P-NMR spectra. Actu-
ally, the unexpectedly highM2 value obtained afterthermal FIGURE 6 Selected3'P-NMRspectraofRBClipidextractswithout(A)
treatment is reflected by the presence ofa very large spec- andwith(B)cholesterol, at25°C.InAamagnification(douedline)anda
tral contribution, with the limit of the very broad powder simulation (dashed line) are shown. The corresponding parameters were
10%fortheisotropiclineand 10%Ao- 20ppm, 10%Ao 90ppm,and
pattern lineshape on the left side at -50 ppm (see magni- 70% Ao/- 40 ppmforthe powder patterns.
2624 Biophysical Journal Volume72 June 1997
ning ofthe observation, the larger liposomes resemble qua- checked for given experimental conditions (temperature,
sispherical or ellipsoidal objects with large thermal fluctu- membrane composition) by recording the thermal fluctua-
ations (not shown). After a short time (-1 min) as T tion of -10 liposomes. This leads to a mean kc and an
decreases, most of these vesicles change their shape to associated error bar (standard deviation) generally smaller
unusual polyhedral forms (Fig. 7). It can be noted that flat than kc/lO that can be used to analyze the relationships
membrane areas are quite rigid at microscope resolution, betweenthe mechanical modulus and any otherbiophysical
whereas the high curvature points fluctuate and seem to be parameter. Wedemonstrateherethatkcistightlyrelatedtothe
responsible for the overall vesicle shape changes. This be- thermodynamic statecharacterizing themembrane, depending
havior is maintained when the cell stays at room tempera- on the phase diagram (temperature and/or composition).
ture for a few days.
Model membranes
DISCUSSION
For pure DMPC bilayers, kc remains constant within the
Since the pioneering workofBrochard andLennon in 1975
experimental error for large temperature changes far above
clearly explaining theorigin oftheRBC flickeringphenom-
Tm. Then it increases to Tm + 3°C (Fig. 4). To explain the
enon, bending elasticities have been measured by using
observedbehavior, we returnto simple microscopic models
different experimental approaches. The thermal fluctuation
relating bending modulus to the most characteristic molec-
analysis of giant vesicles is one of them. It is based on
ular parameters in the case of one-component membranes,
optical observations and image analysis thatdoes not imply
themolecularareaA andthebilayerthicknessb(Petrov and
physical contacts witha solid material suchas glasspipettes
Bivas, 1984; Szleifer et al., 1990):
(Evans and Rawicz, 1990; Waugh et al., 1992). However,
the application of this technique is clearly restricted to bn
sparse objects: we are speaking about giant, isolated, fluc- k KAm n, m'. 1 (19)
tuating, unilamellar vesicles, alarge numberofqualities for
a simple mesoscopic-scale structure. However, from the It is known from x-ray data from DMPC bilayers that a
practical point ofview, their formation rate and yield were temperature decrease induces a larger increase in the mem-
improved by using electroformation to obtain significant brane thickness b in the range 25-30°C than in the range
populations of such objects. 30-40°C (Kirchner and Cevc, 1993), and the thermal area
As already mentioned, giant fluctuating liposomes are expansivity obtained by micromanipulation remains larger
fully characterized by two distinct parameters, the reduced at 29°C than at 35°C (Needham et al., 1988). Considering
membranetension aandthebendingelasticitykc(Fauconet our results, it appears that any changes in b or A are not
al., 1989). Thefirstoneisrelatedto ageometricproperty of large enough to influence kc behavior for temperatures
a particular vesicle (surface/volume ratio), and the second, greater than 30°C. This is no longer the case in the range
kc, is a characteristic of the lipid bilayer itself. This is 27-30°C, whereasmallbut significant increaseis observed
>|N
_ w
q
.49k, la, 11*..
tf.:.
W
FIGURE 7 Videoimages ofliposome suspensions fromsterol-freeRBClipidextractusedforNMRstudiesatroomtemperature. Thebarinthelower
right image corresponds to 10 ,um.
Meleard et al. Bending Elasticities of Membranes 2625
(around 20%). However, it has been reported that a larger poor and rich regions (Almeida et al., 1992; McMullen and
temperature dependence is obtained with unsaturated lipids McElhaney, 1995). This phase separation process may be
(Niggemann et al., 1995). important for mechanical properties, as they are known to
The dependence of kc on the molecular parameters was be related to molecular parameters (Needham and Evans,
also demonstrated by following the behavior of saturated 1988; Needham et al., 1988; Needham and Nunn, 1990;
phosphatidylcholines as a function of their chain length Fernandez-Puente et al., 1994). It may induce large varia-
(Fernandez-Puente et al., 1994). It has been shown experi- tions as the different phases change in size, shape, and
mentallythatthebendingmodulusincreases withthesquare relative amount. Such behavior can explain the lowering of
of the hydrophobic thickness (Fernandez-Puente et al., kc close to Tm at 10 mol% in cholesterol, but we did not
1994), meaningthatthen-exponentinrelation 19isequalto detect any anomalies for kc as a function of T for higher
2 (Petrov and Bivas, 1984) for three saturated phosphati- sterol ratios.
dylcholines (dilauroylPC, dimyristoylPC, anddipalmitoylPC). Nevertheless, it is clear from ourdata that an increase in
To understand the thermal dependence forkc close to Tm, cholesterol in a DMPC membrane induces a large increase
one must consider a local deformation. For one-component in kc for any given temperature. This effect is so important
bilayers, a curvature change induces a compression for the for 50 mol% compared to DMPC bilayers at 300C that it
hydrophobic part of the outer monolayer (located in the was impossible to measure kc at 20°C. At 30 mol% choles-
opposite side compared to the curvature center) and an terol content (T = 30°C), our kc value agrees with those
expansion of the inner monolayer. This is the result of the published, despite the fact that such values were character-
elastic interactions in the monolayer, which are concen- ized by larger error bars (Duwe et al., 1990). Surprisingly,
trated mainly in the proximity of the hydrophilic region. their data for 20 mol% cholesterol at T = 30°C seem to be
Very close to Tm, a small increase in the chain density very closeto ourkc value fora 10 mol% cholesterol bilayer
(related to the lateral tension in the hydrophobic part) after at the same temperature. Other results gave systematic kc
a curvature change would initiate a pressure-induced phase increase with cholesterol content, using PC lipids (Evans
transition toward a pseudophase characterized by a more andRawicz, 1990; Song andWaugh, 1993), withnoticeable
condensed chain region. As a result, a coexistence offluid- differences compared to our measurements. Such differ-
like and gel-like hydrophobic domains will take place. ences may be due totheirdifferenttechnical approaches, as
Changing the curvature will lead to a change of domain already mentioned in Materials and Methods. This should
relative proportion only, without any elastic response ofthe be tested using the different approaches, at a given place,
chain region. Thus the vanishing stretching modulus ofthe similartothe workofNiggemann et al. (1995); this pointis
chain region strongly facilitates the curvature deformation, under study in our laboratory.
explaining the decrease inthe apparent bending modulus of Forthesame30mol% sterolfractionat300C,onemaybe
thebilayerinthevicinity ofthephasetransition temperature surprisedtofindanidenticalkcforDMPC/Chol andDMPC/
(Fernandez-Puente et al., 1994). CholS membranes. This behavior was unexpected, because
WithregardtoFig. 4, weconcludethatthevariation ofkc NMR and fluorescence polarization results showed that the
with temperature for a 10 mol% cholesterol bilayer is sim- ordering properties ofcholesterol sulfate are less important
ilarto thatofpure DMPC membranes. This is probably due than that of cholesterol at the same molecular ratio (Le
to the low amount of cholesterol used. However, Table 1 Grimellec et al., 1984; Faure et al., 1996). Concerning the
shows akc decrease (-10%) when Tis changed from 30°C influence ofthechargedensity onkc, theoretical predictions
to 40°C, whereas the corresponding bilayer thickness vari- are contradictory. The basic idea involves the formation of
ations in the same temperature range are not significantly adouble layerinfrontofchargedmembranes (Russeletal.,
different (Leonard, 1993). This indicates that the micro- 1989). Forarigidinterface,thedouble-layeriondistribution
scopic model presented above cannotsimplybeextendedto is well defined and results from an equilibrium between
other binary membrane systems. The molecular area that repulsiveandattractiveelectricforcesandBrownianmotion
must be used is not defined, for example, as well as the forsolvatedions. Owingtothethermalfluctuationphenom-
leading factorKrelating kc to bn/Am (Eq. 19). Kis modified enon ofthe bilayer, such an ideal equilibrium can never be
when intramolecular forces change within abilayer. This is reached. The double-layer ion distribution must accommo-
the case in the range 25-27°C when one observes a strong date the removal of local osmotic unbalances induced by
decrease in the bending stiffness for pure DMPC mem- local curvature changes. On one hand, a kc increase was
branes (Fernandez-Puente et al., 1994; Hongeretal., 1994), foreseen because ofincreases in the area density charge or
and is especially evident in the present study when both the the Debye length (Winterhalter and Helfrich, 1992),
temperature and the composition are modified. For DMPC/ whereas Lekkerkerker (1989) predicted a negligible effect.
Chol membranes, one must take into account the fact that If the addition of 30 mol% cholesterol sulfate to a mem-
reinforcement of the lipid interactions in the hydrophobic brane results in a superposition ofcharge and sterol effects,
region is usually involved when the sterol amount is in- we conclude by comparison to DMPC/Chol results that the
creased, and a possible phase segregation into cholesterol sterol effect is the dominant
one.