This article was downloaded by: [Umeå University Library] On: 09 October 2013, At: 04:06 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Liquid Crystals Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/tlct20 Phase separation and critical phenomena in biomimetic ternary lipid mixtures Linda S. Hirst a , Pradeep Uppamoochikkal a & Chai Lor a a School of Natural Sciences , University of California , Merced, USA To cite this article: Linda S. Hirst , Pradeep Uppamoochikkal & Chai Lor (2011) Phase separation and critical phenomena in biomimetic ternary lipid mixtures, Liquid Crystals, 38:11-12, 1735-1747, DOI: 10.1080/02678292.2011.615947 To link to this article: http://dx.doi.org/10.1080/02678292.2011.615947 PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http:// www.tandfonline.com/page/terms-and-conditions
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This article was downloaded by: [Umeå University Library]On: 09 October 2013, At: 04:06Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House,37-41 Mortimer Street, London W1T 3JH, UK
Liquid CrystalsPublication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/tlct20
Phase separation and critical phenomena inbiomimetic ternary lipid mixturesLinda S. Hirst a , Pradeep Uppamoochikkal a & Chai Lor aa School of Natural Sciences , University of California , Merced, USA
To cite this article: Linda S. Hirst , Pradeep Uppamoochikkal & Chai Lor (2011) Phase separation and critical phenomena inbiomimetic ternary lipid mixtures, Liquid Crystals, 38:11-12, 1735-1747, DOI: 10.1080/02678292.2011.615947
To link to this article: http://dx.doi.org/10.1080/02678292.2011.615947
PLEASE SCROLL DOWN FOR ARTICLE
Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) containedin the publications on our platform. However, Taylor & Francis, our agents, and our licensors make norepresentations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of theContent. Any opinions and views expressed in this publication are the opinions and views of the authors, andare not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon andshould be independently verified with primary sources of information. Taylor and Francis shall not be liable forany losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoeveror howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use ofthe Content.
This article may be used for research, teaching, and private study purposes. Any substantial or systematicreproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in anyform to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions
Phase separation and critical phenomena in biomimetic ternary lipid mixtures
Linda S. Hirst*, Pradeep Uppamoochikkal and Chai Lor
School of Natural Sciences, University of California, Merced, USA
(Received 1 July 2011; final version received 16 August 2011)
Lipid phase behaviour in biomimetic ternary mixtures has become a rich area of research and this review willprovide a background to the many studies recently carried out, describing important advancements and futureprospects for the field. In the liquid crystal community lipids are traditionally interesting as lyotropic materials andin this sense a large amount of work has been carried out on different systems. This paper will not focus on lyotropicphases but instead will concentrate on the thermotropic phase behaviour of ternary lipid mixtures. We will discussthermotropic phase diagrams and critical phenomena in these systems, including their relationships to biologicalmembranes. Interest in the links between lipid thermodynamics and cell function has grown steadily over the pastthree decades and most of the recent work in these areas has been motivated by a desire to link the phase behaviourof simple lipid mixtures to lateral organisation in the cell membrane. The literature in this field is extensive and canbe intimidating; however, there are still unanswered fundamental questions. As important biological molecules,lipids have the potential to link many interesting physical ideas to how organisms function on a basic level and arecertainly worthy of significant attention.
The cell membrane consists of a lipid bilayer in whicha complex mixture of different lipids, sterols and mem-brane proteins are organised. This composition resultsin a highly selective membrane for transport of mate-rials in and out of the cell.
One of the most exciting and debated subjects inlipid biophysics in recent years has been in miscibil-ity studies of multi-component lipid systems and howresults from these studies can be applied to the struc-ture and dynamics of biological membranes. A largeamount of work has been carried out in trying toreduce the complex biological membrane to a moresimplified ‘model’ system. Experimenters then look atthe phase behaviour of these model systems to try touncover some underlying principles behind membranefunction.
Lipid mixtures and their phase behaviour havebeen studied and reported in the literature for along time, including many different binary systems.However, in a key paper, Simons and Ikonen [1] catal-ysed a surge of interest in the field by emphasising thatphase separation phenomena in biological membranescould be functionally important and relevant.
The real cell membrane is not just a simple lipidbilayer, but a complex structure composed of manydifferent lipid molecules, cholesterol and proteins.Some of these proteins are anchored to the underlying
cytoskeleton or may be connected to the substrateon which the cell can crawl. Over the past decade agreat deal of effort has gone into relating the phasebehaviour observed in simple lipid mixtures to thephysical properties of the biological cell. It would ofcourse be very elegant to find that simple phase sciencecan explain complex cellular behaviour. In biophysicsit is often extremely convenient to reduce and simplifybiological systems, but in doing this with the cell mem-brane it is important to remember the true complexityof the system. Real membranes are higher in proteinconcentration than is generally considered and, as aresult of these proteins, the membranes also vary inlateral heterogeneity and thickness [2]. It is quite achallenge to reconcile data from pure lipid experimentswith the biological membrane.
In this paper we will review the phase behaviour ofsome notable mixtures of biologically relevant lipidsand discuss some interesting current topics in thefield, including controversies over the ternary phasediagrams and some emerging recent work on criticalphenomena in lipid systems.
1.1 Models of the cell membraneUntil fairly recently the dominant model for thecell membrane was the well-known ‘fluid mosaicmodel’. In this model, proposed in 1972 by Singerand Nicolson [3], low concentrations of membrane
proteins are randomly distributed in a lipid ‘sea’.Membrane proteins are able to diffuse freely withinthe two-dimensional (2D) membrane and are assumednot to cluster or interact significantly. You couldconsider this to be an ‘ideal gas’ model for the mem-brane; useful but not necessarily correct. Over thepast 30 years, evidence has grown that the cell mem-brane requires a more complicated model to describeits lateral organisation and not long after the fluidmosaic model was proposed, researchers were alreadynoticing evidence for lateral heterogeneity in lipid mix-tures [4, 5] and postulating their function in the cellmembrane.
A more recently proposed model for membranestructure is the ‘raft model’. In this model, the mem-brane has significant lateral organisation, with thepresence of ordered lipid domains [1, 6]. The mem-brane is a complex mixture of many different lipidspecies and so the idea behind the raft model is thatcertain lipids assemble together to form ‘rafts’ (ordomains) with a differing composition to the sur-rounding membrane. The rafts are proposed to be richin sphingomyelins and cholesterol and may play a rolein the localisation or transport of different proteins, oract as intracellular signalling relay stations. This idea isknown as the ‘raft hypothesis’ and these lipid domainsare often referred to as ‘lipid rafts’. Overall this is anattractive idea as it provides a simplified model for howprotein organisation may be controlled by the cell bytaking advantage of lipid thermodynamics.
In simple ternary lipid mixtures, bilayer hetero-geneity was confirmed in the early 2000s by severalauthors [7–11] using a variety of experimental tech-niques. The accurate completion of even the mostsimple ternary phase diagrams used to model the cellmembrane still remains an active area of research, withmany publications generated over the past 10 years.It is a controversial step to make the link betweenstudies based on simple model lipid mixtures and realbiological membranes that may contain thousands ofdifferent molecular species.
The first question that you might ask is, ‘Havethese “rafts” been observed directly in living cells?’Many of the early papers concerning lipid raftsfocussed on extracted detergent-resistant membranesand have since been identified as potentially problem-atic [12]. Direct observation of the proposed nano-scale domains in a live cell is still a challenge, butindirect studies of protein sorting in the proximity ofpotential domains was actually observed even beforethe recent resurgence in this field [13]. It is now fairlywell accepted in the membrane community that lat-eral organisation of lipids exists in the cell, owing tothe numerous studies that have shown evidence to sup-port this hypothesis. However, there is still significant
debate over the timescale of their composition and sizedistribution.
2. Lipid phase behaviour
Lipids form liquid crystalline phases and so in light ofthe recent surge in interest in this field we should recallthat the first recorded observation of a liquid crys-tal by Reinitzer was of the lipid, cholesterol benzoate.The term lipid incorporates a broad group of differ-ent molecules, including familiar fats, phospholipids,sterols (including cholesterol) and waxes. The commontheme that runs through all lipid compounds is thatthey all contain esterified fatty acid chains. Figure 1shows some examples of different lipids demonstratingthe diversity of these materials. Cholesterol is an essen-tial component of eukaryotic cell membranes [14–16],an amphiphilic molecule with a rigid core and a shortalkyl chain. Although shorter than most membranelipids, cholesterol is still able to take advantage ofthe hydrophobic/hydrophilic properties of lipids andlocalise within the bilayer. Some cell membranes infact contain up to 50 mol% cholesterol [17, 18], a veryhigh percentage considering that the limits on choles-terol solubility in typical biological membranes are notmuch higher [19, 20].
Lipids are surfactants and as a result exhibitan interesting lyotropic phase sequence. The amphi-pathic molecules self-assemble into a variety of differ-ent concentration-dependent phases, subject to theirmolecular geometry. Micellar, hexagonal and lamellarphases can be observed when lipids are dispersed inwater, as well as the particularly fascinating bicontinu-ous phases (although micellar phases are less likely ina system with two flexible chains).
In this review paper we will explore the work thathas been done recently on the thermotropic phases ofphospholipids and lipid mixtures containing phospho-lipids. Because of this focus, the lipids discussed can beassumed to be in a flat bilayer, either a single bilayersheet, a bulk lamellar phase or alternatively bilayershells (either multi-lamellar or uni-lamellar vesicles).All of these bilayer geometries are essentially flat onthe length-scale of the individual molecules. Lipidvesicles are used extensively in this field to visualisemacroscopic membrane domains using fluorescencemicroscopy and as a vehicle for fusing membraneproteins and other membrane-associated molecules.
Phospholipid molecules comprise a hydrophilic‘head-group’ and typically two fatty acid ‘tails’(Figure 1). These tails are hydrocarbon chains andmay vary in flexibility at a given temperature depend-ing on their degree of unsaturation. Lipids withunsaturated bonds in the hydrocarbon chains arelikely to exhibit both trans and gauche conformers,
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Figure 1. Molecular structures of several different relevant lipid molecules: (a) the saturated lipid, sphingomyelin; (b) amixed chain lipid, 1-stearoyl-2-linoleoyl-sn-glycero-3-phosphoethanolamine; (c) NBD-labelled DOPE (1,2-dioleoyl-sn-glycero-3-phosphoethanolamine-N-(7-nitro-2-1,3-benzoxadiazol-4-yl)); and (d) cholesterol.
significantly decreasing the order parameter of themembrane if the temperature is high enough to permita significant number of conformational changes.
Molecules with an average motion that fills a cylin-drical volume pack together well to form a flat bilayer;if the membrane is highly deformed they will diffuseto low curvature regions of the membrane, whereas a‘cone’ shaped or ‘inverted cone’ shaped molecule willpack more efficiently in a membrane with some cur-vature. Although curvature studies are not the focusof this paper it is worthwhile mentioning this stericpacking effect. When lipids phase separate they areeffectively sorting by composition. This means thatlipid domains may have a different intrinsic curvatureto the surrounding regions [21] – an effect that can beapplied in reverse to induce domain formation [22].
2.1 The thermotropic phasesBefore beginning a discussion of lipid phase diagramsand phase coexistence, it is important that we reviewthe more well-known thermotropic lipid phases, start-ing from the lowest temperatures.
2.1.1 Sub-gel
At the lowest temperatures lipids in a bilayer crys-tallise in the sub-gel or Lc’ phases, where the ‘c’ standsfor ‘crystalline’. These phases are not considered
biologically important but for completeness we thinkit is important to include them here. In a sub-gelphase lipid molecules are arranged in a crystalline-like oblique lattice with long-range order within themembrane, although there is no ordering betweenadjacent membranes, so the phase cannot be consid-ered a three-dimensional (3D) crystal [23, 24]. Withinthe membrane the lipids are tilted and cannot diffusearound in the bilayer or rotate.
2.1.2 Gel
On heating the sub-gel phase the next thermotropicphase to occur is the Lβ’ phase, also known as the ‘gel’phase or So. The gel phase is not typically observedin living cells (with a few exceptions, for example thestratum corneum) although may have some biolog-ical importance in the case of nano-scale domains.In fact, many of the lipids found in biological mem-branes would exhibit this phase at body temperatureif they were in their pure state (i.e. not mixed withall the other lipids in the membrane). For exam-ple, the primary component of lung surfactant isthe phospholipid DPPC (1,2-dipalmitoyl-sn-glycero-3-phosphocholine), which exhibits the gel phase up to42◦C, well above body temperature. The gel phase haslong-range orthorhombic in-plane ordering [25] withsome degree of rotational freedom, although lateral
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diffusion is very restricted with extremely low diffu-sion rates. In many lipid materials the lipid ‘tails’ aresignificantly tilted in this phase, so in the bulk lamel-lar state this phase could be considered analogous tothe liquid crystalline smectic-C phase, but with someimportant differences; the gel phase has an extremelylow diffusion rate and long-range molecular order.
2.1.3 Ripple
At temperatures above the gel phase the more unusualripple phase (Pβ’) can occur. This phase is similar tothe gel phase in viscosity, with tilted lipid chains in thebilayer, but the phase exhibits an unusual out-of-planerippled structure [26] that can be identified by x-rayscattering and has been observed in freeze-fractureelectron microscopy [27].
2.1.4 Liquid crystalline
Above a certain temperature, defined as the meltingtemperature (Tm), membrane lipids will exhibit theliquid crystalline phase (Lα). In this phase the lipidmolecules are in a ‘fluid-like’ state in the plane ofthe bilayer. Molecules can freely rotate and diffuselaterally. Above Tm, the lipid head-groups take up alarger area than those in the gel phase, with short-range ordering characteristic of a liquid crystallinephase. In a bulk lamellar sample the Lα phase couldbe compared to the smectic-A phase, with the con-stituent molecules aligned in layers parallel to the layernormal. In biological membranes the overall state ofthe membrane at first glance appears to be liquidcrystalline (Lα); lipids and membrane proteins diffusearound the fluid-like, flexible membrane. As we willsee in this paper, however, lateral phase separationmay play an important role in membrane function,with domains of different compositions being presentin the membrane. The Lα phase therefore representsonly a starting point for linking phase behaviourin simple lipid systems to the state of the complexmixtures that comprise real membranes. Table 1 sum-marises the different phases described above alongwith their important structural characteristics andalternate naming conventions.
2.2 The Lo phaseIn addition to the phases described in the precedingsection, one of the most interesting phenomena internary lipid mixtures is a fluid-fluid two-phase state.This state is described in the literature as liquid disor-dered (Ld)/liquid ordered (Lo) phase separation. TheLo phase comprises a fluid-like bilayer characterisedby a more ordered lipid tail packing than the Ld phase.This new membrane phase was first proposed by Ipsenet al. [28] and investigated by Vist and Davis [29]. TheLo domains observed in ternary mixtures are enrichedin saturated lipids and cholesterol; they are thicker andstiffer than the Ld phase.
In certain ternary lipid compositions, fluid-likedomains in the bilayer matching the Lo phase wereinitially observed in model membranes formed frompure lipid components using microscopy and fluo-rescence spectroscopy techniques. In one experiment,fluorescence microscopy on giant unilamellar vesicles(GUVs) revealed fluid-fluid phase separation into cir-cular domains [7]. Since these first observations, thephase separation phenomenon has been confirmed bynumerous experimental techniques including fluores-cence microscopy [9, 21, 30], atomic force microscopy[31, 32], spectroscopy [10, 33, 34], ion mass spectrom-etry [35], nuclear magnetic resonance (NMR) spec-troscopy [36–38] and x-ray diffraction [39–41]. In fact,since the first associations were made between mem-brane rafts and the Lo phase, hundreds of papershave been published on the subject and the field stillcontinues to be lively and active.
Both NMR and wide-angle x-ray scattering mea-surements have provided quantitative measures ofthe order parameter and in-plane lipid spacings inthe Lo and Ld fluid phases. Both of these compo-sitional sub-phases (Lo and Ld) can be consideredto be liquid crystalline as they have a layered struc-ture and exhibit short-range in-plane ordering. Thisis in clear contrast to the gel phase that producessharp diffraction peaks corresponding to long-rangein-plane order [39]. In addition, in the Lo and Ld
phases the observed diffraction peaks are character-istically different to those observed in the gel phaseowing to suppressed membrane fluctuations. Thesedifferences can be observed using small-angle x-ray
Table 1. Lipid phases and their naming conventions.
Phase Alternative names Characteristics
Lα Liquid crystalline, fluid Liquid disordered (Ld) Short-range hexagonal packing, disordered chainsPβ’ Ripple Out of plane bilayer ripple, tilted chainsLβ’ Gel, So Long-range orthorhombic packing, tilted chainsLo Liquid ordered Short-rangeLc’ Sub-gel Long-range crystalline order
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Figure 2. Schematic demonstrating two different membrane states in a ternary mixture; the orange lipids represent the unsatu-rated component, the grey lipids represent the saturated component and the blue ovals represent cholesterol. (a) A uniform Lomembrane and (b) two-phase Lo/Ld coexistence.
diffraction [40]. Other differences between the Lo andLd phases include lateral diffusion rates (diffusionin the Lo phase is approximately half that of theLd phase) [31, 34, 36] and partitioning of sensitivedye molecules. In addition to conventional fluores-cent dyes that partition differentially, depending on themolecular species present in the different phases, thefluorophore Laurdan has been used successfully to dis-tinguish the phases due to the coupling between orderparameter and the arrangement of water molecules inthe hydrophobic parts of the bilayer [42]. At highertemperatures domains may no longer be present, withthe three lipid components uniformly distributed asdepicted in Figure 2.
In addition to the two-phase Lo/Ld state, it ispossible for a ternary system to adopt three-phasecoexistence with the third phase being the gel phase(or So). Evidence for three phases has been observedby several authors using fluorescence spectroscopy[10], x-ray diffraction [40, 41] and NMR spectroscopy[36, 38]. The composition of the three-phase state canbe determined precisely if an accurate phase diagramcan be drawn, however the range of this three-phaseregion is still controversial [41].
2.3 Model membranes vs extracted membranesMany researchers have based their studies on mem-branes composed of just a few lipid components, thegoal being to capture the underlying phase behaviourof the system without worrying too much about thedetails of a real membrane. A lipid mixture designedto model the composition of the cell membrane willtherefore typically consist of a lipid with saturated
chains (such as sphingomyelin or DPPC where Tm
is above room temperature), a lipid with unsatu-rated chains (such as DOPC (1,2-dioleoyl-sn-glycero-3-phosphocholine) where Tm is below room tempera-ture) and cholesterol. These mixtures are very typicalin the literature and therefore are often referred to as‘canonical’.
An alternative experimental strategy is to extractnative membranes from biological cells and try toobserve lateral organisation [43–45]. In this case thecomplete membrane is extracted, including all of thedifferent membrane proteins. Such a system is morerepresentative of the living cell but characterisation ismuch more difficult. Another idea is to use plasmamembranes extracted by blebbing [46]. In this tech-nique, cells are chemically induced to generate vesiclesthat bud from the membrane. These membranes areexpected to represent the native composition but with-out the influence of the cytoskeleton.
2.4 Phase coexistence and tie-linesIn fluid mixtures, two or more different compositionalphases can occur simultaneously at the same tempera-ture. In this case, the different phase fractions will varyin their compositions depending on the intermolecularforces between different species, total composition ofthe mixture and the temperature of the system. If theaim of a model lipid study is to investigate domain for-mation and the phase behaviour, then the first stagemust be to construct a phase diagram. In ternary lipidmixtures the most common phase diagram used in theliterature has been the three-sided Gibbs triangle. Thisphase diagram represents the equilibrium states of the
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mixtures as a function of composition (in molar per-centage) and temperature. The 2D triangles favouredin the literature represent an isothermal slice throughthe complete phase diagram with T on the z-axis.An example of this construction is shown in Figure 3.Here we can see, as an example, a fictional region oftwo-phase coexistence shaded in grey. At any point onthe triangle the fraction of a particular component inthe mixture can be read by measuring the minimumdistance between the point and the side opposite to thecorresponding vertex for that component.
Another important concept in the phase diagramis the idea of tie-lines. The tie-lines on a phase diagramdenote lines in the two-phase region along which thedifferent phase fractions have consistent compositions.As we move along the tie-line the proportions of eachphase present vary but their compositions do not.
In Figure 3, the two-phase region is indicated,with point X being a composition that separates intotwo phases. Along the tie-line drawn, the proportionsof the two phases vary and the compositions of thephases for all points along this line can be calculated,based on the distance of point X from the ends ofthe tie-line (where the tie-line intersects the boundarywith the one-phase region) using the Lever rule [47].For this reason it is important to know the locationof the ends of tie-lines on the phase diagram; then the
Figure 3. An isothermal slice of a fictitious ternary phasediagram showing a two-phase region (shaded in grey). Eachcorner of the diagram represents a 100% composition of thecomponent assigned to that corner. An imaginary tie-line isalso shown on the diagram passing through point X. All ofthe points along this line are mixtures composed of the sametwo phases in varying proportions; their compositions canbe read by looking at the compositions of the points wherethe tie-line crosses the phase boundary.
composition of the different phases at any point in thephase diagram can be calculated.
So, how can this be applied to lipids? As wehave discussed above, model membrane mixtures con-sisting of just three components – a saturated lipid,an unsaturated lipid and cholesterol – have beenreported to exhibit two- and three-phase coexis-tence. Spurred by early observations, several groupshave prepared phase diagrams for different ternarylipid mixtures designed to mimic the cell mem-brane, the most commonly studied mixtures beingcomposed of DOPC/sphingomyelin/cholesterol, andDOPC/DPPC/cholesterol. Although the differenttechniques used do not agree exactly on the shape ofthe phase boundaries, the presence of phase separationin these mixtures is now well established.
These diagrams are drawn with composition (usu-ally in mol fraction) on each side of the phase tri-angle. These triangles represent an isothermal sliceof the full isobaric phase diagram, and for eachtemperature a new phase diagram must be drawnto represent that isothermal slice. Phase diagramsfor ternary mixtures have been attempted by fluo-rescence microscopy on GUVs [30] and fluorescencespectroscopy [10]. Notably, recent work at differenttemperatures has been carried out [36, 38] (Figure 4)to build up the complete phase diagram using NMRas the characterisation technique, although there arestill large uncertainties about the positions of thephase boundaries. The phase diagrams presented inFigure 4 represent some of the most up-to-date iter-ations for DOPC/DPPC/cholesterol mixtures usingNMR (Figure 4(a)–(c)) and low-angle x-ray scattering(Figure 4(d)). These three groups observe similar areasof phase coexistence at similar temperatures, but withsome important differences in phase boundary slopesand the sizes of the coexistence regions. In particu-lar, the slope of the lower boundary of the three-phaseregion is positive in the data from Veatch et al. [38] butnegative from Davis et al. [36] and Uppamoochikkalet al. [41]. A negative slope could imply that withincreasing proportions of saturated lipid (DPPC) theLo phase forms more readily with increasing choles-terol. This is expected if DPPC and cholesterol havean affinity for each other.
2.5 Membrane domain sizeOne of the open questions in ternary lipid mixturesconcerns the disparity between the macroscopic phaseseparation observed in many experimental model sys-tems and the dynamic nano-scale domains proposedin the raft hypothesis for the living cell. While itis clear that macroscopic micron-scale domains arenot observed in live biological membranes, lateral
inhomogeneities of different macroscopic sizes havebeen observed in cell extracts, blebs and intact cells.Currently, however, it is not possible to image themembrane of a living cell down to the single moleculelevel, so controversy remains on the subject of lipidraft size distribution and its link to the Lo/Ld phaseseparations observed in model membranes. In con-trast, other techniques such as fluorescence spec-troscopy [48] suggest nano-scale domains consistentwith the raft hypothesis, although experimental arte-facts remain problematic.
In a true phase separating mixture in the two-phaseregion of the phase diagram, we expect to see the sys-tem evolve to an equilibrium state consisting of justone large Lo domain in the Ld phase. Such a statecan be seen in the GUV example in Figure 5. Thisis clearly not the case in live cells and a variety ofdifferent micron-scale domain size distributions arealso observed in model systems. When we compare
these artificial systems with the nano-scale domainspostulated for live cells, the discrepancy may beexplained to some extent by the phenomenon ofoxidation-induced domain growth. In 2006 Ayuyanand Cohen [49] reported the apparent formationand growth of Lo domains in GUVs in responseto fluorescence-induced lipid peroxidation, and sincethen further studies have confirmed this effect[50–52]. Other non-optical techniques have estimatedthe domain sizes to be in the range of 20–100 nm, butthe intrinsic domain size and mechanisms for stabilityare still an open question [53]. This debate is somewhatentwined with recent suggestions that the membraneis in a critical state and therefore dynamic raft struc-tures may be explained as critical fluctuations. We willexpand on this idea in the following section.
There have been several published accounts ofdirect and indirect visualisation of membrane raftsin fixed and live cells over the past few years using
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Figure 5. Examples of phase separation in ternary mixtures visualised using (a), (b) laser scanning confocal fluorescencemicroscopy and (c), (d) fluorescence microscopy, with (d) showing an image sequence at different focal planes on the samevesicle (bar = 10 μm). The GUVs are prepared at 1:1:1 molar ratios of DOPC/sphingomyelin/cholesterol, with 0.2 mol%Rh-DPPE. (e) Atomic force microscopy image of a single 1:1:0.22 mol% DPPC/DHA-PE(1-palmitoyl-2-docosahexaenoyl-sn-glycero-3-phosphoethanolamine)/cholesterol bilayer (image is 10μm across). Inset shows a height profile across the domainsmarked by the black line.
fluorescence probes [54–59], atomic force microscopy[60, 61] and other optical techniques [62]. These tech-niques reveal evidence for nano-scale domains in thecell, but all of the techniques are limited in resolu-tion, except, perhaps, for x-ray diffraction, so the directvisualisation of domains remains challenging.
2.6 Controlling domain growth and organisationThe phenomenon of fluid-fluid phase separation inlipid bilayers is a subject not only interesting for itsrelevance to membrane biophysics, but also from amaterials perspective. It is attractive to consider howdomains may be induced or organised in a controlled
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fashion because such directed assembly could leadto applications in ‘soft microfluidics’, templating andmaterials design. Lipids are very amenable to manipu-lation and can be formed into films, tubes and spheres,or combinations of these, depending on the prepara-tion technique applied. For example, lipid tubules canbe grown in a controlled fluid flow [63] and linkedinto branching channel structures connecting differentlipid vesicles [64, 65]. Alternatively, giant vesicles canbe formed by electro-formation, or single bilayers canbe deposited on a smooth or patterned surface.
Membranes can have a curved geometry for tworeasons: either an external force is applied, deform-ing the normally flat bilayer, or the molecules in thebilayer have some intrinsic curvature, promoting a sta-ble curved configuration. These ideas are representedin the classic formula for membrane bending energy,
F =∫ [κ
2(2H + c0)2 + κ̄K
]dA,
where H is the mean curvature, K is the Gaussian cur-vature, c0 is the membrane intrinsic curvature, κ is thebending modulus and κ̄ is the saddle-splay modulus.
In a mixed bilayer, areas of local curvature canbe created by compositional heterogeneities; or con-versely, mechanically induced highly curved regionscan be used to sort lipid species by intrinsic curva-ture. Such experiments were recently carried out bythe Baumgart laboratory, in which a lipid tubule wascarefully pulled from a giant vesicle using an opti-cally trapped bead. Lipid species sorting in responseto local membrane curvature was visualised using fluo-rescence microscopy [66, 67]. An alternative approachis to induce membrane curvature by depositing thebilayer on a defined patterned surface [22, 68]. Bothof these techniques induce the controlled formationof local domains in the membrane similar to the Lo
phase.It has been known for several years that photo-
induced oxidation effects in fluorescently labelled mix-tures can result in domain growth and coalescence[49, 50]. This effect has been noted to be particu-larly important close to the critical line. Recently,Hamada et al. used a photo-responsive amphiphile toreversibly control lateral membrane organisation [69].Additionally, novel bilayer discs and banded tubuleswere observed by inducing the formation of largedomains in lipid tubules formed from ternary mixtures[52, 70]. The Lo phase is apparently stiffer than theLd phase, and as a result Lo domains tend to adopt alower curvature if possible, even in mixtures with nointrinsic curvature; an effect seen clearly in the for-mation of bilayer discs [52] from canonical ternarymixtures. Further evidence for this increased stiffness
is seen in x-ray scattering data from bilayer stacksincluding domains. The Lo phase domains exhibit sup-pressed membrane fluctuations resulting in additionalBragg reflections from this phase [40].
3. Critical phenomena in ternary lipid mixtures
Critical point phenomena are observed in systemsundergoing continuous or second order phase tran-sitions where fluctuations in the order parameterover multiple length-scales occur, leading to the phe-nomenon of critical opalescence – a turbid appearanceof the fluid system under light. A response functionof the order parameter diverges at the critical point,indicating that the system has reached a limit of sta-bility. In fluids, the order parameter is the densitydifference of the coexisting phases, �ρ = (ρl − ρg) andits response function is the isothermal compressibility,KT = ρ−1(∂ρ/∂P)T where P is the pressure. The fluc-tuations are the manifestation of the choice the systemhas to make between two states with infinitesimallysmall differences in free energy. These fluctuationstend to mask the individual characteristics, thus result-ing in striking similarities between systems which areotherwise quite different. The similarity is expressedby universal power-laws which describe the thermo-dynamic and transport properties close to a criticalpoint. The range of the fluctuations (or correlations)is measured by the correlation length ξ (T), whichexhibits a power-law divergence, ξ (T) = ξot−v, towardsthe critical point, t is the scaled reduced temperatureand ξ o is a system dependent parameter of the orderof the molecular size for non-associating simple fluids,also called the bare correlation length. The exponentsdescribing the power-laws are referred to as the criticalexponents, and depend only on very generic featuressuch as the spatial dimensionality d, spin dimension-ality n, i.e. the number of components of the orderparameter, symmetry of the Hamiltonian, etc. Thishas led to the classification of different critical-pointsystems into discrete classes having the same singularbehaviour. The scaling behaviour occurs because ξ (T)is the only characteristic length-scale in the system asit approaches criticality. Systems with identical criticalbehaviours are said to belong to the same universal-ity class, like the 3D Ising, XY, etc. For ferromag-nets, liquid-gas phase transitions, nematic-smectic-A,binary fluid mixtures, etc. the 3D Ising model predictsthe critical exponents [71–77].
The concepts of critical phenomena which firstappeared in condensed-matter physics have beenapplied to different areas, such as high-energy physics,computer science, biology, economics, social science,etc. [78–82]. Over the last decade, critical phenomenain lipid mixtures have received wide attention for good
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reasons. These are quasi-2D structures in the form oflipid bilayers. Biological cell membranes are physicalmixtures of thousands of lipids and proteins, and arepostulated to have a critical composition with exten-sive critical fluctuations close to room temperature [46,83, 84]. These fluctuations give rise to an unusual com-bination of thermodynamic and transport propertiesthat may be advantageously exploited by biologicalcell membranes in a variety of biological functions[85–91].
Electro-formed GUVs and confocal fluorescencemicroscopy techniques have been used widely to studythe lipid organisation in model cell membranes withcoexisting phases [92]. GUVs of ternary lipid mix-tures have been extensively used as models of cellmembranes [82, 92]. Phase diagrams for ternary lipidmixtures with Lo–Ld phase coexistence are shown inFigure 4. An easy way to determine the critical pointor the critical composition is to trace the orientationof the tie-lines in the coexisting phases. The tie-linesmerge to a point on approaching a critical point wherethe two coexisting phases become indistinguishable.Tie-lines form an integral part of any phase diagramand give information on how various components par-tition into the coexisting phases, i.e. the interactionenergies between the lipid species. Various techniques,like spin-echo electron spin resonance (ESR), NMR,low-angle x-ray scattering (LAXS), etc. have been usedto determine tie-lines in lipid mixtures [36, 38, 41,93–95]. However, depending on the type of techniqueand samples (GUVs, oriented bilayer stacks, deuteri-ated lipids, etc.), tie-lines with differences in orienta-tion have been observed. Recent LAXS studies fromthe Nagle group on the DOPC/DPPC/cholesterolmixture (Figure 4d) indicated a positive slope forthe tie-line corresponding to the Ld–Lo side of the
three-phase region and a negative slope for the Ld–So
side [41]. The increasing nature of the positive slope inthe Ld–Lo region indicated the affinity of the choles-terol for the saturated lipid over the unsaturated, andthe negative slope reflected the tendency of the choles-terol to exclude from the gel phase as it tends todisorder it. A slope of zero indicates no preference. Theresults were qualitatively consistent with the theory ofPutzel and Schick [96].
Criticality in ternary lipid mixtures has beenin focus in the recent years [82]. The criticalbehaviour in these 2D systems is accepted tobelong to the 2D Ising universality class [72, 82].Studies by Honerkamp-Smith et al. on the correlationlength, ξ (T), in GUVs of diPhyPC (diphytanoyl-phosphatidylcholine)/DPPC/cholesterol onapproaching the critical temperature, resulted ina 2D Ising value (∼1) for the correlation length expo-nent ν [97]. The correlation length was determinedby analysing the structure factor, S(k), from thefluorescent probe intensity images. Measurement ofother critical exponents for the order parameter β
(difference in lipid composition), osmotic compress-ibility γ (S(k→0)), line tension μ (surface tensionanalogue), etc. also conformed to the 2D Ising uni-versality class [97]. Figure 6(a) displays the build upof composition fluctuations in a critical mixture ofDOPC/DPPC/cholesterol as the critical temperature(Tc ∼31.9oC) is approached. The fluctuations indomain boundaries are optically visible when theenergy of interface fluctuations becomes comparableto the thermal energy. Recent investigations on giantplasma-membrane vesicles (GPMV) isolated from liv-ing rat basophil leukemia (RBL) cells show that theyalso display critical behaviour with critical exponentspredicted by the 2D Ising model [83]. Figure 6(b)
Figure 6. Critical fluctuations in (a) a model membrane lipid mixture (bar = 10 µm) and (b) a GPMV (bar = 5 µm). As Tc
shows critical fluctuations in a GPMV with a criticaltemperature of ∼24.3oC. Correlation lengths of theorder of a few microns were observed within ∼0.5oCof the critical temperature in both model membranesas well as GPMVs. Extrapolation to physiologicaltemperatures yielded composition fluctuations oforders <50 nm in both these membrane systems, andwere consistent with the NMR investigations [38].These observations concluded that the cell plasmamembranes have compositions tuned to a criticalconcentration close to physiological temperatures.Nevertheless, these plasma-membrane vesicles differfrom intact cells in that they do not have connec-tivity with the cytoskeleton network. Furthermore,unlike model membranes, there is no strong evidencefor the existence of macroscopic phase separation(or micrometre to nanometre sized heterogeneities)in intact cells, probably because of their transientand dynamic nature [38, 98, 99]. These heterogeneousstructures, often referred to as ‘lipid rafts’, are believedto participate in the control of trans-membrane signaltransduction, membrane trafficking, endocytosis,viral budding, etc. [1, 6, 100, 101]. Recent simulationstudies on models of the plasma membrane indicatethat membrane lateral heterogeneity is modulatedby coupling to the cortical cytoskeleton [102]. Also,obstacles in the form of integral membrane proteinscan limit the size of the heterogeneities [103].
A mean-field-like [71, 72] treatment of the criticalbehaviour on moving away from the critical temper-ature in ternary lipid mixtures should not be com-pletely ignored, especially if an additional character-istic length-scale (say ξD) exists in the mixture, inaddition to the conventional correlation length of thefluctuations ξ . Such an additional system-dependentlength-scale can modify the approach towards the uni-versal non-classical critical behaviour near the criticalpoint [104–106]. If ξD is strong enough it can sup-press the critical fluctuations and lead to a crossoverto the mean-field-like critical behaviour [107], some-times well within the critical regime [106]. The originof ξD can be due to long-range interactions, molec-ular clustering, etc. [106, 107]. These kinds of sys-tems are classified as associating or complex fluidswhich are homogeneous at macroscopic length-scalesand heterogeneous at mesoscopic length-scales [108].Interactions between the lipid species, in the formof lipid–lipid interaction, lipid–protein interaction orlipid mediated protein-protein interaction, can trig-ger an additional length-scale in lipidic systems. Forsimple fluid mixtures which belong to the 3D Ising uni-versality class ξD ∼ ξ o ∼ of the order of molecularsize [73]. Furthermore, the fact that cell membranesare made up of a large number of lipids implies theexistence of many critical points which can merge
to form higher order critical points, or higher orderthermodynamic states. In fact, a wide distribution ofcritical temperatures is found in GPMVs isolated fromliving cells, indicating that individual GPMVs havecritical compositions [83]. Higher order critical pointsare well known in multi-component mixtures of sur-factants, polymer solutions, aqueous and non-aqueousionic solutions, etc. These higher order thermody-namic states are characterised by critical fluctuationsof magnitudes exceptionally larger than those neara normal critical point [107, 109]. Again, as men-tioned above, strong fluctuations can, in turn, sup-press the molecular structuring (or domain formation)phenomenon. It is quite possible that living cells atphysiological temperature have compositions corre-sponding to higher order critical points, which canbe explored in model membrane mixtures by tuningthe thermodynamic field variables, like temperature,pressure, cholesterol concentration as a field variable,or a fourth component. Closed-loop phase diagramscan be potential systems for this kind of investigation[109, 110]. The phenomenon of molecular structuringcan then be probed as a function of the strength ofthe critical fluctuations using various scattering tech-niques. A direct estimation of ξ o (or the correlationlength far away from the critical point) will then enableus to better understand membrane lateral heterogene-ity. Optical resolutions limit this kind of a systematicapproach. As for the critical behaviour, higher ordercritical points are characterised by renormalised criti-cal exponents with an extended simple-scaling regime[107]. Small changes in ξ o can move the crossovertemperature over large ranges in t [107, 111].
Acknowledgements
We would like to acknowledge generous funding fromthe National Science Foundation division of Biomaterials(DMR: 0852791). Funding for this paper was alsomade possible in part by the UC Merced Center ofExcellence on Health Disparities, funded by grant number1P20MD005049-01 from the National Institute on MinorityHealth and Health Disparities. The views expressed do notnecessarily reflect the official policies of the Departmentof Health and Human Services; nor does mention bytrade names, commercial practices, or organisations implyendorsement by the U.S. Government.[A]
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