Chemistry and Physics of Lipids 170– 171 (2013) 19– 32

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Chemistry and Physics of Lipids

j ourna l ho me p ag e : www.elsev ier .com/ locate /chemphys l ip

Review

Using small-angle neutron scattering to detect nanoscopiclipid domains

Jianjun Pana,!, Frederick A. Heberlea, Robin S. Petruzielob, John Katsarasa,c,d,!!

a Biology and Soft Matter Division, Neutron Sciences Directorate, Oak Ridge National Laboratory, Oak Ridge, TN 37831, United Statesb Department of Physics, Cornell University, Ithaca, NY 14853, United Statesc Canadian Neutron Beam Centre, National Research Council, Chalk River, Ontario K0J 1J0, Canadad Joint Institute for Neutron Sciences, Oak Ridge National Laboratory, Oak Ridge, TN 37831, United States

a r t i c l e i n f o

Article history:Received 9 January 2013Received in revised form 27 February 2013Accepted 28 February 2013Available online xxx

Keywords:Phase separationPhase coexistenceDomain sizeContrast matchingThickness mismatchLine tension

a b s t r a c t

The cell plasma membrane is a complex system, which is thought to be capable of exhibiting non-randomlateral organization. Studies of live cells and model membranes have yielded mechanisms responsiblefor the formation, growth, and maintenance of nanoscopic heterogeneities, although the existence andmechanisms that give rise to these heterogeneities remain controversial. Small-angle neutron scattering(SANS) is a tool ideally suited to interrogate lateral heterogeneity in model membranes, primarily due toits unique spatial resolution (i.e., "5–100 nm) and its ability to resolve structure with minimal perturba-tion to the membrane. In this review we examine several methods used to analyze the SANS signal arisingfrom freely suspended unilamellar vesicles containing lateral heterogeneity. Specifically, we discuss ananalytical model for a single, round domain on a spherical vesicle. We then discuss a numerical methodthat uses Monte Carlo simulation to describe systems with multiple domains and/or more complicatedmorphologies. Also discussed are several model-independent approaches that are sensitive to membraneheterogeneity. The review concludes with several recent applications of SANS to the study of membraneraft mixtures.

© 2013 Published by Elsevier Ireland Ltd.

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201.1. The roadmap for rafts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201.2. Phase separation in model membranes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201.3. The role of scattering techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2. Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.1. Analytical treatment of a single round domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.2. The Monte Carlo method for analyzing domains of complex morphology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.2.1. Introduction of the Monte Carlo method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.2.2. Monte Carlo method for multiple scattering objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.2.3. Effect of number of domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.2.4. Effect of domain area fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.2.5. What phase do the round domains correspond to?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.3. Model independent analysis of membrane heterogeneity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.3.1. The Porod invariant method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.3.2. The power law scattering method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.3.3. The forward scattering method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

! Corresponding author at: Oak Ridge National Laboratory, P.O. Box 2008 MS-6453, Oak Ridge, TN 37831, United States. Tel.: +1 865 576 5841.!! Corresponding author. Tel.: +1 865 274 8824.

E-mail addresses: jianjunp@gmail.com, panj@ornl.gov (J. Pan), katsarasj@ornl.gov (J. Katsaras).

0009-3084/$ – see front matter © 2013 Published by Elsevier Ireland Ltd.http://dx.doi.org/10.1016/j.chemphyslip.2013.02.012

20 J. Pan et al. / Chemistry and Physics of Lipids 170– 171 (2013) 19– 32

3. Applications of SANS to membrane rafts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.1. SANS confirms heterogeneity in probe-free raft mixtures, and is consistent with multiple rather than single domains . . . . . . . . . . . . . . . . . . 283.2. Vesicle curvature may influence domain area fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.3. Domain size depends on acyl chain thickness mismatch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

1. Introduction

The cell plasma membrane (PM) is composed of proteins, sterols,and amphiphilic lipids. It is therefore not surprising that sucha complex system is capable of exhibiting non-random lateralorganization. Indeed, heterogeneities in multiple-component lipidmixtures have been known since the early 1970s. However, inthe intervening years a rather surprising hypothesis has takenshape around those observations, namely that the non-randomorganization of lipids and proteins has explicit functionality in bio-logical membranes. These functional lipid/protein microdomains,or membrane rafts, are enriched in sphingomyelin (SM) and choles-terol (Chol). In the current view, rafts effectively compartmentalizethe cell PM into ordered and disordered regions, separating pro-teins based on their preferential interaction with certain types oflipids. Nevertheless, despite nearly two decades of intense research,the existence of rafts remains controversial, primarily due to theirsmall size and possible transient nature.

1.1. The roadmap for rafts

In 1972, Singer and Nicolson proposed the fluid mosaic model,which postulated that the PM is a homogeneous, relatively inert,two-dimensional fluid matrix that provides a medium for proteindiffusion, and a substrate for protein interactions and protein-directed processes (Singer and Nicolson, 1972). In short, lipidswere treated as passive structural components, and proteins werethought to control membrane architecture and organization, possi-bly through interactions with the cytoskeleton. Soon after, studiesof various lipid-only systems proposed the possible existence oftemperature-dependent lipid clustering in the membrane (Leeet al., 1974). The lipid clusters were thought to exist in an orderedfluid state (Wunderlich et al., 1978) relative to their surroundingdisordered liquid crystalline lipids. In 1982, Karnovsky and cowork-ers advanced the concept of membrane domains (Karnovsky et al.,1982) after observing heterogeneous fluorescence lifetime decayin both model lipid bilayer mixtures and isolated cell membranes.They proposed several lines of inquiry, some of which are stillbeing investigated today, including the forces behind the formation,maintenance, and fluctuation of lipid domains.

Interest in the roles of lipids and sterols in the lateral organiza-tion and chemical functions of the PM followed these observations.For example, sphingolipids and cholesterol were found to beenriched in the apical membranes of epithelial cells (Simons andVanmeer, 1988). It was also observed that protein partitioningand function were affected by lipid composition in model sys-tems (Dibble et al., 1993; Florine and Feigenson, 1987). Brownand Rose found that certain proteins localized with sphingolipidsand cholesterol in detergent-resistant membrane fractions, whichwere presumed to exist in the membrane as ordered domainsprior to detergent solubilization (Brown and Rose, 1992). In modelmembranes made up of three lipid components, liquid–liquidimmiscibility was first reported in 1996 (Silvius et al., 1996).

The findings from live cells and model membranes led to themembrane raft description of the PM (Ahmed et al., 1997; Simonsand Ikonen, 1997). The raft hypothesis postulated that the PM is

organized into functional domains with different average com-positions, compared to the bulk lipids (presumably due to thepreferential association of SM with cholesterol). These domainsorganize proteins and control their function by influencing proteindiffusion and local concentration. Analysis of lipids by mass spec-trometry has elucidated the lipid composition of rafts. For example,compared to the bulk PM, SM levels in rafts are elevated by about50% (Fridriksson et al., 1999), cholesterol levels are double (Pikeet al., 2002), while phosphatidylcholine (PC) levels are similar. Sincethe raft concept was formalized, membrane domains have beenimplicated in many cellular functions, including cell signaling path-ways (Foster et al., 2003; Simons and Toomre, 2000), protein sorting(Anderson and Jacobson, 2002), protein activity modulation (Jensenand Mouritsen, 2004), and cytoskeletal connections (Su et al., 2012).

A continuing source of controversy is the lack of visual (e.g.,fluorescence micrograph) evidence for rafts in resting (unstimu-lated) cells. Rafts are currently thought to be ordered domainsof nanoscopic dimensions that can coalesce to form larger, sta-ble platforms upon cell stimulation (e.g., external crosslinking ofa membrane component), and exclude certain proteins (Lingwoodand Simons, 2010). Evidence for such nanoscale heterogeneities inthe resting PM is accumulating. For example, Sharma and cowork-ers used homo and hetero-FRET (Förster resonance energy transfer)to detect small clusters (<5 nm) of certain proteins in the PM(Sharma et al., 2004). FRET between fluorescent lipid analogs inthe PM’s outer leaflet revealed nanoscale heterogeneity in cells(Sengupta et al., 2007). Electron spin resonance (ESR) studies in livecells found order and rotational diffusion parameters consistentwith distinct liquid-ordered (Lo) and liquid-disordered (Ld) phases(Swamy et al., 2006). New tools with enhanced spatial resolutionare also proving helpful (Simons and Gerl, 2010). Super resolutionmicroscopy methods, including fluorescence photoactivation local-ization microscopy (FPALM), are capable of detecting nanoscaleheterogeneities in cells (Hess et al., 2006). Moreover, stimulatedemission depletion (STED) far-field nanoscopy inferred the pres-ence of nanoscopic domains in live cells through the detection ofsphingolipids with hindered diffusion (Eggeling et al., 2009).

1.2. Phase separation in model membranes

Complementing the research with live cells, chemically sim-plified model systems with well-defined lipid compositions haveproven to be powerful tools for elucidating the thermodynamicsgoverning the lateral heterogeneity of membrane lipids. Lipids inthe outer leaflet of the mammalian PM can be broadly groupedbased on fluidity: high-melting (high-TM) lipids, including SM,undergo a transition from the gel to the fluid phase near or abovephysiological temperatures, while low-TM lipids in the outer leafletare fluid at ambient temperature. A three-component model forthe cell membrane outer leaflet can be constructed using one com-ponent from each of these categories, together with cholesterol,the most abundant lipid in the PM by mole fraction. These mix-tures often exhibit lateral segregation of the Ld and Lo phases overa broad range of composition and temperature. Importantly, thephase diagrams of these model systems provide critical informationfor understanding lipid–lipid interactions governing raft formation.

J. Pan et al. / Chemistry and Physics of Lipids 170– 171 (2013) 19– 32 21

Considerable effort has gone toward solving such phase diagramsfor a variety of ternary mixtures, discussed below. For a compre-hensive overview of binary and ternary lipid phase diagrams, thereader is referred to the excellent reviews by Marsh and Feigenson(Marsh, 2009, 2010; Feigenson, 2009).

The first observations of micron-sized coexisting Ld + Lo phasesin model membranes were reported in bSM (brain-SM)/DOPC (1,2-dioleoyl-sn-glycero-3-phosphocholine)/Chol (Dietrich et al., 2001)and eSM (egg-SM)/DOPC/Chol (Samsonov et al., 2001). (N.B. We willrefer to phase coexistence that can be detected with conventionalmicroscopy as “macroscopic”.) Subsequently, the macroscopiccoexistence of Ld + Lo phases was found in other ternary mixtures,often including lipids such as DOPC and DPhPC (1,2-diphytanoyl-sn-glycero-3-phosphocholine), lipids chosen for their poor mixingproperties with saturated lipids and SM. Examples of ternary phasediagrams with macroscopic Ld + Lo phase coexistence includeDPPC (1,2-dipalmitoyl-sn-glycero-3-phosphocholine)/DOPC/Chol(Veatch and Keller, 2003), DPPC/DPhPC/Chol (Veatch et al., 2006),DSPC (1,2-distearoyl-sn-glycero-3-phosphocholine)/DOPC/Chol(Heberle et al., 2010; Zhao et al., 2007a), PSM (N-palmitoyl-d-erythro-sphingosylphosphorylcholine)/DOPC/Chol (Nyholm et al.,2011; Veatch and Keller, 2005a), SSM (N-stearoyl-d-erythro-sphingosylphosphorylcholine)/DOPC/Chol (Farkas and Webb,2010), and bSM/DOPC/Chol (Petruzielo et al., 2013).

As rafts are now widely considered to be structures withnanometer dimensions (Lingwood and Simons, 2010), the rele-vance of model lipid mixtures that exhibit nanoscopic domainshas been heightened. Ld + Lo coexistence regions, which areundetectable by fluorescence microscopy, were inferred fromFRET measurements in DPPC/DLPC (1,2-dilauroyl-sn-glycero-3-phosphocholine)/Chol, in the first report of nanoscopic Ld + Lodomains (Feigenson and Buboltz, 2001). Further studies employedspectroscopic techniques with nanoscale resolution to investigateLd + Lo phase coexistence in ternary systems, whereby the low-TMlipid DOPC was replaced with the more biologically relevant lipidPOPC (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine). Phasediagrams were reported for DSPC/POPC/Chol (Heberle et al., 2010),PSM/POPC/Chol (de Almeida et al., 2003; Halling et al., 2008;Ionova et al., 2012; Veatch and Keller, 2005a), and bSM/POPC/Chol(Pokorny et al., 2006; Petruzielo et al., 2013). It is believed thatsystems with nanoscopic heterogeneity better model the cellu-lar PM, and their study is important for gaining insight into themechanisms responsible for the stability of nanoscale domains(Elson et al., 2010). Results from several studies suggest thatnanoscopic assemblies exist in cells, but their stability and lifetimesare presently not known.

1.3. The role of scattering techniques

As with macroscopic phase separation in model membranemixtures, it is useful to employ equilibrium thermodynamics toexamine how phase behavior and domain size vary with com-position and temperature in biologically relevant outer leafletmembrane models. Proposed mechanisms for the formation andmaintenance of nanoscopic heterogeneity can be refined throughmodel and live cell studies, as well as theoretical treatments. Asa first step, the disparity between measurements of nanoscaleLd + Lo domains in model systems and rafts in cells must be rec-onciled through studies combining multiple, minimally disruptivetechniques with different spatial sensitivities. In this respect, small-angle scattering techniques are important tools capable of resolvingnanometer-scale heterogeneity with minimal perturbation to thenative lipid composition.

X-ray solution scattering has been successfully used to inter-rogate the phase behavior of unoriented lipid bilayer vesiclesuspensions (i.e., powder samples) by establishing the presence

of multiple lamellar Bragg reflections (D) or wide-angle (d) spa-cings in the scattering pattern. Multiple D-spacings in multilamellarvesicles (MLVs) indicate three-dimensional phase separation: theyarise from lateral phase separation within the plane of eachbilayer, with phase domains aligned in multiple adjacent bilay-ers in the multilamellar stack (Chen et al., 2007; Yuan et al., 2009;Boulgaropoulos et al., 2012). In contrast, multiple d-spacings arisefrom coexisting phases with different chain packing parameterswithin a single bilayer (Boulgaropoulos et al., 2012). A weakness ofthis method is that the absence of multiple peaks does not implythe absence of phase separation. For example, large differences inphase lamellar repeat distances may introduce packing frustrationthat favors anti-alignment of phase domains in adjacent bilayers,such that only a single, average D-spacing is observed. At the otherextreme, coexisting phases with similar D- or d-spacings may sim-ply not be resolved. This is an especially significant drawback forthe use of multiple wide-angle spacings to detect coexisting Ldand Lo phases, both of which exhibit broad wide angle X-ray scat-tering peaks at or near 4.5 A. This obstacle can be circumventedwith oriented bilayer stacks, which provide additional off-axisscattering, normally obscured in powder samples. The angularextent of off-axis scattered intensity is related to the distribu-tion of chain tilt angles, which in favorable cases can be extractedfrom the two-dimensional scattering pattern (Mills et al., 2008a).Importantly, Ld and Lo phases have substantially different chainorientational order. Mills and coworkers exploited this property toprobe liquid–liquid phase separation in ternary mixtures, by deter-mining if two chain tilt distributions were required to model thescattering data for different compositions in the DPPC/DOPC/Cholsystem (Mills et al., 2008b). The results of their analysis were consis-tent with GUV (giant unilamellar vesicle) and NMR phase diagrams.

Ultimately, the usefulness of small-angle X-ray scattering(SAXS) for probing lipid domains is limited by the lack of contrast(i.e., differences in electron density) between the different lipidphases. On the other hand, neutron scattering exhibits a remark-ably different sensitivity to hydrogen and its isotope, deuterium.By varying the hydrogen/deuterium ratio in both sample and/orsolvent, features of interest can be highlighted. Neutron scatteringhas therefore traditionally been used to investigate matter distri-bution in hydrogen-rich biological systems (Heberle et al., 2012;Pan et al., 2012a,b). For the study of membrane domains, a typicalsmall-angle neutron scattering (SANS) experiment involves choos-ing an H2O/D2O ratio for the aqueous solvent that minimizes thescattering contribution from the bilayer as a whole. In addition,by labeling specific lipid components (e.g., the acyl chains of thehigh-TM species) with deuterium (replacing hydrogen), the scat-tering contrast between the domain phase and the surroundingmembrane (bulk phase) can be enhanced, leading to an observ-able scattering signal that depends on domain composition, size,and morphology. SANS is an important tool capable of resolvingstructures of "5–100 nm with minimal perturbation to the nativelipid composition (requiring only partial deuteration of a lipidcomponent). Importantly, domain sizes obtained from SANS mea-surements bridge micrometer-sized domains observed in GUVsand nanometer-sized domains obtained from FRET measurements(Fig. 1). SANS therefore offers a unique possibility to assess thevarious physicochemical parameters that control domain size.

A simple, well-characterized platform for studying lipiddomains using SANS is the one composed of unilamellar vesicles(ULVs) suspended in aqueous solvent. One advantage of the ULVsystem is that vesicle size can be precisely controlled by mechani-cal extrusion through polycarbonate filters with defined pore sizes.Second, the absence of inter-bilayer interference, which is com-monly seen in MLVs, significantly simplifies data analysis. Finally,the geometrical constraint imposed by vesicle size yields laterallysegregated domains on the scale of tens of nanometers, a domain

22 J. Pan et al. / Chemistry and Physics of Lipids 170– 171 (2013) 19– 32

Fig. 1. Domain length scales accessible by different experimental techniques. Thetechniques that are able to determine the sizes of domains are highlighted in green(i.e., AFM, super resolution imaging including PALM, STORM, NSOM and STED, NMR,FM, FRET and SANS). The techniques that are only capable of detecting the pres-ence of multiple environments (i.e., phase coexistence) are highlighted in blue (i.e.,FRET at large length scales, FS and ESR). (AFM: atomic force microscopy; PALM:photoactivated localization microscopy; STORM: stochastic optical reconstructionmicroscopy; NSOM: near-field scanning optical microscopy; STED: stimulated emis-sion depletion; NMR: nuclear magnetic resonance; FM: fluorescence microscopy;FRET: Förster resonance energy transfer; SANS: small-angle neutron scattering; FS:fluorescence spectroscopy; ESR: electron spin resonance).

size that may be more relevant to the transient membrane raftsthat occur in live cells. For these reasons, ULVs in aqueous solu-tion present a suitable platform for examining nanoscopic lateralheterogeneity in model membranes.

Here, we review several methods used to analyze SANS datafrom ULVs exhibiting lateral heterogeneity. In particular, we dis-cuss an analytical model for the scattered intensity originating froma ULV with a single, round domain, which can be used to estimatedomain size. We then present a numerical approach, which usesMonte Carlo simulation, to address the case of multiple domains.We illustrate the effects of domain size and its area fraction basedon simulated neutron scattering profiles. Also discussed are sev-eral model-independent approaches that have been used to assessmembrane heterogeneity. We conclude with examples pertainingto membrane heterogeneity using SANS data, as analyzed using theaforementioned methods.

2. Methodology

2.1. Analytical treatment of a single round domain

In this section we review an analytical model for scatteringfrom a single, round domain on a spherical shell, mimicking theULV geometry. The assumption of a single domain results in arelatively simple expression for the scattered intensity in termsof domain size and scattering length density (SLD), and which issuitable for use in non-linear least-squares data fitting. The sin-gle domain model corresponds to the so-called “infinite phaseseparation limit”, and is based on the notion that following nuclea-tion, smaller domains will ultimately coalesce into a single, largedomain in order to minimize the energetic cost associated with theboundary.

Anghel and coworkers first presented the mathematical treat-ment of this model (Anghel et al., 2007). It was assumed that the SLDdistribution of the ULV is uniform within each phase and assumesthe values !1(r) for the domain phase and !2(r) for the bulk phase.This is equivalent to a uniform SLD of W(r) = !2(r) over the entireshell, with an additional SLD contribution of V(rr) = v(r) # w(r) forthe domain phase, where v(r) = !1(r) $ !2(r) and w(r) is an angu-lar term that assumes a value of zero in the bulk phase and unityin the domain phase. Using a spherical polynomial expansion, theangular averaged scattered intensity I(q, R) can be written as:

I(q, R) = 1q2 [2ZW (q, R) + Z0(q, R)X0(˛)]2

+ 1q2

!%

l=1(2l + 1)2Z2

l (q, R)X2l (˛) (1)

ZW (q, R) = q

" %

0W(r)r2j0(qr)dr, (2)

Zl(q, R) = q

" %

0v(r)r2jl(qr)dr, (3)

Xl(˛) = 1l

[cos ˛Pl(cos ˛) $ Pl+1(cos ˛)], (4)

where q is the scattering vector, R is the mean radius of the vesi-cle, Pl(cos") is the Legendre polynomial of order l, and jl(qr) isthe spherical Bessel function of order l. The angle is half of themaximum angle formed by the domain boundary and the cen-ter of the vesicle, and is related to the domain area fraction adby:

= cos$1(1 $ 2ad) (5)

The first term in Eqn. (1) arises from the SLD difference (contrast)between the average vesicle lipid composition and the surroundingaqueous solvent, and contains no information about lateral hetero-geneity. The contribution from domains is manifested in the secondterm, which is a series summation that depends on the integer l.Since we are only interested in the scattering signal from lateraldomains, it is important to minimize the first term by matchingthe average vesicle and solvent SLDs. For the remainder of this dis-cussion, we assume that the average vesicle and solvent SLDs areequal to zero. It should be pointed out that the scattered intensityarising from lateral domains is proportional to the square of theSLD difference between the domain and bulk phases. This differ-ence depends on the precise lipid composition of the two phases.In the case of protiated lipids, the SLD difference between saturatedand unsaturated acyl chains is too small to generate a useful scatter-ing signal, even when large domains are present. Experimentally,the SLD difference between the domain and bulk phases can, how-ever, be greatly enhanced through the use of chain-perdeuterateddi-saturated lipids (e.g., DPPC-d62 or DSPC-d70), which partitionpreferentially into the ordered phase, thereby enhancing the SLDcontrast between the two phases. In cases where a deuteratedhigh-TM lipid is not available or is prohibitively expensive to pur-chase, commercially available sn-1 perdeuterated low-TM lipids(e.g., POPC-d31 or SOPC-d35) may provide sufficient contrast todetect domains (Petruzielo et al., 2013).

The scattered intensity [Eqn. (1)] depends not only on the scat-tering vector q, but also on the vesicle’s radius R. Vesicle sizepolydispersity of 20–40% is frequently observed in extruded vesi-cles. ULV heterogeneity can be approximated using the Schulzdistribution (Pencer et al., 2005):

G(R) =#

m + 1Ra

$m+1 Rm

# (m + 1)exp

#$R(m + 1)Ra

$, (6)

J. Pan et al. / Chemistry and Physics of Lipids 170– 171 (2013) 19– 32 23

Fig. 2. Series truncation effect on the single-domain scattering profile based onthe second term in Eqn. (1), calculated for a domain area fraction ad = 0.25. A thinbilayer approximation with a thickness of 30 A was used. The scattered intensityversus scattering vector q was averaged over different vesicle sizes drawn from aSchulz distribution with an average vesicle radius Ra of 300 A and a polydispersity$ of 25%. Inclusion of the second order increases the integrated intensity by 40%(solid green line to cyan line), while the further addition of the third order has nodiscernible effect (solid cyan line overlaps dashed brown line).

where Ra is the average vesicle radius, m describes the degree ofpolydispersity, and # is the gamma function. Vesicle size varianceis defined as %2 = R2

a/(m + 1), and the relative polydispersity isdefined as & =

%1/(m + 1). Information on Ra and & is usually

obtained from a separate scattering experiment, where the sameULV sample is suspended in fully deuterated water. This results ina large contrast between the solvent and the vesicle, and an accu-rate determination of vesicle size and polydispersity can be made.Taking polydispersity into account, the final scattered intensity canbe expressed as:

I(q) =" Rmax

Rmin

I(q, R)G(R)dR/

" Rmax

Rmin

G(R)dR, (7)

where Rmin and Rmax are the smallest and largest vesicle sizes,respectively. Using Eqns. (1) and (7), information on the domainand bulk phases, including !1, !2, and ˛, can be obtained by fittingthe experimentally obtained scattered intensity using a non-linearleast-squares fit.

The intensity arising from vesicle lateral heterogeneity isexpressed as the summation of an infinite series in Eqn. (1). Toassess the truncation effect, Fig. 2 plots predicted intensities forthe first three orders of the series. The figure demonstrates thatthe major contribution to the scattered intensity comes from thefirst order. Inclusion of the second order increases the integratedintensity by about 40% and slightly shifts the maximum position toa larger q value, while the addition of the third order has no dis-cernible effect. Therefore, only the first two orders in Eqn. (1) arerequired for the analytical data analysis of domains (Anghel et al.,2007).

Using the analytical single domain model described by Eqns.(1)–(7), Anghel and coworkers (Anghel et al., 2007) analyzed SANSdata from a 1:1 DPPC:DLPC mixture, a system known to exhibitgel/fluid immiscibility over a range of temperatures (Feigensonand Buboltz, 2001; Tenchov, 1985) due to a large hydrocarbonchain-length mismatch (Kucerka et al., 2011). Within the phasecoexistence region (20 &C), SANS data were found to be consistentwith the model, while no enhanced scattering was observed justabove the liquidus line at 30 &C.

Masui and coworkers performed a similar single domain analy-sis for small unilamellar vesicles (SUVs) of "20 nm diameter usinga ternary mixture composed of DPPC/DOPC/Chol = 4/4/2 (Masuiet al., 2008). Based on the established phase diagram (Buboltz et al.,

Fig. 3. An illustrative representation showing experimental SANS data deviatingfrom the scattered intensity calculated using the single domain model, thus indicat-ing the possible existence of multiple-domains. The simulated experimental datawere generated from a 3-domain model using MC simulation. Random noise wasadded to better approximate experimental data. The analytical curve was obtainedthrough non-linear least-squares fitting to the simulated data by varying the singledomain area fraction.

2007; Kahya et al., 2004; Mills et al., 2008b; Scherfeld et al., 2003;Veatch and Keller, 2003; Veatch et al., 2007), this mixture exhibitsLd + Lo phase coexistence at 15–30 &C. Indeed, a well-resolved scat-tering peak centered at q = 0.03 A$1 was observed at 26 &C (Masuiet al., 2008). Using a domain area fraction ad obtained from flu-orescence micrographs of GUVs, the authors found that althoughthe single domain model predicted some of the important featuresseen in their SANS data (e.g., peak position), a significant deviationwas observed at the right shoulder region of the scattering peak(Fig. 3), which could not be fitted by simply varying the domainarea fraction ad. Based on this observation, the authors concludedthat instead of a single round domain, their samples consisted ofmultiple domains.

To summarize, the analytical model derived for a single, rounddomain serves two purposes in examining membrane lateral het-erogeneity. First, structural parameters relating to domain size,area fraction, and composition can be estimated by fitting theanalytical expressions to experimentally obtained data. Second,discrepancies between the predicted intensity and the experi-mental data may indicate the presence of more complex domainmorphologies, such as the presence of multiple domains (Masuiet al., 2008).

2.2. The Monte Carlo method for analyzing domains of complexmorphology

2.2.1. Introduction of the Monte Carlo methodBiological structures often possess complex morphologies

whose scattering profiles cannot be well described by analyticalmathematical expressions. As mentioned in the previous sec-tion, examples pertaining to lipid domain studies include multipledomains on a single vesicle and domains with irregular shapes(Bagatolli and Kumar, 2009; Feigenson and Buboltz, 2001; Korlachet al., 1999; Li and Cheng, 2006; Scherfeld et al., 2003; Veatchand Keller, 2003, 2005b; Zhao et al., 2007a; Zhao et al., 2007b;Konyakhina et al., 2011; Goh et al., 2013). Numerical approacheshave proven invaluable for circumventing the obstacle of analyticalintractability. All of these approaches are based on the fundamentalDebye formula for isotropic systems, namely:

I(q) '!

i

!j /= i

fifjsin qrij

qrij, (8)

24 J. Pan et al. / Chemistry and Physics of Lipids 170– 171 (2013) 19– 32

where rij is the distance between objects i and j, and fi and fj are theircorresponding scattering powers (i.e., electron density or neutronSLD).

By dividing the total scattering volume (e.g., a multiple-domainprotein or a vesicle, which we will refer to as a “compositescatterer”) into simpler objects (e.g., cubes or spheres) with adefined position and scattering power (Barnes and Zemb, 1988),the pairwise distances in Eqn. (8) can be statistically sampledvia Monte Carlo (MC) simulation (McAlister and Grady, 2002).This technique has been widely used to model and predict struc-tures of single strand DNA (Zhou et al., 2006), the thylakoidmembrane (Kirkensgaard et al., 2009), phospholipid bilayer nan-odiscs encapsulated by scaffold proteins (Skar-Gislinge et al., 2010),a polymer-silica nanocomposite (Balmer et al., 2011), and theimmune stimulating complex (Pedersen et al., 2012).

The MC method proceeds by generating random points withineach object making up the composite scatterer in proportion to theobject’s SLD contrast with its surrounding aqueous solvent. Whenall objects have the same SLD, the number of random points withineach object is proportional to its volume (Hansen, 1990). Whenthe composite scatterer contains scattering objects with differentSLD (e.g., a domain and bulk phase that differ in their concentra-tion of deuterated lipid), a modified algorithm is required (Pantoset al., 1996). In the next section we discuss such an algorithm,which was proposed by Henderson (Henderson, 1996). The finalscattering profile is obtained by a simple Fourier transform of thepair-distance probability of all of the generated random points (Sec-tion 2.2.2).

Similar to the analytical model analysis, the MC method requiressome knowledge of the scattering objects in advance. Randompoints are then generated within these objects, followed by cal-culating the scattering profile based on pair-distances between theset of all random points. Characteristics of the scattering objectscan then be varied systematically (e.g., changing an object’s size orSLD) and compared. The most probable morphology is obtainedwhen the difference between the simulated scattering profileand the experimentally observed profile is minimized, based onsome predefined criterion (McAlister and Grady, 2002; Pedersen,1997).

The above-described procedure assumes negligible interferencebetween the individual composite scatterers in the system, whichin our case corresponds to large inter-vesicle distances (i.e., a dilutesuspension). If this is not the case, an additional term describingthe interactions between scatterers (a “structure factor”) shouldbe included (Pedersen and Schurtenberger, 1996; Potschke et al.,2000; Svergun and Koch, 2003).

2.2.2. Monte Carlo method for multiple scattering objectsHenderson proposed an MC algorithm to describe scattering

from dissimilar objects (Henderson, 1996). The solvent-excludedtotal scattering volume of the composite scatterer (e.g., the vesicleshell) is first divided into multiple objects with defined geome-tries (e.g., spherical caps corresponding to round domains). Eachobject i is then filled with ki random coordinates (x,y,z), whereki is proportional to the product of the object’s volume and itsSLD contrast with the solvent. A weighting term wi is applied tothe ki points to account for the sign of the object’s SLD contrast(i.e., wi = +1 for positive contrast and $1 for negative contrast).Finally, the distance between each unique pair of points p(x,y,z),q(x,y,z) in the composite scatterer is calculated, weighted by theproduct wpwq, and then binned into probabilities as a function ofdistance r to construct a total pair-distance histogram P(r). It isworth noting that pair-distances between points from objects withopposite contrast subtract from the pair-distance histogram, whichcan result in negative probabilities. This is in fact the hallmark of a

Fig. 4. (a) Pair-distance probability P(r) for a spherical shell composite scatterercomposed of a single round domain (object 1 with area fraction 0.25) surroundedby a bulk phase of opposite SLD (object 2). The domain and bulk phases wereassigned positive and negative SLDs, respectively. The total P(r) histogram (solidblack line) is equal to the sum of contributions from intra-object pairs (P1,1 andP2,2) and inter-object pairs (P1,2). Note that the weighting terms for each probabilitydistribution were implicitly included in the calculation of the pair-distance distri-bution histograms, resulting in positive probabilities for objects 1 and 2 (P1,1 andP2,2 , respectively), and negative probabilities for the cross-pairs P1,2 . (b) Scatteringprofile calculated from the total P(r) in (a) based on Eqn. (9). The intensity was aver-aged over a Schulz distribution of vesicles with an average radius of 300 A and apolydispersity of 25%. The shell thickness was 30 A.

contrast-matched system, as will be discussed later on. Based onthe Debye formula, the scattered intensity is:

I(q) = 1/4!

" %

0P(r)

sin(qr)qr

dr, (9)

where P(r) denotes the total pair-distance probability function forthe composite scatterer.

To demonstrate the algorithm, we use the single domain modelpresented in Section 2.1. The composite scatter (a 300 A radius ULVwith a 30 A shell thickness) is composed of two objects: a round sin-gle domain phase (object 1), surrounded by a bulk phase (object 2).Under a bilayer/solvent contrast matching condition, the domainand bulk phases have SLD contrasts of opposite sign. The intra- andinter-object pair-distance probabilities for this system are shownin Fig. 4a, with weighting terms implicitly included. It is clear thatthe probabilities within each phase assume positive values at alldistances (dashed green and cyan lines). Although the shapes aredifferent, due to the different area fractions of the two phases, bothprobabilities exhibit a similar trend: an initial increase, followedby a decrease to zero intensity with increasing r. Due to the oppo-site SLD contrast of the domain and bulk phases, the cross-pairprobability is negative (dashed brown line). The total pair-distanceprobability P(r) takes on positive values at small distances, and

J. Pan et al. / Chemistry and Physics of Lipids 170– 171 (2013) 19– 32 25

Fig. 5. (a) An illustrative representation showing different numbers of round domains on a spherical shell. The total area fraction occupied by the domain phase was fixed at0.25. (b) Pair-distance probabilities for different number of round domains on a spherical shell corresponding to (a). Multiple-domain curves (i.e., 2, 3 and 4 domains) weregenerated by averaging an ensemble of pair-distance histograms obtained by randomly placing non-overlapping domains on the spherical shell with a radius of 300 A and athickness of 30 A.

negative values at larger distances (solid black line). If the systemis contrast matched, the number of positive pair-distances (thesum of all intra-object histograms) must equal the number ofnegative pair-distances (the sum of all inter-object histograms)in the limit of a large number of sampled points. In this case, theintegral of P(r) over all distances is zero. This feature is shared byall systems whose average SLD match that of the solvent, and isthe fundamental cause of zero forward scattered intensity I(0) inthese systems (Fig. 4b), as illustrated by the following equation:

I(0) ' limq(0

" %

0P(r)

sin(qr)qr

dr =" %

0P(r)dr = 0. (10)

Using Eqn. (9) and the total pair-distance probability P(r) fromFig. 4a, the SANS scattering profile I(q) is readily calculated, asshown in Fig. 4b. The data were averaged over a large number ofvesicles, with their radii drawn from the Schulz distribution. Notethat when averaging pair-distance probabilities between differentsized vesicles, the number of generated random points within eachvesicle should be proportional to the vesicle’s spherical shell vol-ume, as the scattering power is proportional to the material in eachvesicle. Similar to the scattering profile obtained from the analyti-cal expression in Section 2.1 (Fig. 2), the scattering profile in Fig. 4bshows a well-defined peak, whose width and position are relatedto the size of the round domain phase.

2.2.3. Effect of number of domainsAs pointed out, the power of the MC method lies in its abil-

ity to model complex morphologies whose scattering profiles (orequivalently pair-distance probability distributions) lack a simplesolution. Unlike the round single domain model presented in Sec-tion 2.1, the interference term arising from multiple, randomlyarranged domains on a sphere cannot be expressed analytically.On the other hand, it is straightforward to model the inter-domaininterference using the MC method (Fig. 5a). Multiple domains ofa defined radius are randomly placed on a spherical shell. Withinthe vesicle, we assume an excluded volume interaction betweendomains (i.e., no domain overlap). The total contrast weightedpair-distance histogram is then calculated as previously described.This process is then repeated with different random domain con-figurations to generate a statistical ensemble, and the overallpair-distance probability (or scattered intensity) is obtained byaveraging the results.

Fig. 5b shows the total pair-distance probability P(r) forthe multiple-domain model with a fixed domain area fraction,ad = 0.25. Increasing the number of domains Nd (or equivalently,

decreasing the individual domain size) systematically moves thezero-crossover point (where the probability switches from posi-tive to negative values) to smaller values of r. The effect of Nd onP(r) can further be demonstrated by calculating the correspondingscattering profile using Eqn. (9), as shown in Fig. 6. One notable fea-ture is that increasing Nd shifts the position of maximum intensityto larger q values. Furthermore, the peak width increases system-atically and asymmetrically with increasing Nd, with a markedintensity increase on the right side of the peak. This feature ofmultiple-domain scattering was utilized by Masui and coworkers– where a similar deviation between the single domain analyti-cal model and the experimental data was observed –to infer theexistence of multiple domains (Masui et al., 2008).

2.2.4. Effect of domain area fractionAnother important parameter for characterizing membrane het-

erogeneity is the total area fraction of the domain phase. Using theMC method we calculated SANS profiles for a contrast-matchedvesicle with two randomly arranged round domains of total areaad, and whose area was then systematically varied from 0.05 to0.45. The intensity curves were relatively scaled based on the Porodinvariant (Section 2.3.1), which is proportional to ad # (1 $ ad). Sev-eral interesting features are evident from the plots in Fig. 7. First,

Fig. 6. Theoretical scattering profiles for the multiple-domain models shown inFig. 5 as derived from MC simulation. The intensity profiles were obtained by aver-aging an ensemble of vesicles described by the Schulz distribution, with an averageradius of 300 A and a polydispersity of 25%. The intensities were scaled to preservethe Porod invariant Q =

&I(q)q2dq, which does not vary when the total domain area

fraction is fixed (Section 2.3.1). The dashed arrow is a guide to the eye highlightingthe trend of maximum intensity positions using a second order polynomial fit.

26 J. Pan et al. / Chemistry and Physics of Lipids 170– 171 (2013) 19– 32

Fig. 7. Theoretical scattering profiles for the two-domain model as a function of areafraction ad occupied by the domain phase. The intensities were scaled according tothe Porod invariant, which is proportional to ad(1 $ ad). The dashed arrow highlightsthe trend of the maximum intensity position as a function of ad .

the scattered intensity decreases with ad. This observation is impor-tant as it can be used to set a lower spatial resolution limit onthe method, below which no usable scattering signal is detected(Anghel et al., 2007). Second, a decreasing ad results in peak broad-ening, primarily due to the relatively enhanced intensity occurringin the right shoulder region. This is similar to the case where Ndincreases, while ad is fixed (Section 2.2.3). Third, the position ofthe maximum intensity is insensitive to ad. At first glance it seemscounterintuitive that a smaller length scale would yield scatteringat larger reciprocal space. However, such consideration neglectsthe contribution from the relative positions between the differentdomains, which are constrained on the spherical shell. Specifically,the maximum length scale between different domains is equal tothe vesicle’s diameter, regardless of ad. This explains the essentiallyconstant peak position in Fig. 7. However, the situation is differentwhen there is only one domain. In this case, the peak position con-tinually moves to a larger q as a function of a decreasing ad (datanot shown).

2.2.5. What phase do the round domains correspond to?For macroscopically phase-separated systems, it is usually the

case that either the Ld or Lo phase can be the continuous (percolat-ing) phase, depending on the lipid composition (Crane and Tamm,2004; Veatch and Keller, 2003; Zhao et al., 2007a). For example, athigher concentrations of the high-TM lipid, the sample is closer to

the Lo tieline endpoint, therefore the Ld phase has a smaller areaand mole fraction, and consequently discontinuous Ld domains inan Lo matrix are observed. (The opposite holds when the low-TMlipid makes up the majority of the sample.) Near the middle of thephase coexistence region, where mole fractions of Ld and Lo phasesare approximately equal, a percolation threshold marks the transi-tion between these two types of behaviors. There is no theoreticalbasis of which we are aware for predicting the precise compositionof the percolation threshold, and in the absence of direct visualiza-tion with fluorescence microscopy, the assignment of continuousand discontinuous phases is not always clear.

To test if SANS is capable of distinguishing the phase of the dis-continuous domains, we consider a case where the Lo phase is75 mol%. Assuming that the average lipid area is 45 A2 in the Lophase and 60 A2 in the Ld phase (Pan et al., 2008; Pan et al., 2009),the area fraction of the Lo phase is then 0.69. In the continuous Lophase model (Fig. 8a, top), two round domains were used to modelthe Ld phase with total area fraction of 0.31, while in the discon-tinuous Lo phase model (Fig. 8a, bottom), two round domains witha total area fraction of 0.69 were used to model the Lo phase. Thecorresponding scattering profiles averaged over an array of vesiclesdrawn from the Schulz distribution (an average radius of 300 A anda polydispersity of 25%) are shown in Fig. 8b.

It is clear that the profile for the discontinuous Lo phase modelshows an enhanced right shoulder (relative to the peak inten-sity), compared to that of the continuous Lo phase model. Thedifference is mainly due to the cross term of the pair-distance prob-ability [Eqn. (9)] which changes the zero-crossover point, similar toFig. 5b. Therefore, SANS is capable of distinguishing the continuousphase when the area fraction of the Lo phase is not near ad = 0.5,at which point the SANS profile is the same upon switching theLo and Ld phases. Note that the change of the SANS profiles byswitching the Lo and Ld phases in Fig. 8b resembles that of varyingdomain size (or number of domains) in Fig. 6. Thus, additional con-straints are required when using SANS to establish the percolationthreshold.

2.3. Model independent analysis of membrane heterogeneity

2.3.1. The Porod invariant methodBoth the analytical and MC methods described above compare

experimental scattering data to a calculated profile, from whichrelevant parameters pertaining to a domain’s morphology (i.e.,composition and size) are determined. However, these methods

Fig. 8. (a) An illustrative representation showing continuous (top) and discontinuous Lo phase (bottom) models. The Lo phase is colored in blue and occupies 69% of the shellarea in both models (Ld phase is depicted in brown). Two round domains were used to model the Ld phase in the continuous Lo phase model. Two round domains were alsoused to model the Lo phase in the discontinuous Lo phase model. (b) Scattering profiles for the continuous and discontinuous Lo phase models in (a). The scattering profileswere scaled to preserve the Porod invariant, which is the same for both models.

J. Pan et al. / Chemistry and Physics of Lipids 170– 171 (2013) 19– 32 27

are strictly dependent on the model used, and often prove to betime consuming. A straightforward model-free analysis involvingthe Porod scattering invariant was proposed by Pencer and cowork-ers, and used to robustly detect the presence of lateral membraneheterogeneity in ULV suspensions (Pencer et al., 2006). Althoughthe method cannot be used to simultaneously determine domainsize and composition, it has proven useful for detecting the onset oflateral segregation, and the corresponding phase boundaries, as afunction of temperature or lipid composition (Pencer et al., 2007b).

The method is based on the concept that the Porod invariantQ =

&I(q)q2dq can be decomposed into three additive terms cor-

responding to: (1) the SLD contrast between the average vesiclecomposition and the solvent; (2) radial SLD fluctuations arisingfrom the different average SLDs of the lipid head and acyl chainregions; and (3) lateral SLD fluctuations arising from domainsof different average acyl chain composition. As mentioned, SANSexperiments capable of detecting lateral domains are nearly alwaysdesigned to eliminate or greatly suppress the first term of the Porodinvariant by matching the solvent SLD to that of the average vesi-cle composition, and to enhance the contribution of the third termthrough chain-perdeuteration of one lipid component (typically thedi-saturated, high-TM lipid). The second term of the Porod invari-ant is often neglected (Czeslik et al., 1997; Hirai et al., 2006; Masuiet al., 2006; Masui et al., 2008; Nicolini et al., 2004; Vogtt et al.,2010), despite the fact that the headgroup and acyl chain regionsof PC bilayers have markedly different average SLDs. In fact, radialSLD fluctuations can contribute significantly to the scattered inten-sity and should be minimized experimentally whenever possible.For example, in many cases the ratio of deuterated and protiateddi-saturated lipid (e.g., DPPC and DPPC-d62), as well as the D2Ofraction in the solvent can be adjusted to simultaneously matchthe average SLD of the acyl chains, headgroups, and solvent (Anghelet al., 2007; Pencer et al., 2006; Heberle et al., 2013).

After eliminating or minimizing the contribution from the firsttwo terms, the Porod invariant can be approximated by:

Q ' ad(1 $ ad)(ı!ac)2, (11)

where ı!ac is the SLD difference between the acyl chain compo-sition of the domain and bulk phases. Based on Eqn. (11), severalconclusions can be drawn. First, the Porod invariant is related toboth the domain area faction and composition. As a result, it is notpossible to simultaneously determine these two quantities basedon Q alone. Second, the Porod invariant reaches a maximum whenthe domain phase occupies half of the vesicle area. Third, underideal contrast matching conditions (i.e., no contribution from thefirst and second terms of the Porod invariant), evaluation of Q canbe used to sensitively detect domain formation (i.e., ad deviatesfrom zero), for example as temperature is reduced through an uppermiscibility transition (Pencer et al., 2005).

2.3.2. The power law scattering methodIt has been shown that for MLVs whose average SLD matches

that of the solvent, the obtained SANS signal is governed, over agiven q range, by the power law I(q) ' q$D (Vogtt et al., 2010). Theexponent D is a parameter that characterizes the geometrical prop-erties of the lateral heterogeneity in the system. When D is between0 and 3, it represents a mass fractal Dm = D that describes bulk struc-ture, and when D is between 3 and 6, it represents a surface fractalDs = D $ 3 that describes surface structure. Because the power lawbehavior is only valid when a$1 < q < b$1 (a is the cutoff distanceof the fractal object and b is the characteristic size of the scatteringobject), an estimate of the size scale of a membrane’s heterogeneitycan be obtained by pinpointing where the power law relationshipdeviates (Fahsel et al., 2002).

Using this method, Winter and coworkers found that for aDPPC/DOPC/Chol mixture D decreased from 3.5 to 3.2 as the

temperature decreased from 50 to 10 &C (Vogtt et al., 2010), anobservation that is consistent with the system’s known phasebehavior (Buboltz et al., 2007; Kahya et al., 2004; Mills et al.,2008b; Scherfeld et al., 2003; Veatch and Keller, 2003; Veatch et al.,2007). Similarly, it was found that the addition of cholesterol to abSM/DOPC mixture led to an increase of the mass-fractal dimensionDm from 2.7 to 3.0, indicating an enhanced spacing-filling capabilityby cholesterol (Nicolini et al., 2004). For the binary mixture DPPCand ergosterol, the surface-fractal dimension Ds was determinedto be 2.7 in the Lo/gel two-phase region. Increasing temperatureled to a smaller Ds of 2.4, suggesting a smoother scattering inter-face (Krivanek et al., 2008). Moreover, chain length mismatch wasfound to play an important role in dictating the power law behaviorfor lipid mixtures in the gel/fluid coexistence region. Specifically,surface-fractal fluctuations dominate when the mismatch is small,whereas mass-fractal fluctuations become more important whenthe mismatch is large (Czeslik et al., 1997; Winter et al., 1999).Gramcidin D was found to dramatically decrease concentrationfluctuations and increase the lower cutoff of the correlation lengthin a DSPC/DMPC (1,2-dimyristoyl-sn-glycero-3-phosphocholine)mixture (Fahsel et al., 2002), equivalent to an increase in domainsize.

2.3.3. The forward scattering methodKnoll and coworkers proposed a forward scattering method that

makes use of the solvent’s SLD to interrogate membrane hetero-geneities in MLVs (Knoll et al., 1981a). The method is based on thenotion that the coherent forward scattering I(0), as q approaches 0,is proportional to the SLD difference between the lipid phases andthe solvent, namely:

I(0) '!

iVi(!i $ !s)2, (12)

where Vi is the volume fraction of phase i, and !i and !s are theSLDs of phase i and the solvent, respectively. I(0) is obtained byextrapolating a linear section of the logarithmic Kratky–Porod plot(I # q2 versus q2) to the ordinate (i.e., q2 = 0). Several vesicle sam-ples with identical lipid composition, but different solvent SLDs, areprepared by varying the ratio of D2O/H2O. When the lipids form asingle, homogeneous phase,

%I(0) changes linearly as a function

of !s and crosses zero when the solvent’s SLD equals that of theaverage lipid composition. However, when there is lateral hetero-geneity in the vesicles, the linear relationship between

%I(0) and

!s no longer holds. Moreover,%

I(0) does not go to zero at any !s.

Therefore, by monitoring the behavior of%

I(0) as a function of !s,information such as phase boundaries can be determined. A mod-ified procedure (the so-called inverse contrast variation) was laterproposed by the same authors, whereby they varied the deuteratedand protiated ratio of one lipid component, while keeping the sol-vent’s SLD fixed (Knoll et al., 1985a). Based on Eqn. (12), the samecriteria for

%I(0) versus !s can be used for

%I(0) versus !L (lipid

SLD) to probe membrane heterogeneity.To demonstrate the effectiveness of the forward scattering

method, Knoll et al. obtained a linear relationship between%

I(0)and !s for a homogeneous mixture (i.e., DMPC/DMPC-d54), whilea non-linear relationship was observed for a DSPC/DMPC mixtureat temperatures known to exhibit gel/fluid coexistence. Interest-ingly, even at high temperatures (60 &C) where DSPC/DMPC waspresumed to form a homogeneous fluid phase,

%I(0) did not go to

zero (Knoll et al., 1981a). The authors attributed this observationto critical fluctuations arising from a hidden consolute point ofthe solid/solid miscibility gap (Knoll et al., 1983), highlightingthe exquisite sensitivity of SANS to detect lateral membraneheterogeneity.

28 J. Pan et al. / Chemistry and Physics of Lipids 170– 171 (2013) 19– 32

Although the forward scattering method (contrast variation andinverse contrast variation) seems to be successful in studying phasebehaviors of several lipid mixtures (Henkel et al., 1989; Hirai et al.,2006; Knoll et al., 1981a; Knoll et al., 1981b; Knoll et al., 1985a;Knoll et al., 1985b; Knoll et al., 1991; Knoll et al., 1983), it was laterbrought into question by Pencer and coworkers, who recognizedthat under perfect contrast matching conditions, I(0) must be zeroregardless of the miscibility of individual lipid components in thevesicle, as demonstrated by Eqn. (10) (Pencer et al., 2007a). It turnsout that the weakness of the forward scattering method stems fromEqn. (12), which only accounts for the contrast between the individ-ual lipid phases and the solvent, but neglects the contrast betweenthe different lipid phases (which gives rise to inter-domain inter-ference). Therefore, the forward scattering method is only validfor small, uniform, and uncorrelated lipid domains (Pencer et al.,2007a).

3. Applications of SANS to membrane rafts

We conclude this review with several recent examples of SANSand membrane raft mixtures. To provide some additional contextfor these experiments, it is useful to follow the thread of lipid phasediagram studies through the early 2000s. In a pioneering study, Kor-lach and coworkers demonstrated that coexistence of micron-sizedphases could be directly observed with conventional fluorescencemicroscopy, provided that suitable contrast agents were addedto the lipid mixture (typically small concentrations of fluorescentlipids) (Korlach et al., 1999). This development stimulated inter-est in solving three-component phase diagrams for lipid mixturesmimicking the composition of the mammalian PM (i.e., a low- andhigh-TM lipids, together with cholesterol), as the entire compositionspace could be sampled at reasonably high resolution, with flu-orescence micrographs providing easily interpreted (yes/no) dataregarding phase coexistence. It was soon recognized that certainlow-TM lipids (especially those with multiple acyl chain unsatura-tions, such as DOPC) consistently showed micron-sized coexistingliquid phases (Ld + Lo) over a wide range of composition and tem-perature. In part because of this propensity to form large domains,relatively complete phase diagrams were subsequently reportedfor DOPC-containing mixtures including: DPPC/DOPC/Chol (Veatchet al., 2007), DSPC/DOPC/Chol (Zhao et al., 2007a), PSM/DOPC/Chol(Veatch and Keller, 2005a), bSM/DOPC/Chol (Smith and Freed,2009; Petruzielo et al., 2013), and SSM/DOPC/Chol (Farkas andWebb, 2010). In particular, the DPPC/DOPC/Chol phase diagram ofVeatch and coworkers (Veatch et al., 2007) proved highly influen-tial, and served as a standard for many experimental and theoreticalstudies of raft-like phenomena in model membranes.

The picture for the more biologically relevant monounsaturatedlow-TM lipids (including POPC and SOPC) was however not as clear:micron-sized liquid domains were reported by some researchers(Veatch and Keller, 2005a), while in other studies only gel/liquidcoexistence was observed at low cholesterol concentrations (Zhaoet al., 2007b). In any event, small domains in the liquid coexis-tence region could often be inferred from spectroscopic techniques,including FRET and ESR for the POPC-containing mixtures, andphase diagrams with a prominent Ld + Lo coexistence region werereported for PSM/POPC/Chol (de Almeida et al., 2003; Veatch andKeller, 2005a), bSM/POPC/Chol (Pokorny et al., 2006; Petruzieloet al., 2013), and DSPC/POPC/Chol (Heberle et al., 2010).

In an important study, Ayuyan and Cohen showed that thegeneration of lipid peroxides and the subsequent breakdown ofunsaturated bilayer components, initiated by the excitation of flu-orescent probes, could strongly affect domain properties (Ayuyanand Cohen, 2006). Among the effects of photoinduced lipid break-down was a propensity to form larger domains, and the authors

suggested that this experimental artifact might explain the discrep-ancy between some fluorescence microscopy and spectroscopicstudies. To summarize, in the mid-2000s the extent to whichexisting phase diagrams constructed from microscopy data wereaffected by artifacts was unknown, which elevated the importanceof obtaining independent confirmation of liquid–liquid phase sep-aration from probe-free techniques, like SANS (Petruzielo et al.,2013).

3.1. SANS confirms heterogeneity in probe-free raft mixtures, andis consistent with multiple rather than single domains

Pencer et al. examined “canonical” 1:1:1 mixtures ofDPPC/DOPC/Chol and DPPC/SOPC/Chol using 50 nm ULVs (Penceret al., 2005). While the size of these vesicles imposes an uppercutoff on domain radius of "80 nm (for a single domain withan area fraction of 0.5), it is nevertheless advantageous to use50 nm vesicles for two reasons. First, extrusion through pore sizes>100 nm often results in a small fraction of MLVs in the sample,which then introduces a structure factor (i.e., the interferencebetween repeating lamellae) that can complicate data analysis.Second, larger domains move the signature domain scatteringpeak to smaller q (Fig. 6), and potentially below the minimum q of aSANS instrument (typically 0.003 A$1 at a 15 m sample-to-detectordistance and a 6 A wavelength).

Using the model-free Porod analysis, phase coexistence wasobserved for the DPPC/DOPC/Chol mixture over a temperaturerange that was consistent with published phase diagrams obtainedfrom microscopy (Veatch and Keller, 2005a), NMR (Veatch et al.,2007), and FRET (Buboltz et al., 2007) data. In contrast, only agradual increase in total scattered intensity with decreasing tem-perature was found for the 1:1:1 DPPC/SOPC/Chol mixture, whichwas interpreted as evidence of uniform mixing over the tempera-ture range of 25–50 &C. Data for the DPPC/DOPC/Chol system werefitted with the MC method using SLDs and phase area fractionscalculated from the published phase diagram, and varying onlythe number of domains per vesicle (or equivalently the domainsize). At 20 and 25 &C, the scattering curves could not be success-fully modeled assuming a single, round domain, and rather multiplesmall domains were required. In some cases, the data were fit asa weighted sum of curves with different numbers of domains, andinterpreted accordingly. For example, it was reported that 95% ofthe ULVs contain "30 domains of radius 8 nm, with the remaining5% of vesicles containing either 1 or 8 domains of 40 or 14 nmradius. It should be noted that an intermediate scattering peaklike those shown in Figs. 4–7 was not seen, indicating a large for-ward scattering contribution, presumably due to imperfect contrastmatching. No attempt was made to match the headgroup and acylchain regions, which should then have resulted in a radial scatteringcontribution (Section 2.3.1).

Masui et al. examined a different composition system, namely,4/4/2 DPPC/DOPC/Chol, using SUVs of "20 nm diameter preparedby sonication (Masui et al., 2008). SANS data could not be ade-quately fit with the analytical single domain model. Instead,MC-simulated curves were used in the analysis, and a weightedsum of single domain and two domain curves provided a goodfit to the experimental data at all temperatures studied (12–26 &C,with 28 and 30 &C falling outside the phase coexistence region). Itwas found that both the fraction of single domain vesicles and thecontrast between the domain and the bulk phase decreased withincreasing temperature, indicating increased miscibility of the lipidcomponents and an overall reduction in domain size with increas-ing temperature.

Vogtt et al. looked at both MLVs and extruded 30 nm diam-eter ULVs under contrast matching conditions of vesicle/solvent,but not headgroup/acyl chain, at the composition 27/45/28

J. Pan et al. / Chemistry and Physics of Lipids 170– 171 (2013) 19– 32 29

DPPC-d62/DOPC/Chol (Vogtt et al., 2010). This composition is nearthe upper boundary of Ld + Lo phase coexistence at 10–20 &C (pos-sibly near a critical point), and consists of a single, uniform phaseat temperatures >25 &C (Veatch et al., 2007). Minimal scatter-ing was observed at 35 &C, where the bilayer is well mixed, andincreased scattering was reported at 14, 10, and 6 &C, consistentwith the phase diagram. The q-range of increased scattering was0.003–0.05 A$1, corresponding to real space lengths (domain sizes)of 1–20 nm. The high temperature sample (35 &C), as well as apure Ld composition, showed forward scattering which the authorsattributed to “unmatchable” radial contrast from differences in SLDbetween the headgroup and acyl chains. The ULV data were suc-cessfully fitted to a model of cylindrical discs with 15 nm radiusand 2.5 nm thickness (corresponding to the hydrocarbon thicknessof the bilayer, which was the primary source of contrast in theexperiment).

To summarize, the results from these three studies (in everycase, DPPC/DOPC/Chol bilayers) were best described by multiplesmall domains, rather than a single large round domain. It may besignificant that in the Vogtt and Pencer studies, the vesicle compo-sitions were close to a critical point at their respective temperatures(Veatch et al., 2007), where line tensions are expected to be small,and the total number of domains per vesicle was larger than inthe study by Masui et al. The latter study, for which the SANSdata were best described by only one or two domains per vesi-cle, was performed at a lower cholesterol concentration (20 mol%),a composition which is well within the Ld + Lo region.

3.2. Vesicle curvature may influence domain area fraction

Anghel et al. first published an analytical model for SANS datafrom a phase-separated ULV composed of a single, round domain,and reported on a binary mixture composed of DPPC and DLPC inthe region of gel/fluid coexistence (Anghel et al., 2007). The best-fit phase area fractions (or equivalently, the phase boundaries)were found to be inconsistent with phase diagrams determinedfrom differential scanning calorimetry (Tenchov, 1985). Anghelet al. concluded that membrane curvature may in part be respon-sible for the discrepancy. A follow-up study examined a 45/45/10DPPC/DOPC/Chol mixture using three different vesicle sizes: 50,100, and 200 nm (nominal) diameter. The SANS data for the twosmallest vesicle sizes, which had diameters of 44 nm and 73 nm,were fitted using the single domain analytical model (Section 2.1).The best-fit domain area fraction increased from 0.1 in the case ofthe 73 nm diameter ULVs, to 0.21 for the 44 nm diameter ULVs, aresult that was interpreted as evidence for enhanced lipid demix-ing in highly curved vesicles. Though not commented upon by theauthors, neither of the reported area fractions are consistent withthe phase diagram at 10 &C (Veatch et al., 2007), which indicatesnearly equal mole fractions of gel and fluid phases for the lipid com-position in question. Given estimates for phase molecular areas of60 A2 for Ld and 40 A2 for gel, a gel domain area fraction of "0.4 isexpected.

While the authors’ interpretation of the data raises the issue ofthe influence of vesicle curvature on domain size, there are severalimportant caveats that must be considered. First, the negativelycharged lipid phosphatidylserine (PS) was added to the mixture ata concentration of 5 mol% to provide charge repulsion sufficient toprevent the formation of MLVs. Phosphatidylglycerol (PG) is oftenused to achieve this effect in studies where ULVs are desirable(Akashi et al., 1996; Zhao et al., 2007a), as corresponding PC/PGlipids have the same melting transition temperature (Pan et al.,2012c). In contrast, PS lipids have melting temperatures nearly10 &C higher than PCs with the same acyl chains, and might beexpected to alter the phase diagram. Nevertheless, the change indomain area with increasing curvature cannot be simply explained

by the presence of additional mixture components. Second andmore importantly, at 10 &C the mixture exhibits a gel/fluid coex-istence, rather than a fluid/fluid coexistence. In gel/fluid mixtures,highly ramified domain patterns are typically observed, rather thansingle domains (Bagatolli and Kumar, 2009; Feigenson and Buboltz,2001; Korlach et al., 1999; Scherfeld et al., 2003; Veatch and Keller,2005b; Zhao et al., 2007a; Zhao et al., 2007b). It is therefore notclear that the single domain model is applicable to the data in ques-tion. Indeed, the domain area fraction reported for the more highlycurved vesicles is closer to that expected from the phase diagram,whereas one would expect the observed area fraction to approachthat of the published phase diagram (obtained from study of low-curvature, giant vesicles) as vesicles become larger, if curvaturewas in fact influencing the phase behavior. An alternative explana-tion is that the size of multiple smaller domains, rather than thephase area fraction of a single round domain, is responsible for thechanges observed in the SANS data.

3.3. Domain size depends on acyl chain thickness mismatch

Recent work from Feigenson and coworkers has investi-gated a domain size transition in the four-component mixtureDSPC/DOPC/POPC/Chol (Konyakhina et al., 2011; Goh et al., 2013),which may yield insight into the ways cells can exploit lipid compo-sition changes to alter the size and connectivity of domains. In thisline of research, the low-TM lipid POPC is systematically replacedwith DOPC, which causes the size of fluid domains to increase froma few nanometers (as determined by FRET and ESR) to microns (vis-ible with fluorescence microscopy of GUVs) (Heberle et al., 2010).

The low end of this size regime was further investigatedwith SANS (Heberle et al., 2013). SANS intensity was mea-sured for 39/39/22 DSPC-d70/(DOPC + POPC)/Chol, with the ratio! = DOPC/(DOPC + POPC) defined to indicate the DOPC concentra-tion in the low-TM fraction. SANS curves from the MC method weregenerated using previously determined phase diagrams (Heberleet al., 2010; Zhao et al., 2007a) to constrain the compositions (SLDs)and volume fractions of the coexisting phases at 20 &C, such thatthe only remaining variable parameter was the number (or equiv-alently size) of domains. The geometric model considered everyvesicle to have the same number N of monodisperse domains anddomain area fraction, independent of vesicle size (which was drawnfrom the Schulz distribution). This simple model provided a goodfit to the data, and domain size was found to increase from 6.8 to16.2 nm as ! was varied from 0 to 0.35. Fig. 9 shows SANS curvesas a function of temperature for the ! = 0.1 sample, as well as thebest-fit curve at 20 &C.

Interestingly, the scattering curve for the ! = 1 sample (knownto exhibit macroscopic phase separation in GUVs) was not well-described by a single value of N, but could be satisfactorily fit witha linear combination of N = 1 and N = 4 curves. This result was inter-preted as evidence for a distribution of domain sizes at high DOPCfractions, such that a few large domains are present at equilib-rium, consistent with incomplete domain coalescence that is oftenobserved in fluorescence micrographs of GUVs. It is also likely thatdomain polydispersity is present at lower DOPC fractions, thoughthe good quality of the fits to a monodisperse model suggests thatthe size distribution may be relatively narrow. A domain size dis-tribution can be accounted for with a simple modification of theMC method described in Section 2.2.2, with an additional fittingparameter (the width of the distribution).

From the phase diagram the compositions of the coexisting Ldand Lo phases are known for each of the compositions studied,and measurements of bilayer thickness were made for thesecompositions. The Lo phase thickness was essentially invariant asthe DOPC concentration was varied, but the Ld thickness decreasedfrom 38.4 to 35.1 A as DOPC increased from 0 to 100% of the low-TM

30 J. Pan et al. / Chemistry and Physics of Lipids 170– 171 (2013) 19– 32

Fig. 9. SANS curves at different temperatures reveal phase coexistence in themixture DSPC-d70/DOPC/POPC/Chol = 0.39/0.04/0.35/0.22. Under solvent contrastmatching conditions, minimal scattering above background is observed at 50 &C(purple solid line) and 40 &C (yellow solid line). However, an abrupt increase in scat-tering occurs upon further lowering the temperature to 30 &C (brown solid line),which persists at 20 &C (green solid line) and 10 &C (cyan solid line). 20 &C datawere fitted with the MC method (smooth black line) using constraints providedby the four-component phase diagram for this system, as described in the text. Theinset shows the total integrated scattered intensity (Porod invariant) as a functionof temperature, further demonstrating the enhanced scattering observed at lowertemperatures. Note that although the SLD contrast between the lipids and solventwas near zero at 50 &C, it increases with decreasing temperature, mainly due totheir different volume contractivity. This accounts for the observed deviation of thescattering curves from zero at q = 0 A$1 (i.e., 10 and 20 &C data).

lipid fraction. The thickness difference between coexisting Ld andLo phases therefore increased with increasing !, such that thedomain size correlated positively with the thickness mismatch, asshown in Fig. 10. This observation is consistent with line tensiontheories that predict a quadratic dependence of line tension onthickness mismatch. Presumably, increased line tension drives thecoalescence of small domains into fewer, larger domains to reducethe total domain perimeter. This effect was expected but had notpreviously been observed in freely suspended vesicles.

As mentioned previously, there is an artificial domain size trun-cation due to the finite size of the 60 nm diameter vesicles studied.For the compositions studied, the infinite phase separation condi-tion was not fulfilled up to ! = 0.35. On the other hand, data at ! = 1were consistent with a few large domains, though the quality ofthe fit was not as good. SANS curves for the single-phase compo-sitions required an asymmetric SLD profile, though compositionalasymmetry was not accounted for in the domain size modeling. It isalso likely that water penetration into the bilayer is different in the

Fig. 10. Domain size versus bilayer thickness mismatch for different mixture com-positions in the four-component system DSPC/DOPC/POPC/Chol. Both domain sizeand thickness mismatch of the coexisting Ld and Lo phases increased with increasingacyl chain unsaturation in the bilayer, as described in the text.

inner and outer leaflets due to differential packing of the lipid head-groups (looser packing in the outer leaflet), which would result inan asymmetric SLD profile, accounting for the asymmetry observedin the scattering profile (Risselada and Marrink, 2009).

4. Conclusions

The last decade has seen significant advances in the applica-tion of SANS to the study of lateral heterogeneities in membranes.SANS offers several important advantages for studying membranedomains, namely: 1) SANS is sensitive to nanometer distance scales,which arguably seem to be the natural size scale of both lipid raftsin resting cells and of Ld + Lo phase domains in a class of lipid mix-tures containing POPC or SOPC as the low-TM lipid; and 2) SANSdoes not require the use of extrinsic probe molecules, which maybe important for systems that are prone to light-induced artifactualphase separation (Ayuyan and Cohen, 2006; Petruzielo et al., 2013).While early work was primarily focused on validating the method-ology and developing suitable analyses, recent work has advancedour understanding of the mechanisms responsible for domain sizetransitions in increasingly biologically-relevant model mixtures.

For future development, it will be important to examine theinfluence of curvature and structural asymmetry across bilayerleaflets on phase separation. Such work will involve the use of largervesicles, and consequently the use of ultra-small-angle neutronscattering (USANS) instruments, which are capable of achievingsmaller reciprocal space distances. It may ultimately be possibleto use SANS to probe for lateral heterogeneities in live cells, whichcould provide important insight into the mechanisms responsiblefor raft formation and growth in physiologically relevant environ-ments.

Acknowledgment

J.K. is partly supported by ORNL’s Laboratory Directed Researchand Development (LDRD) program.

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