Article pubs.acs.org/Langmuir
Slow Relaxation of Shape and Orientational Texture in Membrane Gel Domains Jonas Camillus Jeppesen,*,† Vita Solovyeva,† Jonathan R. Brewer,‡ Ludger Johannes,§ Per Lyngs Hansen,† and Adam Cohen Simonsen† †
Department of Physics, Chemistry and Pharmacy and ‡Department of Biochemistry and Molecular Biology, University of Southern Denmark, DK-5230 Odense, Denmark § Institut Curie, UMR3666 CNRS, U1143 INSERM, 26 rue d’Ulm, 75248 Paris Cedex 05, France ABSTRACT: Gel domains in lipid bilayers are structurally more complex than fluid domains. Growth dynamics can lead to noncircular domains with a heterogeneous orientational texture. Most model membrane studies involving gel domain morphology and lateral organization assume the domains to be static. Here we show that rosette shaped gel domains, with heterogeneous orientational texture and a central topological defect, after early stage growth, undergo slow relaxation. On a time scale of days to weeks domains converge to circular shapes and approach uniform texture. 1,2-Dipalmitoyl-sn-glycero-3phosphocholine (DPPC) enriched gel domains are grown by cooling 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC):DPPC bilayers into the solid−liquid phase coexistence region and are visualized with fluorescence microscopy. The relaxation of individual domains is quantified through image analysis of time-lapse image series. We find a shape relaxation mechanism which is inconsistent with Ostwald ripening and coalescence as observed in membrane systems with coexisting liquid phases. Moreover, domain texture changes in parallel with the changes in domain shape, and selective melting and growth of particular subdomains cause the texture to become more uniform. We propose a relaxation mechanism based on relocation of lipids from high-energy lattice positions, through evaporation−condensation and edge diffusion, to low-energy positions. The relaxation process is modified significantly by binding Shiga toxin, a bacterial toxin from Shigella dysenteriae, to the membrane surface. Binding alters the equilibrium shape of the gel domains from circular to eroded rosettes with disjointed subdomains. This observation may be explained by edge diffusion while evaporation− condensation is restricted, and it provides further support for the proposed overall relaxation mechanism.
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The gel phase is less investigated than fluid phases because the gel phase has been thought to be of less biological importance. This presumption comes from the fact that most lipid membranes do not form gel phases at physiological temperatures. However, gel phases have been reported to exist in membranes reconstituted from lipids extracted from human stratum corneum, at skin physiological temperature. 6 In general, the biological significance of lipid domain formation and the role of specific equilibrium phases remains to be clarified.7,8 Gel domains are structurally more complex than fluid domains. When raft-mimicking ternary membranes are cooled into the liquid−liquid phase coexistence region, lateral separation occurs. Here fluid domains assume a circular shape as a result of line tension. In contrast, gel domains assume a variety of shapes through more complex growth mechanisms. In supported bilayers and giant unilamilar vesicles (GUVs)
INTRODUCTION Biomembranes are complex, quasi two-dimensional structures, with a self-assembled lipid bilayer as backbone, which serve to compartmentalize living organisms. The lipid bilayer consists of multiple lipid species, with proteins embedded in and attached to it.1 In vivo, biomembranes are not in equilibrium, but are subject to energy-consuming processes such as active transport and turnover.2 It remains an open question which aspects of the equilibrium behavior of lipid bilayers are relevant for biomembranes.3 The complexity of biomembranes in terms of composition, shape, and structure makes it difficult to study fundamental mechanisms in biomembranes, and model membranes consisting of one to three lipid species continue to serve as important model systems for fundamental biophysical studies.1 Important model membrane systems include freestanding bilayers4 and solid supported bilayers.5 Freestanding bilayers, in the form of vesicles, are more representative of the bilayers found in biomembranes, but being spherical and in liquid suspension makes them unideal for long-term imaging of a fixed region of interest. © 2015 American Chemical Society
Received: August 24, 2015 Revised: October 26, 2015 Published: October 26, 2015 12699
DOI: 10.1021/acs.langmuir.5b03168 Langmuir 2015, 31, 12699−12707
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nonequilibrium state and the rosette shaped gel domains should be assumed to be out of equilibrium. Here, we are aiming at identifying the relevant equilibrium state of gel domains and the time scale required for reaching it. We show that gel domains undergo relaxation in both shape and orientational texture, in parallel. Using time-lapse fluorescence microscopy, we investigate the relaxation of gel domains in solid supported DOPC:DPPC bilayers. A quantitative analysis of the temporal evolution is provided on time scales of days to weeks. We seek to obtain further information about the domain relaxation mechanism by restricting the lipid mobility through protein binding to the membrane. We have recently shown that Shiga toxin, a bacterial toxin produced by Shigella dysenteriae, alters lipid ordering in gel domains if present during domain growth.24 Shiga toxin is comprised of a toxic A unit and a nontoxic pentameric B unit (STxB) responsible for membrane binding. STxB binds to the glycosphingolipid globotriaosylceramide (Gb3), present in the membrane as illustrated in Figure 1c.25 We show that DOPC:DPPC bilayers (1:1, 0.5% Gb3) with STxB bound relax toward a different equilibrium state than bilayers without STxB bound.
formed from binary mixtures, a combination of reaction-limited and diffusion-limited growth mechanisms is giving rise to rosette shaped gel domains.9−11 Figure 1a shows examples of
Figure 1. (a) Bilayer with gel domains (dark rosettes). (b) Gel domain with vortex texture. Director angles are indicated by black lines and colors according to the color wheel in panel d. (c) Schematic illustration of bilayer (not to scale) with Shiga toxin subunit B (STxB) pentamers bound to Gb3 lipids (green heads, dashed chains). (d) Schematic explanation of the P2FM technique.
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MATERIALS AND METHODS
Materials. 1,2-Dioleoyl-sn-glycero-3-phosphocholine (DOPC) and 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) were purchased from Avanti Polar Lipids. Porcine globotriaosylceramide (Gb3) was purchased from Matreya, LLC. The fluorescent probes, 6-dodecanoyl2-dimethylaminonaphthalene (Laurdan) and 1,1′-dioctadecyl-3,3,3′,3′tetramethylindodicarbocyanine, 4-chlorobenzenesulfonate salt (DiD), were purchased from Molecular Probes (a Life Technologies brand). All lipids and probes were used without further purification. Shiga toxin subunit B (STxB) was supplied by Prof. Ludger Johannes, Institut Curie, UMR144 Curie/CNRS, Paris, France.26 All other chemicals were of HPLC grade, purchased from Sigma-Aldrich. Milli-Q water was used for all steps involving water. HEPES buffer (10 mM HEPES, 148 mM NaCl) was prepared at pH 7.0 by mixing appropriate amounts of HEPES acid, HEPES base, and NaCl. Muscovite mica was purchased from Plano GmbH, Germany. Sample Preparation. Supported lipid bilayers were prepared by hydrating dry lipid films.27,28 Dry lipid films on mica were prepared by spin-coating. A droplet (V ∼ 40 μL) of 10 mM stock lipid solution (DOPC:DPPC, 1:1), containing 0.5% Laurdan and 0.5% DiD, in a mixture of hexane and methanol (97:3 by volume), was applied to a freshly cleaved piece of mica, using a syringe, and spun on a KW-4A spinner (Chemat Technology, Inc., Northridge, CA, USA) at 3000 rpm for 40 s. The coated samples were placed under vacuum for 12−24 h to ensure complete evaporation of the solvent, yielding dry multilamellar lipid films. Multilamellar bilayers self-assemble from the dry lipid films when immersed aqueous buffer, referred to as hydration of the dry films. Hydration was done in a temperature controlled fluid cell designed for inverted microscopes, TSA02i (Instec, Inc., Boulder, CO, USA). The dry films on mica were immersed in buffer, heated to 60 °C, and allowed to hydrate for 1 h. Hydration was performed at 60 °C, which is above the melting temperature for both DOPC and DPPC, to ensure the bilayers form and equilibrate in the fluid phase, where the lipids are the most mobile. Excess lipid bilayers were removed mechanically by flushing the hydrated samples with 60 °C buffer, using a pipet. Imaging the sample while flushing allowed removal of all bilayers but the one proximal to the mica substrate. The presence of a single bilayer was verified by rinsing certain areas to an extend where holes appear in the bilayer, i.e., areas with no membrane and hence no fluorescence signal. The contrast between a hole and surrounding bilayer establishes the fluorescence signal of a single bilayer. After flushing, the entire buffer volume was exchanged multiple times to remove membrane debris in suspension. After exchanging buffer, the mica
several rosette shaped domains in an 1,2-dioleoyl-sn-glycero-3phosphocholine:1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DOPC:DPPC) membrane. In the gel phase the acyl chains of the lipids can be tilted with respect to the bilayer normal, creating a degree of freedom associated with the projection of the acyl chains in the plane of the bilayer, called the director. The lateral distribution of the director is termed orientational texture or just texture. The rosette shaped gel domains have a vortex-like texture around a central topological defect;12,13 for an example see Figure 1b. The texture and defects are similar to those observed for liquid crystals in the smectic-C phase14−16 After nucleation and early stage growth of domains, the free energy of the bilayer system is lowered through various mechanisms. Coarsening lowers the interfacial energy by increasing the area to perimeter ratio. It does so via two possible mechanisms:17 (1) collision and coalescence, where smaller domains merge to form larger domains, and (2) Ostwald ripening, sometimes called evaporation−condensation, where lipids evaporate from the boundary of small domains and condense on larger domains.18 Both mechanisms cause the radius of domains to grow as ⟨r⟩ ∝ tα, or equivalently the area as ⟨A⟩ ∝ t2α, where t is time and α is a constant, called the growth exponent.19 Studies of coarsening of gel domains are scarce compared to coarsening of fluid domains. Previously, the shape and texture of gel domains have been studied.11−13,20−22 In these studies, gel domains were typically grown over a period of 5−30 min by either a rapid temperature quench or by cooling at a rate of ∼1 °C min−1 into the phase coexistence region, and then studied for 1−5 h. Observations include the physical shape of the domains, area, perimeter length, spatial distribution of domains, and texture. It is generally assumed that nonequilibrium growth is the origin of the complex shapes of gel domains, but the long-term stability of the domains is rarely addressed. It is typically assumed that gel domains are static throughout the observation window.11,23 In general, fast crystal growth can indeed trap systems in a 12700
DOI: 10.1021/acs.langmuir.5b03168 Langmuir 2015, 31, 12699−12707
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Langmuir sample was turned upside down so the bilayer faced the microscope objective. This was necessary to allow excitation with polarized light (mica is birefractive) and to avoid imaging the bilayer through the mica. After the temperature stabilized at 60 °C again, the sample was cooled to 20 °C at a rate of 1 °C min−1. Before imaging began, the temperature was allowed to stabilize at 20 °C, to ensure no temperature driven growth was recorded, and then held at 20 °C for the rest of the experiment. For the experiments involving STxB, the dry lipid films would be prepared from a lipid solution containing 0.5% Gb3 and STxB would be added to the buffer surrounding the sample to a final concentration of 0.2 μM, before the temperature ramp was initiated. Further details about the STxB experimental protocol can be found in ref 24. Microscopy. Microscopy was done on modified Nikon Eclipse Ti-E microscopes, and Micro-Manager29 was used to control and automate the image acquisition process. Wide-field imaging was used to study the shape of gel domains over large areas of membrane. A motorized stage allowed imaging of multiple regions automatically, and a computer controlled shutter was used to switch off illumination between image acquisitions. The Perfect Focus System (PFS) on the Eclipse Ti-E microscope was used to keep the sample in focus throughout the observation window (several days). Images were captured with a 20×, 0.75 NA air objective. To study the texture of the gel domains during relaxation, we used polarized two-photon fluorescence microscopy (P2FM). The technique is described in detail in refs 12 and 13; what follows is a short review. In the following, refer to Figure 1d for symbols and geometry of the P2FM technique. Laurdan is sensitive to the tilt of surrounding lipids because its transition moment P aligns parallel to the acyl chains of the surrounding lipids. The emission intensity of Laurdan depends on the angle between the polarization of the excitation light E and the azimuth orientation of the probe P, φc − φ.30 Images recorded as a function of polarization angle will hence contain information about the director orientation. The director angle φc can be found in each pixel by Fourier transforming the intensity image series, as the phase angle of the transform. To obtain the strongest dependence on the angle of polarization, and to minimize damage to the sample, two-photon excitation was used. Excitation was performed with a Ti:sapphire laser working at 780 nm. The emission wavelength of Laurdan in the gel phase is λgel = 440 nm,31 selected with a dichoric mirror splitting at 475 nm, followed by a 438 ± 12 nm band-pass filter, and detected with a photomultiplier (Hamamatsu Photonics, H7422P-40). Images were formed with a 60×, 1.2 NA, water immersion objective. The temperature of the objective was actively matched to that of the sample, using a water cooling system, to avoid thermally induced growth or melting of domains when bringing the water immersion objective into contact with the sample.
of membrane were recorded throughout that period. Figure 2a,b shows representative wide-field images, with changes in domain
Figure 2. Domains in a DOPC:DPPC (1:1) bilayer (a) 0 and (b) 78 h after early stage domain growth. (c) Gel area fraction as a function of time for the system seen in panels a and b.
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RESULTS Bilayers were prepared well above the liquid−gel phase transition temperature, and cooled into the liquid−gel phase coexistence region. Gel domains nucleate when the liquid−gel phase boundary is crossed and continue to grow in size as the temperature is lowered. Using a constant cooling rate of 1 °C min−1, the domains grow over a period of ∼20 min, and the final domain size is dictated by the final temperature of the system and phase diagram for the lipid mixture used, via the lever rule. The state of the system after cooling and temperature stabilization is referred to as the initial state of the system, and growth of domains due to the temperature ramp is referred to as early stage growth. Our observations of slow relaxation start with the system in its initial state, just after the early stage growth of gel domains. Unless stated otherwise, the sample was actively maintained at a constant temperature of 20 ± 1 °C throughout the whole observation period. To verify the rosette shaped gel domains are indeed out of equilibrium, the shapes of the domains were observed for 3 days. Wide-field images of several 100 μm × 100 μm patches
shape from Figure 2a to Figure 2b readily observable. The domains circled and labeled suggest three different behaviors: growing (domain 1), shrinking (domain 2), and merging (domains 3). To quantify the observed changes, the images were segmented to allow determination of the area and perimeter of each individual gel domain, as a function of time. The segmentation was done with MATLAB, using a single threshold, chosen to preserve as many features, visible in the raw images (see Figure 2a,b), as possible. From the segmented images, geometric information on single domains, such as area and perimeter, was extracted. To investigate whether the system was in phase equilibrium during observations, the fraction of the total area covered by gel phase, Agel/(Aliq + Agel), was found as a function of time. Figure 2c shows the gel area fraction, which remained a constant 0.25 ± 0.1 throughout the observation window. With the system confirmed to be in thermodynamic equilibrium and early stage growth completed, we proceeded to investigate the dynamics of the slow relaxation. Area time 12701
DOI: 10.1021/acs.langmuir.5b03168 Langmuir 2015, 31, 12699−12707
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Langmuir series for individual domains are shown in Figure 3a, and they confirm the qualitative observations made from the raw images
Figure 3. Area and perimeter of individual gel domains as a function of time after early stage growth, i.e., t = 0 corresponds to the end of the temperature ramp. (a) Area of domains from Figure 2, normalized with respect to the initial area of the individual domains. (b) Normalized perimeter, and (c) normalized area to perimeter ratio. (d) Membrane patch from Figure 2a segmented. Green domains are growing, red domains are shrinking, and black domains are excluded from analysis. The scale bar is 50 μm.
(Figure 2a,b); some domains increase their area with time while others decrease. Correspondingly, Figure 3b shows the perimeter time series and Figure 3c shows the area-to-perimeter ratio time series. All individual domains were categorized as growing or shrinking, based on the slope of a line fitted to each individual area time series in Figure 3a. Figure 3d shows a segmented patch of membrane at t = 0, with domains color coded as green for growing and red for shrinking. Black domains were excluded from analysis because either they merge with another domain, or membrane debris settled on them during imaging. The distributions of the initial area A0 of growing and shrinking domains, respectively, are shown in Figure 4a. The two distributions are indistinguishable at the significance level 5% implying that the fate of domains during relaxation does not correlate with their initial area. The distributions of area-to-perimeter ratios for the two populations were also indistinguishable (not shown). The rate of domain area growth or shrinkage, however, does show a significant dependence on initial domain area. Figure 4b shows the growth rates, found from the area time series in Figure 3a, as a function of initial domain area. A line fitted to the rate data has a positive slope of (5 ± 2) × 103 h−1, which is significantly different from zero using a significance level of 5%. A positive slope implies that, within the population of growing domains, large domains grow faster than smaller domains. Similarly for the shrinking domains, smaller domains shrink faster than larger domains. Up to now we have not considered the texture of the domains. It might influence the shape relaxation investigated above, or at least we expect it to change along with the shape. Texture of domains within a patch of membrane was imaged with the P2FM technique after early stage growth, and then every 24 h for 1 week. Figure 5a−d shows the domains and
Figure 4. (a) Histograms of initial domain sizes for growing and shrinking domains. (b) Initial area A0 as a function of average growth rate, and linear fit with slope (5 ± 2) × 103 h−1.
their texture on days 1, 3, 5, and 7. Marked are domains shrinking (1), growing (2), and merging (3). The heterogeneity of domain textures appears unaffected by time, except that certain subdomains (spatially separate regions with distinct texture, e.g., the leaves of the rosettes) grow in area while others shrink or maintain a constant area. Uneven growth or shrinkage of subdomains leads to a change in the overall texture of the domains. Consider domain 2 in Figure 5a,d. Two of the five subdomains grow significantly in size, while the remaining three maintain their initial area. The uneven growth can be quantified by histograms of the director angles (φc) within the domain. Figure 5e shows a histogram of φc within domain 2 at t = 0, and Figure 5f shows a histogram of φc within domain 2 at t = 144 h. Three peaks are visible in both histograms, one for each of the distinct director orientations within the domain, but the peaks do not grow proportionally, as the area percentages on the peaks show. The positions of the peaks are also shifted (10−20°) during the 144 h observation, which can also be seen from the texture images as a slight change in subdomain color with time. The data presented thus far indicate that equilibrium shape and equilibrium texture are not reached after 3−7 days; e.g., changes in shape and texture are still visible from Figure 5c to Figure 5d. To probe the long-term equilibrium of the gel domains, 12702
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Figure 5. Orientational texture of domains in DOPC:DPPC bilayer (a) 0, (b) 48, (c) 96, and (d) 144 h after early stage domain growth. (e) Histograms of director angles ϕc within the domain labeled 2, (e) at time t = 0 h and (f) at time t = 44 h. The histograms in panels e and f have been divided into three regions with boundaries midway between peaks. The percentages at each peak indicate the fraction of directors (proportional to number of lipids) located within the peaks.
circular shapes, the domains appear to preserve the rosette shape, albeit with thinner leafs and eroded centers. To quantify the difference between bilayers with and without STxB bound, the isoperimetric coef f icient Q = 4πA/P2, also called the circularity, was calculated for the domains in each experiment at t = 0 and t = 27 days. The isoperimetric coefficient relates the perimeter P of a closed curve to the area A of the enclosed region, and is a measure of compactness of a shape relative to a circle. Q varies from Q = 1 for circles to Q ≪ 1 for fractal-like objects, e.g., Q ∼ 0.79 for a square and Q ∼ 0.21 for a quadrifolium. Initially, at t = 0, the circularity is Q = 0.4 ± 0.1 for the domains without STxB (Figure 7a) and QSTxB = 0.5 ± 0.1 for the domains with STxB (Figure 7c). After 4 weeks, at t = 27 days, the circularity had changed to Q = 0.8 ± 0.2 for the domains without STxB (Figure 7b) and QSTxB = 0.4 ± 0.2 for the domains with STxB (Figure 7d). The domains with STxB bound see a small reduction in Q, whereas the domains without STxB see a large increase in Q. This confirms the initial observation that domains with STxB bound relax toward less compact shapes compared to the pure DOPC:DPPC domains and the DOPC:DPPC:Gb3 control domains.
the samples were kept protected from light and at constant temperature after they were removed from the microscope, allowing the membranes to be imaged ∼30 days after early stage growth. Figure 6a show two typical domains at this late stage. Both domains are more circular and uniform in texture compared to the domains shown at earlier stages. Domain I has almost been reduced to two subdomains, and the topological defect is now located on the boundary of the domain, a so-called boojum.32 The texture histograms in Figure 6b (domain I) and Figure 6c (domain II) are different from the histograms shown in Figure 5e,f. Peaks are broader and closer spaced, indicating a more uniform texture. To obtain more insight into the relaxation mechanism, the system was perturbed by binding of STxB to the bilayer. STxB will cross-link Gb3 embedded in the membrane, forming larger and less mobile lipid clusters within the membrane, possibly lowering the overall diffusivity of the lipids. Gb3 was added to the DOPC:DPPC membranes in a concentration of 0.5%, facilitating STxB binding to the bilayer. STxB was added to the buffer before cooling the system into the liquid−gel coexistence region. This allowed STxB to bind to Gb3 while the system was still in the mobile fluid phase. The bilayers with STxB bound, and controls with Gb3, but without STxB, were imaged immediately after early stage domain growth and then on a weekly basis for 4 weeks. Panels a and b of Figure 7 show a control DOPC:DPPC:Gb3 bilayer at t = 0 and t = 27 days, respectively. Qualitatively the relaxation resembles that of the pure DOPC:DPPC system (see Figure 2a,b). Initially domains are rosette shaped, and with time they become more circular. Panels c and d of Figure 7 show a DOPC:DPPC:Gb3 bilayer with STxB added, at t = 0 and t = 27 days, respectively. Initially, at t = 0, the domains resemble those in membranes without STxB. The long-term equilibrium, however, appears different from that of the pure DOPC:DPPC system and the DOPC:DPPC:Gb3 control system. Instead of relaxing toward
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DISCUSSION AND CONCLUSIONS
Gel domains, coexisting with a liquid phase, in a solid supported bilayer, were observed to change shape on a time scale of hours to days. It was found that the area covered by gel phase remained constant throughout observations, confirming the system to be in thermodynamic equilibrium. If this was not the case, the phenomenon observed might not have been relaxation of shape but phase equilibration. From Figure 2c, the constant value found for the gel area fraction was Agel/(Aliq + Agel) = 0.25 ± 0.01. This value can be compared to one calculated from the DOPC:DPPC phase diagram. Using the 12703
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Figure 7. (a) Control sample (DOPC:DPPC with 1% Gb3) immediately after early stage domain growth. (b) Same sample after 27 days. (c) Sample with STxB bound (DOPC:DPPC with 1% Gb3 and STxB added), immediately after early stage domain growth. (d) Same sample 27 days later. (e) Schematic illustration of mechanisms for mass transport: evaporation (I), condensation (II), and edge diffusion (III). Not to scale. (f) Schematic illustration of STxB−Gb3 cluster within a bilayer (top view). Not to scale.
species: agel = aDPPC,gel = 47.9 Å2 and aliq = aDOPC,liq = 72.5 Å2.33 This approximation has previously been used when comparing images to phase diagrams.34 The only available phase diagram for a DOPC:DPPC mixture, needed to supply values for Wgel and Wliq, is a phase diagram for multilamilar DOPC:DPPC vesicles in bulk, constructed using X-ray scattering.35 From this phase diagram we find Wgel = 0.92 ± 0.05 and Wliq = 0.36 ± 0.05. Evaluating eq 1 gives a gel area fraction of 0.24 ± 0.06 (assuming the uncertainty on agel and aliq is 2 Å2). This value is in agreement with our experimental finding of 0.25 ± 0.01. Three different behaviors (growing, shrinking, and merging) were observed during relaxation of shape, as exemplified in Figure 2a,b. The different behaviors were quantified in Figure 3a−c, which shows time series of area, perimeter, and areato-perimeter-ratio for the individual domains. The time series confirm the initial observation of domains growing and shrinking; areas are seen to increase and decrease in approximately equal numbers. The area-to-perimeter time series show a strong tendency for domains to become more compact. Changes in area and area-to-perimeter ratio indicate the shapes of the domains are out of equilibrium after early stage growth. Classifying domains according to whether they grow or shrink (Figure 3d), revealed no obvious dependence of the two populations on initial shape or area. Histograms of initial area A0 and area-to-perimeter ratio for the two populations were found to be indistinguishable. But a weak dependence of the growth rate on initial area was found.
Figure 6. (a) Two gel domains ∼30 days after early stage growth. The sample did not stay on the microscope for 30 days, but was kept protected from light at T = 20 ± 2 °C. The black dots on the domains mark the approximate location of the topological defect. (b) Texture histogram for domain I. (c) Texture histogram for domain II.
lever rule to find the molar percentage weight of the gel and liquid phase, the gel area fraction can be found as Agel agelXgel = Agel + Aliq agelXgel + aliq Xliq =
agel(X − Wliq) agel(X − Wliq) + aliq (Wgel − X )
(1)
where X = 0.50 ± 0.02 is the molar fraction of DPPC in the 1:1 mixture, Wgel and Wliq are the DPPC percentage weights at the solidus and liquidus, and agel and aliq are the area per lipid in the liquid and gel phases. The area per lipid should ideally be measured values for the two phases with this specific composition and temperature. But we will assume the area per lipid in the two phases to be that of the predominant 12704
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coalesce via this mechanism. This is because of the interactions with the solid support, which make collective motion of whole domains impossible. Collective motion of gel domains is possible in freestanding membranes,39 but long-term studies of coarsening of gel domains in GUVs are not realistic. The second mechanism of coarsening is Ostwald ripening, or evaporation−condensation, where individual lipids evaporate (melt) from the boundary of small domains and condense (solidify) on the boundary of larger domains.17,18 This was observed. We observed domains of all initial sizes growing and shrinking, which is not consistent with Ostwald ripening. Evaporation and condensation must, however, be occurring since it is the only mechanism by which domains can change area in the absence of coalescence. The general evaporation and condensation processes are illustrated in Figure 7e as processes I and II, respectively. Changes in shape, without changes in area, can also happen through edge diffusion10 as illustrated in Figure 7e, process III. We propose, as an explanation for the observed changes in shape and texture, a combination of edge diffusion and evaporation−condensation, removing lipids from lattice positions of high energy, and redepositing them at positions of lower energy. The two contributions to the free energy, i.e., texture and shape, associate different positions with high and low energy. Consider the positions labeled 1 and 2 in Figure 7e. Position 1, at the bottom of a gap between two leaves, is a low energy position in terms of shape, since the interface is concave, maximizing the number of neighbors a newly condensed lipid can achieve. Position 2, on the other hand, is a high energy position in terms of shape, since the interface at this location is convex, providing fewer neighbors for a condensed lipid. In terms of texture, position 1 has the higher energy, since the texture is highly nonuniform where two leaves join to form a line defect, compared to positions where the texture is more uniform (position 2). The rate at which lipids evaporate and condense at a given boundary position depends on the energy of that position; higher energy means faster evaporation, and lower energy means faster condensation. This could explain why small subdomains (leaves) appear to melt, while larger subdomains appear to grow. Large subdomains have the least convex domain boundary, giving them the lowest interfacial energy, and the largest interface exposing low-energy uniform subdomain texture. Edge diffusion will likely make individual subdomains more round, but not the domain as a whole. If the domains had uniform textures, edge diffusion would act to fill out the gaps between leaves (position 1 in Figure 7e), since these positions would entail low interfacial energy. Positions between leaves are, however, high-energy positions in terms of texture because a line defect between two individual subdomain textures has to form for the gap to be filled. Lipids diffusing along the edge, from one subdomain to another, would need to pass through this high-energy region between the subdomains, and therefore lipids are not thought to diffuse from one subdomain to another along the edge. The two equilibrium states defined by uniform texture and circular shape are approached in parallel. Changes in shape appear to drive the changes in texture; the overall domain texture appears to change only as a result of individual subdomains growing and shrinking. This suggests a coupling between the two relaxation processes. Perturbing the system prior to gel domain formation via membrane binding of STxB was found to alter the long-term
Extracting a growth exponent from the domain area time series was not possible because the slopes of the time series in Figure 3a do not change significantly with time. One other study has reported growth exponents for gel domains in DOPC:DPPC bilayers following a temperature quench.36 They report compact circular gel domains of diameter ∼1 μm growing with an exponent α ≈ 0.7 for 20−30 min followed by a change in growth exponent to α ≈ 0.1. The growth reported by ref 36 is, however, an early stage growth, where the system is still moving toward thermodynamic equilibrium, and therefore cannot be compared to our findings. Significantly, the texture was observed to change in parallel with shape; see Figure 5a−d. Certain subdomains were observed to grow and others to shrink, leading to an overall more homogeneous texture. Figure 6 indicates that the longterm equilibrium for the domains might be circular with uniform texture, and the topological defect excluded, but such a final state was not reached during our 1 month of observations. Obtaining uniform texture requires eliminating the central topological defect. The topological defect appears fixed in position, but we see indications that it is excluded by selectively melting one side of the domain while growing the other, eventually causing the defect to be located on the domain boundary. The process was very slow, requiring weeks to show significant changes. A closed system minimizes its free energy as it tends toward equilibrium. Two contributions to the free energy of a gel domain are (1) the energy associated with phase boundary, or interface, under the influence of line tension, and (2) the energy associated with heterogeneous texture, and the topological defects needed to have heterogeneous texture. Minimal interfacial energy for a domain with constant area implies maximal area-to-perimeter ratio, which implies a circular shape. While the gel domains may not become completely circular on the time scales observed in this study, they do relax toward elongated, round shapes with a much higher area-to-perimeter ratio than the initial rosette shapes. The texture with minimal energy is a uniform texture, if there are no boundary conditions.37 Boundary conditions on the director orientation will lead to nonuniform textures with defects. Textures with defects observed in surfactant monolayers have been successfully modeled as systems with a director field subject to boundary conditions.37 The director field of the gel domains with vortex texture, however, are not subject to any boundary conditions.38 This can also be seen from the domains in Figures 1b, 5a−d, and 6a, where directors do not align with the domain boundary in any particular orientation. Our observations indicate that the gel domains relax their shape in a manner which causes the texture to become more uniform and the defect located closer to the boundary, possibly tending toward boojums. The observed relaxation differs from the coarsening phenomena reported for systems with liquid−liquid phase coexistence. The framework of coarsening do not take into account internal structures of the objects undergoing coarsening, nor changes to shape. Changes in both shape and internal structure were observed for the gel domains. The first of the two coarsening mechanisms is coalescence, where domains undergo Brownian motion, collide, and coalesce. This behavior was not observed in our study. Three pairs of close-lying domains were observed to merge (the black domains in Figure 3d), but the domains came into contact by growing, not by collective motion. The gel domains do not undergo Brownian motion, and hence do not 12705
DOI: 10.1021/acs.langmuir.5b03168 Langmuir 2015, 31, 12699−12707
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(FNU), Grant DFF-1323-00134, and the Villum Foundation. The experiments were performed on the facilities of DaMBIC Danish Molecular Biomedical Imaging Center.
equilibrium significantly. The long-term equilibrium of the DOPC:DPPC:Gb3 control system (Figure 7b) and the pure DOPC:DPPC system was found to be the same: enlarged rounded domains. As expected, the addition of 0.5% Gb3 did not alter the long-term equilibrium significantly. In contrast, the membranes with bound STxB (Figure 7c,d) relaxed toward eroded rosette-shaped domains, rather than larger rounded domains. The difference in the relaxaiton outcome was quantified by the isoperimetric coefficient, or circularity, Q. The control system (with Gb3 but without STxB) exhibited an increase in average domain circularity, whereas the system with STxB showed a decrease. Domains with bound STxB appear frozen terms of their shape. STxB is known to bind up to 15 Gb3 lipids (three on each of the five subunits),25 forming STxB−Gb3 complexes; this is illustrated in Figure 7f. Other lipids get trapped between the cross-linked Gb3 lipids and become highly immobilized. The complexes are subject to slow diffusion on account of their size, and we suggest they lower the diffusivity of the surrounding lipids as well, by acting as obstacles which the lipids have to diffuse around. An overall slower diffusion would slow evaporation and condensation because the lipids condensing onto a domain need to be transported to the domain by diffusion, and lipids evaporating need to be transported away by diffusion. If edge diffusion became the predominant mechanism for mass transport, the area of the domains would become fixed while changes in shape would remain possible. As previously suggested, edge diffusion is unlikely to transport lipids from one subdomain to another, because doing so would require diffusion through the positions of high texture−energy in the gaps between leaves (position 1 in Figure 7e). Edge diffusion could, however, transport lipids away from the gaps, thereby eroding the centers of the domains and removing energetically costly defect lines in the process. This could explain the eroded rosette shapes we see in in Figure 7d. To summarize, we have demonstrated that gel domains in supported bilayers, coexisting with a liquid phase, can undergo internal reorganization where the orientational texture and shape relax toward uniform and circular, respectively. The relaxation process is slow, taking place on time scales of days to weeks, in contrast to the coarsening phenomena observed in ternary mixtures with liquid−liquid phase coexistence, which occur over tens of minutes to hours.17 We propose that the mechanism is a combination of evaporation−condensation and edge diffusion, relocating lipids on the domain boundary, from high-energy positions to low-energy positions. Perturbation of the system by the binding of STxB to the membrane was found to significantly alter the outcome of relaxation. Under this condition domains did not relax toward a more rounded morphology, as expected for systems subject to line tension, but instead, they progressed toward eroded rosette shapes, which exhibited a lower circularity than the initial rosette shapes.
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[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We thank the following sources for financial support: The Danish Council for Independent Research, Natural Sciences 12706
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