Morphometric Image Analysis of Giant Vesicles: A New Tool for Quantitative Thermodynamics Studies of Phase Separation in Lipid Membranes

Abstract

We have developed a strategy to determine lengths and orientations of tie lines in the coexistence region of liquid-ordered and liquid-disordered phases of cholesterol containing ternary lipid mixtures. The method combines confocal-fluorescence-microscopy image stacks of giant unilamellar vesicles (GUVs), a dedicated 3D-image analysis, and a quantitative analysis based in equilibrium thermodynamic considerations. This approach was tested in GUVs composed of 1,2-dioleoyl-sn-glycero-3-phosphocholine/1,2-palmitoyl-sn-glycero-3-phosphocholine/cholesterol. In general, our results show a reasonable agreement with previously reported data obtained by other methods. For example, our computed tie lines were found to be nonhorizontal, indicating a difference in cholesterol content in the coexisting phases. This new, to our knowledge, analytical strategy offers a way to further exploit fluorescence-microscopy experiments in GUVs, particularly retrieving quantitative data for the construction of three lipid-component-phase diagrams containing cholesterol.

Introduction

Fluorescence microscopy experiments on giant unilamellar vesicles (GUVs) have become a popular method of studying phase-coexistence phenomena in model lipid membranes (1–3). Until now, however, only few researchers have attempted to perform a quantitative characterization of thermodynamic phase equilibria and phase diagrams from these type of experiments. We recently introduced an image-analysis method that allows morphometric data to be extracted from 3D confocal stacks of GUVs rather than wide confocal planes. In turn, this allows a global characterization of the membrane lateral structure with fully obtainable resolution at every point (4). In particular, by using the area fraction of coexisting domains in GUVs composed of 1,2-dilauroyl-sn-glycero-3-phosphocholine (DLPC)/1,2-palmitoyl-sn-glycero-3-phosphocholine (DPPC) and using the lever rule, it was found that the observed lipid domains indeed correspond with equilibrium solid-ordered (s_o) and liquid-disordered (l_d) thermodynamic phases (4). This image-analysis method has been recently improved in our laboratory by generating a 2D representation of the entire GUV surface from the 3D stacks, thus allowing for full-surface histograms, compensation for the photoselection effects of fluorescent probes, and a more versatile quantitative characterization of the geometry of lipid-domain structures on the surface, including efficient measurement of domain areas (5). The large size of the coexisting domains allows for accurate determinations of the fractional areas of the coexisting phases in a single vesicle. This makes possible a quantitative comparison of single-vesicle experiments with ensemble-averaged information derived from bulk methods using multilamellar vesicles. In a recent work, Juhasz et al. conducted comparative experiments using quantitative confocal fluorescence microscopy of GUVs and ²H-NMR spectroscopy within the two-phase region (6), i.e., liquid-ordered (l_o)-l_d, using 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC)/DPPC/cholesterol mixtures. These authors used a simple fitting routine to identify large circular domains as ellipses in confocal images of the top and bottom halves of a vesicle. Specifically, they found a quantitative agreement between the measured area fractions of coexisting fluid phases from a large population of GUVs and the phase fractions deduced from ²H-NMR (6), which supports the interpretation that the observed membrane domains in GUVs correspond to coexisting l_o-l_d equilibrium thermodynamic phases.

All of the aforementioned results validate the reliability of quantitative fluorescence microscopy of GUVs as an approach to performing studies of membrane-phase equilibria. For the determination of tie lines, however, fluorescence-microscopy information obtained from GUV experiments has not been exploited so far, i.e., GUV experiments are rather used as a supplementary technique. As an example, studies reporting on the lateral structure of GUVs composed of DOPC/DPPC/cholesterol mixtures performed computation of tie lines in the l_o-l_d phase coexistence region using ²H-NMR data obtained from multilamellar membrane structures (6–8). Using the same lipid mixture, Uppamoochikkal et al. (9) obtained from decomposition of x-ray diffraction data information about the orientation of tie lines in the same phase coexistence region. From all these reported data (7–9), discrepancies in determinations of l_o-l_d phase coexistence regions and/or tie lines are evident, so this calls for further investigation of other methods, such as fluorescence imaging using GUVs. This method makes available a visual measurement of the fractional areas of the coexisting phases, thereby providing a direct observable of the extensive variables defining the miscibility gap. Tie lines give information about composition and fraction of each coexisting phase at a given state, and thus, they constitute a key parameter in characterizing phase-separation phenomena. To explore whether or not tie-line length and orientation can be extracted solely from GUVs/fluorescence microscopy experiments, we have used our previously reported image-analysis strategy (4,5) in combination with general equilibrium thermodynamic considerations.

Materials and Methods

Materials

DOPC, DPPC, cholesterol, and 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine-N-(lissamine rhodamine B sulfonyl) (Rh-DOPE) were purchased at Avanti Polar Lipids (Alabaster, AL) as powders. Naphthopyrene was purchased from Sigma-Aldrich (St. Louis, MO).

Methods

Preparation of GUVs

DPPC, DOPC, and cholesterol stock solutions (10 mg/ml) were prepared in Cl₃CH by dissolving the appropriate mass of lipid previously weighed by balance (Mettler Toledo AX205 delta range, d = 0.01 mg). The DOPC and POPC concentrations in these stocks were confirmed by phosphorus analysis (10). Cholesterol concentration was determined by gravimetric analysis. The associated error in the concentration of our stock solutions was <1%. Different mixtures containing DOPC, DPPC, and cholesterol with the fluorescent probes were prepared in Cl₃CH/MetOH 2:1 v/v (total lipid concentration, 0.2 mg/ml). Probes were 0.5 and 0.2 mol % with respect to total lipids for naphthopyrene and Rh-DOPE, respectively. Stock solutions of both fluorescent probes where prepared in Cl₃CH and their concentrations were determined using spectrophotometry. For information about the different DOPC/DPPC/cholesterol compositions used in our study, see Table 1. GUVs were prepared according to the electroformation method described by Angelova et al. (11) using a custom-built chamber (12). Briefly, aliquots of the desired lipid mixture containing the fluorescent probes were deposited on each Pt electrode (4 μl/wire), and the solvent was removed under vacuum for 2 h. After removal of the organic solvent, the chamber was filled with a 200 mM sucrose solution, and an AC field was applied to the chamber using a function generator (Vann Draper Digimess Fg 100, Stenson, Derby, United Kingdom) with an amplitude of 1.3 V and a frequency of 10 Hz. The electroformation was carried out for 60 min at a temperature of 55°C for all samples. Subsequently, the GUVs chamber was cooled to room temperature in a time span of ∼5 h in an oven (J. P. Selecta, Barcelona, Spain) using a temperature ramp (∼0.2°C/min). The last step was performed to achieve equilibrium conditions in our samples. Once the solution reached room temperature, the vesicles were transferred to an iso-osmolar glucose solution in a special chamber (200 μl of glucose + 50 μl of the GUVs in sucrose in each of the eight wells of the plastic chamber used (Lab-Tek Brand, Nalgenunc International, Naperville, IL)). The density difference between the interior and exterior of the GUVs causes the vesicles to sink to the bottom of the chamber, and within a few minutes, the vesicles are ready to be observed using an inverted laser scanning confocal fluorescence microscope. The temperature during image acquisition was controlled to 20.0 ± 0.5°C.

Table 1.

Measured area fractions (A_lo/A) of l_o phase for the various compositions sampled

Sample	N	xCHOL	xDOPC	xDPPC	Alo/A	σ(Alo/A)
1	5	0.45	0.20	0.35	0.816	0.068
2	5	0.45	0.08	0.47	0.897	0.023
4	5	0.40	0.25	0.35	0.706	0.064
5	5	0.40	0.13	0.47	0.824	0.020
6	4	0.35	0.42	0.23	0.513	0.139
7	6	0.35	0.30	0.35	0.669	0.126
8	5	0.35	0.18	0.47	0.771	0.022
9	5	0.35	0.10	0.55	0.875	0.048
a	10	0.30	0.47	0.23	0.091	0.090
b	11	0.30	0.35	0.35	0.467	0.098
c	10	0.30	0.23	0.47	0.675	0.044
d	10	0.30	0.15	0.55	0.850	0.045
10	5	0.25	0.47	0.28	0.314	0.066
11	5	0.25	0.35	0.40	0.574	0.053
12	5	0.25	0.23	0.52	0.688	0.067
13	5	0.25	0.15	0.60	0.779	0.084
14	5	0.20	0.60	0.20	0.190	0.047
15	5	0.20	0.47	0.33	0.431	0.058
16	5	0.20	0.35	0.45	0.535	0.140
17	5	0.20	0.23	0.57	0.704	0.088
18	5	0.20	0.15	0.65	0.850	0.062

The standard deviation (σ(A_lo/A)) for each composition is indicated as well. N is the number of vesicles analyzed.

Laser scanning confocal fluorescence microscopy experiments

Confocal Image stacks were acquired on a Zeiss LSM 510 Meta confocal laser scanning fluorescence microscope. A C-Apochromat 40× water immersion objective, NA 1.2, was used in our experiments. Two-channel image stacks were acquired using multitrack mode. Argon and NeHe lasers (458 and 543 nm) were used as excitation sources. The laser lines were reflected to the sample through the objective using two different dichroic mirrors (HFT 488/543/633 and HFT 458 for exciting Rh-DOPE and naphthopyrene, respectively). The fluorescence emission collected through the objective was directed to the photomultiplier-tube (PMT) detectors using a mirror. A beam splitter was used to eliminate remnant scattering from the laser sources (NFT 545) in a two-channel configuration. Additional filters were incorporated in front of the PMT detectors in the two different channels to measure the fluorescent intensity, i.e., a long-pass filter, >560 nm, for Rh-DOPE and a band-pass filter, 500 ± 20 nm, for naphthopyrene. The acquired intensity images were checked to avoid PMT saturation and loss of offsets by carefully adjusting the laser power, the detector gain, and the detector offset. The image stacks were acquired at a sampling rate slightly above the Nyquist frequency, which was calculated to be 40 nm for Δx and Δy and 140 nm for Δz with Huygens Scripting Software (Scientific Volume Imaging, Hilversum, The Netherlands). The sampling above the Nyquist frequency was necessary to guarantee sufficient scan speed to minimize undesirable effects due to vesicle movement. The obtained confocal raw fluorescence image stacks were deconvolved with Huygens Scripting Software using an algorithm based on the classic maximum-likelihood estimator. The distinct preference of Rh-DOPE and naphthopyrene for disordered and ordered liquid phases, respectively was corroborated by LAURDAN GP experiments (1) in DOPC/DPPC/cholesterol mixtures at the l_o-and-l_d phase-coexistence regime (data not shown). The preferential partition of these two probes is in agreement with previous observations performed in brain sphingomyelin/DOPC/cholesterol mixtures also displaying l_o-l_d phase coexistence (13).

Image analysis

The confocal image data are processed using the software and method described by us in an earlier article (5). The procedure is sketched in Fig. 1. As a starting point, a confocal image stack is used to generate a surface image on a triangulation of a spherical surface, i.e., a surface mesh, which represents the lateral variation of fluorescence intensities throughout the surface of the imaged GUV. The triangles of the mesh are used as pixels for the surface image, and their intensity values are derived from the local volumetric fluorescence-intensity data. This representation, although it maps out a complete spherical surface, is topologically 2D, which greatly simplifies the characterization of lateral structures on the surface. Domains are easily identified based on intensity thresholds on the triangles of the mesh, and domain areas are obtained simply by adding up the areas of triangles.

Figure 1.

A confocal imaging stack (left) of a GUV is used to generate a surface image (upper right), which represents the variation in fluorophore concentration throughout the entire spherical surface on a mesh of ∼250,000 triangles. A histogram of channel intensities on the surface (lower right) is used to quantify the separate phases in the system and to guide a choice of threshold for segmentation of the surface into domains. The histogram values are in units of surface area (normalized to the unit sphere, i.e., solid angle) per intensity unit squared, such that the integral of a region of the histogram gives the total area of triangles on the mesh with intensities in that region. The domain boundaries, identified using the indicated threshold line in the histogram, are shown on the surface image as white curves.

From the surface image representation, a histogram of the intensities of the two channels over the entire surface is generated and inspected to identify the separate phases in the membrane. As shown in Fig. 1, a clear separation into two phases is observed as two peaks in the histogram, which has the red (naphthopyrene, l_o phase) and green (Rh-DOPE, l_d phase) intensities on the axes. To segment the surface into these phases, an adequate threshold criterion, which separates these peaks in the histogram, must be chosen. For this experiment, a threshold in the form of the simple criterion that a triangle of the mesh is deemed red (l_o phase) if the red intensity exceeds the green intensity was found adequate for all the sampled image stacks and was used for the quantification. The white curves on the surface image in Fig. 1 indicate the domain boundaries resulting from this choice. The areas of the two phases are calculated as the sum of the areas of triangles with intensities on either side of the threshold. Alternatively, this can be thought of as the integral of the histogram value over each of the two parts of the histogram separated by a straight line through the origin with slope 1.

Results

To perform the analysis, we first acquired confocal image stacks from GUVs composed of DOPC/DPPC/cholesterol mixtures of varying composition within the l_o-l_d-phase-coexistence region (6,8) and retrieved domain area fractions using our image-analysis approach described in the previous section. The computed domain area fractions with the associated standard deviations for the different DOPC/DPPC/cholesterol compositions are recorded in Table 1. The experiments and analyses were done for 21 different compositions, with 5–10 GUVs/composition.

To evaluate the choice of threshold, a family of threshold curves parameterized by a single variable, ϕ, is investigated in Fig. 2 for a GUV from sample 5 (see Table 1). Here, the threshold is the criterion that the green intensity must be greater than tan(ϕ) times the red intensity for a triangle to be deemed green (l_d). This threshold corresponds to the straight line through the origin of the coordinate system of the two channel intensities (the coordinate system of the histogram shown in Fig. 1) with an angle ϕ from the red axis. According to this parameterization, the choice of threshold defined in the Image analysis section, which is used for all imaged GUVs, corresponds to the value $\varphi =\pi /4$. Fig. 2 shows a histogram in terms of the value of ϕ, which indicates the sensitivity of the choice near the value $\varphi =\pi /4$. A confidence interval for the value of ϕ is obtained by inspecting the resulting domain boundaries on the surface image. The surface image in Fig. 2 shows the domain boundaries. These boundaries correspond to the two values of ϕ indicated in the histogram (ϕ = 0.635 and ϕ = 0.935) as white and yellow curves. Inspection of this image provides a reasonable confidence that the actual area fractions of the two phases correspond to a choice of threshold between these values. The value $\varphi =\pi /4$ is at the center of the interval. Here, the l_o area was determined as 10.46 ± 0.12 in solid angle. Although this example is typical for the GUVs analyzed in this study, a few are more problematic, with poorer separation between the phases in the histogram. We do not, however, see a systematic bias to one side or the other, so we find it reasonable to stick with a fixed choice of threshold for consistency and to let the problematic vesicles show up as a higher standard deviation for these compositions. These standard deviations are used as error estimations for the error analysis in the tie-line determination described in the next section.

Figure 2.

The surface image on the left shows domain boundaries for two choices of threshold (ϕ = 0.635 and ϕ = 0.935; see Results for the definition of ϕ) and gives an impression of the range of reasonable values. The histogram on the right reveals the sensitivity of the total l_o area to the choice of threshold. The l_o area is 10.462 (solid angle) at $\varphi =\pi /4$ and 10.351 and 10.583 at the lower and upper bounds, i.e., an area determination of 10.46 ± 0.12. This uncertainty is typical among the imaged GUVs, although we observed a few cases where the analysis is more ambiguous.

Calculation of tie lines for the DOPC/DPPC/cholesterol system

We now describe the procedure for determination of the l_o-l_d tie line from the experimental data presented in Table 1, which were obtained by the methodology given in the Materials and Methods section. For nonexpert readers, a general introduction focused on basic thermodynamics aspects of phase coexistence has been included in the Supporting Material.

Three main steps are considered. First, we argue that the area ratios given in Table 1 give the approximate degree of transition, t, along a tie line. Second, we find some simple conditions for the dependence of t on the composition along the tie line. Finally, the estimation of the tie lines from the experimental data and the associated error propagation are given. For convenience, we introduce a short-hand notation for the molar fractions: x₁ = x_chol, x₂ = x_DOPC, and x₃ = x_DPPC. Since x₁ + x₂ + x₃ = 1, we can choose x₁ and x₂ as the independent variables.

The area ratio, ${\rho }_{l_o}$, for each composition x = (x₁, x₂) can be expressed by the degree of transition, t:

$${\rho }_{l_o}\equiv \frac{A_{l_o}}{A_{l_o}+A_{l_d}}=\frac{t{a}_{l_o}}{\left(1-t\right)a_{l_d}+t{a}_{l_o}}.$$ (1)

$a_{l_o}$ and $a_{l_d}$ are the average molecular cross-sectional areas in each of the two phases. To a good approximation, we can identify ${\rho }_{l_o}$ with the degree transition, t, since $\Delta a=a_{l_d}-a_{l_o}$ is small. This is seen by expanding Eq. 1 in $\Delta a/a_{l_o}$:

$${\rho }_{l_o}=t-t\left(1-t\right)\frac{\Delta a}{a_{l_o}}+O\left(t{\left(\left(1-t\right)\frac{\Delta a}{a_{l_o}}\right)}^2\right)$$ (2)

Here, $0<t\left(1-t\right)<1/4$ for 0 < t < 1, and $\Delta a/a_{l_o}<0.1$ (estimate obtained from Pan et al. (14)) varies along the l_o-l_d coexistence region. Therefore, the difference between ${\rho }_{l_o}$ and t can be considered small—below the error in the estimates of ${\rho }_{l_o}$. This situation is very different from the s_o-l_d phase coexistence, where the molecular area difference is substantial and needs to be taken into account in the analysis (4).

The obtained degree of transition, t(x), is associated with a particular tie line (s) from the family of tie lines comprising the coexistence region,

$$\mathbf{x}=\left(1-t\right){\mathbf{x}}^{l_d}\left(s\right)+t{\mathbf{x}}^{l_o}\left(s\right),$$ (3)

where ${\mathbf{x}}^{l_d}\left(s\right)$ and ${\mathbf{x}}^{l_d}\left(s\right)$ are the compositions of the two phases. We will now try to identify this tie line from the functional behavior of t(x). First, notice from Eq. 3 that along the tie line, we have

$${\left(\frac{\partial \mathbf{x}}{\partial t}\right)}_s=\Delta \mathbf{x}={\mathbf{x}}^{l_o}\left(s\right)-{\mathbf{x}}^{l_d}\left(s\right).$$ (4)

Therefore, applying the chain rule to t(x) along a tie line and Eq. 4, it follows that the condition

$$1=\frac{\partial t}{\partial x_1}\Delta x_1+\frac{\partial t}{\partial x_2}\Delta x_2$$ (5)

must be fulfilled for the tie line. Repeated application of the chain rule and Eq. 4 gives

$$0=\frac{{\partial }^{2}t}{\partial x_1\partial x_2}{\left(\Delta x_1\right)}^2+\frac{{\partial }^{2}t}{\partial x_2\partial x_2}{\left(\Delta x_2\right)}^2+\frac{2{\partial }^{2}t}{\partial x_1\partial x_2}\Delta x_1\Delta x_2.$$ (6)

Equations 5 and 6 must thus be fulfilled for the vector Δx. In general, these equations do not provide a sufficient condition to determine Δx. However, for a nonzero matrix ${\partial }^{2}t/\partial x_i\partial x_j$, i, j = 1, 2, there are at most two orientations that fulfill the condition in Eq. 6 (15). The corresponding lengths of Δx are fixed by Eq. 5. Thus, the knowledge of the first and second derivatives of t(x) strongly limits the possible tie lines.

In practice, this analysis is implemented by estimation of the derivatives of t(x) from the discrete set of t^(k) and x^(k) obtained from the experiments from the approximation:

$$t^{\left(k\right)}\approx {\tilde{t}}^{\left(k\right)}\left(\mathbf{b},\mathbf{C}\right)=t\left({\mathbf{x}}_0\right)+\mathbf{b}\left({\mathbf{x}}^{\left(\mathit{k}\right)}-{\mathbf{x}}_0\right)+\frac{1}{2}\left({\mathbf{x}}^{\left(\mathit{k}\right)}-{\mathbf{x}}_0\right)\mathbf{C}\left({\mathbf{x}}^{\left(\mathit{k}\right)}-{\mathbf{x}}_0\right),$$ (7)

where the vector b is an estimate of $\partial t/\partial x_i$, whereas the matrix C is an estimate of ${\partial }^{2}t/\partial x_i\partial x_j$ at x₀. For convenience, the reference composition x₀ is chosen among the sampled compositions, such that t(x₀) is known. The estimates of b and C and their errors σ²(b) and σ²(C) are obtained from linear least-squares minimization based on the measured data (16), i.e., minimizing the χ² function:

$${\chi }^2\left(\mathbf{b},\mathbf{C}\right)={\sum _k\left(\frac{t^{\left(k\right)}-{\tilde{t}}^{\left(k\right)}\left(\mathbf{b},\mathbf{C}\right)}{{\sigma }_k}\right)}^2,$$ (8)

where t^(k) and σ_k are the error estimates from the individual compositions given in Table 1. We have used the approach to calculate Δx and the corresponding tie line using each of the reference compositions a, 7, and c in Table 1. These references are chosen because they exhibit intermediate degrees of transition. The resulting tie lines are shown in Fig. 3. The orientation of Δx is obtained from Eq. 6, with the estimate C_ij for ${\partial }^{2}t/\partial x_i\partial x_j$, and its extent is determined by Eq. 5 with the estimate b_i for $\partial t/\partial x_i$. Equation 6 gives two possible orientations of Δx, but only one has a length, found by Eq. 5, which allows for construction of the tie line within the barycentric domain (0 < x₁ < 1, 0 < x₂ < 1, x₁ + x₂ < 1). The tie lines are constructed as

$$\mathbf{x}={\mathbf{x}}_0+\Delta \mathbf{x}\left(t-t\left({\mathbf{x}}_0\right)\right)$$ (9)

The three tie lines are shown in Fig. 3, where the endpoints represent the phase boundaries corresponding to t = 0 and t = 1.

Figure 3.

The l_o area fractions from Table 1 are visualized using a color map overlaid on the three-component phase diagram, with a red color indicating the value 1, i.e., the entire surface is in the l_o phase, and a green color indicating the value 0, i.e., all l_d phase. The straight lines are tie lines calculated from the area information, with the blue crosses indicating the estimated errors in the end-point positions. For comparison, the gray-shaded regions are the l_o-l_d coexistence regions reported by Veatch et al. (8) at 20°C (lighter shading) and 25°C (darker shading). Our results suggest the existence of a critical point in the left region of our calculated tie line that used composition a as the reference.

The error propagation in this procedure is obtained by writing Δx = |Δx|e_θ, where e_θ = (e₁, e₂) = (cos θ, sin θ) is the unit vector along the tie line with orientation angle θ. The error σ(θ) is derived from Eq. 6:

$${\mathbf{e}}_{\theta }\mathbf{C}{\mathbf{e}}_{\theta }=0\Rightarrow {\sigma }^2\left(\theta \right)=\frac{\sum _{i,j=1,2}{e}_i^2{e}_j^2{\sigma }^2\left(C_{ij}\right)}{{\left(\sum _{i=1,2}{e}_i{C}_{ij}{e}_j\right)}^2},$$ (10)

and the error in Δx follows from the use of Eq. 5:

$$\left|\Delta \mathbf{x}\right|{\mathbf{e}}_{\theta }\mathbf{b}=1\Rightarrow \frac{{\sigma }^2\left(\left|\Delta \mathbf{x}\right|\right)}{{\left|\Delta \mathbf{x}\right|}^2}=\frac{\sum _{i=1,2}{e}_i^2{\sigma }^2\left(b_i\right)}{{\left(\sum _{i=1,2}{e}_i{C}_{ij}{e}_j\right)}^2}.$$ (11)

The calculated errors are presented in Fig. 3 (blue crosses).

Discussion

Our analysis of the l_o-l_d-phase-coexistence region of the phase diagram is based on the observation that the domain areas (A_lo and A_ld), to a very good approximation, give the degree of transition, t, between the l_d and l_o phases along a particular tie line. Thus, t is a simple linearly increasing quantity as the composition is changed from the l_d phase boundary along the tie line to the l_o phase boundary. For other changes in composition, we will in general not find a global linear relationship in the l_o-l_d coexistence region of the phase diagram. The estimate of t(x_DPPC, x_chol) from our measurements in the coexistence region gives us the possibility of analyzing its functional behavior. In particular, we can estimate the orientation of the tie lines as orientations in (x_DPPC, x_chol) variables, where t(x_DPPC, x_chol) increases linearly and the corresponding phase boundaries are at t = 0 and t = 1 from the measured t(x_DPPC, x_chol).

The data presented in Table 1 and Fig. 3 stand for compositions where macroscopic phase separation is detected. The end points of the tie lines are also a result of the calculation (the points given by t = 0 and t = 1) and thus provide a determination of the boundaries of the l_o-l_d coexistence region. These estimated phase boundaries are consistent with compositions where GUVs display single-liquid phase reentrance. The identified phase boundaries are in good agreement with the l_o-l_d coexistence region obtained by ²H-NMR studies by Veatch et al. (8), whereas the orientations of the tie lines differ significantly from those presented in this study. Veatch et al. argue, based on NMR analysis, that the cholesterol content is similar in the two phases, leading to a critical point at high cholesterol content (8). However, our findings indicate tie lines between l_o and l_d phases, with increasing cholesterol content toward the l_o phase, suggesting a critical demixing point at low DPPC content and close-to-equal amount of DOPC and cholesterol. Veatch et al. also find that most of the detected phase boundaries are robust to temperature variations between 20°C and 25°C, except in the region of low DPPC content, where our results suggest the presence of a critical point. It is characteristic of critical regions that the locations of the phase boundaries are very sensitive to changes in the thermodynamic conditions, so that small differences in temperature could give rise to a shift in the coordinates of the critical point. Davis et al. (7) have suggested a location of the critical point in the same region suggested from our results (see Fig. 3). However, it is important to clarify that it is not possible to precisely locate the critical point with the applied techniques, since detection of two distinct signals from the coexisting domains is absolutely required to properly perform the analysis. When approaching the neighborhood of a critical point, the compositional differences between the phases vanish. This hampers the possibility of obtaining accurate signals from the different phases. In the particular case of fluorescence microscopy, the big limitation is the resolution of the microscope (∼300 nm radial), i.e., it will limit the detection accuracy when the proliferation of the phases into small (below-resolution) domains occurs near the critical point.

The orientations of our computed tie lines are, on the other hand, in very good agreement with the ²H-NMR study of Davis et al. (7) based on spectral decomposition methods (17). The extent of their reported l_o-l_d coexistence region, however, is significantly smaller than what we find in this study. The orientation of our computed tie lines is also in overall agreement with those obtained by Uppamoochikkal et al. (9), who develop an indirect method based on lamellar spacing measurements using x-ray diffraction. In this last case, the extent of the l_o-l_d coexistence region of our phase diagram could not be compared, since this information cannot be obtained with the reported x-ray diffraction method. Finally, the three-phase l_d/l_o/s_o region reported by Davis et al. (7) extends to relatively low DPPC content and includes compositions where we observed only a two-phase separation, assuming the three phases would be distinguishable with the fluorophores used. Although the mere use of fluorescence-intensity images has been reported to be ineffective in detecting three-phase coexistence, the use of fluorescence-lifetime imaging in DOPC/DPPC/cholesterol GUVs labeled only with Rh-DOPE was reported to be a successful method to detect this region (18). This adds further to the possibilities of using fluorescence-microscopy-related techniques to obtain comprehensive phase diagrams of ternary lipid mixtures. At present, our partial characterization of the phase diagram is complementary to those reported with other experimental methodologies. In particular, we describe the phase behavior of single free-standing bilayers, whereas the other studies (7–9) used bulk measurements of multilamellar systems, and coupling effects among bilayers could perturb the nature of the phase diagram.

In conclusion, our results demonstrate that image-analysis methods applied to fluorescence-microscopy experiments on GUVs can provide a robust quantitative tool. The information retrieved not only allows correlation between lipid domains on vesicles and equilibrium thermodynamic phases (4), but also allows, in combination with equilibrium thermodynamic considerations, the construction of phase diagrams and in particular the computation of tie lines for phase-separated membranes composed of ternary lipid mixtures.