INTRODUCTION

TOP ABSTRACT INTRODUCTION THEORY SIMULATIONS EXPERIMENTAL PROBE PHOTOPHYSICS AND... FRET MEASUREMENTS AND... CONCLUSION REFERENCES

Cholesterol is a major component of mammalian cells, and its action upon the physical properties of lipid bilayers has been studied actively in the last three decades. Some consensual results have emerged from these efforts, particularly that cholesterol concentrations of approximately 10-30% produce phase separation above the main transition temperature of dimyristoylphosphatidylcholine (DMPC) and dipalmitoylphosphatidylcholine (DPPC). The monotetic phase diagram for the DMPC/cholesterol mixture is shown in Fig. 1 (Almeida et al., 1992). The two coexisting phases, the so-called liquid-ordered (l_o) and liquid-disordered (l_d) phases, have been thoroughly characterized in terms of physical properties. Although l_d resembles the pure lipid fluid, l_o has intermediate properties between those of pure phospholipid fluid and gel. The notable effects of cholesterol include condensation of area/lipid molecule (e.g., Smaby et al., 1997), reduction in passive permeability of the bilayer (e.g., Xiang and Anderson, 1997), increase in orientational order of the phospholipid acyl chains (e.g., Lafleur et al., 1990) and increase in bending elasticity (e.g., Méléard et al., 1997), relative to the values in pure phospholipid fluid membranes. McMullen and McElhaney (1996) have recently reviewed this field and pointed out that, despite all research on the effect of cholesterol on phospholipid bilayers, a complete molecular-level rationalization of these changes is still lacking.

View larger version (24K): [in this window] [in a new window]   FIGURE 1   Phase diagram of DMPC/cholesterol (Almeida et al., 1992). The points indicate the mixtures and temperatures addressed in this study.

The usual hypotheses of cholesterol molecular organization at high molar fractions involve formation of sterol/phospholipid complexes of a given stoichiometry, most commonly 1:1. Vanderkooi (1994) performed energy-minimization calculations for an equimolar DMPC/cholesterol mixture and obtained two relative minima, the lowest of which corresponds to nonidentical nearest neighbors. Subsequent molecular dynamics simulations have used these packing structures as starting points and have generally confirmed the observed physical effects of cholesterol on DMPC/cholesterol (Gabdoulline et al., 1996) and DPPC/cholesterol (Smondyrev and Berkowitz, 1999) bilayers. However, as pointed out by the latter authors, this choice of initial arrangement is certainly not unique. Moreover, although the recent progress in computational techniques has led to interesting accordance between observed and predicted physical properties for either very high (1:1; Gabdoulline et al., 1996, Smondyrev and Berkowitz, 1999) or very low (1:9 or 1:8; Robinson et al., 1995; Tu et al., 1998; Smondyrev and Berkowitz, 1999) cholesterol:phospholipid ratios, for which a sole phase (l_o or l_d, respectively) is expected, little advance has been made recently regarding the intermediate composition range, for which domains of l_o and l_d phases are expected to coexist. This region of the phase diagram is, however, especially important as a study model of heterogeneity in fluid biological membranes. This latter phenomenon has considerable biological relevance, because the existence of small membrane domains can influence membrane functions by concentrating some species in particular membrane regions, or rather by excluding molecules from them (Edidin, 1997).

In this regard, several experimental techniques have been used in the experimental study of phosphatidylcholine/cholesterol mixtures. DSC (Mabrey et al., 1978; Vist and Davis, 1990) is useful regarding the study of non-ideality of lipid mixtures, but does not give topological information. A number of spectroscopic techniques, such as ²H-NMR (e.g., Vist and Davis, 1990), ESR (e.g., Sankaram and Thompson, 1990, 1991) and steady-state and time-resolved fluorescence (e.g., Lentz et al., 1980; Mateo et al., 1995) are also sensitive to the environment surrounding the spectroscopic probes, but are not usually informative regarding the lateral organization of each phase. Fluorescence recovery after photobleaching has been used to estimate phase microdomain sizes in multibilayers containing cholesterol, DMPC and distearoylphosphatidylcholine (DSPC; Almeida et al., 1993). However, these values were obtained only for coexistence of one solid and one liquid phase, and not in the (probably most relevant to biological membranes) fluid-fluid coexistence region.

Fluorescence resonance energy transfer (FRET; reviewed in Van der Meer et al., 1994; Lakowicz, 1999) is a photophysical process that causes quenching of the fluorescence of one species (the donor), by nonradiative transfer of its excitation energy to another species (the acceptor), which absorption spectrum overlaps the emission spectrum of the donor. The strong dependence (sixth power) of the FRET rate on the intermolecular distance has led to its wide use in biochemistry in the last three decades as a "spectroscopic ruler" for determination of distances in the 1-10 nm range (Stryer, 1978). If, instead of an isolated donor/acceptor pair at a single defined distance, there is a distribution of donor and acceptor molecules in three-dimensional space or in a plane (the geometry relevant for membranes), donor fluorescence becomes dependent on the acceptor concentration surrounding the donors.

In this paper, we show that, for a microheterogeneous binary lipid system, by the means of simple relationships, it is possible to extract information on the partition of both donor and acceptor probes in each environment, and on the lipid mixture phase diagram boundaries, from the parameters of the donor fluorescence decay in presence of acceptor. Additionally, using Monte-Carlo simulations together with global analysis of fluorescence decays, we show that deviations to the theoretical decay laws (derived assuming large domain sizes) can provide unique information on the size of the lipid domains. This approach is then carried out for three DMPC/cholesterol mixtures (cholesterol mole fractions x_chol = 0.15, x_chol = 0.20, x_chol = 0.25) for two temperatures within the fluid-fluid phase coexistence range (30 and 40°C; see Fig. 1). Labeled phospholipids were selected as fluorescent probes. N-(7-nitrobenz-2-oxa-1,3-diazol-4-yl)-dimyristoylphosphatidylethanolamine (NBD-DMPE) was used as FRET donor, and N-(lissamine^TM-rhodamine B)-dipalmitoylphosphatidylethanolamine (Rh-DMPE; acceptor) was the FRET acceptor.

	THEORY

TOP ABSTRACT INTRODUCTION THEORY SIMULATIONS EXPERIMENTAL PROBE PHOTOPHYSICS AND... FRET MEASUREMENTS AND... CONCLUSION REFERENCES

Consider a planar system of two infinite separated phases, labeled 1 and 2. If the fluorescence decay of the donor in each phase is a single exponential,

(1)

then, upon incorporation of acceptor probe with a concentration of n_i molecules/area unit, the decay becomes complex (e.g., Hauser et al., 1976),

(2)

where

(3)

In this equation, R_0i is the Förster critical distance for phase i, and  is the complete gamma function. Considering the whole biphasic system, the donor decay in the absence of acceptor is now

(4)

where A_i is proportional to the number of donor molecules in phase i, and, in presence of acceptor, the decay law becomes

(5)

or, equivalently,

(6)

This equation shows clearly that the decay of donor fluorescence in the presence of acceptor contains information on the amounts of donor and acceptor probes within each phase of the system. For biexponential decay of donor within each phase, and bilayer (rather than planar; Davenport et al., 1985) geometry of FRET, Eqs. 4 and 5 are still valid, with the following alterations:

(7)

(8)

where _ji are the different donor lifetime components in phase i, q_i is their amplitude ratio, and

(9)

In this latter definition, R_0i and d_i are, respectively, the Förster critical distance for FRET and the bilayer width in phase i, and

(10)

The distribution of probes between two lipid phases, 1 and 2 (the actual type of phases involvede.g., gel, fluid, liquid-orderedis not important in the following) is commonly described on the basis of a partition equilibrium,

(11)

The partition coefficient of this probe between phases 1 and 2 is given by (e.g., Davenport, 1997)

(12)

In this equation, P₁ is the probe mole fraction in lipid phase 1, and X₁ is the lipid phase 1 mole fraction (therefore, P₂ = 1  P₁ and X₂ = 1  X₁). Combining Eqs. 6 and 12, it is easy to show that the partition coefficients of donor (K_pD) and acceptor (K_pA) probes can be calculated straightforwardly from the FRET decay parameters,

(13)

(14)

where a_i is the area per lipid molecule in phase i (usually known from X-ray diffraction studies; a good collection is given in Marsh, 1990).

Consider now a composition x (which represents the overall mole fraction of the lipid component that predominates in phase 2) that, at a given temperature T, corresponds to a (x, T) point within the phase 1/phase 2 coexistence range (note that this discussion is independent of the actual shape of the hypothetical phase diagram); let the phase coexistence boundaries at this temperature be x₁ (X₂ = 0) and x₂ (X₁ = 1). For the (x, T) point, X₁ and X₂ can be easily calculated from the lever rule

(15)

(16)

Now consider that the phase diagram for the lipid mixture is unknown. Let then F be the overall acceptor mole fraction (acceptor moles/total moles; it is an experimentally accessible amount), and let F₁ and F₂ be the acceptor mole fractions within each phase. F₁ (acceptor molecules in phase i/total lipid molecules in phase i) and n_i (acceptor molecules in phase i/area of phase i) are related according to

(17)

Combining Eqs. 3 and 17, one obtains the relationship between F_i and c_i,

(18)

Once both F_i are computed, from the acceptor mass balance equation,

(19)

it is easy to calculate X₁ and X₂, even for an unknown phase diagram.

In this situation, if, at a given temperature, X₁ are known for two points, A(x_A, T) and B(x_B, T), which are known to be located inside the phase coexistence range, one obtains a system of two linear equations, which unknowns, x₁ and x₂, are given by

(20)

(21)

which allows one to calculate the compositions of phases 1 and 2 at that temperature from time-resolved FRET data. If this procedure is repeated for several temperatures, the phase diagram is obtained.

	SIMULATIONS

TOP ABSTRACT INTRODUCTION THEORY SIMULATIONS EXPERIMENTAL PROBE PHOTOPHYSICS AND... FRET MEASUREMENTS AND... CONCLUSION REFERENCES

The preceding considerations refer to an infinite-phase binary lipid mixture (that is, one in which the domains of phase i are R_0i). To study their applicability to microheterogeneous mixtures in which the size of the domains is only a few times larger than the Förster distance (i.e., typically <50 nm), we carried out Monte-Carlo simulations. After assuming a shape and a size for the domains of the least abundant phase (dispersed inside the complementary phase), and the X₁ and X₂ values, their locations were generated randomly (with the restriction of nonoverlap of different domains). Suitable K_pD and K_pA values were then chosen a priori. Finally, chosen numbers of donors and acceptors were distributed inside and outside the domains, according to their partition coefficient values. The probe distribution within each phase was random. A triangular lattice of 10³ × 10³ molecules was considered.

The hypothetical system had phase compositions x₁ = 0.08 and x₂ = 0.72 at a given temperature, and two different values for X₁ were assumed: 0.50 (which corresponds to a global composition x = 0.40; in this case, domains of phase 1 dispersed in phase 2 were generated) and 0.80 (which corresponds to a global composition x = 0.21; in this case, domains of phase 2 dispersed in phase 1 were generated). For each X₁ value, two different sizes of square domains were considered: 400 (20 × 20) molecules and 2500 (50 × 50) molecules. These domain sizes were chosen to be of the order of magnitude of those estimated by Sankaram et al. (1992) for a dilauroylphosphatidylcholine/distearoylphosphatidylcholine mixture (which exhibits gel/fluid phase coexistence). Obviously, a uniform domain size distribution is very unlikely. However, although the FRET decays are undoubtedly affected by the domain size, it is, at this point, impossible to recover multiple parameters of a nonuniform domain size distribution of a given family from experimental data, hence this model restriction. For each of these domain sizes, the values K_pD = 1.00 and K_pA = 1.00, 2.00, and 0.50 were considered. A total of 12 simulations was run, each with different K_p, domain size, and phase ratio. For the sake of brevity, only the characterization of the simulations with X₁ = 0.50 is given as example in Table 1. Each lattice location represented a molecule with 9-Å diameter. N_D = 2 × 10³ donors and N_A = 5 × 10³ acceptors were distributed in each simulation run. Donor lifetimes (typical dye lifetimes in fluid and gel lipid phases, respectively; Davenport, 1997) were ₁ = 0.8 ns and ₂ = 1.32 ns. R₀₁ = 47.2 Å and R₀₂ = 50.1 Å were considered for all simulations. For a donor j, located in phase i, the decay law is given by (Förster, 1949)

(22)

where R_jk is the distance between donor j and acceptor k (for the calculation of this distance in a triangular lattice, see Snyder and Freire, 1982). We assume that there is a single R₀ parameter for every (donor in phase i, acceptor in either phase) pair (this condition is met in the dynamic orientational regime; note that the spectral overlap is usually phase independent) and neglect energy migration among donors (this can be experimentally achieved choosing a donor with no absorption/emission overlap or using low donor concentration). Periodic boundary conditions are used in the calculation of _j(t). The macroscopic decay is obtained by averaging over donors:

(23)

The generated decays were then convoluted with an experimental instrumental response function, and Poisson noise was added to them. They were then analyzed using Eq. 6 and software based on the Marquardt algorithm (Marquardt, 1963). Each FRET decay thus generated was analyzed globally together with an "experimental" (obtained from Eq. 4, after convolution and adding of Poisson noise) donor decay, for the lifetime parameters to be better recovered. Statistically acceptable fits were obtained for all simulations (global ² < 1.1). From the recovered c_i and A_i parameters, K_pD, K_pA, X₁, x₁, and x₂ were calculated from Eqs. 13-14 and 18-21. The values thus obtained are represented in the lower part of Table 1, for the simulations with X₁ = 0.50 (the simulations with X₁ = 0.80 resulted in identical trends).

As is shown in Table 1, for simulations 1 and 4 (K_pA = 1.00), the values recovered for c₁ and c₂ are virtually identical, as expected. The recovered K_pA is very close to 1.00. For all other simulations, K_pA was given the input value 2.0 (simulations 2 and 5) or 0.5 (simulations 3 and 6). In these cases, the highest c value (c₁ for K_pA = 0.5, c₂ for K_pA = 2.0) is always underestimated, whereas the lowest c value (c₂ para K_pA = 0.5, c₁ for K_pA = 2.0) is consistently overestimated. This is due to the small domain size: many of the donors located in phase 1 are sensitive to acceptors in phase 2, and conversely for the donors located in phase 2. This effect is more pronounced for the domain phase than for the continuous phase, especially when the former is more abundant.

As a consequence of these deviations, the K_pA values are always closer to unity than expected (between 1.0 and 2.0 for simulations 2 and 5 in Table 1; between 0.5 and 1.0 for simulations 3 and 6). In contrast, the parameters are consistently recovered with a smaller error when the domain size increases from 400 molecules (~3.5 R₀; simulations 2 and 3) to 2500 molecules (~9 R₀; simulations 5 and 6), as the system approaches the "infinite separated phases" hypothesis. In any case, even for the simulations in which the domain size is 400 molecules, the accuracy is relatively satisfactory, even for the phase diagram limit compositions (x₁ and x₂). Therefore, this method compares well with established procedures such as NMR difference spectroscopy (e.g., Vist and Davis, 1990). Some of the above equations of our method are reminiscent of NMR difference spectroscopy (both methods are based on the lever rule), but there are important differences, which arise from the experimental technique. Our method relies on the accurate recovery of the FRET decay parameters (see below), but is not limited by the slow time scale of NMR (~10⁴ times slower than fluorescence).

In the Theory section, it is shown that time-resolved FRET measurements can be used as a novel method to quantitate partition of probes in a biphasic lipid system and to estimate the phase boundary compositions for each temperature, and, ultimately, the phase diagram. However, Eqs. 13-14 and 18-21, which relate the decay parameters with the partition coefficients and the phase diagram information, are, on the whole, ill-conditioned, because of the divisions and subtractions involved in some of them, and also because the calculation of some parameters involves a "train" of equations, each contributing to error propagation.

This was the reason that led us to obtain synthetic FRET decays by Monte-Carlo techniques and compare the parameters recovered (after convoluting, adding noise, and analyzing the decays) with those used as input for the simulations. From comparison of the input and recovered parameters in Table 1, the results are largely satisfactory. Deviations in the recovered K_pA values are due to the small domain size, being much less important for 2500-molecule domains than for 400-molecule ones. A crucial part in the success of the present method is certainly played by the use of global analysis of the FRET decays (see e.g., Beechem et al., 1991 for a review on global analysis, or Loura et al., 1996 for a FRET application). If the donor-acceptor decays were analyzed alone, using Eq. 6, one would attempt to recover six different parameters (A₁, A₂, c₁, c₂, ₁, ₂) from a single decay curve. However, by analyzing the donor decay together with the respective donor-acceptor decay, three parameters become largely restricted (the lifetimes and the ratio A₁/A₂), leaving only the two acceptor concentrations and one pre-exponential factor to be completely optimized from a sole donor-acceptor decay. In this situation, the parameter recovery problem becomes certainly less critical than, e.g., for three-lifetime fitting, commonly used in protein and peptide fluorescence studies.

Of course, K_p values can be obtained by a plethora of established methods, including other photophysical techniques (Davenport, 1997). The uniqueness of FRET in this respect resides in the dependence of the "apparent K_p", the value recovered after analysis, on the size of the phases, as revealed from our simulations. Other fluorescent properties often used for calculation of K_p, like fluorescence intensity, lifetime, or anisotropy, are only dependent on the immediate environment of the probe (at least for common dyes, with lifetimes smaller than 10 ns), and are insensitive to the domain size. In this way, a procedure for obtaining information on the size of membrane domains would be the following:

i.  Measure K_p by distance-independent methods; ii.  Obtain time-resolved FRET data and calculate K_pA from global analysis; iii.  Compare the K_pA values obtained in i. and ii. and, from their eventual difference, conclude about domain sizes; iv.  This would allow an "educated guess," which could in turn be confirmed from adequate Monte-Carlo simulations. Theoretical decay laws would thus be obtained and compared with the experimental ones.

	EXPERIMENTAL

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Materials

Cholesterol was purchased from Merck (Darmstadt, Germany). DMPC and the fluorescent species NBD-DMPE and Rh-DMPE were obtained from Avanti Polar Lipids (Birmingham, AL). All materials were used without further purification.

Vesicle preparation

Adequate amounts of stock solutions of host lipids and probes in chloroform and methanol, respectively, were mixed, dried until complete evaporation, and suspended in buffer (tris-HCl 50 mM, NaCl 100 mM, EDTA 0.2 mM, pH = 7.4; tris-HCl from BDH (London, U.K.) and NaCl and EDTA from Merck (Darmstadt, Germany) were used). Large unilamellar vesicles (LUV) were then prepared by the extrusion method (Hope et al., 1985). The probes were assumed to be symmetrically distributed between the two bilayer leaflets. For the FRET measurements, the NBD-DMPE and Rh-DMPE content in the vesicles was 0.1 and 0.5 mol%, respectively. To ensure that the lipid mixtures were in an equilibrium state, the prepared vesicles rested overnight at 25°C, and the measurements took place on the following day.

Instrumentation

Fluorescence decay measurements were carried out with a time-correlated single-photon counting system, which is described elsewhere (Loura et al., 2000). For the experiments at 30°C, time scales of 44.7 ps/ch and 34.0 ps/ch were used in the measurement of NBD-DMPE decays (excitation at 340 nm, emission at 520 nm) in the absence and presence of acceptor, respectively. For the experiments at 40°C, the time scales were 34.0 ps/ch in the measurement of NBD-DMPE decays in the absence of acceptor and 21.6 ps/ch in the presence of acceptor. For measurement of fluorescence decays of Rh-DMPE, the same instrument was used, but excitation was now at 570 nm using Rhodamine 6G as the laser dye, and emission was detected at 610 nm. The time scale was 15.3 ps/ch for measurements at both temperatures. Data analysis was carried out using a nonlinear, least squares iterative convolution method based on the Marquardt algorithm (Marquardt, 1963) using global analysis (e.g., Loura et al., 1996). The goodness of the fit was judged from the individual experiments' ² values, global chi-square value, and weighted residuals and autocorrelation plots.

Fluorescence steady-state measurements were carried out with an SLM-Aminco 8100 Series 2 spectrofluorimeter (Rochester, NY; with double excitation and emission monochromators, MC-400) in a right-angle geometry. The light source was a 450-watt Xe arc lamp and the reference was a Rhodamine B quantum counter solution. Correction of excitation and emission spectra was performed using the apparatus correction software. 5 × 5-mm quartz cuvettes were used. Temperature was controlled to ±0.5°C by a thermostatted cuvette holder. Both emission and excitation spectral bandwidths were 4 nm.

The steady-state anisotropy, r, was calculated from (Jaboski, 1960)

(24)

where the different intensities I_ij are the steady-state vertical and horizontal components of the fluorescence emission with excitation vertical (I_VV and I_VH, respectively) and horizontal (I_HV and I_HH, respectively) to the emission axis. The latter pair of components is used to calculate the G factor (G = I_HV/I_HH; Chen and Bowman, 1965). Polarization of excitation and emission light was achieved using Glan-Thompson polarizers. Absorption spectra were carried out in a Jasco V-560 spectrophotometer.

	PROBE PHOTOPHYSICS AND PARTITION FROM NON-FRET MEASUREMENTS

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NBD-DMPE

This probe shows biexponential decays for all studied samples. The longer recovered component measured 10-12 ns at T = 30°C and 8-10 ns at T = 40°C, depending on x_chol, with amplitude ~60-70%. The shorter and lesser component measured 1.9-2.2 ns at 30°C and 1.3-1.6 ns at 40°C. These values agree with those measured by Duportail et al. (1995), who also reported biexponential decays for the identical (with the same fluorophore, and just two additional methylene groups in each chain) N-(7-nitrobenz-2-oxa-1,3-diazol-4-yl)-dipalmitoylphosphatidylethanolamine (NBD-DPPE) probe in dipalmitoylphosphatidylglycerol vesicles.

A detailed study of the NBD-DMPE fluorescence decay was carried out as a function of x_chol (Fig. 2 A), revealing that increases monotonously up to x_chol = 0.28, undergoes maxima for this composition both at 30 and 40°C, and decreases with further increase of cholesterol content. The maximum composition coincides with the l_o + l_d tie-line end at 30°C (see Fig. 1), and differs slightly from this point at 40°C. From Fig. 1, it was expected that the composition for which there is a single l_o phase at 40°C would be ~31 mol%. Of course, as a consequence of Eq. 4, the decay for a sample in the phase coexistence range should be a linear combination of the decays in each pure phase, with coefficients proportional to the amount of probe in each phase. should thus have a monotonous variation along the tie-line, and nonmonotonous variations have no physical meaning and are incompatible with global analysis (for optimization of lifetimes and donor pre-exponential ratios) of the decays. In this way, 28 mol% was taken as the composition for which the FRET decays are characteristic of pure l_o phase for both temperatures (instead of a higher value, e.g., 0.40, for which there would also be solely l_o phase, but with composition different from that in the coexistence region). Although this singularity was not observed at the opposite end of the tie-line, samples with x_chol = 0.075 and 0.14 were chosen (from the phase diagram, Fig. 1) as those for which the FRET decays are characteristic of pure l_d phase for 30 and 40°C, respectively (instead of, e.g., x_chol = 0).

View larger version (11K): [in this window] [in a new window]   FIGURE 2   Variation of (A) average lifetime and (B) steady-state anisotropy of NBD-DMPE (0.1 mol%) in DMPC/cholesterol LUV, as a function of (A) global vesicle composition or (B) lo phase fraction, for T = 30°C () and T = 40°C (). The lines in A are mere guides to the eye, whereas the lines in B are fitting curves using Eqs. 12 and 25, with Kp (30°C) = 1.1 and Kp (40°C) = 2.6.

Using as reference, the fluorescence quantum yield value (NBD-DPPE) = 0.32 (Chattopadhyay, 1990), the values (30°C, l_d) = 0.26, (30°C, l_o) = 0.29, (40°C, l_d) = 0.21, and (40°C, l_o) = 0.25 were obtained. No major absorption or emission spectral or intensity alterations were apparent upon varying the cholesterol content of the vesicles. In this regard, the l_o/l_d partition coefficient for this probe, K_pD, was determined from fluorescence anisotropy measurements. Using Weber's law of additivity of anisotropy (Weber, 1952), the anisotropy in a l_o/l_d mixture is given by

(25)

In Eq. 25, _i is the molar absorption coefficient, _i is the fluorescence quantum yield, g_i is the fluorescence intensity at the emission wavelength in a normalized spectrum, for pure i phase, and P_i has the same meaning as in Eq. 12 (i =  or  for l_d and l_o, respectively). Assuming  = , g = g, and / = /, and using P/P = K_p(1X)/X (from Eq. 12), the only unknown parameter is K_p, which can be determined by fitting. This is shown in Fig. 2 B, and the values K_pD(30°C) = 1.1 and K_pD(40°C) = 2.6 are obtained.

Rh-DMPE

Rh-DMPE shows a significant decrease in fluorescence and absorption intensity with increasing cholesterol (results not shown). The absorption maximum undergoes a shift from  = 571 nm (x_chol = 0) to  = 574 nm (x_chol = 0.28). This latter value coincides with the absorption maximum in buffer. The absorption intensity in this medium is approximately half of that in the l_d phase and similar to that in the l_o phase. However, the shoulder observed in buffer at ~530 nm, indicating the presence of excitonic species, is not apparent in vesicles, even those with large x_chol. When x_chol increases from 0 to 0.40, emission intensity is reduced by 60%, but the spectra's shape is unchanged (_max = 591 nm).

Rh-DMPE decays are exponential up to x_chol = 0.15 at 30°C and 0.20 at 40°C (² < 1.2), two exponentials being needed in the x_chol = 0.20-0.25 range, and three exponentials are necessary for x_chol = 0.40 for an adequate description (the new components are short-lived; result not shown). The fact that Rh-DMPE decays become gradually faster and more complex with increasing x_chol is probably due to an increased solvation of the lipid head groups for higher cholesterol content. This would result from steric restrictions imposed by cholesterol, which molecules would act as spacers between otherwise neighboring phospholipids, thus reducing the latter's intermolecular interactions and rendering their head groups more accessible to water, as verified by Ho et al. (1995). The increased polarity in the head group microenvironment also explains the shift of the absorption spectra.

Figure 3 shows the steady-state fluorescence intensity I_F and the lifetime averaged quantum yield of Rh-DMPE as a function of the fraction of l_o in the vesicles, X. The variations of the two parameters are identical, and only for pure l_o small deviations between the relative values of I_F and are detected. The fact that this discrepancy is verified solely for this sample and not for any other (not even for some samples characterized by a large X value) is related to either a poorer fitting of decay data or probably to the appearance of a static self-quenching component.

View larger version (10K): [in this window] [in a new window]   FIGURE 3   Variation of steady-state fluorescence intensity (IF (a.u.); ; ex = 560 nm, em = 590 nm) and average lifetime (; ) of Rh-DMPE as a function of lo phase fraction (X), for (A) T = 30°C and (B) T = 40°C. The curves are fits to IF (Eqs. 12 and 26) with Kp (30°C) = 0.30 and Kp (40°C) = 0.27.

Contrary to NBD-DMPE, the steady-state anisotropy variation is not useful to study Rh-DMPE partition, because of the very efficient energy homotransfer among Rh-DMPE molecules, leading to strong emission depolarization. In this way, K_p should be calculated from the variation in I_F. The relationship between this parameter and the probe fraction within each phase for dilute samples (total absorbency < 0.1) is given by (e.g., Ameloot et al., 1991)

(26)

where K includes a geometric factor and the intensity of inciding light. Using again P/P = K_p(1  X)/X, there are only two fitting variables, K and K_p. The curves in Fig. 3 were obtained this way, K_p(30°C) = 0.30 and K_p(40°C) = 0.27 being recovered. Thus, unlike NBD-DMPE, Rh-DMPE prefers unequivocally the l_d phase rather than the l_o phase, even tough the two probes have essentially the same lipid structure (only differing in the fluorescent label in the phospholipid head). This interesting difference is not readily explained.

	FRET MEASUREMENTS AND DISCUSSION

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From the spectral overlap of NBD-DMPE emission and Rh-DMPE absorption, as well as the donor fluorescence quantum yields (_D) obtained above and the measured maximum molar absorption coefficient _max(Rh-DMPE, phase l_d) = 88 × 10³ M¹cm¹, the critical FRET distances R₀ were calculated using

(27)

where ² is the FRET orientation factor, n is the refractive index, and  is the wavelength. ² was taken as 5/4 (value for isotropic planar distribution of dipoles in the dynamic regime), the value used by Medhage et al. (1992) in their study of N-(lissamine^TM-rhodamine B)-dipalmitoylphosphatidylethanolamine (Rh-DPPE) energy migration in bilayers, while n = 1.4 was considered (Davenport et al., 1985). If the  units used in Eq. 27 are nm, the calculated R₀ has Å units. The values obtained were R₀ (30°C) = 59.9 Å, R₀ (40°C) = 57.7 Å, R₀ (30°C) = 61.1 Å, and R₀ (40°C) = 59.4 Å.

Because both probes were mixed with adequate volumes of stock solutions of the host lipids, there is a bilayer geometry, and the decays should be analyzed using Eqs. 4, 5, 7, and 8. For this analysis, the interplanar distance in phase i, d_i, is required. Although the bilayer width varies with the cholesterol content (increases for T above the main transition temperature of the phospholipid, T_m; Ipsen et al., 1990), we did not find literature values for this effect in DMPC vesicles (the theoretical study of Ipsen et al. (1990) refers to DPPC). In any case, for DPPC at temperatures ~7°C above T_m and x_chol = 0.25, the bilayer width varies only 3 Å (visual inspection of Fig. 3 from Ipsen et al., 1990). In our study, this would be an approximation to T = 30°C and x_chol = 0.25, respectively, the lowest temperature and the highest cholesterol mole fraction studied inside the phase coexistence range. For larger T (40°C) or smaller x_chol (0.15, 0.20), the effect is even less pronounced. Because this variation in d is much smaller than R₀, a good approximation will certainly be to use the bilayer width for pure fluid DMPC, 35.5 Å (Marsh, 1990). This value should be increased by the distance between the Rh-DMPE chromophore and the lipid water interphase, which, according to Medhage et al. (1992), is ~3.5 Å. In contrast, the NBD-DMPE fluorophore is expected to be located at the interphase (Chattopadhyay and London, 1987). Therefore, the interplanar distance is taken as d = d = 39 Å.

Table 2 shows the results of global analysis of the FRET decays. The energy transfer efficiency, E, calculated from the donor decays in absence and presence of acceptor (_D(t) and _DA(t), respectively), according to

(28)

is represented in Fig. 4 for both studied temperatures. From this figure it is clear that E decreases for both temperatures inside the phase coexistence range, and increases again (possibly not significantly for T = 40°C) at the phase coexistence limit. This happens because donor and acceptor have affinity for different phases, as was shown above. When phase separation occurs, the acceptor concentration around the majority of the donors is reduced, leading to less donor quenching and smaller E. For higher cholesterol concentration, there is a single phase again, and this compartmentalization effect disappears.

View larger version (13K): [in this window] [in a new window]   FIGURE 4   Variation of FRET efficiency of NBD-DMPE/Rh-DMPE in DMPC/cholesterol LUV, as a function of the cholesterol mole fraction, for (A) T = 30°C and (B) T = 40°C. The error bars' extremes are the results of two different measurements. The dotted vertical lines represent the phase coexistence limits according to the phase diagram of Fig. 1.

One can now apply the methodology presented above to calculate the apparent K_p values of both probes. For this system, Eqs. 13 and 14 should be written as

(29)

(30)

where c_i is proportional to the amount of acceptor in phase i (according to Eq. 3), a_i is the average area per lipid molecule in phase i, i =  or  for phase l_d or l_o (respectively), and q is the pre-exponential ratio A/A. q and c_i result directly from the decay analysis, whereas X_i (the molar fraction of phase i in the sample) comes from the phase diagram. As for a and a, one must take into account the bilayer condensation effect produced by cholesterol. In this way, the values of Smaby et al. (1997) obtained for non-ideal condensation in monolayers at 30 mN/m (Table 1 in this reference), together with those reported by Marsh (1990) for the area per DMPC molecule in pure bilayers (0.652 nm² at 30°C, 0.622 nm² at 40°C) are used to estimate a (30°C) = 0.601 nm², a (30°C) = 0.488 nm², a (40°C) = 0.535 nm², and a (40°C) = 0.452 nm². Table 3 shows the K_p values from Eqs. 29 and 30, which are compared with those obtained in the previous section from anisotropy or fluorescence intensity measurements.

Another interesting comparison is that of the experimental c and c values with the theoretical values. Using the K_pA values from steady-state fluorescence, for each composition X, the acceptor mole fraction inside each phase (P and P = 1  P) is calculated from Eq. 12, and used to calculate the surface acceptor concentration (n_i) according to

(31)

where F is the bulk acceptor:lipid ratio, kept to 0.005 in our experiment. In turn, from n_i and Eq. 3, one obtains c_i. Figure 5 shows the theoretical and experimental c_i inside the phase coexistence range.

View larger version (11K): [in this window] [in a new window]   FIGURE 5   Theoretical values ( and - - -, respectively) and experimental fitting values ( and , respectively) for c and c, the c parameters (proportional to acceptor concentration) associated to lo and ld phases (respectively) for NBD-DMPE/Rh-DMPE in DMPC/cholesterol LUV. The open circles represent points where one of the functions c or c is not defined. (A) T = 30°C; (B) T = 40°C.

The results of Table 3 and Fig. 5 prompt the following considerations:

1.	The donor partition coefficient values obtained from analysis of the decay data are very close to those obtained by anisotropy measurements. Considering a normal distribution of KpD estimates, with 80% confidence level, one obtains KpD (30°C) = 1.3 ± 0.3 and KpD (40°C) = 2.4 ± 1.0. This proximity between FRET and anisotropy estimates of KpD corresponds to the agreement of input and recovered KpD values in the Simulations section (see Table 1).
2.	Turning our attention now to KpA, the values obtained for the samples with 25 mol% are the ones closest to those obtained from IF variation. The fact that the apparent FRET KpA are somewhat smaller than the KpA obtained from IF for this composition at both temperatures could result from several factors. One hypothesis, suggested by the decrease of absorption and emission intensity, is the existence of a certain degree of acceptor aggregation in the lo phase. This would indeed lead to a negative error in the recovered c, and, consequently, KpA (Eq. 29). In any case, note that, for Rh-DMPE, there is little static fluorescence self-quenching in that phase, which could mean that this effect is not too significant. Moreover, despite the reduction in absorption intensity, the spectra shape remains the same, apart from a small bathochromatic shift. In particular, the shoulder at ~535 nm is not enhanced (as observed in buffer, where there is certainly substantial Rh-DMPE aggregation). Another equally probable hypothesis is the uncertainty associated to the used a and a values. Still, the agreement between the KpA recovered from the FRET formalism for the sample with xchol = 0.25 and the values obtained from IF measurements is quite reasonable.
3.	An equivalent point is the proximity between the ci recovered from FRET analysis of experimental decays and the theoretical curves for xchol = 0.25 (the sample with the larger lo phase fraction X inside the lo/ld coexistence range). The fact that the experimental c is larger than expected (especially for T = 40°C) may be due to one of the factors mentioned above, or to inaccuracy in the theoretical curves (which would occur if the experimental acceptor:total lipid ratio were not exactly 0.005, or if there were errors in the KpA calculated from IF measurements), or probably to the difficulty in recovery of the correct FRET decay fitting parameters, due to their correlation. In any case, an identical tendency, described below, is clear for both studied temperatures.

The FRET recovered apparent K_pA value decreases from the sample with x_chol = 0.15 to that with x_chol = 0.20 at 30°C (being invariant at 40°C), and from the latter to that with x_chol = 0.25 at both temperatures. The fact that, for x_chol = 0.15 and x_chol = 0.20, one recovers FRET k_pA values larger than those measured from I_F measurements is not due to aggregation in either the l_o phase (which would have the opposite effect) or the l_d phase (which is similar to pure phospholipid fluid phase, in which the probes disperse randomly; Loura et al., 1996). Figure 5 suggests the most probable cause for this observation. For x_chol = 0.15 and x_chol = 0.20 (the studied samples with smaller X in the l_o/l_d coexistence range), the experimental c value (which would always be expected to be larger than c, according to the K_pA calculated from I_F measurements) is smaller than expected, whereas the opposite is true for c. This behavior recalls the Monte-Carlo simulations, which showed that FRET K_pA values closer to unity than expected from the input distributions are recovered due to the existence of small domains of the minor phase.

At this point, it is interesting to compare the relative deviations between the FRET-recovered K_pA and the theoretical values (for the simulations) or the I_F-recovered values (for the experimental study). Note that both the theoretical K_pA values and those obtained experimentally from I_F measurements are the "real" K_pA values, unaffected by the domain size of the coexistence phases, whereas the FRET-recovered value, as shown in the Simulations section, is sensitive to this variable. In these studies, the average relative deviation in K_pA (excluding the simulations which had homogeneous distributions of acceptors) is 27% for domains of size 3.5 R₀ and 10% for domains of size 9 R₀. The deviations for the present study, calculated from 100% × |K_pA(FRET)  K_pA(I_F)|/K_pA(I_F), are 143% (T = 30°C, x_chol = 0.15), 40% (T = 30°C, x_chol = 0.20), 74% (T = 40°C, x_chol = 0.15), and 81% (T = 40°C, x_chol = 0.20).

These numbers should be viewed cautiously, because there is not exact matching between input simulation variables and the experimental parameters, and the simulated domains had a shape and size distribution that probably differs from the actual ones, but they clearly indicate the following:

• In the systems that have smaller amount of l_o phase (x_chol = 0.15 and 0.20 for T = 40°C, x_chol = 0.15 for T = 30°C), the considerable deviation between K_pA (FRET) and K_pA(I_F) suggests that the l_o domains, dispersed in l_d phase, should be very small, of the order of magnitude of R₀, that is, a few nm. The fact that these deviations are much larger than those calculated for simulations for domain size 3.5 R₀ (~20-25 nm for this system) indicates that the l_o domains should be smaller than this value.
• This effect is apparently more