Article pubs.acs.org/JPCB
Viscosity Heterogeneity inside Lipid Bilayers of Single-Component Phosphatidylcholine Liposomes Observed with Picosecond TimeResolved Fluorescence Spectroscopy Yuki Nojima and Koichi Iwata* Department of Chemistry, Faculty of Science, Gakushuin University, 1-5-1 Mejiro, Toshima-ku, Tokyo 171-8588, Japan ABSTRACT: A number of biochemical reactions proceed inside biomembranes. Because the rate of a chemical reaction is influenced by chemical properties of the reaction field, it is important to examine the chemical properties inside the biomembranes, or lipid bilayer membranes, for understanding biochemical reactions. In this study, we estimate viscosity inside the lipid bilayers of liposomes with picosecond time-resolved fluorescence spectroscopy. trans-Stilbene is solubilized in the lipid bilayers formed by phosphatidylcholines, DSPC, DOPC, DPPC, DMPC, and DLPC, with 18, 18, 16, 14, and 12 carbon atoms in their alkyl chains, respectively, and egg-PC. Viscosity inside the lipid bilayer is estimated from the photoisomerization rate constant and from the rotational relaxation time of the first excited singlet state of trans-stilbene. The effect of the hydrocarbon chain length and temperature on viscosity is examined. The presence of two solvation environments within the lipid bilayer is indicated from the two independent estimations. One environment is 30 to 290 times more viscous than the other. Even single-component lipid bilayers are likely to have heterogeneous structures.
1. INTRODUCTION
The lipid bilayer is a major component of biomembranes. It is often formed in water from phospholipids. Because it is thermodynamically more stable when their hydrophobic groups are not exposed to water, they form a vesicle with the lipid bilayer forming a sphere. A vesicle made of lipid bilayers is also called a liposome. The liposomes are widely studied as a model of biomembranes.21−23 The liposome has a capsule-like structure, and thus hydrophilic substrates are enclosed in the inner aqueous phase and hydrophobic substrates are solubilized inside the lipid bilayer. Liposomes are often used as drugdelivery carriers because of this structure.24−26 The lipid bilayer shows two major phases depending on the temperature: the gel phase and the liquid crystal phase. The conformation and motion of the hydrocarbon chains of lipids that form the lipid bilayer are different between the two phases.27,28 The hydrocarbon chains have the all-trans conformation in the gel phase while the hydrocarbon chains in the liquid crystal phase contain gauche-conformations as well as the trans-conformation. The hydrocarbon chains move more freely in the liquid crystal phase compared with the gel phase. The lipid molecules in the lipid bilayer diffuse more freely when the motion of their hydrocarbon chains is less restricted. Therefore, the lipid bilayer in the liquid crystal phase is more fluid compared with the lipid bilayer in the gel phase. It is believed that the lipid bilayer of biomembranes, which are formed by multiple phospholipids, takes mostly the liquid crystal phase. However, the lipid raft model presumes that the
Biomembranes serve as structural components or boundaries in a cell. At the same time, a number of biochemical reactions proceed at the biomembranes. Biochemical reactions are often catalyzed by membrane proteins. The membrane proteins are buried in the lipid bilayer of biomembranes, and thus the lipid bilayer serves as a reaction field for biochemical reactions. Because a rate of a chemical reaction is determined by chemical properties of the reaction field such as viscosity and polarity, it is necessary to know the environment inside the lipid bilayer as a chemical reaction field to understand biochemical reactions. In this study, we focus on viscosity, one of the fundamental chemical properties that characterize a chemical reaction field, of the lipid bilayer. The structure of biomembranes has been studied extensively,1−6 although the number of studies that evaluate lipid bilayers as a chemical reaction field is still limited.7−13 The lipid raft has been proposed and is an influential model that explains the structure and functions of biomembranes.14−16 It is assumed in this model that the biomembrane is mostly composed of a fluid lipid bilayer. A stiff structure, which is rich in cholesterol and sphingomyelin, also assumed in the model, is called a lipid raft. The cholesterol and sphingomyelin molecules are reported to be packed tightly and form a micro domain or raft.17 Lipid rafts are considered to be floating in a lipid bilayer and to repeat formation and decomposition. Diameter of a lipid raft is estimated to be 26 nm18 or smaller than 20 nm.19,20 Some membrane proteins are contained in the lipid raft. Incorporation of membrane proteins will enable efficient information propagation inside the cell. © 2014 American Chemical Society
Received: April 22, 2014 Revised: June 2, 2014 Published: June 26, 2014 8631
dx.doi.org/10.1021/jp503921e | J. Phys. Chem. B 2014, 118, 8631−8641
The Journal of Physical Chemistry B
Article
coefficient of a lipid with a fluorescence probe inside the DLPC lipid bilayer was reported to be 3 × 10−8 cm2 s−1. This value is ∼1000 times smaller compared with the self-diffusion coefficient of water (2.30 × 10−5 cm2 s−140). Because the diffusion coefficient correlates with viscosity, the result indicates that viscosity of a lipid bilayer is considerably larger than that of water. Estimations of viscosity inside lipid bilayers with fluorescence spectroscopy previously mentioned suggest that the lipid bilayer is more viscous than alkanes or water by two to three orders of magnitude. In this study, we solubilize trans-stilbene inside the lipid bilayers of liposomes and have measured its fluorescence decay kinetics with a picosecond time-resolved fluorescence spectrometer with a typical response time of 15 ps. We estimate viscosity inside the lipid bilayers of the liposomes from the photoisomerization rate constant and from the rotational relaxation time of trans-stilbene obtained from the fluorescence decay kinetics. It has been shown in our previous study on an egg-PC bilayer41 that the lipid bilayer of egg-PC has two solvation environments with different viscosity values. One environment is 50 to 100 times more viscous than the other. Because egg-PC is a mixture of lipids obtained from egg-yolk, the number of carbon atoms and CC bonds in the hydrocarbon chain is not uniform. It is possible that the observed environments with different viscosities originate from the varieties in the length or in the number of CC bond in the lipid hydrocarbon chain. To eliminate effects that the distribution of hydrocarbon chains possibly has on the structure of the lipid bilayer, we prepare liposome solutions from a single lipid, with five different synthetic phospholipids. Each of them has a uniform length and CC bond location in the hydrocarbon chains. We examine how viscosity inside the lipid bilayer changes depending on the character of the hydrocarbon chain of the phospholipids. We also examine the temperature dependence of viscosity inside the lipid bilayer. We discuss the structure of the liposome lipid bilayer from the obtained results.
biomembranes contain both a liquid-crystal-phase-like lipid bilayer (disordered liquid phase, Ld) and a gel-phase-like lipid bilayer (ordered liquid phase, Lo). Lipid bilayers in the Lo phase form a domain structure, or a lipid raft, with cholesterol. AFM observations revealed that the lipid raft was floating in the Ld phase lipid bilayer.29,30 Viscosity inside the lipid bilayer has been estimated with fluorescence techniques such as steady-state fluorescence anisotropy measurement,31 detection of excimer formation,32 determination of fluorescence quantum yield,33 and timeresolved fluorescence spectroscopy.34−36 Estimated viscosity, however, tends to depend on the choice of the fluorescence probe and on the method of the measurement. In most of the previous studies, environment inside the lipid bilayer is considered to be homogeneous. Shinitzky and Barenholz estimated the viscosity inside an egg-PC (egg-yolk phosphatidylcholine) lipid bilayer with steady-state fluorescence anisotropy measurement of perylene and DPH (diphenyl hexatriene).31 Viscosity of the egg-PC bilayer at room temperature was estimated to be 80 mPa s for both of the probes. Vanderkooi and Callis estimated viscosity inside an egg-PC bilayer at room temperature from excimer fluorescence of pyrene.32 Viscosity was estimated to be 60 mPa s. Kung and Reed estimated the viscosity inside DPPC (dipalmitoylphosphatidylcholine) bilayer from the fluorescence quantum yield of a fluorescent probe CCVJ (9-(2-carboxy-2cyanovinyl)julolidine).33 Phase-transition temperature of the DPPC bilayer has been reported to be 41 °C.34 Viscosity inside the DPPC bilayer at 10 °C (gel phase) was estimated to be 120 mPa s, while it was estimated to be 70 mPa s at 60 °C (liquid crystal phase). Kinoshita et al. estimated the viscosity inside a lipid bilayer formed by biological membrane extracts with timeresolved fluorescence anisotropy measurements of DPH.35 The viscosity inside the lipid bilayer composed of purple membrane extracts was estimated to be 273 mPa s at 10 °C and 87 mPa s at 35 °C. Wu et al. examined the local viscosity inside the lipid bilayers of single lipid vesicles and phase-separated vesicles from the fluorescence lifetime.36 They observed two environments with the different viscosity (160 and 1300 mPa s) inside the gel-phase lipid bilayer, while only one environment was observed inside the liquid-crystal-phase lipid bilayers. Holmes et al. estimated the viscosity inside the DPPC bilayer with time-resolved fluorescence measurements of trans-stilbene solubilized within the lipid bilayer.37 Viscosity inside the DPPC bilayer is estimated to be 320 mPa s at 20 °C (gel phase) and 150 mPa s at 50 °C (liquid-crystal phase). Viscosity inside the lipid bilayer estimated with trans-stilbene was approximately two times larger than other estimated values. Viscosity estimated within the bilayer tends to be larger when the fluorescent probe is smaller. Holmes et al. presumed that the DPPC bilayer had several solvation environments because the two fluorescence lifetimes of trans-stilbene were observed for the two different phases. However, fluorescence anisotropy decay curve showed one decay component. They mentioned that they did not observe a fast anisotropy decay component probably because of the limited instrumental time resolution. Estimations of the viscosity of lipid bilayers suggest that it is 26 to 120 times more viscous inside of the lipid bilayer than in hexadecane (2.77 mPa s38). Reported diffusion coefficients of lipids also indicate that the lipid bilayer is viscous in its interior. Translational diffusion in the DLPC (dilauroyl-phosphatidylcholine) bilayer was measured with fluorescence correlation spectroscopy by Korlach et al.39 Translational diffusion
2. EXPERIMENTAL METHODS 2.1. Sample Preparation. Liposome solutions were prepared by the method reported by Bangham and Horne.42 Phospholipid and trans-stilbene were dissolved in a mixture of chloroform and methanol. The solvent was then removed and a lipid thin film was obtained. Distilled water was added to the thin film. The liposome solutions thus obtained were filtered under high pressure with an “extruder.” The diameter of the liposomes after the filtration was estimated to be 100 nm.43 Liposomes were prepared from six phospholipids: distearoylphosphatidylcholine (DSPC), dipalmitoyl-phosphatidylcholine (DPPC), dimyristoyl-phosphatidylcholine (DMPC), dilauroylphosphatidylcholine (DLPC), dioleoyl-phosphatidylcholine (DOPC), and egg-yolk phosphatidylcholine (egg-PC). Phospholipids and trans-stilbene were purchased from Wako Pure Chemical Industries. The six lipids have different numbers of carbon atoms and CC bonds in the hydrocarbon chains. DSPC has 18, DPPC has 16, DMPC has 14, DLPC has 12, and DOPC has 18 carbon atoms in their hydrocarbon chains. Because egg-PC is a mixture of lipids obtained from natural egg-yolk, the number of carbon atoms in the hydrocarbon chains varies from 16 to 20. DSPC, DPPC, DMPC, and DLPC are saturated lipids, with no CC bond in the hydrocarbon chains. DOPC and egg-PC, however, are unsaturated lipids. DOPC has one CC bond in each 8632
dx.doi.org/10.1021/jp503921e | J. Phys. Chem. B 2014, 118, 8631−8641
The Journal of Physical Chemistry B
Article
hydrocarbon chain. Egg-PC has two or three CC bonds in the hydrocarbon chains. The difference in the hydrocarbon chain among these six lipids results in the difference in the phase-transition temperature of the lipid bilayers they form. Reported temperature for the phase transition of the lipid bilayer from the gel phase to the liquid crystal phase is 56 °C for the DSPC lipid bilayer, 42 °C for DPPC, 24 °C for DMPC, −2.1 °C for DLPC, −22 °C for DOPC, and −15 to −7 °C for egg-PC.44 At room temperature (25 °C), DSPC and DPPC lipid bilayers are in the gel phase, while DMPC, DLPC, DOPC, and egg-PC lipid bilayer are in the liquid crystal phase. 2.2. Picosecond Time-Resolved Fluorescence Spectroscopy. Fluorescence decay kinetics was measured with a picosecond time-resolved fluorescence spectrometer. The fourth harmonic (300 nm, 1 kHz) of the output from an optical parametric amplifier (Coherent OPerA Solo), pumped by a Ti:sapphire regenerative amplifier (Coherent Legend EliteUSP) seeded by a Ti:sapphire oscillator (Coherent, Micra), was used as the pump pulse for the fluorescence excitation. Emitted fluorescence was passed through a polarization analyzer and a depolarizer and was focused into an imaging spectrograph (Chromex 250IS). A UV cut filter was placed in front of the entrance slit of the spectrograph to eliminate the scattered excitation light. The collected fluorescence was detected by a streak camera (Hamamatsu C2909).45 A part of the output from the Ti:sapphire regenerative amplifier was used as a trigger pulse for the streak camera. It took ∼30 nanoseconds from the input of the trigger pulse for the streak camera to start a recording. The measurement by the streak camera was synchronized with the photoexcitation with an optical delay of 11 m (35 ns) in the light path of the pump pulse. Sample solutions were circulated by a magnet gear pump to avoid photodeterioration during the fluorescence measurements. For measuring the temperature dependence of the fluorescence lifetime, sample solutions were kept in a quartz cell. The sample solutions were stirred by a magnetic stirrer. Temperature of the sample solutions was controlled by a temperature-controllable cell holder. The temperature of the sample solutions was measured before and after each fluorescence measurement. The temperature of the solutions was kept constant within 0.1 °C during the measurement. Fluorescence signals polarized at the magic angle (54.7°) with respect to the excitation polarization were collected for the fluorescence lifetime measurements. Observed fluorescence decay curve was fitted with a convolution of a doubleexponential decay function and a Gaussian response function. For the anisotropy measurements, fluorescence decay was measured with the polarization parallel with and perpendicular to the excitation polarization separately. The fluorescence anisotropy decay curve was then calculated from a set of fluorescence decay curves observed for the two polarization conditions.
Figure 1. Absorption spectrum of trans-stilbene inside DLPC liposome.
this absorption band originates from trans-stilbene solubilized within the lipid bilayer of the liposome. The absorption band of trans-stilbene was also observed for other liposome solutions formed by DMPC, DPPC, DSPC, DOPC, and egg-PC. The vibronic bands were observed at the same position for all samples. The number of trans-stilbene molecules solubilized in a single liposome sphere is estimated from the obtained absorption spectra. For the DLPC liposome, for example, absorbance of the trans-stilbene band at 298 nm is 2.02. If we assume that the molar extinction coefficient of trans-stilbene in the DLPC liposome is the same as that in chloroform (3.1 × 104 mol−1 dm3 cm−1), the average concentration of transstilbene for the whole liposome solution is estimated to be 6.7 × 10−5 mol dm−3. By calculating the number of DLPC liposomes and the number of stilbene molecules contained in the sample solution and by estimating the number of the DLPC molecules contained in a liposome of a diameter of 100 nm, the number of trans-stilbene molecules contained in a single DLPC liposome is estimated to be 5000. The surface area of a liposome that one trans-stilbene should occupy is 6.3 nm2 in average. The concentration of stilbene inside the lipid bilayer should be 5.0 × 10−2 mol dm−3. The numbers of stilbene molecules solubilized in a single liposome varied depending on the phospholipid. The estimated number of trans-stilbene molecules contained in a single liposome was 8000 for the DMPC liposome, 5000 for the DPPC liposome, 600 for the DSPC liposome, 5000 for the DOPC liposome, and 300 for the egg-PC liposome. Absorption spectra of liposome solutions did not indicate any sign of stilbene aggregates. 3.2. Estimation of Viscosity Inside Lipid Bilayer of Liposomes. 3.2.1. Viscosity Estimation from Photoisomerization Rate Constant of S1 trans-Stilbene. Fluorescence decay kinetics of trans-stilbene solubilized within the liposome lipid bilayer was measured with a picosecond time-resolved fluorescence spectrometer. Observed fluorescence decay kinetics for the DLPC liposome and the DPPC liposome are shown in Figure 2. The DLPC lipid bilayer is in the liquidcrystal phase, while the DPPC lipid bilayer is in the gel phase at room temperature (25 °C). As shown in the Figure, the fluorescence intensity of trans-stilbene in the liquid-crystal phase liposome (Figure 2A) decreases faster than that of transstilbene in the gel-phase liposome (Figure 2B). The observed fluorescence decay curves of trans-stilbene (a and d, dotted trace, in Figure 2) were fitted with a doubleexponential decay function (b and e, solid curves) and with a single-exponential decay function (c and f, dotted lines). For all samples, observed decay curves were fitted well with a doubleexponential decay function. This suggests the presence of two solvation environments within the lipid bilayer. A fluorescence decay curve of trans-stilbene in an organic solvent is mostly
3. RESULTS AND DISCUSSION 3.1. Absorption Spectra of trans-Stilbene Solubilized in Liposome Lipid Bilayer. We measured the steady-state absorption spectra of liposome samples to confirm that transstilbene molecules are solubilized inside the liposome lipid bilayer. Figure 1 shows an absorption spectrum of trans-stilbene in a DLPC liposome solution. The absorption band of transstilbene with its characteristic vibrational structure was observed at ∼300 nm, with maxima at 298, 311, and 325 nm. Because trans-stilbene is insoluble in water, we conclude that 8633
dx.doi.org/10.1021/jp503921e | J. Phys. Chem. B 2014, 118, 8631−8641
The Journal of Physical Chemistry B
Article
photoisomerization rate constant kiso is calculated from the following equation, kiso = 1/τf − kr, where τf is the fluorescence lifetime and kr is the radiative decay rate constant. The kr value has been reported to be 6.06 × 108 s−1.54 Two photoisomerization rate constants, which are calculated from the fluorescence lifetimes of 90 and 270 ps for the DLPC liposome, are 1.1 × 1010 and 3.1 × 109 s−1, respectively. The photoisomerization rate constants calculated from the fluorescence lifetimes of 230 ps and 1.0 ns for the DPPC liposome are 3.8 × 109 and 4.0 × 108 s−1, respectively. We assume that the solvation environment of trans-stilbene inside the lipid bilayer is similar to that of alkanes because it is more likely that hydrophobic trans-stilbene molecules, insoluble in water, are surrounded by the hydrocarbon chains of phospholipids than by charged head groups. Thus, viscosity within the lipid bilayer of liposomes is estimated from the known correlation between the photoisomerization rate constant and the viscosity of alkanes. The reported values38 are presented in Figure 3 with crosses. The correlation curve
Figure 2. Fluorescence decay curve of trans-stilbene inside the DLPC lipid bilayer (A) and the DPPC lipid bilayer (B). Dotted traces (a,d) represent the observed decay curves while solid curves (b,e) and dotted lines (c,f) represent double-exponential and single-exponential decay functions, respectively.
fitted well with a single-exponential decay function. It has been reported that the fluorescence decay curve of trans-stilbene included in β-cyclodextrin is fitted well with a doubleexponential decay function.46 The result suggests the presence of two stilbene-cyclodextrin complexes. Obtained fluorescence lifetimes for the DLPC liposome are 90 and 280 ps, respectively. The amplitude of the faster decay component is larger than that of the slower component by a factor of 4. Obtained fluorescence lifetimes for the DPPC liposomes are 230 ps and 1.0 ns, respectively, with the amplitude of the faster decay component larger than the slower component by a factor of 2. Photoirradiation of trans-stilbene induces the isomerization reaction to the cis configuration. The rate constant of the photoisomerization reaction of trans-stilbene in the first excited singlet (S1) state is a sensitive measure of the solvent properties. The photoisomerization rate constant of S1 transstilbene is known to show a good correlation with the viscosity of the solvent.38,47−49 The solvent dependence of the photoisomerization rate constant and the dependence of the position and shape of the CC stretch vibration of S1 transstilbene has been explained well by the “dynamic polarization model”.50,51 In this article, however, we characterize the solvation environment in the lipid bilayer membranes with viscosity, although it is an index describing a property of a bulk liquid. We estimate the viscosity within the lipid bilayer of liposomes from the photoisomerization rate constant of S1 trans-stilbene. The two fluorescence decay components suggest the presence of two solvation environments with different viscosity values inside the lipid bilayer of the liposomes. The photoisomerization rate constant of S1 trans-stilbene was calculated from the obtained fluorescence lifetime. It has been established that the photoisomerization is the dominant nonradiative decay process for S1 trans-stilbene.52,53 The
Figure 3. Correlation between photoisomerization rate constant of S1 trans-stilbene and solvent viscosity. Crosses represent the correlation for alkanes reported by Courtney et al.38 Estimated viscosity for lipid bilayers is plotted as well. ηfluid shows values estimated from the faster fluorescence decay component, while ηviscous shows values estimated from the slower component.
represented with a dotted trace in the Figure was calculated by the least-squares-fitting analysis, with the use of a power function as the model function. The obtained correlation is k iso = −1.6 + 12.2η−0.244
(1)
where the photoisomerization rate constant, kiso, and viscosity, η, are represented in 109 s−1 and in mPa s, respectively. Viscosities estimated for the six liposome samples are summarized in Table 1. We refer to the smaller viscosity value as ηfluid and the larger value as ηviscous hereafter. ηfluid and ηviscous inside the DLPC lipid bilayer are estimated to be 1.0 and 54 mPa s, respectively, and ηfluid and ηviscous for the DPPC lipid bilayer are estimated to be 28 and 1500 mPa s. Viscosity values estimated for the DPPC lipid bilayer in the gel phase are ∼30 times larger than those for the DLPC lipid bilayer in the liquid crystal phase. The ratio between the two viscosity values, ηviscous/ηfluid, is 290 for the DSPC lipid bilayer, 54 for the DPPC lipid bilayer, 65 for the DMPC lipid bilayer, 54 for the DLPC lipid bilayer, 33 for the DOPC lipid bilayer, and 57 for the egg-PC lipid bilayer. The viscosity of lipid bilayers in the gel phase (DSPC and DPPC) tends to be larger than the viscosity of lipid bilayers in the liquid-crystal phase (DMPC, DLPC, DOPC, and EggPC). Viscosity values estimated for the lipid bilayer composed of egg-PC, whose hydrocarbon chain length and the numbers 8634
dx.doi.org/10.1021/jp503921e | J. Phys. Chem. B 2014, 118, 8631−8641
The Journal of Physical Chemistry B
Article
Table 1. Viscosity inside the Lipid Bilayer of Liposomes Estimated by Photoisomerization Rate Constant of S1 trans-Stilbene DSPC (18:0) DPPC (16:0) DMPC (14:0) DLPC (12:0) DOPC (18:1) Egg-PC (16−20:2−3)
ηfluid/mPa S
ηviscous/mPa S
(Iviscous/(Ifluid + Iviscous))
5.2 28 1.5 1.0 1.5 5.1
1500 1500 97 54 49 290
0.23 0.33 0.17 0.23 0.17 0.090
moment of the molecule. Immediately after the photoexcitation, the emitted fluorescence is mostly polarized parallel to the polarization of the excitation light if the absorption and emission transition moments are parallel with each other. Emitted fluorescence becomes less polarized as the alignment of the molecules relaxes due to the rotational reorientation of the excited molecules. The degree of polarization is expressed by fluorescence anisotropy, r(t), defined as
of CC bonds are not uniform, are between the liquid crystal phase (DLPC, DMPC, and DOPC) and the gel phase (DPPC and DSPC). The estimated viscosity increases as the hydrocarbon chain length increases for saturated lipids (DSPC, DPPC, DMPC, and DLPC). Although DOPC has 18 carbon atoms and a CC bond in each hydrocarbon chain, the estimated viscosity values are 3.5 and 31 times smaller than those of the lipid bilayer composed of DSPC, which also has 18 carbon atoms but no CC bond in the hydrocarbon chain. This is probably caused by the relatively loose packing of the hydrocarbon chains for DOPC. Because DOPC has a CC bond in each hydrocarbon chain, its chains do not take the straight all-trans configuration as saturated hydrocarbon chains do. The hydrocarbon chains of DOPC bend at the CC bond and provide more space for trans-stilbene molecules. The friction that the stilbene molecules feel decreases and the rate of the photoisomerization increases. The packing condition of the hydrocarbon chains is reflected in the thickness of the lipid bilayer. The thickness of the lipid bilayer composed of saturated lipid, such as DPPC, has been reported to be 4 to 15% larger than that of unsaturated lipids, such as DOPC.29,55,56 Viscosity for the less viscous or fluid environment is similar to the values of alkanes except for the DPPC lipid bilayer. The viscosity values for the viscous environment suggest the presence of wellpacked domains in the liposome lipid bilayers, even for lipid bilayers formed by a single lipid. By fitting a fluorescence decay curve with a doubleexponential decay function, I(t) = Ifast exp(−t/τfast) + Islow exp(−t/τslow), relative intensities for the two decay components are obtained. Because the fluorescence lifetime of trans-stilbene has a correlation with the viscosity of the surrounding medium, the relative intensity of a fluorescence decay component should represent the number of stilbene molecules in the fluid environment or in the viscous environment within the lipid bilayer. Thus, Islow/(Ifast + Islow) is proportional to the ratio of trans-stilbene in the viscous environment within the lipid bilayer. The ratios for six different lipids are listed in Table 1. The ratio of stilbene molecules in the viscous environment is larger for the lipid bilayers in the gel phase than those in the liquid crystal phase. This tendency is more evident in the results for temperature dependence of fluorescence lifetime mentioned in Section 3.3. 3.2.2. Viscosity Estimation from Rotational Relaxation Time of S1 trans-Stilbene. We estimate the viscosity inside the lipid bilayers by a different method, from the rotational relaxation time of S1 trans-stilbene. The rotational relaxation time is obtained from the measurement of fluorescence anisotropy decay. When a molecule is excited with linearly polarized light, the probability for the molecule to be excited depends on its orientation. The probability of the excitation is proportional to cos2 θ, where θ represents the angle between the direction of polarization of the excitation light and the absorption transition
r(t ) = (I//(t ) − I⊥(t ))/(I//(t ) + 2I⊥(t ))
(2)
where I∥(t) and I⊥(t) are the intensities of the fluorescence component at time t with the polarization parallel with and perpendicular to the excitation light, respectively. Decay of the fluorescence anisotropy is often expressed by an exponentialdecay function: r(t ) = r(0) exp( −t /τrot)
(3)
where τrot is the rotational relaxation time. The rotational relaxation time represents how fast a molecule changes its orientation. The Stokes−Einstein−Debye (SED) equation (eq 4) gives a correlation between the rotational relaxation time and the viscosity of the solvent. τrot = ηV /kT
(4)
In eq 4, η is the viscosity of the solvent, V is the volume of the probe molecule, k is the Boltzmann constant, and T is the temperature. With the Stokes−Einstein-Debye equation, it is possible to estimate the viscosity of the solvent from the rotational relaxation time. We measured I∥(t) and I⊥(t) of S1 trans-stilbene separately and calculated the time dependence of the fluorescence anisotropy with eq 2. Observed fluorescence anisotropy decay curves for the DLPC and DPPC liposomes are shown in Figure 4. The DLPC lipid bilayer is in the liquid-crystal phase at 25 °C, or 298 K, while the DPPC lipid bilayer is in the gel phase. Decay curves observed for the DLPC liposome and for the DPPC liposome (dotted traces in Figure 4) are fitted well with a double-exponential decay function (solid curves), whereas the fluorescence anisotropy decay curve of trans-stilbene is fitted well with a single-exponential decay function in most of the organic solvents. Fluorescence anisotropy decreases to zero in
