KAWATO, KINOSITA, AND IKECiAMl11> c ' I 'JU L 4,K -cnz 0.1wI-zcWzt-QE\>a0Et-0m-ZQ0.0''h/I" 0 20 40 60t (nsec)FIGURE 2: Time dependence <strong>of</strong> the emission anisotropy r(t) at differenttemperatures (zigzag <strong>cu</strong>rves) and <strong>of</strong> the total fluorescence intensity l ~(t)(dots) at 9.2 OC <strong>of</strong> DPH in liquid paraffin. The concentration <strong>of</strong> DPH was5 X M. Thin solid line: the best fit <strong>cu</strong>rve for double exponential approximation.Thin dashed line: the best fit <strong>cu</strong>rve for a single exponentialapproximation. Thin chain line: g'(X,,, f), A, = 455 nm.process <strong>of</strong> extrapolation to time zero induces a wide error.Therefore, the value <strong>of</strong> ro = 0.395 f 0.01 was used in the followinganalysis.The fluorescence lifetime 7 <strong>of</strong> DPH in liquid paraffin, hydrophobicsolution, is much larger than that in glycerin, hydrophilicsolution. It is interesting that the lifetime 7 is independent<strong>of</strong> temperature in completely hydrophobic environment,but it depends on temperature in hydrophilic environment.DPH in Liposome. Time courses <strong>of</strong> fluorescence intensityand depolarization <strong>of</strong> DPH embedded in DPPC liposomes weremeasured at various temperatures. Typical decays <strong>of</strong> zT(f) andr(t) measured with sonicated liposomes are shown in semilogarithmicplots in Figure 3. Similar results were obtainedwith unsonicated liposomes when the effect <strong>of</strong> scattering wascorrected. A significant feature <strong>of</strong> decay <strong>cu</strong>rves is that the<strong>cu</strong>rves r(t) do not follow a single exponential decay but can beseparated into two phases: an initial fast decreasing phase anda second almost constant phase. Similar decay <strong>cu</strong>rves havebeen observed in an excitable membrane (Wahl et al., 1971).On the other hand, the <strong>cu</strong>rves I,(t) follow a single exponentialdecay as pointed out <strong>by</strong> Lentz et al. (1976a). The <strong>cu</strong>rves IT(^)were analyzed <strong>by</strong> setting N = 1 and 2 in eq 7, and the cal<strong>cu</strong>latedbest fit <strong>cu</strong>rves are shown in Figure 3. No significantprogress in <strong>cu</strong>rve fitting was observed <strong>by</strong> setting N = 2.The <strong>cu</strong>rves r(t) were analyzed <strong>by</strong> settingr*(t) = (ro- rffi)e-r/@l + rffi (14)The best fit <strong>cu</strong>rves are shown <strong>by</strong> thin solid lines in Figure 3.FIGURE 3: Time dependence <strong>of</strong> the emission anisotropy r(r) at differenttemperatures (zigzag <strong>cu</strong>rves) and the total fluorescence intensity IT(I)at 5.2 'C (dots) <strong>of</strong> DPH in DPPC liposomes. The concentrations <strong>of</strong> DPPCand DPH were 3 mg/mL and 5 X M. Thin solid line: the best fit <strong>cu</strong>rve<strong>of</strong> IT(t) for double exponential approximation and that <strong>of</strong> r(t) <strong>ac</strong>cordingto eq 14. Thin dashed line: the best fit <strong>cu</strong>rve <strong>of</strong> IT(?) for a single exponentialapproximation and that <strong>of</strong> r(t) for double exponential approximation. Thinchain line: g'(A,,, t), A, = 455 nm.i60030230OO 20 40 01T("C)FIGURE 4: Temperature dependence <strong>of</strong> r, (0) and <strong>of</strong> the cone angle (0)for DPH in DPPC liposomes.For several cases, r(t) was deconvoluted <strong>by</strong> setting M = 2 ineq 8, that is, two exponential approximation. The best fit <strong>cu</strong>rvesfor r(t) are shown <strong>by</strong> thin dashed lines in Figure 3. In all casesexamined, values <strong>of</strong> 42 obtained <strong>by</strong> deconvolution were verylarge. Thus, r6(t) can be expressed well <strong>by</strong> eq 14.The obvious interpretation <strong>of</strong> the results is that the orientationaldistribution <strong>of</strong> DPH embedded in the hydrocarbonregion is anisotropic even at equilibrium state; r, representsthe degree <strong>of</strong> anisotropy in equilibrium distribution <strong>of</strong> DPHand 41 represents the relaxation time to appro<strong>ac</strong>h the anisotropicequilibrium distribution <strong>of</strong> excited DPH. The "orderparameter" commonly used in spin-label studies should correspondto the equilibrium anisotropy ratio r,/rO. As shown2322 BIOCHEMISTRY, VOL. 16, NO. 11, 1977
NANOSECOND FLUORESCENCE STUDY OF LIPID BILAYERS”In 04 0.1 50-II-0 1uOO 20 40 60T(T)FIGURE 6: Temperature dependence <strong>of</strong> the fluorescence lifetime T (0)and <strong>of</strong> the ratio <strong>of</strong> the steady-state fluorescence intensity to the fluorescencelifetime 1~~ T (0) for DPH in DPPC liposomes.O‘OIJ 005G L0 20 40 60T(T)FIGURE 5: (A) Temperature dependence <strong>of</strong> the relaxation time 61 <strong>of</strong> DPHin DPPC liposomes. (B) Temperature dependence <strong>of</strong> the wobbling diffusionconstant D, (0) and <strong>of</strong> the viscosity in the cone qc (0) for DPH inDPPC liposomes.in Figure 4, rm decreases sharply near the transition temperature40 ‘C. Highly anisotropic distribution <strong>of</strong> DPH in liposomesbelow the transition temperature Tt becomes almostisotropic <strong>by</strong> the transition. On the other hand, the apparentrelaxation time 41 is very short, ranging from 0.4 to 1.3 ns, andmarkedly “increases” near T, as shown in Figure 5.Temperature dependence <strong>of</strong> the fluorescence lifetime 7 isshown in Figure 6. Below T,, the value <strong>of</strong> 7 is the same orsomewhat higher than that in liquid paraffin, indicating almostcomplete hydrophobic environment. At the transition region,7 decreases rather sharply and decreases farther above T,.Dis<strong>cu</strong>ssionAnisotropic Distribution and Wobbling Diffusion. Results<strong>of</strong> the emission anisotropy r(t) summarized <strong>by</strong> eq. 14 indicatethat the orientational distribution <strong>of</strong> DPH in liposomes inequilibrium is anisotropic. The emission anisotropy at sufficientlylong time after the excitation, rm, does not vanish butremains constant even above the transition temperature. Then,the orientational motion <strong>of</strong> DPH in liposomes must be described<strong>by</strong> the wobbling or tumbling restricted <strong>by</strong> a certainanisotropic potential.The ex<strong>ac</strong>t treatment <strong>of</strong> the wobbling diffusion should bk verycomplicated, for the mole<strong>cu</strong>lar motion is affected <strong>by</strong> the shape<strong>of</strong> potential and local diffusion constants. Here we assume asimple square well potential and a uniform diffusion constant.The wobbling diffusion <strong>of</strong> the excited DPH is confined withina cone around the normal <strong>of</strong> the membrane with the cone angle8, (0’ I 8, I 90’). The “wobbling diffusion constant” D, isconstant throughout the cone and the orientational distribution<strong>of</strong> DPH in the cone is uniform at equilibrium. Even in thissimple model, the wobbling diffusion cannot be expressed <strong>by</strong>a single relaxation time but <strong>by</strong> many relaxation times (Kinositaet al., 1977). The resultant expression <strong>of</strong> r(t) is <strong>of</strong> the formwhere Ai and ui are constants which depend only on 8,. Thecone angle 0, is related to the equilibrium anisotropy ratioasThen, the single relaxation time $1 obtained experimentallycan be expressed approximately <strong>by</strong> the average <strong>of</strong> relaxationtimes asThe average relaxation time (4) increases with increase <strong>of</strong> thecone angle 8, because the time needed for the equilibrium ina wider angle is longer. That is, the apparent relaxation timefor the restoration <strong>of</strong> equilibrium in the cone does not expressthe “diffusion rate”.Wobbling Diffusion Constant and Cone Angle. The “wobblingdiffusion constant” D, cal<strong>cu</strong>lated <strong>by</strong> eq 17 and the coneangle 8, <strong>by</strong> eq 16 are plotted against temperature in Figures4 and 5. The change in 8, at T1 is sharper than that in D, at Tt,and, though the temperature dependence <strong>of</strong> BC is sigmoidal, that<strong>of</strong> D, is like the exponential function. Thus, the apparent“increase” in 41 due to the transition in Figure 5 is attributedto the effect <strong>of</strong> drastic increase in 8, which overcomes the effect<strong>of</strong> increase in D, near Tt.Viscosity in the Cone. From the wobbling diffusion constant,the “viscosity in the cone” can be estimated. The rotationaldiffusion constant D <strong>of</strong> an ellipsoid is generally expressed<strong>by</strong>D=- kT6.11 Vdwhere 7 denotes the viscosity <strong>of</strong> the solvent, V, and f denotethe effective volume and shape f<strong>ac</strong>tor <strong>of</strong> the probe. The samerelation can be applied between the wobbling diffusion constantand the “viscosity in the cone”.Here we assumed that the value <strong>of</strong> V, in hydrocarbon chains<strong>of</strong> lipids is the same as that in liquid paraffin because <strong>of</strong> thesimilar mole<strong>cu</strong>lar nature <strong>of</strong> both solvents. Then the “viscosityin the cone”, v,, was estimated using the average value <strong>of</strong> V$estimated in liquid paraffin (see Table I). The results (seeFigure 5) are an order <strong>of</strong> magnitude smaller than the values<strong>of</strong> “microviscosity” estimated from the steady-state fluorescenceanisotropy <strong>of</strong> perylene and DPH in DPPC vesicles(Cogan et al., 1973; Lentz et al., 1976a).The main source <strong>of</strong> the large difference between vC andiBIOCHEMISTRY, VOL. 16, NO. 11, 1977 2323