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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 of the emission anisotropy r(t) at differenttemperatures (zigzag curves) and of the total fluorescence intensity l ~(t)(dots) at 9.2 OC of DPH in liquid paraffin. The concentration of DPH was5 X M. Thin solid line: the best fit curve for double exponential approximation.Thin dashed line: the best fit curve for a single exponentialapproximation. Thin chain line: g'(X,,, f), A, = 455 nm.process of extrapolation to time zero induces a wide error.Therefore, the value of ro = 0.395 f 0.01 was used in the followinganalysis.The fluorescence lifetime 7 of DPH in liquid paraffin, hydrophobicsolution, is much larger than that in glycerin, hydrophilicsolution. It is interesting that the lifetime 7 is independentof temperature in completely hydrophobic environment,but it depends on temperature in hydrophilic environment.DPH in Liposome. Time courses of fluorescence intensityand depolarization of DPH embedded in DPPC liposomes weremeasured at various temperatures. Typical decays of zT(f) andr(t) measured with sonicated liposomes are shown in semilogarithmicplots in Figure 3. Similar results were obtainedwith unsonicated liposomes when the effect of scattering wascorrected. A significant feature of decay curves is that thecurves 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 curves havebeen observed in an excitable membrane (Wahl et al., 1971).On the other hand, the curves I,(t) follow a single exponentialdecay as pointed out by Lentz et al. (1976a). The curves IT(^)were analyzed by setting N = 1 and 2 in eq 7, and the calculatedbest fit curves are shown in Figure 3. No significantprogress in curve fitting was observed by setting N = 2.The curves r(t) were analyzed by settingr*(t) = (ro- rffi)e-r/@l + rffi (14)The best fit curves are shown by thin solid lines in Figure 3.FIGURE 3: Time dependence of the emission anisotropy r(r) at differenttemperatures (zigzag curves) and the total fluorescence intensity IT(I)at 5.2 'C (dots) of DPH in DPPC liposomes. The concentrations of DPPCand DPH were 3 mg/mL and 5 X M. Thin solid line: the best fit curveof IT(t) for double exponential approximation and that of r(t) accordingto eq 14. Thin dashed line: the best fit curve of IT(?) for a single exponentialapproximation and that of r(t) for double exponential approximation. Thinchain line: g'(A,,, t), A, = 455 nm.i60030230OO 20 40 01T("C)FIGURE 4: Temperature dependence of r, (0) and of the cone angle (0)for DPH in DPPC liposomes.For several cases, r(t) was deconvoluted by setting M = 2 ineq 8, that is, two exponential approximation. The best fit curvesfor r(t) are shown by thin dashed lines in Figure 3. In all casesexamined, values of 42 obtained by deconvolution were verylarge. Thus, r6(t) can be expressed well by eq 14.The obvious interpretation of the results is that the orientationaldistribution of DPH embedded in the hydrocarbonregion is anisotropic even at equilibrium state; r, representsthe degree of anisotropy in equilibrium distribution of DPHand 41 represents the relaxation time to approach the anisotropicequilibrium distribution of 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 of the fluorescence lifetime T (0)and of the ratio of 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 of the relaxation time 61 of DPHin DPPC liposomes. (B) Temperature dependence of the wobbling diffusionconstant D, (0) and of 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 of DPH in liposomesbelow the transition temperature Tt becomes almostisotropic by 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 of the fluorescence lifetime 7 isshown in Figure 6. Below T,, the value of 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,.DiscussionAnisotropic Distribution and Wobbling Diffusion. Resultsof the emission anisotropy r(t) summarized by eq. 14 indicatethat the orientational distribution of 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 of DPH in liposomes must be describedby the wobbling or tumbling restricted by a certainanisotropic potential.The exact treatment of the wobbling diffusion should bk verycomplicated, for the molecular motion is affected by the shapeof potential and local diffusion constants. Here we assume asimple square well potential and a uniform diffusion constant.The wobbling diffusion of the excited DPH is confined withina cone around the normal of the membrane with the cone angle8, (0’ I 8, I 90’). The “wobbling diffusion constant” D, isconstant throughout the cone and the orientational distributionof DPH in the cone is uniform at equilibrium. Even in thissimple model, the wobbling diffusion cannot be expressed bya single relaxation time but by many relaxation times (Kinositaet al., 1977). The resultant expression of r(t) is of 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 $1 obtained experimentallycan be expressed approximately by the average of relaxationtimes asThe average relaxation time (4) increases with increase of thecone angle 8, because the time needed for the equilibrium ina wider angle is longer. That is, the apparent relaxation timefor the restoration of equilibrium in the cone does not expressthe “diffusion rate”.Wobbling Diffusion Constant and Cone Angle. The “wobblingdiffusion constant” D, calculated by eq 17 and the coneangle 8, by eq 16 are plotted against temperature in Figures4 and 5. The change in 8, at T1 is sharper than that in D, at Tt,and, though the temperature dependence of BC is sigmoidal, thatof D, is like the exponential function. Thus, the apparent“increase” in 41 due to the transition in Figure 5 is attributedto the effect of drastic increase in 8, which overcomes the effectof increase in D, near Tt.Viscosity in the Cone. From the wobbling diffusion constant,the “viscosity in the cone” can be estimated. The rotationaldiffusion constant D of an ellipsoid is generally expressedbyD=- kT6.11 Vdwhere 7 denotes the viscosity of the solvent, V, and f denotethe effective volume and shape factor of the probe. The samerelation can be applied between the wobbling diffusion constantand the “viscosity in the cone”.Here we assumed that the value of V, in hydrocarbon chainsof lipids is the same as that in liquid paraffin because of thesimilar molecular nature of both solvents. Then the “viscosityin the cone”, v,, was estimated using the average value of V$estimated in liquid paraffin (see Table I). The results (seeFigure 5) are an order of magnitude smaller than the valuesof “microviscosity” estimated from the steady-state fluorescenceanisotropy of perylene and DPH in DPPC vesicles(Cogan et al., 1973; Lentz et al., 1976a).The main source of the large difference between vC andiBIOCHEMISTRY, VOL. 16, NO. 11, 1977 2323
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