J . Phys. Chem. 1989, 93, 8371-8376
8371
Electronic Energy Transfer In Anisotropic Systems. 2. 2,5,8,1l-Tetra-tert-butylperylene in Vesicles Bjorn Kalman,? Lennart B.-A. Johansson,*qt Maria Lindberg,t and Sven Engstrod Department of Physical Chemistry, University of UmeB, S-901 87 UmeB, Sweden, and Division of Food Technology, Chemical Centre, P. 0. Box 124, S- 221 00 Lund, Sweden (Received: April 3, 1989)
The electronic energy transfer between 2,5,8,1l-tetra-tert-butylperylene(TBPe) molecules solubilized in lipid membranes of 1,2-dioleoyl-sn-glycer0(3)phosphocholine(DOPC)has been studied by steady-stateand time-resolved fluorescence spectroscopy. The membranes were dispersed as unilamellar vesicles in a glycerol-water solution and cooled below 273 K to reduce the rotational rate of TBPe. The Forster radius (R,) of TBPe was determined spectroscopicallyto 33.4 1 A, which is smaller than the typical vesicle radius. The order parameter of TBPe solubilized in macroscopically aligned DOPC bilayers was small, suggesting a broad orientational distribution. The formation of excimers and dimers could be excluded since the fluorescence lifetime did not depend on TBPe's concentration. The TBPe-vesicle system was used to model the incoherent energy migration, among randomly distributed donors in two dimensions that are isotropically oriented. The experimental fluorescence anisotropy was compared with that obtained from Monte Carlo (MC) simulations and the Baumann-Fayer (BF) theory and found to be in good agreement, without using any adjustable parameter. From the MC simulations, the , be calculated. At a reduced concentration of one, (RZ(t))'I2 mean square displacement of the excitation energy, ( R Z ( t ) )could = Ro,which is much shorter than what is found for the corresponding three-dimensional case.
I. Introduction The radiationless electronic energy transfer1V2among molecules in viscous solutions has been studied intensively during the past 40 years. For such systems, a quantitative agreement between theory and experiments has been established r e ~ e n t l y . ~ -In ~ complex and chemically more interesting systems, such as membranes and proteins, a quantitative comparison is still lacking. The general theoretical treatment of incoherent energy transfer in these anisotropic systems is a matter of considerable complexity. This is due to the fact that the interacting molecules are distributed anisotropically with respect to both distances and orientation. Baumann and Faye# have treated theoretically the excitation transport in anisotropic and disordered two- and three-dimensional systems. The theory is based on the two-particle approximation proposed by Huber et al.,'v8 where only the interaction between pairs of molecules is considered. A more general approach for describing transfer is the Monte Carlo algorithm developed re~ e n t l y . ~In this method, the interactions between an excited molecule and any other molecule in the system are taken into account. The time dependence of the fluorescence anisotropy and the mean square displacement of the excitation can be calculated for any spatial and orientational ensemble. The fluorescence anisotropy gives in a straightforward way information about the excitation transport among identical molecules or so-called donor-donor transfer. Anfinrud et a1.I0 have measured the time-resolved anisotropy of rhodamine 3B adsorbed on amorphous quartz. The excitation transfer is restricted in two dimensions, since the dye forms a submonolayer. Anfinrud et al." have also studied the energy transfer of octadecyl-rhodamine B situated in Langmuir-Blodgett monolayers of 1,2-dioleoyl-sn-glycero(3)phosphocholine (DOPC). These systems are however a less suitable model for donor-donor transfer in two dimensions since the rhodamines did form aggregates that served as excitation traps. Vesicles can be used as model systems for investigating energy transfer in lipid bilayers.'* In such a system, the chromophores could be localized at the lipid-water interface as exemplified by octadecylrhodamines (6G, B, 101) and rhodamine B-lissamine-dioleoylphosphatidylethanolamine.'2~14 The excitation transport is then pseudo-two-dimensional with an energy migration across and parallel to the lipid bilayer. In this work, we have studied the hydrophobic molecule, 2,5,8,11 -tetratert-butylperylene (TBPe), which is solubilized in the hydrocarbon region of a bilayer. The lipid used here is DOPC. We found that University of UmeA. *Chemical Centre.
f
TBPe is localized preferentially in the middle of the lipid bilayer and the excitation transport is therefore considered as two-dimensional. The rotational rates of aromatic molecules and dyes in vesicles and lyotropic liquid crystals occur typically on the time scale of nanoseconds.'*J5J6 The rates of transfer and rotations are then comparable, and both contribute to the fluorescence anisotropy. Another complication is that the excitation transfer depends on the rotational rates, and these cannot be separated easily. In the present theories, it is assumed that the rotational motions, of the interacting molecules, are either much slower or faster as compared to the transfer rates. These limits are often referred to as the slow and fast cases, respectively. Therefore, a quantitative comparison between these theories and experiments using vesicles and lyotropic liquid crystals is not relevant. In order to investigate energy transfer in two dimensions for the slow case, we have modified the vesicle system used in ref 12. Vesicles are prepared normally with water, but here, we show that vesicles also form in mixtures of glycerol and water. These systems enable cooling below 273 K so that the effects of rotational motions become small. There are advantages in using vesicles instead of micelles or liquid crystals as model systems in the study of energy transfer. The local concentration of the interacting molecules in a vesicle can be kept very high although the total concentration in the system is very low. The vesicles prepared in the solvent mixture show much less light scattering as compared to those in ( I ) Forster, Th. Natunvissenschaften 1946, 33, 166. (2) FBrster, Th. Ann. Phys. ( h i p r i g ) 1948, 2, 5 5 . (3) Gochanour, C. R.; Andersen, H. C.; Fayer, M. D. J . Chem. Phys. 1979, 70, 4254. (4) Gochanour, C. R.; Fayer, M. D. J . Phys. Chem. 1981, 85, 1989. (5) Anfinrud, P. A.; Struve, W. S. J. Chem. Phys. 1987, 87, 4256. (6) Baumann, J.; Fayer, M. D. J . Chem. Phys. 1986,85, 4087. (7) Huber, D. L.; Hamilton, D. S.; Barnett, B. Phys. Reu. B 1977, 16, 4642. (8) Ching, W. Y.; Huber, D. L.; Barnett, B. Ibid. 1978, 17, 5025. (9) Engstrom, S.;Lindberg, M.; Johansson, L. B.-A. J . Chem. Phys. 1988, 89, 204. (10) Anfinrud, P. A.; Hart, D. E.; Struve, W. S. J . Chem. Phys. 1988,92, 4067. (1 1) Anfinrud, P. A.; Hart, D. E.; Hedstrom, J. F.; Struve, W. S. J . Chem. Phys. 1986, 90, 3116. (12) Johansson, L. B.-A.; Niemi, A. J . Phys. Chem. 1987, 91, 3020. (13) Kawski, A. Photochem. Photobiol. 1983, 38, 487. (14) Kalman, B.; Johansson, L. B . - k To be published. (15) Johansson, L. B.-A.; Molotkovsky, J. G.; Bergelson, L. D. J. Am. Chem. SOC.1987, 109, 7374. (16) Zannoni, C.; Arcioni, A,; Cavatorta, P. Chem. Phys. Lipids 1983, 32, 179.
0022-3654/89/2093-8371$01.50/00 1989 American Chemical Society
8312
The Journal of Physical Chemistry, Vol. 93, No. 26, 1989
Kalman et al.
water. Therefore, the vesicle concentration in glycerol-water mixtures can thus be kept higher, while still the energy transfer between the vesicles can be omitted. TBPe is a new fluorescent probe whose spectroscopic properties are given el~ewhere.’~J’ TBPe’s absorption and fluorescence spectra are very similar to those of perylene. The fluorescence lifetime is about 5 ns and weakly dependent on the kind of host medium. This lifetime is slightly longer than that of perylene in the same media. The rotation of perylene and TBPe is different. While both molecules rotate as an oblate symmetric top in paraffin oil, the rotation of perylene and TBPe obeys to partly slipping and sticking boundary conditions, respectively. This discrepancy is due to the four tert-butyl groups that make TBPe more bulky as compared to perylene.” For TBPe in lipid bilayers, it is found that the rotation can be described as that of an oblate in a solvent under partly slipping boundary conditions. In section 111, we derive from the Baumann-Fayer (BF) theory the anisotropy decays due to energy transfer in vesicles. In the BF theory, the interacting molecules are assumed to be isotropically oriented, which should be a good approximation to the situtation of TBPe in lipid bilayers. A vesicle is here considered as a planar lipid bilayer, which is true provided that the transfer distances are small in comparison to the vesicle’s curvature. Since we find that the TBPe molecules are located preferentially in the middle of the bilayer, the energy transfer becomes two dimensional. Hence, the BF theory can be experimentally tested for energy migration among isotropically oriented donors in two dimensions. The prerequisites of the Monte Carlo simulations of energy transfer are also summarized in this section. In section IV, we give evidence for the existence of lipid vesicles in mixtures of glycerol with water. The physicochemical properties of these bilayers are discussed briefly. Furthermore, the experimental results obtained a t different temperatures and concentrations of TBPe in the vesicles are given. It is shown that the energy transfer is solely due to donor-donor interaction, which means that the influence of excitation traps is negligible. The fluorescence anisotropy decay is dominated by energy transfer at temperatures below 250 K where the rotational motions of TBPe become small but not negligible. The experimental results approximate the slow case and are therefore of great interest for comparisons with models. We compare the experimental anisotropy decay with those obtained by the BF theory and Monte Carlo simulations.
The refractive indices were measured at 439 and 589 nm with an Abbe refractometer (Model A, Zeiss). A Bruker Model WM-250 NMR spectrometer equipped with a superconducting magnet was used for recording the spectra. The linear dichroism was conveniently recorded on a Cary Model 219 (Varian, USA) absorption spectrophotometer supplemented with sheet polarizers (HNP’B, Polarizers Ltd., UK). The technique for studying macroscopically aligned lamellar liquid crystals is presented e1se~here.I~The steady-state fluorescence spectra and anisotropies were obtained with a SPEX Fluorolog Model 112 instrument (SPEX Industries, New Jersey, USA), equipped with Glan-Thompson polarizers. The spectral bandwidths were 5.6 and 2.7 nm for the excitation and emission monochromators, respectively. A PRA Model 3000 system (Photophysical Research Associates Inc., Canada) was used for single-photon-counting measurements of the fluorescence decay. The excitation source is a thyratrongated flash lamp (Model 510C, PRA) filled with deuterium gas and operated at about 30 kHz. The excitation wavelengths were selected by interference filters (Omega/Saven AB, Sweden) centered at 409.4 nm (HBW = 13.0 nm). The fluorescence emission was observed above 470 nm through a long-pass filter Schott Model KV 470 (Schott, West Germany). The maximum absorbance of all samples was kept below 0.08, which corresponds to a total concentration of less than 10” M. The time-resolved polarized fluorescence decay curves were measured by repeated collection of photons during 200 s, for each setting of the polarizers. The emission polarizer was fixed and the excitation polarizer rotated periodically. In each experiment, the decay curves Fzz(t) and F d t ) were collected. The subscripts refer to the settings of the excitation (first subscript) and emission (second subscript) polarizers which are either being parallel (22) or perpendicular ( Y Z ) . From these, a sum curve s ( f )= Fzz(t) + 2GFYZ(t) and a difference curve W t ) = Fzz(t) - G F d t ) were calculated. The correction factor, G, was obtained by normalizing the total number of counts Fzzand FYZ collected in Fzz(t) and FyZ(t), respectively, to the steady-state anisotropy, rsras G = (1 - rJ(1 + 2r,)-’FZz(Fn)-l
11. Materials and Methods 2,5,8,11 -Tetra-tert-butylperylene (TBPe) was synthesized by Friedel-Crafts alkylation of perylene. Further details concerning the synthesis and the purification are given elsewhere.15J8 1,2Dioleoyl-sn-glycero( 3)phosphocholine (DOPC) was purchased from Avanti Polar Lipids (USA). The punty was better than 99% as checked by thin-layer and gas chromatography in our laboratory. Glycerol (Omnisolv, BDH; spectroscopic grade) was used after checking the fluorescence background. The lamellar liquid crystalline phase was composed of 80 wt % DOPC in a solvent mixture of glycerol and water. This solvent mixture of 91 wt % glycerol in water was also used in the preparation of DOPC vesicles. The vesicles were prepared by sonication as follows. Solutions of DOPC dissolved in chloroform and TBPe dissolved in ethanol were mixed. The solvents were evaporated, and the mixture of DOPC and TBPe was dried at 320 K and 0.1 Torr for 2 h. Then, 3 mL of the glycerol-water mixture was added, and the suspension was sonicated 8 times in intervals of 5 min. During the sonication, the sample was cooled at about 283 K. The sonicator is a Soniprep 150 (MSE Scientific Instruments, England) supplemented with an exponential microprobe. The level of amplitude used was 10-14 hm. After sonication, the sample were centrifuged at 5000g during 15 min.
The data were analyzed with a MINC-11/03 computer, using the deconvolution software (DECAY V3.0a, ATROPY V1 .O) developed by PRA. The fluorescence quantum yield, @, of TBPe in vesicles at 243 K has been determined. Perylene in ethanol was used as a standard with a reported2w22quantum yield of 0.92. The quantum yield was calculated from @TBPe
=
FTBPe @Pep
- exp(-APe
1°)lnGW2
FPe [I - exp(-ATspe In lO)InEtoH2 Here, F denotes the integral of the corrected fluorescence spectrum and A is the absorbance at the excitation wavelength. The refractive indices of ethanol (nEtOH) and the glycerol-water (nGW) mixture are 1.36 and 1.48, respectively. We obtain that = 0.85 0.07. The Forster radius (R,) of TBPe in vesicles at 243 K was determined in the following way. The corrected fluorescence spectrum, F ( e ) , of TBPe solubilized in vesicles at 243 K was determined. The spectral bandwidth was 1 nm. Quinine bisulfate and rhodamine 6G were used as reference substances for the c o r r e c t i ~ n . ~ ~The * * ~molar absorptivity as a function of wavenumbers, €(e), was determined from the absorption spectrum of
*
(19) Johansson, L. B.-A.; Davidsson, A. J . Chem. Soc., Faraday Trans.
(17) Kalman, B.;Clarke, N.; Johansson, L. B.-A. J . Phys. Chem. 1989, 93, 4608. (18) Minsky, A.; Meyer, Y . ;Rabinovitz, M. J . Am. Chem. Soc. 1982, 104, 2475.
I 1985, 81, 1373. (20) (21) (22) (23)
Melhuish, W. H. J . Phys. Chem. 1960, 64, 762. Demas, J. N.; Crosby, G. A. J . Phys. Chem. 1961, 65, 229. Dawson, W. R.; Winsor, M . W. J . Phys. Chem. 1968, 72, 3251. Kubin, R. F.; Fletcher, A. N. J . Lumin. 1982, 27, 455.
The Journal of Physical Chemistry, Vol. 93, No. 26, 1989 8373
Electronic Energy Transfer in TBPe in Vesicles TBPe in vesicles. From t(s) and the modified Strickler-Berg equation24
,.
J F(s) d3
1
- = 2.88 x 10-9n2 TO
SF(s)s-’ d s
2
St(i~)a-’dij
=
a radiative lifetime r 0 of 5.5 f 0.2 ns is obtained. Since the fluorescence lifetime is known from the time-resolved decay and equal to 4.8 ns, a quantum yield of 0.88 f 0.07 is obtained from T = 9.~~. This value is in good agreement with that determined independently and given above. The Forster radius as defined by KawskiI3 reads 9000(ln 1o)(K2)@h ROF
=
ed-state processes are independent of its orientational dynamics (see, for example, ref 16 and papers cited therein). Within this assumption, one obtains
128aSn4NA
75
m=-2
(@t%[QML.(o)]
@i*[QMrL,(t)l)
which is the orientational correlation function written on the basis of second-rank irreducible Wigner rotational matrices.25 The orientation of the molecules at the time of excitation and at a time t later is described by the Eulerian angles Q(0) and Q ( t ) . The subscripts indicate that the transformation is from a molecule-fmed (M, M’) to a laboratory-fixed (L) frame. The intial anisotropy r(0) = 2/S, if the absorption transition dipole moment is parallel with the emission transition dipole. For fluorophores in a liquid solvent, r(t) decays to zero with time since the equilibrium orientation is random. In general, this is however not the situation for fluorophores residing in an anisotropic system such as vesicles. It can be shown16that for such a system the equilibrium anisotropy r(t,) = &S2
N A and n denote the Avogadro constant and the refractive index of the medium. ( K ~ is ) a mean value of the orientational part of a dipole-dipole interaction. In order to calculate an explicit value on the Forster radius, it is convenient to choose ( K ~ = ) 2/3 as a reference state. This mean value is relevant for an interaction between rapidly and isotropically rotating dipoles, which is often referred to as the dynamic limit or the fast case. We denote this Forster radius by Ro and obtain Ro = 33.4 f 1 A for TBPe solubilized in a lipid bilayer of DOPC at 243 K. We have used n = 1.52, which was determined at 439 nm for a lamellar phase of DOPC and the glycerol-water mixture. 111. Basic Theory Linear Dichroism. Some lyotropic lamellar liquid crystals align spontaneously between quartz slides and form macroscopically uniaxial systems with the optic axis being perpendicular to the bilayers. The orientational distribution of chromphoric molecules solubilized in such systems is uniaxially anisotropic. If linearly polarized light propagates at an angle of tilt to the optic axis, its absorption will depend on the direction of the polarization plane. The difference, in absorption of light polarized in and out of the plane of the bilayer defines the linear dichroism, LD. LD yields information about the average orientation of the transition dipole moment of a particular chromophore in terms of an order parameter, S:I9
S=
Lr
1/2(3 cos2 /3 - l)f(/3) sin /3 d/3
(1)
Here, /3 is the angle between the transition dipole moment and the normal to the lipid bilayer andf(0) is the normalized orientational distribution function. The order parameter is a number between -1/2 and 1 where the limits correspond to a perfect orientation perpendicular and parallel to the normal of the bilayer, respectively. In particular, for an isotropic orientational distribution, S = 0. Fluorescence Anisotropy. The properties of the distribution of electronically excited molecules in a macroscopically isotropic system are described conveniently by the time-resolved fluorescence anisotropy
(24) Birks, J. B. Phorophysics of Aromatic Molecules; Wiley-Interscience: London, 1970.
(4)
provided that the transition dipoles are parallel and that the ground- and excited-state orientational distributions are the same. For pure rotational motion of a fluorophore in a solvent the explicit time dependence of the anisotropy can be described very well theoretically. r(t) for a fluorophore rotating in an anisotropic system is much more complicated, and models have been developed for highly symmetric molecules.16 In the presence of energy transfer, the evaluation of eq 3 involves taking into account all possible patterns of interaction between the fluorophores, which is a formidable problem, even in the absence of rotational motion. Two approaches are the Baumann-Fayer model and the Monte Carlo simulations presented below. Baumann-Fayer Model. Baumann and Fayer describe incoherent energy transfer on the basis of an interaction between two molecules, an excited donor and an unexcited donor.6 This approach of pairwise interactions was originally proposed by Huber et al.’ The BF model is developed for the transfer among isotropically oriented molecules randomly distributed in a one-, two-, and three-dimensional space for the slow and the fast cases, but the model also treats the transfer in a two-dimensional system, where the transition dipoles are oriented in a plane. The slow case and transfer among isotropically oriented donors in two dimensions is used as a model in the analysis of the fluorescence anisotropy of TBFe in vesicles. From the BF model, one obtains f f ( t ) ,which is the probability that the excitation is on the initially excited donor, according to Gs(t) = exp[-O).7223C(t / T ) (5) Equation 5 is relevant for a uniform excitation probability of the donors. This is the case of energy transfer in planes that are randomly oriented. The reduced concentration of the donors is defined according to C = paRo2 (6) which corresponds to an average number of donors within an area of one Forster radius, R,,. p is the number density of donors. The observed emission consists of two contributions: the first one originating from the ensemble of initially excited molecules and the second from those molecules to which the energy has been transferred. In the so-called Galanin a p p r o x i m a t i ~ n , ~con~~~’ tributions from the latter distribution are neglected. The fluorescence anisotropy then becomes r(t) = YSGs(t)
Fzz(t) ,and FyZ(t) denote the fluorescence emission when the excitation and the emission polarizers are set mutually parallel (22) and perpendicular (YZ).It can be shown that r(t) depends only on the orientational dynamics of the molecule if the excit-
(3)
(7)
Hence, the BF model predicts a t 1 I 3 time dependence of the anisotropy decay. Contrary to the Monte Carlo simulations discussed below, the BF model yields no information about the (25) Brink, D. M.; Satchler, G. R. Angular Momentum; Oxford University Press: Oxford, 1968. (26) Galanin, M. D. T r . Fiz. Ins?. Akad. Nauk. USSR 1950, 5, 341. (27) Jablonski, A. Acta Phys. Pol. 1970, ,438, 453.
8374
The Journal of Physical Chemistry, Vol. 93, No. 26, 1989
spatial displacement of the excitation from its initial position. Monte Carlo Simulations. In a previous paper? we have shown how Monte Carlo (MC) simulations may be used to study electronic energy transfer in isotropic three-dimensional donor systems. The simulations were undertaken in order to test the validity of existing analytical theories like the so-called GAF theory3 and the two-particle model of Huber et al.738 It was found that the agreement between the simulations and the GAF theory was excellent for the fast-rotating case. For the slow-rotating case, the agreement was also good but only if an approximate term was included in the GAF treatment. The Galanin approximation, Le., eq 7, was shown to be valid in comparison with the simulation data. In this work, the MC algorithm was extended to treat twodimensional systems. An advantage with computer simulations is that the model can be made very complex, regarding the interaction between both the particles and their spatial and orientational distributions. We have performed the simulations with up to 50 donors in the system. For the decay of the excitation probability of the initially excited donor as well as for the anisotropy, this number of donors is more than enough, but in order to describe the excitation transport properly, we have introduced an approximation that takes into account the donors (actually treating them as acceptors) out to infinity. The transfer rate caused by the medium outside the so-called cutoff radius may be written as
+
*>,:(.
w,o = Az 1
10
7- 1
where i is the donor on which the excitation resides, 0 denotes a jump out from the cutoff sphere (circle, line), A is the dimensionality of the system ( A = 2, in this case), R, is the cutoff radius (Le., within a radius R, from donor i, all other donors are treated explicitly in the simulation), and 7 is the emission lifetime (in the absence of energy transfer). Equation 8 is valid only if Ro/R,
