Measurements of fluorescence lifetimes by use of a hybrid time-correlated and multifrequency phase fluorometer

Measurements of homogeneous and heterogeneous fluorescence intensity decays using a hybrid time-correlated single photon counting/multifrequency phase fluorometer are reported. A trio of fluorophores exhibiting a range of decay profiles was selected. p-Terphenyl, 1,4-bis[2-(4-methyl-5-phenyloxazolyl)]benzene [(Me)2POPOP], and p-bis[2-(5-phenyloxazolyl)]benzene (POPOP), commonly used reference fluorophores, were analyzed initially; their emissions were characterized by monoexponential decay functions. Additionally, emissions from two single tryptophan proteins with different decay profiles were measured. Scorpion neurotoxin variant 3 required three exponentials to fit the emission decay properly (average lifetime approximately 500 ps). At pH 5.5, the fluorescence emission of ribonuclease T1 showed a monoexponential decay with a measured lifetime of approximately 4.0 ns. Thus, in each case, the results from both measurements were consistent between the two detection systems, confirming the view that the two approaches for measuring fluorescence lifetimes are equivalent.     

Analysis of multi-component fluorescence emission by phase-sensitive detection using one modulation frequency

We describe the use of phase-sensitive detection of fluorescence to resolve the lifetimes and fractional intensities from multi-component fluorescence samples, using data obtained at a single modulation frequency. Phase-sensitive spectra of the mixture are recorded at arbitrarily chosen detector phase angles. The steady-state spectrum of each component must be known. The phase-sensitive spectra are fitted, using a nonlinear least-squares algorithm, to obtain the lifetimes and fractional intensities of each fluorophore in the mixture. Simulations for two- and three-component mixtures are presented to illustrate how the resolution is affected by spectral overlap and lifetime separation. Experimentally, we resolved two- and three-component mixtures of protein-like fluorophores (N-acetyl-L-tyrosinamide, N-acetyl- L-tryptophanamide, indole and 2,3-dimethylindole) using data collected at 30 MHz. These fluorophores have closely spaced lifetimes of 1.5, 2.9, 4.5 and 4.3 ns, respectively, and display extensive spectral overlap. These results demonstrate that phase-sensitive spectra, recorded at only one modulation frequency with a standard phase fluorometer, can be used to resolve multi-component emissions.     

The use of isochronal reference standards in phase and modulation fluorescence lifetime measurements

Errors in phase and modulation lifetime measurements observed with the only commercially available instrument are readily apparent when the Debye-Sears modulation tank is not perfectly tuned. Unfortunately, we have found that exact tuning was extremely difficult to achieve and maintain. We report that these errors could be reduced by using single-lifetime (homogeneous) reference standards whose fluorescence lifetime approximated that of the unknown sample (isochronal standards). A number of useful standards are suggested. In the proposed method, the phase shift and relative modulation of the sample emission are measured using the isochronal standard as a reference to determine the effective characteristics of the sinusoidal excitation. The importance of the improvement in accuracy accomplished by the proposed methods is illustrated by the accurate resolution of fluorescence lifetime heterogeneity for two known heterogeneous samples.     

Fluorescence lifetime imaging.

We describe a new fluorescence imaging methodology in which the image contrast is derived from the fluorescence lifetime at each point in a two-dimensional image and not the local concentration and/or intensity of the fluorophore. In the present apparatus, lifetime images are created from a series of images obtained with a gain-modulated image intensifier. The frequency of gain modulation is at the light-modulation frequency (or a harmonic thereof), resulting in homodyne phase-sensitive images. These stationary phase-sensitive images are collected using a slow-scan CCD camera. A series of such images, obtained with various phase shifts of the gain-modulation signal, is used to determine the phase angle and/or modulation of the emission at each pixel, which is in essence the phase or modulation lifetime image. An advantage of this method is that pixel-to-pixel scanning is not required to obtain the images, as the information from all pixels is obtained at the same time. The method has been experimentally verified by creating lifetime images of standard fluorophores with known lifetimes, ranging from 1 to 10 ns. As an example of biochemical imaging we created life-time images of Yt-base when quenched by acrylamide, as a model for a fluorophore in distinct environments that affect its decay time. Additionally, we describe a faster imaging procedure that allows images in which a specific decay time is suppressed to be calculated, allowing rapid visualization of unique features and/or regions with distinct decay times. The concepts and methodologies of fluorescence lifetime imaging (FLIM) have numerous potential applications in the biosciences. Fluorescence lifetimes are known to be sensitive to numerous chemical and physical factors such as pH, oxygen, temperature, cations, polarity, and binding to macromolecules. Hence the FLIM method allows chemical or physical imaging of macroscopic and microscopic samples.     

Fluorescence lifetime imaging: multi-point calibration, minimum resolvable differences, and artifact suppression

BACKGROUND: Frequency-domain fluorescence lifetime imaging microscopy (FLIM) is finding increasing use in the analysis of biological systems. However, the calibration, determination of resolvable lifetime differences, and evaluation of artifacts have not been extensively treated. We describe a multi-point method for calibrating a frequency-domain FLIM system, characterize the minimum detectable heterogeneity and intra- and inter-image lifetime differences, discuss the statistical treatment of FLIM data, and suggest methods for minimizing artifacts. METHODS: A set of solutions exhibiting single-component lifetimes suffice for accurately calibrating a reference material with a single-component lifetime, even in the absence of accurate data on the lifetimes of the individual solutions or the reference material. We used a set of rhodamine 6G solutions quenched with varying concentrations of iodide, leading to lifetimes of 0.5--4.0 ns, to calibrate a 1 microM reference solution of rhodamine 6G in water. RESULTS: We measured a value of 4.11 ns with an estimated absolute error of +/-0.05 ns for the rhodamine 6G reference solution. With 57.7 MHz modulation, the minimum detectable inter-image lifetime difference was 0.1--0.15 ns and the minimum detectable intra-image lifetime difference was 4--5 ps, allowing solutions differing in lifetime by 40 and 70 ps to be easily distinguished. The minimum detectable lifetime heterogeneity was 50--80 ps. Evaluation of replicate measurements of single solutions demonstrated that inter-image instrument errors exceeded those predicted from intra-image statistics by more than an order of magnitude. We also measured lifetimes and heterogeneity in 4 GFP variants (WTGFP, EGFP, S65T, and EYFP) with the technique. CONCLUSION: The multi-point calibration method is applicable to any system consisting of single-component lifetimes. Applying the method in our FLIM microscope allowed us to demonstrate a previously unreported degree of lifetime resolution in a FLIM microscope. Cytometry 43:248-260;2001.     

Resolution of mixtures of fluorophores using variable-frequency phase and modulation data

We measured fluorescence phase shift and modulation data for one-, two- and, three-component mixtures of fluorophores at modulation frequencies ranging from 1 to 140 MHz. These data were analyzed using the least-squares procedure described in the preceding paper (Lakowicz, J. R., G. Laczko, M. Cherek, E. Gratton, and M. Limkeman, 1984, Biophys. J., 46:463-477). Using data obtained at a single emission bandpass, the lifetimes and preexponential factors of two-component mixtures could be easily resolved if the lifetimes differed by a factor of 2. With currently available instrumental stability, three-component mixtures could be resolved when the overall range of decay times was 10-fold, (e.g., 1.3, 4.4, and 12 ns). Measurement of phase and modulation data at several emission wavelengths, where the ratio of the preexponential factors varied, enhanced our ability to resolve closely spaced two and three-component decays. Two-component mixtures could then be resolved if the lifetimes differed by 30% (4.4 and 6.2 ns). Also, the multiple-wavelength data allowed the lifetimes and emission spectra of the three-components of a mixture to be resolved. These results demonstrated that resolution of multiexponential decay laws was possible using frequency-domain phase-modulation fluorometry.     

Resolution of multiple fluorescence lifetimes in heterogeneous systems by phase-modulation fluorometry

Procedures are described for the treatment of phase and modulation lifetime data in fluorescent systems having multiexponential decay. All computer procedures (called FIT programs) arise from the lifetime resolution theory for phase-modulation measurements (Weber, G (1981) J. Phys. Chem. 85, 949–953). The programs most successful in resolving heterogeneous lifetimes use a Monte Carlo approach in which phase and modulation lifetime data at three modulation frequencies are simultaneously utilized. These programs are shown to have more utility than the final closed form procedure presented by Weber (1981). The FIT routines are simple and require little computer time while yielding excellent results. To illustrate the applicability of these programs, defined binary (carbazole and pyrene) and ternary systems (carbazole, pyrene and POPOD) were examined. In most cases, the resolved lifetimes were within 5% of the independently measured value and the fractional fluorescence contributions were within 10% of that expected. These results demonstrate that phase-modulation measurements analyzed by appropriate computer programs are capable of solving for lifetimes in both binary and, in selected cases, ternary systems. An example is given from the recent literature (Dalbey, R., Weiel, J. and Yount, R.G. (1983) Biochemistry 22, 4696–4706) in which the above programs allowed the resolution of both binary and ternary lifetimes of a dansyl label on myosin, where Förster energy transfer was occuring. These lifetimes] were used to quantify changes in distances between two activity-related thiols on myosin upon the addition of Mg-ATP or its analogs.     

Fluorescence lifetime spectroscopy in multiply scattering media with dyes exhibiting multiexponential decay kinetics

To investigate fluorescence lifetime spectroscopy in tissue-like scattering, measurements of phase modulation as a function of modulation frequency were made using two fluorescent dyes exhibiting single exponential decay kinetics in a 2% intralipid solution. To experimentally simulate fluorescence multiexponential decay kinetics, we varied the concentration ratios of the two dyes, 3,3-diethylthiatricarbocyanine iodide and indocynanine green (ICG), which exhibit distinctly different lifetimes of 1.33 and 0.57 ns, respectively. The experimental results were then compared with values predicted using the optical diffusion equation incorporating 1) biexponential decay, 2) average of the biexponential decay, as well as 3) stretched exponential decay kinetic models to describe kinetics owing to independent and quenched relaxation of the two dyes. Our results show that while all kinetic models could describe phase-modulation data in nonscattering solution, when incorporated into the diffusion equation, the kinetic parameters failed to likewise predict phase-modulation data in scattering solutions. We attribute the results to the insensitivity of phase-modulation measurements in nonscattering solutions and the inaccuracy of the derived kinetic parameters. Our results suggest the high sensitivity of phase-modulation measurements in scattering solutions may provide greater opportunities for fluorescence lifetime spectroscopy.     

Analysis of excited-state processes by phase-modulation fluorescence spectroscopy

Fluorescence phase shift and demodulation methods were used in the analysis of excited-state reactions and to investigate solvent relaxation around fluorophores in viscous solvents. The chosen samples illustrate the results expected for fluorophores bound to biological macromolecules. These moderately simple samples served to test the theoretical predictions described in the preceding paper (J.R. Lakowicz and A.B. Balter, Biophys. Chem. 16 (1982) 99.) and to illustrate the characteristic features of phase-modulation data expected from samples which display time-dependent spectral shifts. The excited-stale protonation of acridine and exciplex formation between anthracene and diethylaniline provided examples of one-step reactions in which the lifetimes of the initially excited and the reacted species were independent of emission wavelength. Using these samples we demonstrated the following: (I) Wavelength-dependent phase shift and demodulation values can be used to prove the occurrence of an excited-state process. Proof is obtained by observation of phase angles (φ) larger than 90° or by measurement of ratios of m/cos φ > 1, where m is the modulation of the emission relative to that of the excitation. (2) For a two-state process the individual emission spectra of each state can be calculated from the wavelength-dependent phase and modulation data. (3) The phase difference or demodulation factor between the initially excited and the reacted states reveals directly the fluorescence lifetime of the product of the reaction. (4) Phase-sensitive detection of fluorescence can be used to prove that the lifetimes of both the initially excited and the reacted states are independent of emission wavelength. (5) If steady-state spectra of the individual species are known, then phase-sensitive emission spectra can be used to measure the lifetimes of the individual components irrespective of the extent of spectral overtap. (6) Spectral regions of constant lifetime can be identified by the ratios of phase-sensitive emission spectra. In addition, we examined 6-propionyl-2-dimethylaminonaphthalene(PRODAN) and N-acetyl-l-tryptophanamide (NATA) in viscous solvents where the solvent relaxation times were comparable to the fluorescence lifetimes. Using PRODAN in n-butanol we used m/cos φ measurements, relative to the blue edge of the emission, to demonstrate that solvent relaxation requires more than a single step. For NATA in propylene glycol we used phase-sensitive detection of fluorescence to directly record the emission spectra of the initially excited and the solvent relaxed states. These measurements can be easily extended to fluorophores which are bound to proteins and membranes and are likely to be useful in studies of the dynamic properties of biopolymers.     

Texture analysis of fluorescence lifetime images of nuclear DNA with effect of fluorescence resonance energy transfer

BACKGROUND: Fluorescence lifetime imaging microscopy (FLIM) is becoming an important tool in cellular imaging. In FLIM, the image contrast is concentration insensitive, whereas it is sensitive to the local environment and interactions of fluorophores such as fluorescence resonance energy transfer (RET). METHODS: Fluorescence microscopy, lifetime imaging, and texture analysis were used to study the spatial distribution of fluorophores bound to nuclear DNA. 3T3-Swiss albino mice fibroblast nuclei were labeled with Hoechst 33258 (Ho), an AT-specific dye, and 7-aminoactinomycin D (7-AAD), a GC-specific dye. Ho is a RET donor to the 7-AAD acceptor. RESULTS: Texture analysis of 50 alcohol-fixed nuclei quantitatively showed changes of spatial distribution of apparent donor lifetimes. RET increased the spatial heterogeneity in the phase and modulation lifetime images. In most of the doubly stained cells (about 80%), the phase and modulation lifetime distributions were spatially homogeneous. In about 20% of the cells, we noticed that lower phase and modulation lifetimes caused by RET were correlated with regions of high Ho intensity in the nuclei. CONCLUSIONS: The spatial lifetime heterogeneity of Ho in presence of 7-AAD seems to be caused by RET between closely spaced strands in the three dimensionally condensed regions of DNA.     

Fluorescence lifetime imaging of calcium using Quin-2.

We describe the use of a new imaging technology, fluorescence lifetime imaging (FLIM), for the imaging of the calcium concentrations based on the fluorescence lifetime of a calcium indicator. The fluorescence lifetime of Quin-2 is shown to be highly sensitive to [Ca2+]. We create two-dimensional lifetime images using the phase shift and modulation of the Quin-2 in response to intensity-modulated light. The two-dimensional phase and modulation values are obtained using a gain-modulated image intensifier and a slow-scan CCD camera. The lifetime values in the 2D image were verified using standard frequency-domain measurements. Importantly, the FLIM method does not require the probe to display shifts in the excitation or emission spectra, which may allow Ca2+ imaging using other Ca2+ probes not in current widespread use due to the lack of spectral shifts. Fluorescence lifetime imaging can be superior to stationary (steady-state) imaging because lifetimes are independent of the local probe concentration and/or intensity, and should thus be widely applicable to chemical imaging using fluorescence microscopy.     

Development and characterization of green fluorescent protein mutants with altered lifetimes

Multiple-probe fluorescence imaging applications demand an ever-increasing number of resolvable probes, and the use of fluorophores with resolvable fluorescence lifetimes can help meet this demand. Green fluorescent protein (GFP) and its variants have been widely used in spectrally resolved multiprobe imaging, but as yet, there has not been a systematic set of mutants generated with resolvable lifetimes. Therefore, to generate such mutants, we have utilized error-prone PCR and fluorescence lifetime imaging to screen for mutants of UV-excited green fluorescent protein (GFPuv) that exhibit altered fluorescence decay lifetimes. This has resulted in the isolation of GFPuv mutants displaying at least three distinctly different lifetimes in the range of 1.9-2.8 ns. Mutation of Y145 to either histidine or cysteine was found to shift the fluorescence lifetime of GFPuv from 3.03 +/- 0.03 to 2.78 +/- 0.05 ns for the Y145H mutant and to 2.74 +/- 0.05 ns for Y145C. Some of the shorter-lifetime mutants exhibited excitation peaks that were red-shifted relative to their maximal absorption, indicating that the mutations allowed the adoption of additional conformations relative to wtGFPuv. The utility of these mutants for applications in simultaneous imaging and quantification is shown by the ability to quantify the composition of binary mixtures in time-resolved images using a single detector channel. The application of the screening method for generating lifetime mutants of other fluorescent proteins is also discussed.     

In vivo resolution of multiexponential decays of multiple near-infrared molecular probes by fluorescence lifetime-gated whole-body time-resolved diffuse optical imaging

The biodistribution of two near-infrared fluorescent agents was assessed in vivo by time-resolved diffuse optical imaging. Bacteriochlorophyll a (BC) and cypate-glysine-arginine-aspartic acid-serine-proline-lysine-OH (Cyp-GRD) were administered separately or combined to mice with subcutaneous xenografts of human breast adenocarcinoma and slow-release estradiol pellets for improved tumor growth. The same excitation (780 nm) and emission (830 nm) wavelengths were used to image the distinct fluorescence lifetime distribution of the fluorescent molecular probes in the mouse cancer model. Fluorescence intensity and lifetime maps were reconstructed after raster-scanning whole-body regions of interest by time-correlated single-photon counting. Each captured temporal point-spread function (TPSF) was deconvolved using both a single and a multiexponental decay model to best determine the measured fluorescence lifetimes. The relative signal from each fluorophore was estimated for any region of interest included in the scanned area. Deconvolution of the individual TPSFs from whole-body fluorescence intensity scans provided corresponding lifetime images for comparing individual component biodistribution. In vivo fluorescence lifetimes were determined to be 0.8 ns (Cyp-GRD) and 2 ns (BC). This study demonstrates that the relative biodistribution of individual fluorophores with similar spectral characteristics can be compartmentalized by using the time-domain fluorescence lifetime gating method.     

Deconvolution of single photon counting data with a reference method and global analysis

A method based on quenched references and global analysis was used to deconvolute timeresolved single photon counting data. The results from both computer simulated data and real experiments showed that highly accurate and reliable deconvolutions were possible. Fluorescence lifetimes and Stern-Volmer quenching constants for quenching with NaI were determined for the reference substances para-terphenyl, PPO (2,5-diphenyloxazol), POPOP (1,4-bis-(5-phenyl-2-oxazolyl)-benzene), and dimethyl-POPOP, all in ethanol. The fluorescence from a mixture of POPOP, anthracene, and diphenylanthracene in ethanol at different wavelengths was successfully resolved into the known relative contributions from the species at each wavelength. Fluorescence intensity decays of tryptophan in solution were studied at different wavelengths and globally analyzed with the method. Also, fluorescence anisotropy described by isotropic and anisotropic rotations in homogeneous and heterogeneous emitting systems were simulated and successfully deconvoluted. The method was applied to real fluorescence anisotropy data of diphenylanthracene and POPOP in paraffin oil, as well as to data from experiments on the blue copper-containing protein stellacyanin and its apo-form. In these cases, the method both corrected for errors due to, for example, the wavelength-dependent transit-times in the photomultiplier, and realized global deconvolutions of the total, parallel, and perpendicular components of the fluorescence. General algorithms for arbitrary fluorescence impulse responses are given.A preliminary account of this work was presented at the NATO ASI in Acireale, Italy (Löfroth 1985a, in press)     

Tryptophan fluorescence lifetimes in lysozyme.

Tryptophan fluorescence lifetimes at pH 2 and pH 8 have been obtained for lysozyme and for lysozyme derivatives in which tryptophan-62 or tryptophan-108 or both are nonfluorescent. The lifetimes range from about 0.5 ns to 2.8 ns for the various emitting tryptophans. The tryptophan lifetimes appear to increase with exposure of tryptophan to solvent, but intramolecular contacts, probably with cystine residues, can considerably shorten the lifetime. Intertryptophanyl interactions can also affect fluorescence lifetimes. The trytophan-108 lifetime in lysozyme is shorter than in the derivative in which tryptophan-62 is oxidized; this is ascribed to energy transfer from tryptophan-108 to tryptophan-62. From the lifetime results the relative intensities emitted by specific tryptophans can be estimated, and these values also support the existence of intertryptophanyl energy transfer. The emission intensity from tryptophan-62 is greater in the presence of tryptophan-108, and the emission intensity of tryptophan-108 appears to be greater in the absence of tryptophan-62. Conformational effects accompanying chemical modification of tryptophan cannot be completely ruled out, however. The tryptophan-62 lifetime at pH 8 in lysozyme is shorter than in the derivatives, which might indicate a subtle conformational effect. Studies with tri-(N-acetyl-glucosamine)-protein complexes indicate that both the tryptophan lifetimes and the number of emitting tryptophans may be changing upon complexation. The results illustrate the usefulness and the limitations of lifetime measurements in understanding protein fluorescence.     

Spectral characteristics of fluorophores formed via interaction between all-trans-retinal with rhodopsin and lipids in photoreceptor membrane of retina rod outer segments

It is shown that all-trans-retinal under model conditions of its excessive accumulation in photoreceptor membranes interacts with amino groups of rhodopsin and lipids, forming at least three distinct fluorophores with fluorescence quantum yield 20–40 times higher than that of free all-trans-retinal. These retinal derivatives are likely precursors of photo- and cytotoxic fluorophores of lipofuscin and in particular of A2E. Spectral characteristics of fluorophores have been described. Picosecond time-resolved laser fluorescence spectroscopy was used to study kinetics of fluorescence decay of both free and bound all-trans-retinal; fluorophores were determined and their lifetimes have been measured. Based on calculations it is shown that the decay kinetics of all-trans-retinal derivatives consists of three components with lifetimes equal to 48, 208, and 900 ps; kinetics of free all-trans-retinal is monoexponential with lifetime of 31 ps. The chemical nature of fluorophores with the lifetimes obtained is discussed.     

Tryptophanyl fluorescence lifetime distribution of hyperthermophilic beta-glycosidase from molecular dynamics simulation: a comparison with the experimental data

A molecular dynamics simulation approach has been utilized to understand the unusual fluorescence emission decay observed for beta-glycosidase from the hyperthermophilic bacterium Solfolobus sulfotaricus (Sbeta gly), a tetrameric enzyme containing 17 tryptophanyl residues for each subunit. The tryptophanyl emission decay of Sbeta gly results from a bimodal distribution of fluorescence lifetimes with a short-lived component centered at 2.5 ns and a long-lived one at 7.4 ns (Bismuto E, Nucci R, Rossi M, Irace G, 1999, Proteins 27:71-79). From the examination of the trajectories of the side chains capable of causing intramolecular quenching for each tryptophan microenvironment and using a modified Stern-Volmer model for the emission quenching processes, we calculated the fluorescence lifetime for each tryptophanyl residue of Sbeta gly at two different temperatures, i.e., 300 and 365 K. The highest temperature was chosen because in this condition Sbeta gly evidences a maximum in its catalytic activity and is stable for a very long time. The calculated lifetime distributions overlap those experimentally determined. Moreover, the majority of trytptophanyl residues having longer lifetimes correspond to those originally identified by inspection of the crystallographic structure. The tryptophanyl lifetimes appear to be a complex function of several variables, such as microenvironment viscosity, solvent accessibility, the chemical structure of quencher side chains, and side-chain dynamics. The lifetime calculation by MD simulation can be used to validate a predicted structure by comparing the theoretical data with the experimental fluorescence decay results.     

Determination of the excited-state lifetimes of the tryptophan residues in barnase, via multifrequency phase fluorometry of tryptophan mutants.

A multifrequency phase fluorometric study is described for wild-type barnase and engineered mutant proteins in which tryptophan residues have been replaced by less fluorescent residues which do not interfere with the determination of the tryptophan emission spectra and lifetimes. The lifetimes of the three tryptophans in the wild-type protein have been resolved. Trp-35 has a single fluorescence lifetime, which varies in the different proteins between 4.3 and 4.8 ns and is pH-independent between pH 5.8 and 8.9. Trp-71 and Trp-94 behave as an energy-transfer couple with both forward and reverse energy transfer. The couple shows two fluorescence lifetimes: 2.42 (+/-0.2) and 0.74 (+/-0.1) ns at pH 8.9, and 0.89 (+/-0.05) and 0.65 (+/-0.05) ns at pH 5.8. In the mutant Trp-94----Phe the lifetime of Trp-71 is 4.73 (+/-0.008) ns at high pH and 4.70 (+/-0.004) ns at low pH. In the mutant Trp-71----Tyr, the lifetime of Trp-94 is 1.57 (+/-0.01) ns at high pH and 0.82 (+/-0.025) ns at low pH. From these lifetimes, one-way energy-transfer efficiencies can be calculated according to Porter [Porter, G.B. (1972) Theor. Chim. Acta 24, 265-270]. At pH 8.9, a 71% efficiency was found for forward transfer (from Trp-71 to Trp-94) and 36% for reverse transfer. At pH 5.8 the transfer efficiency was 86% for forward and 4% for reverse transfer (all +/-2%). These transfer efficiencies correspond fairly well with the ones calculated according to the theory of F?rster [F?rster, T. (1948) Ann. Phys. (Leipzig) 2, 55-75].(ABSTRACT TRUNCATED AT 250 WORDS)