Review of fluorescence anisotropy decay analysis by frequency-domain fluorescence spectroscopy

This didactic paper summarizes the mathematical expressions needed for analysis of fluorescence anisotropy decays from polarized frequency-domain fluorescence data. The observed values are the phase angle difference between the polarized components of the emission and the modulated anisotropy, which is the ratio of the polarized and amplitude-modulated components of the emission. This procedure requires a separate measurement of the intensity decay of the total emission. The expressions are suitable for any number of exponential components in both the intensity decay and the anisotropy decay. The formalism is generalized for global analysis of anisotropy decays measured at different excitation wavelengths and for different intensity decay times as the result of quenching. Additionally, we describe the expressions required for associated anisotropy decays, that is, anisotropy decays where each correlation time is associated with a decay time present in the anisotropy decay. And finally, we present expressions appropriate for distributions of correlation times. This article should serve as a reference for researchers using frequency-domain fluorometry.

Anisotropy decays of indole, melittin monomer and melittin tetramer by frequency-domain fluorometry and multi-wavelength global analysis

We used frequency-domain fluorescence spectroscopy to measure the fluorescence lifetime and anisotropy decays of indole in propylene glycol, and of the tryptophan emission of melittin monomer and tetramer in water solutions at 5 degrees C. We obtained an increase in resolution of the anisotropy decays by using multiple excitation wavelengths, chosen to provide a range of fundamental anisotropy values. The multi-excitation wavelength anisotropy decays were analyzed globally to recover a single set of correlation times with wavelength-dependent anisotropy amplitudes. Simulated data and kappaR2 surfaces are shown to reveal the effect of multi-wavelength data on the resolution of complex anisotropy decays. For both indole and melittin, the anisotropy decays are heterogeneous and require two correlation times to fit the frequency-domain data. For indole in propylene glycol at 5 degrees C we recovered correlation times of 0.59 and 4.10 ns, which appear to be characteristic of the rigid and asymmetric indole molecule. For melittin monomer the correlation times were 0.13 and 1.75 ns, and for melittin tetramer 0.12 and 3.96 ns. The shorter and longer correlation times of melittin are due to segmental motions and overall rotational diffusion of the polypeptide.

Anisotropy decays of single tryptophan proteins measured by GHz frequency-domain fluorometry with collisional quenching

We used harmonic-content frequency-domain fluorometry to determine the anisotropy decays of a variety of single tryptophan peptides and proteins. Resolution of the rapid and complex anisotropy decays was enhanced by global analysis of the data measured in the presence of quenching by either oxygen or acrylamide. For each protein, and for each quencher, data were obtained at four to six quencher concentrations, and the data analyzed globally to recover the anisotropy decay. The decrease in decay times produced by quenching allows measurements to an upper frequency limit of 2 GHz. The chosen proteins provided a range of exposures of the tryptophan residues to the aqueous phase, these being ACTH, monellin, Staphylococcus nuclease and ribonuclease T1, in order of decreasing exposure. Examination of indole and several small peptides demonstrates the resolution limitations of the measurements; a correlation time of 12 ps was measured for indole in methanol at 40 degrees C. Comparison of the anisotropy decays of gly-trp-gly with leu-trp-leu revealed stearic effects of the larger leucine side chains on the indole ring. The anisotropy decay of gly-trp-gly revealed a 40 ps component for the indole side chain, which was resolved from the overall 150 ps correlation time of the tripeptide. Only the longer correlation time was observed for leu-trp-leu. With the exception of ribonuclease T1, each of the proteins displayed a subnanosecond component in the anisotropy decay which we assign to independent motions of the tryptophan residues. For example, Staphylococcus nuclease and monellin displayed segmental tryptophan motions with correlation times of 80 and 275 ps, respectively. The amplitudes of the rapid components increased with increasing exposure to the aqueous phase. These highly resolved anisotropy decays for proteins of known structure are suitable for comparison with molecular dynamic simulations.

Detection of three rotational correlation times for a rigid asymmetric molecule using frequency-domain fluorometry

We measured the frequency response of the polarized emission of Yt-base in propylene glycol at 10 degrees C. Data were obtained for excitation wavelengths of 290, 312 and 346 nm, for which the fundamental anisotropies are 0.05, 0.19 and 0.32, respectively. Additionally, data were obtained using CCl4, to decrease the mean decay time from 9.1 to 4.2 ns. These nine sets of data were analyzed globally to recover the anisotropy decay law. Three correlation times were needed to fit the data, 0.8, 3.0 and 5.6 ns, a range of only 7-fold. We believe this is the first reported detection of three correlation times for a rigid molecule.

Analysis of fluorescence decay kinetics measured in the frequency domain using distributions of decay times

We describe the theoretical and practical aspects of analyzing complex fluorescence decay kinetics using continuous distributions of decay times. Our analysis uses frequency-domain data, provides for global analysis of multiple data sets and includes the possibility of excited-state processes. Simulated data were used to estimate the types of distributions which can be reasonably recovered from the measurements. Additionally, we describe a variety of distributions recovered from experimental data. For mixtures of one, two or three exponentially decaying fluorophores we recovered narrow lifetime distributions, which are essentially identical to a multiexponential decay. Similarly, a two-state excited-state reaction also yielded a narrow distribution with negative preexponential factors. The presence of time-dependent spectral relaxation of labeled lipids results in a wide distribution of decay times, which becomes narrower for faster relaxation rates at higher temperatures. Hence, the decay-time distributions appear to be sensitive to the dynamics of the environment surrounding the fluorophore. Additionally, distributions of decay times were observed to result from transient effects in collisional quenching, from energy transfer in the presence of a range of donor-to-acceptor distances, and for several single-tryptophan proteins.

Demonstration of an associated anisotropy decay by frequency-domain fluorometry

We used frequency-domain fluorometry to demonstrate the presence of an associated decay of fluorescence anisotropy. In such systems the individual correlation times are associated with distinct emitting species, each with its own characteristic lifetime and rotational correlation times. We obtained an associated system using 1-anilino-8-naphthalenesulfonic acid (ANS) in the presence of increasing amounts of apomyoglobin. When both free and apomyoglobin-bound ANS contributed to the emission the differential polarized phase angles become negative at particular frequencies, even though the fundamental anisotropy (r0) is greater than zero. Additionally, the modulated anisotropy decreases at high frequencies. Both observations appear to be the unique consequence of an associated anisotropy decay, and are not possible for a multiexponential anisotropy decay of a single species.

Enhanced resolution of fluorescence anisotropy decays by simultaneous analysis of progressively quenched samples. Applications to anisotropic rotations and to protein dynamics

Enhanced resolution of rapid and complex anisotropy decays was obtained by measurement and analysis of data from progressively quenched samples. Collisional quenching by acrylamide was used to vary the mean decay time of indole or of the tryptophan fluorescence from melittin. Anisotropy decays were obtained from the frequency-response of the polarized emission at frequencies from 4 to 2,000 MHz. Quenching increases the fraction of the total emission, which occurs on the subnanosecond timescale, and thereby provides increased information on picosecond rotational motions or local motions in proteins. For monoexponential subnanosecond anisotropy decays, enhanced resolution is obtained by measurement of the most highly quenched samples. For complex anisotropy decays, such as those due to both local motions and overall protein rotational diffusion, superior resolution is obtained by simultaneous analysis of data from quenched and unquenched samples. We demonstrate that measurement of quenched samples greatly reduces the uncertainty of the 50-ps correlation time of indole in water at 20 degrees C, and allows resolution of the anisotropic rotation of indole with correlation times of 140 and 720 ps. The method was applied to melittin in the monomeric and tetrameric forms. With increased quenching, the anisotropy data showed decreasing contributions from overall protein rotation and increased contribution from picosecond tryptophan motions. The tryptophan residues in both the monomeric and the tetrameric forms of melittin displayed substantial local motions with correlation times near 0.16 and 0.06 ns, respectively. The amplitude of the local motion is twofold less in the tetramer. These highly resolved anisotropy decays should be valuable for comparison with molecular dynamics simulations of melittin.

Resolution of multicomponent fluorescence emission by phase sensitive detection at multiple modulation frequencies

Phase sensitive emission spectra recorded at multiple frequencies were used to determine the lifetimes and steady-state spectra of the fluorophores In two-component mixtures. This analysis does not require any previous knowledge of the lifetimes, fractional Intensities, or the emission spectra and is thus an Improvement over single frequency phase sensitive detection which requires known emission spectra or known lifetimes. Phase sensitive emission spectra are recorded at several frequencies and arbitrarily chosen detector phase angles. The data are analyzed by use of nonlinear least squares to recover the lifetimes and wavelength-dependent fractional Intensities. The latter values determine the emission spectrum and relative intensity of each component in the mixture. Using this technique, we resolved two-component mixtures of fluorescein and 9-amlnoacrldlne, 2-(p -toluidinyl)-naphthalene-6-sulfonlc acid and 6-proplonyl-2-(dlmethylamlno)naphthalene, and N -acetyl-l -tyrosinamide and N -acetyl-l -tryptophanamide. In these mixtures the lifetimes differ by about 2-fold. Analysis of simulated data is presented to Illustrate the requirements for a satisfactory resolution. For simulated two-component mixtures, the components can be resolved If the lifetimes differ by 2-fold or greater, even with extensive overlap of the emission spectra.

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.

Measurement of subnanosecond anisotropy decays of protein fluorescence using frequency-domain fluorometry

We report the first anisotropy decays of protein fluorescence obtained using a frequency-domain fluorometer. The ultraviolet light source (300 nm) was a ring dye laser equipped with an intracavity frequency doubler, pumped by an argon ion laser. The data, measured at modulation frequencies from 2 to 200 MHz, reveal the presence of subnanosecond motions (0.1-0.2 ns) of the single tryptophan residues in melittin and monellin. For melittin the data also indicate the presence of slower motions near 1 ns, which may be the result of concerted motions of several peptide units. Smaller amplitude motions, on a similar timescale, were observed for the single tryptophan residue in staphylococcal nuclease. We demonstrate using N-acetyl-L-tryptophanamide in water that the method of frequency-domain fluorometry is capable of measuring correlation times as short as 50 ps. This method can provide data for the direct comparison of measured anisotropy decays with those predicted from molecular dynamics calculations.

A new method for resolution of two- and three-component mixtures of fluorophores by phase-sensitive detection of fluorescence

We describe a new method for the analysis of phase-sensitive fluorescence emission spectra. This method permits the resolution of three-component mixtures using spectra measured at a single modulation frequency. Phase-sensitive spectra are recorded using one modulation frequency, at a number of arbitrary detector phase angles. It is not necessary to suppress any one component. The spectra are then used to estimate the component lifetimes and steady-state fractional intensities using a nonlinear least-squares analysis procedure. The only requirement for the analysis is the knowledge of the steady-state spectra of the individual components. This procedure allowed the resolution of a two-component mixture of 9-methylanthracene (4.5 ns) and 9,10-diphenylanthracene (5.9 ns). It should be noted that resolution of two lifetimes which differ by only 30% is a difficult task. Additionally, we resolved a three-component mixture with lifetimes that differed fourfold: p-bis[2-(5-phenyloxazolyl)]benzene (1.3 ns), 9-methylanthracene (4.5 ns), and 9,10-diphenylanthracene (5.9 ns). Conveniently, the technique utilizes a commercially available fixed-frequency phase fluorometer.

Time-resolved fluorescence anisotropies of diphenylhexatriene and perylene in solvents and lipid bilayers obtained from multifrequency phase-modulation fluorometry

Time-resolved decays of fluorescence anisotropy were obtained from frequency-domain measurements of the phase angle difference between the parallel and perpendicular components of the polarized emission and the ratio of the modulated amplitudes. These data were measured at modulation frequencies ranging from 1 to 200 MHz. To demonstrate the general applicability of this method, we describe the resolution of both simple and complex decays of anisotropy. In particular, we resolved single, double, and triple exponential decays of anisotropy and the hindered rotational motions of fluorophores within lipid bilayers. The ease and rapidity with which these results were obtained indicate that frequency-domain measurements are both practical and reliable for the determination of complex decays of anisotropy.

Analysis of fluorescence decay kinetics from variable-frequency phase shift and modulation data

Recently it has become possible to measure fluorescence phase-shift and modulation data over a wide range of modulation frequencies. In this paper we describe the analysis of these data by the method of nonlinear least squares to determine the values of the lifetimes and fractional intensities for a mixture of exponentially decaying fluorophores. Analyzing simulated data allowed us to determine those experimental factors that are most critical for successfully resolving the emissions from mixtures of fluorophores. The most critical factors are the accuracy of the experimental data, the relative difference of the individual decay times, and the inclusion of data measured at multiple emission wavelengths. After measuring at eight widely spaced modulation frequencies, additional measurements yielded only a modest increase in resolution. In particular, the uncertainty in the parameters decreased approximately as the reciprocal of the square root of the number of modulation frequencies. Our simulations showed that with presently available precision and data for one emission bandpass, two decay times could be accurately determined if their ratio were greater than or equal to 1.4. Three exponential decays could also be resolved, but only if the range of the lifetimes were fivefold or greater. To reliably determine closely-spaced decay times, the data were measured at multiple emission wavelengths so that the fractional intensities of the components could be varied. Also, independent knowledge of any of the parameters substantially increased the accuracy with which the remaining parameters could be determined. In the subsequent paper we present experimental results that broadly confirm the predicted resolving potential of variable-frequency phase-modulation fluorometry.

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.

Determination of time-resolved fluorescence emission spectra and anisotropies of a fluorophore-protein complex using frequency-domain phase-modulation fluorometry

We report the first time-resolved fluorescence emission spectra and time-resolved fluorescence anisotropies obtained using frequency-domain fluorescence spectroscopy. We examined the fluorophore p-2-toluidinyl-6-naphthalenesulfonic acid (TNS) in viscous solvents and bound to the heme site of apomyoglobin using multifrequency phase fluorometers. Fluorescence phase shift and modulation data were obtained at modulation frequencies ranging from 1 to 200 MHz. For time-resolved emission spectra, the impulse response for the decay of intensity at each emission wavelength was obtained from the frequency response of the sample at the same emission wavelength. The decays have negative pre-exponential factors, consistent with a time-dependent spectral shift to longer wavelengths. These multiexponential decays were used to construct the time-resolved emission spectra, which were found to be in good agreement with earlier spectra obtained from time-domain measurements. Additionally, time-resolved anisotropies were obtained from the frequency-dependent phase angle differences between the parallel and perpendicularly polarized components of the emission. The rotational correlation times of TNS bound to apomyoglobin are consistent with those expected for this probe rigidly bound to the protein. TNS in propylene glycol also displayed a single exponential decay of anisotropy. These results, in conjunction with the previous successful resolution of multiexponential decays of fluorescence intensity (Lakowicz, J. R., Gratton, E., Laczko, G., Cherek, H., and Limkeman, M. (1984) Biophys. J., in press; Gratton, E., Lakowicz, J. R., Maliwal, B. P., Cherek, H., Laczko, G., and Limkeman, M. (1984) Biophys. J., in press) demonstrate that frequency-domain measurements provide information which is, at a minimum, equivalent to that obtainable from time-domain measurements.

Rotational freedom of tryptophan residues in proteins and peptides

We studied the rotational motions of tryptophan residues in proteins and peptides by measurement of steady-state fluorescence anisotropies under conditions of oxygen quenching. By fluorescence quenching we can shorten the fluorescence lifetime and thereby decrease the average time for rotational diffusion prior to fluorescence emission. This method allowed measurement of rotational correlation times ranging from 0.03 to 50 ns, when the unquenched fuorescence lifetimes are near 4 ns. A wide range of proteins and peptides were investigated with molecular weights ranging from 200 to 80 000. Many of the chosen substances possessed a single tryptophan residue to minimize the uncertainties arising from a heterogeneous population of fluorophores. In addition, we also studied a number of multi-tryptophan proteins. Proteins were studied at various temperatures, under conditions of self-association, and in the presence of denaturants. A wide variety of rotational correlation times were found. As examples we note that the single tryptophan residue of myelin basic protein was highly mobile relative to overall protein rotation whereas tryptophan residues in human serum albumin, RNase T1, aldolase, and horse liver alcohol dehydrogenase were found to be immobile relative to the protein matrix. These results indicate that one cannot generalize about the extent of segmental mobility of the tryptophan residues in proteins. This physical property of proteins is highly variable between proteins and probably between different regions of the same protein.

Correction of timing errors in photomultiplier tubes used in phase-modulation fluorometry

The measurement of fluorescence lifetimes is known to be hindered by the wavelength-dependent and photocathode area-dependent time response of photomultiplier tubes. A simple and direct method is described to minimize these effects in photomultiplier tubes used for phase-modulation fluorometry. Reference fluorophores of known lifetime were used in place of the usual scattering reference. The emission wavelengths of the reference and sample were matched by either filters or a monochromator, and the use of a fluorophore rather than a scatterer decreases the differences in spatial distribution of light emanating from the reference and sample. Thus photomultiplier tube artifacts are minimized. Five reference fluorophores were selected on the basis of availability, ease of solution preparation, and constancy of lifetime with temperature and emission wavelength. These compounds are p-terphenyl, PPO, PPD, POPOP and dimethyl POPOP. These compounds are dissolved in ethanol to give standard solutions that can be used over the temperature range from -55 to +55 degrees C. Purging with inert gas is not necessary. The measured phase and modulation of the reference solution is used, in conjunction with the known reference lifetime, to calculate the actual phase and modulation of the excitation beam. The use of standard fluorophores does not require separate experiments to quantify photomultiplier effects, and does not increase the time required for the measurement of fluorescence lifetimes. Examples are presented which demonstrate the elimination of artifactual photomultiplier effects in measurements of the lifetimes of NADH (0.4 ns) and indole solutions quenched by iodide. In addition, the use of these reference solutions increases the accuracy of fluorescence lifetime measurements ranging to 30 ns. We judge this method to provide more reliable lifetime measurements by the phase and modulation method. The test solutions and procedures we describe may be used by other laboratories to evaluate the performance of their phase fluorometers.

Phase-sensitive fluorescence spectroscopy: a new method to resolve fluorescence lifetimes or emission spectra of components in a mixture of fluorophores

A novel phase fluorometric method is described which permits direct recording of individual emission spectra from a mixture of two fluorescent compounds. Additionally, the lifetimes of each component may be determined by examination of the phase-sensitive fluorescence spectra. The method utilizes phase-sensitive detection of the sinusoidally modulated emission from a phase fluorometer. Resolution of the individual emission spectra in the mixture requires different fluorescence lifetimes for each component. Determination of the individual lifetimes requires knowledge of the steady-state emission spectra of the components. Use of low-frequency (approximately equal to 10(6) Hz) cross-correlated signals eliminates the need for high-frequency (approximately equal to 10(6) HZ) phase-sensitive detection. A mixture of 2-p-toluidinyl-6-naphthalenesulfonic acid (TNS) and 6-propionyl-2-(dimethylamino)naphthalene (PRODAN) was used to demonstrate the possibility of phase resolution of fluorophore mixture and to confirm theoretical predictions. A mixture of dibenzo[a,h]anthracene and dibenzo[c,g]carbazole was used to demonstrate that phase resolution is possible for spectra which overlap strongly and which are highly structured. In addition, the possibility of using phase-sensitive emission spectra for the resolution of excited-state reactions was demonstrated with anthracene and its diethylaniline exciplex. From a sample whose steady-state emission displayed both components we directly recorded the emission spectrum of anthracene monomer and the exciplex. For all these samples the dependence of the individual intensities on the phase angle of the detector agreed precisely with that expected on the basis of the individual fluorescence lifetimes. The detector phase angles chosen for suppression of each component in the mixture also agreed with the measured lifetimes. Thus, phase-sensitive fluorescence spectra can reveal individual spectral distributions or lifetimes. This method will be useful in the analysis of heterogeneous fluorescence emissions which frequently occur from proteins, membranes and other biological samples.

Dipolar relaxation in proteins on the nanosecond timescale observed by wavelength-resolved phase fluorometry of tryptophan fluorescence

We used phase fluorometry to investigate the wavelength dependence of the fluorescence lifetimes of N-acetyl-L-tryptophanamide (NATA) in solvents of varying viscosity and the lifetimes of tryptophan in human serum albumin, melittin, and liver alcohol dehydrogenase. In highly fluid solvents, and in completely vitrified solvents, the lifetime of NATA was constant across its emission spectrum. In viscous solvents, such as propylene glycol at -9 degrees C, the lifetimes of NATA increased across its emission spectrum, with the values being 3.3, 5.5, and 8.1 ns at 317, 344, and 400 nm, respectively. These wavelength-dependent lifetimes appear to be a result of reorientations of solvent dipoles around the excited state dipole moment of the indole moiety. For the three proteins investigated, the fluorescence lifetimes of tryptophan increased with increasing wavelength in a manner comparable to that observed for NATA in propylene glycol. These observations indicate that these protein matrices can reorientation around their tryptophan residues on the nanosecond timescale, and illustrate the potential of phase fluorometry for quantifying the details of these dipolar relaxation processes.