Constrained analysis of fluorescence anisotropy decay:application to experimental protein dynamics

Hydrodynamic properties as well as structural dynamics of proteins can be investigated by the well-established experimental method of fluorescence anisotropy decay. Successful use of this method depends on determination of the correct kinetic model, the extent of cross-correlation between parameters in the fitting function, and differences between the timescales of the depolarizing motions and the fluorophore's fluorescence lifetime. We have tested the utility of an independently measured steady-state anisotropy value as a constraint during data analysis to reduce parameter cross correlation and to increase the timescales over which anisotropy decay parameters can be recovered accurately for two calcium-binding proteins. Mutant rat F102W parvalbumin was used as a model system because its single tryptophan residue exhibits monoexponential fluorescence intensity and anisotropy decay kinetics. Cod parvalbumin, a protein with a single tryptophan residue that exhibits multiexponential fluorescence decay kinetics, was also examined as a more complex model. Anisotropy decays were measured for both proteins as a function of solution viscosity to vary hydrodynamic parameters. The use of the steady-state anisotropy as a constraint significantly improved the precision and accuracy of recovered parameters for both proteins, particularly for viscosities at which the protein's rotational correlation time was much longer than the fluorescence lifetime. Thus, basic hydrodynamic properties of larger biomolecules can now be determined with more precision and accuracy by fluorescence anisotropy decay.     

Analysis of nonexponential fluorescence decay data by a method of moments.

A method of moments is presented for the analysis of convoluted fluorescence decay data when the impulse response function is given by f(t) = alpha exp (-At - Bt1/2). Examples of this method are given using both simulated and measured fluorescence decays. It is also shown that this method, used with moment index displacements, will correct for light-scatter leakage, zero-point time shifts, and slow lamp drift.     

Simulation of convoluted and exact emission anisotropy decay profiles

We have Simulated the convolution of the emission anisotropy decay function with both a delta-pulse excitation function (exact solution) and a pulse function of either Gaussian or other functional form. It can be readily shown that convolution with a pulse of finite width leads to lower r0 values (anisotropy at time zero). Especially in the case of short-lived fluorescence, it can be demonstrated that the convoluted anisotropy lags behind the exact anisotropy leading to longer apparent rotational correlation times. Contour plots of r corrections as a function of both fluorescence lifetime and rotational correlation time were constructed for two different pulse profiles. Inspection of these contour diagrams can lead to an estimate of the relative error involved, when anisotropy data are not deconvoluted.     

Application of a reference convolution method to tryptophan fluorescence in proteins. A refined description of rotational dynamics

A reference method for the deconvolution of polarized fluorescence decay data is described. Fluorescence lifetime determinations for p-terphenyl, p-bis[2-(5-phenyloxazolyl)]benzene and N-acetyltryptophanamide (AcTrpNH2) show that with this method more reliable fits of the decays can be made than with the scatterer method, which is most frequently used. Analysis of the AcTrpNH2 decay with p-terphenyl as the reference compound yields an excellent fit with lifetimes of 2.985 ns for AcTrpNH2 and 1.099 ns for p-terphenyl (20 degrees C), whereas the AcTrpNH2 decay cannot be satisfactorily fitted when the scatterer method is used. The frequency of the detected photons is varied to determine the conditions where pulse pile-up starts to affect the measured decays. At detection frequencies of 5 kHz and 15 kHz, which corresponds to 1.7% and 5% respectively of the rate of the excitation photons no effects are found. Decays measured at 30 kHz (10%) are distorted, indicating that pile-up effects play a role at this frequency. The fluorescence and fluorescence anisotropy decays of the tryptophan residues in the proteins human serum albumin, horse liver alcohol dehydrogenase and lysozyme have been reanalysed with the reference method. The single tryptophan residue of the albumin is shown to be characterized by a triple-exponential fluorescence decay. The anisotropy decay of albumin was found to be mono-exponential with a rotational correlation time of 26 ns (20 degrees C). The alcohol dehydrogenase has two different tryptophan residues to which single lifetimes are assigned. It is found that the rotational correlation time for the dehydrogenase changes with excitation wavelength (33 ns for lambda ex = 295 nm and 36 ns for lambda ex = 300 nm at 20 degrees C), indicating a nonspherical protein molecule. Lysozyme has six tryptophan residues, which give rise to a triple-exponential fluorescence decay. A single-exponential decay with a rotational correlation time of 3.8 ns is found for the anisotropy. This correlation time is significantly shorter than that arising from the overall rotation and probably originates from intramolecular, segmental motion.     

The use of moment index displacement in analyzing fluorescence time-decay data

Moment index displacement automatically corrects a number of significant nonrandom instrumental errors in fluorescence time-decay measurements. Three-component data, obtained by measuring the fluorescence decay of three different species mixed in the same solution, were used as a test sample. It was shown, as predicted by theory, that moment index displacement corrects three nonrandom instrumental errors: (1) the presence of scatter in the data; (2) time origin shifts between lamp and fluorescence data; and (3) lamp drift, or time-dependent changes in the shape of the excitation curve. The data clearly show that the use of the method of moments with moment index displacement to analyze fluorescence decay data is not a curve-fitting procedure. This procedure will accurately obtain decay parameters for multiple-exponential decays from certain badly distorted data, yielding a calculated curve very different from the actual data.     

Determination of rotational correlation times from deconvoluted fluorescence anisotropy decay curves. Demonstration with 6,7-dimethyl-8-ribityllumazine and lumazine protein from Photobacterium leiognathi as fluorescent indicators

The experimental and analytical protocols required for obtaining rotational correlation times of biological macromolecules from fluorescence anisotropy decay measurements are described. As an example, the lumazine protein from Photobacterium leiognathi was used. This stable protein (Mr 21 200) contains the noncovalently bound, natural fluorescent marker 6,7-dimethyl-8-ribityllumazine, which has in the bound state a long fluorescence lifetime (tau = 14 ns). Shortening of the fluorescence lifetime to 2.6 ns at room temperature was achieved by addition of the collisional fluorescence quencher potassium iodide. The shortening of tau had virtually no effect on the rotational correlation time of the lumazine protein (phi = 9.4 ns, 19 degrees C). The ability to measure biexponential anisotropy decay was tested by the addition of Photobacterium luciferase (Mr 80 000), which forms an equilibrium complex with lumazine protein. Under the experimental conditions used (2 degrees C) the biexponential anisotropy decay can best be described with correlation times of 20 and 60 ns, representing the uncomplexed and luciferase-associated lumazine proteins, respectively. The unbound 6,7-dimethyl-8-ribityllumazine itself (tau = 9 ns) was used as a model compound for determining correlation times in the picosecond time range. In the latter case rigorous deconvolution from the excitation profile was required to recover the correlation time, which was shorter (100-200 ps) than the measured laser excitation pulse width (500 ps).     

Effect of orientational order on the decay of the fluorescence anisotropy in membrane suspensions. A new approximate solution of the rotational diffusion equation

We discussed the time-dependence of fluorescent emission anisotropy of a cylindrical probe in membrane vesicles. We showed that, if the motion of the probe were described as diffusion in an anisotropic environment, it would be possible to determine not only the second-rank but also the fourth-rank orientational order parameter from the decay of the fluorescence anisotropy. The approximations involved were based on an interpolation of short-time and long-time behavior of the relevant correlation functions. A general expression was derived for the time dependence of the fluorescence anisotropy in closed form, which applies to any particular distribution model. It was shown to be in good agreement with previously reported results for the cone model and the Gaussian model. Finally, the applicability of the theory to time-resolved and differential phase fluorescence depolarization experiments was discussed.     

Detection and correction of blinking bias in image correlation transport measurements of quantum dot tagged macromolecules

Semiconductor nanocrystals or quantum dots (QDs) are becoming widely used as fluorescent labels for biological applications. Here we demonstrate that fluorescence fluctuation analysis of their diffusional mobility using temporal image correlation spectroscopy is highly susceptible to systematic errors caused by fluorescence blinking of the nanoparticles. Temporal correlation analysis of fluorescence microscopy image time series of streptavidin-functionalized (CdSe)ZnS QDs freely diffusing in two dimensions shows that the correlation functions are fit well to a commonly used diffusion decay model, but the transport coefficients can have significant systematic errors in the measurements due to blinking. Image correlation measurements of the diffusing QD samples measured at different laser excitation powers and analysis of computer simulated image time series verified that the effect we observe is caused by fluorescence intermittency. We show that reciprocal space image correlation analysis can be used for mobility measurements in the presence of blinking emission because it separates the contributions of fluctuations due to photophysics from those due to transport. We also demonstrate application of the image correlation methods for measurement of the diffusion coefficient of glycosyl phosphatidylinositol-anchored proteins tagged with QDs as imaged on living fibroblasts.     

Conformational dynamics and intersubunit energy transfer in wild-type and mutant lipoamide dehydrogenase from Azotobacter vinelandii. A multidimensional time-resolved polarized fluorescence study.

Time-resolved fluorescence and fluorescence anisotropy data surfaces of flavin adenine dinucleotide bound to lipoamide dehydrogenase from Azotobacter vinelandii in 80% glycerol have been obtained by variation of excitation energy and temperature between 203 and 303 K. The fluorescence kinetics of a deletion mutant lacking 14 COOH-terminal amino acids were compared with the wild-type enzyme to study a possible interaction of the COOH-terminal tail with the active site of the enzyme. The flavin adenine dinucleotide fluorescence in both proteins exhibits a bimodal lifetime distribution as recovered by the maximum entropy method of data analysis. The difference in standard enthalpy and entropy of associated conformational substates was retrieved from the fractional contributions of the two lifetime classes. Activation energies of thermal quenching were obtained that confirm that the isoalloxazines in the deletion mutant are solvent accessible in contrast to the wild-type enzyme. Red-edge spectroscopy in conjunction with variation of temperature provides the necessary experimental axes to interpret the fluorescence depolarization in terms of intersubunit energy transfer rather than reorientational dynamics of the flavins. The results can be explained by a compartmental model that describes the anisotropy decay of a binary, inhomogeneously broadened, homoenergy transfer system. By using this model in a global analysis of the fluorescence anisotropy decay surface, the distance between and relative orientation of the two isoalloxazine rings are elucidated. For the wild-type enzyme, this geometrical information is in agreement with crystallographic data of the A. vinelandii enzyme, whereas the mutual orientation of the subunits in the deletion mutant is slightly altered. In addition, the ambiguity in the direction of the emission transition moment in the isoalloxazine ring is solved. The anisotropy decay parameters also provide information on electronic and dipolar relaxational properties of the flavin active site. The local environment of the prosthetic groups in the deletion mutant of the A. vinelandii enzyme is highly inhomogeneous, and a transition from slow to rapid dipolar relaxation is observed over the measured temperature range. In the highly homogeneous active site of the wild-type enzyme, dipolar relaxation is slowed down beyond the time scale of fluorescence emission at any temperature studied. Our results are in favor of a COOH-terminal polypeptide interacting with the active site, thereby shielding the isoalloxazines from the solvent. This biological system forms a very appropriate tool to test the validity of photophysical models describing homoenergy transfer.     

Fluorescence anisotropy decay due to rotational brownian motion of ethidium intercalated in double strand DNA

The transient fluorescence of solutions of ethidium bromide . DNA complexes has been measured by pulse fluorimetry at different temperatures and in solvents containing various amounts of sucrose. The molar ratio of ethidium to nucleotides was low. Under these conditions the anisotropy decay was due to the Brownian motion of ethidium molecules intercalated in the double strand DNA molecules. This anisotropy decay could be described by a sum of 3 exponential terms, with correlation times 01, 02, 03 which were linear functions of the ratio of the solvent viscosity to the absolute temperature (n/T). The amplitude of the exponential term characterized by the shortest correlation time (01) has been found to depend on temperature while the ratio of the amplitude of the two other terms (characterized by 02 and 03) was independent of temperature. These results were interpreted as follows: 01 corresponds to a fast motion of the dye in its site. 02 and 03 describe a tortional motion of the ethidium bromide. DNA complex, involving several nucleotide pairs.     

Analysis of fluorescence decay curves by means of the Laplace transformation.

A computational procedure is described for the analysis of fluorescence decay data convolved with a lamp flash of finite width. The computer program calculates the ratio of the Laplace transforms of the decay and the lamp flash for different values of s to give the transforms of the impulse response for each value of s. These are set equal to the analytical Laplace transforms of the decay law involved. Solution of the nonlinear simultaneous equations yields the desired decay parameters. The method can be modified to analyze data that contains a component due to scattered light and can also provide essential information regarding transit time changes of the photomultiplier with changes in emission wavelength. The method was tested by the analysis of real and simulated data. The accuracy of the analysis depends on the degree of correlation among the parameters.     

Dynamic depolarization of interacting fluorophores. Effect of internal rotation and energy transfer.

Effects of internal rotation on the fluorescence decay functions and time-dependent anisotropies of fluorophores bound to a spherical macromolecule are theoretically investigated in the presence of the intramolecular energy transfer interaction by solving relevant rotational diffusion equations. The model system examined is one in which the energy donor is internally rotating around an axis fixed at the macromolecule and the acceptor is fixed at a definite position in the macromolecule. The effect of internal rotation in the system is described by Hill's functions with two cosine terms. The fluorescence decay function and anisotropy decay are functions of the ratio of energy-transfer probability averaged over the internal rotation angle to the rotary diffusion co-efficient. When the internal rotation is much faster than energy transfer, the decay function of the donor is predicted to be a single exponential, and the anisotropy decay is essentially described by the expression derived by Gotlieb and Wahl (1963. J. Chim. Phys. 60:849-856). However, deviation from it becomes pronounced as the rotation becomes slower. Methods of numerical analysis are presented for decay function and anisotropy decay, as well as relative quantum yield and polarization anisotropy under steady-state excitation, and examined for a simplified system under the variation of the diffusion coefficient.     

Nanosecond spectroscopy of retinol.

Nanosecond fluorescence spectroscopy was used to study the unique binding site of the retinol-binding protein (RBP) from human serum. At pH 7.4, the binding of retinol to RBP caused the following spectroscopic changes in the ligand: (a) an enhancement of the fluorescence decay time (gamma = 8 ns); and (b) an increase in the emission anisotropy (A = 0.29). Retinol in hexane has a fluorescent decay time of 4.2 ns and a low emission anisotropy (A = 0.02). The increase in the fluorescence decay time of bound retinol is not due to dielectric relaxation effects of polar groups, since nanosecond time-resolved emission spectra of either retinol in glycerol or retinol bound to RBP, failed to show any time-dependent shifts in emission maxima during the time period investigated 0 to 30 ns. The degree of rotational mobility of bound retinol was investigated by time emission anisotropy measurements. The observed rotational correlation time (theta = 7.2 ns) is consistent with a rigid compact macromolecule of 21,000 molecular weight.     

Fluorescence quenching dynamics of tryptophan in proteins. Effect of internal rotation under potential barrier.

In many proteins fluorescence from single tryptophan exhibits a nonexponential decay function. To elucidate the origin of this nonexponential decay, we have examined the fluorescence decay function and time-resolved fluorescence anisotropy of a fluorophore covalently bound to a macromolecule by solving a rotational analogue of the Smoluchowski equation. An angular-dependent quenching constant and potential energy for the fluorophore undergoing internal rotation were introduced into the equation of motion for fluorophore. Results of numerical calculations using the equations thus obtained predict that both the fluorescence decay function and time-resolved anisotropy are dependent on rotational diffusion coefficients of fluorophore and potential energy for the internal rotation. The method was applied to the observed fluorescence decay curve of the single tryptophan in apocytochrome c from horse heart. The calculated decay curves fit the observed ones well.     

Environmental modulation of M13 coat protein tryptophan fluorescence dynamics

The effects of detergent [deoxycholate (DOC) and phospholipid [dimyristoylphosphatidylcholine (DMPC)] environments on the rotational dynamics of the single tryptophan residue 26 of bacteriophage M13 coat protein have been investigated by using time-resolved single photon counting measurements of the fluorescence intensity and anisotropy decay. The total fluorescence decay of tryptophan-26 is complex but rather similar in DOC as compared to DMPC when analyzed in terms of a lifetime distribution (exponential series method). This similarity, in conjunction with the almost identical steady-state fluorescence spectra, indicates only minor differences between the tryptophan environments in DOC and DMPC. The reorientational dynamics of tryptophan-26 are dominated by slow rotation of the entire protein in both detergent and phospholipid environments. The resolved anisotropy decay in DOC can be approximated by a simple hydrodynamic model of protein/detergent micelle rotational diffusion, although the data indicative slightly greater complexity in the rotational motion. The tryptophan fluorescence anisotropy is not sensitive to protein conformational changes in DOC detected by nuclear magnetic resonance on the basis of pH independence in the range 7.5-9.1. In DMPC bilayers, restricted tryptophan motion with a correlation time of approximately 2 ns is observed together with a second very slow reorientational component. Resolution of the time constant for this slow rotation is obscured by the tryptophan fluorescence time window being too short to clearly locate its anisotropic limit. The possible contribution made by axial rotational diffusion of the protein to this slow rotational process is discussed.(ABSTRACT TRUNCATED AT 250 WORDS)     

A new method for decay-associated fluorescence spectroscopy. Application to the tryptophan zwitterion

We describe a new method for decay associated fluorescence spectroscopy using synchrotron radiation as the excitation pulse and a photon counting technique. This method is based on the determination of the difference between the barycenters of the exciting pulse and of the fluorescence response at several wavelengths. It is applicable to the case where individual decay times are independent of emission wavelength. Coupled to the analysis of the decay curve at only one emission wavelength, this method reduces the time devoted to the numerical analysis and avoids the spectral distortion due to the lamp profile. The results obtained by this method on indole, the tryptophan zwitterion, and N-acetyl-tryptophan are presented. Results are compared to those obtained by two other methods: Determination of the fluorescence decay parameters by deconvolution analysis at several emission wavelengths. Photon counting of the fluorescence spectrum emitted during a selected time window after the excitation pulse.     

Analysis of time-resolved fluorescence anisotropy in lipid-protein systems

The subnanosecond fluorescence and motional dynamics of the tryptophan residue in the bacteriophage M13 coat protein incorporated within pure dioleoylphosphatidylcholine (DOPC) as well as dioleoylphosphatidylcholine/dioleoylphosphatidylglycerol (DOPC/DOPG) and dimyristoylphosphatidylcholine/dimyristoylphosphatidylglycerol (DMPC/DMPG) bilayers (80/20 w/w) with various L/P ratio have been investigated. The fluorescence decay is decomposed into four components with lifetimes of about 0.5, 2.0, 4.5 and 10.0 ns, respectively. In pure DOPC and DOPC/DOPG lipid bilayers, above the phase transition temperature, the rotational diffusion of the protein molecules contributes to the depolarization and the anisotropy of tryptophan is fitted to a dual exponential function. The longer correlation time, describing the rotational diffusion of the whole protein, shortens with increasing temperature and decreasing protein aggregation number. In DMPC/DMPG lipid bilayers, below the phase transition, the rotational diffusion of the protein is slowed down such that the subnanosecond anisotropy decay of tryptophan in this system reflects only the segmental motion of the tryptophan residue. Because of a heterogeneous microenvironment, the anisotropy decay must be described by three exponentials with a constant term, containing a negative coefficient and a negative decay time constant. From such a decay, the tryptophan residue within the aggregate undergoes a more restricted motion than the one exposed to the lipids. At 20 degrees C, the order parameter of the transition moment of the isolated tryptophan is about 0.9 and that for the exposed one is about 0.5.     

One- and two-photon excited fluorescence lifetimes and anisotropy decays of green fluorescent proteins

We have used one- (OPE) and two-photon (TPE) excitation with time-correlated single-photon counting techniques to determine time-resolved fluorescence intensity and anisotropy decays of the wild-type Green Fluorescent Protein (GFP) and two red-shifted mutants, S65T-GFP and RSGFP. WT-GFP and S65T-GFP exhibited a predominant approximately 3 ns monoexponential fluorescence decay, whereas for RSGFP the main lifetimes were approximately 1.1 ns (main component) and approximately 3.3 ns. The anisotropy decay of WT-GFP and S65T-GFP was also monoexponential (global rotational correlation time of 16 +/- 1 ns). The approximately 1.1 ns lifetime of RSGFP was associated with a faster rotational depolarization, evaluated as an additional approximately 13 ns component. This feature we attribute tentatively to a greater rotational freedom of the anionic chromophore. With OPE, the initial anisotropy was close to the theoretical limit of 0.4; with TPE it was higher, approaching the TPE theoretical limit of 0.57 for the colinear case. The measured power dependence of the fluorescence signals provided direct evidence for TPE. The general independence of fluorescence decay times, rotation correlation times, and steady-state emission spectra on the excitation mode indicates that the fluorescence originated from the same distinct excited singlet states (A*, I*, B*). However, we observed a relative enhancement of blue fluorescence peaked at approximately 440 nm for TPE compared to OPE, indicating different relative excitation efficiencies. We infer that the two lifetimes of RSGFP represent the deactivation of two substates of the deprotonated intermediate (I*), distinguished by their origin (i.e., from A* or B*) and by nonradiative decay rates reflecting different internal environments of the excited-state chromophore.     

Fluorescence anisotropy decay studies upon hemoglobin A and its subunits

Fluorescent conjugates of hemoglobin A, its isolated β-chain, and the apo-derivative of the β-chain have been prepared in which the β-93 sulfhydryl was conjugated with 1,5-AEDANS. Radiationless enery transfer to the heme group results in a major decrease in fluorescence intensity and decay time. Measurements of the time decay of fluorescence anisotropy, employing single-photon counting, indicate that the apparent rotational correlation time is, in each case, substantially reduced from the value expected for a rigid molecule of the same molecular weight. This observation raises the possibility that internal degrees of rotational freedom exist.     

Monitoring membrane protein rotational diffusion using time-averaged phosphorescence

Rotational motions of membrane proteins have previously been measured using time-dependent phosphorescence techniques. This paper discusses a method of examining membrane protein mobility at temperatures relevant to biological systems, using a technique similar to steady-state fluorescence. The method is demonstrated using sarcoplasmic reticulum ATPase labelled with erythrosin isothiocyanate, both in its natural condition and crosslinked by incubation with glutaraldehyde. The experimentally-observed dependence of phosphorescence anisotropy on temperature is compared to a calculated anisotropy-temperature curve. Comparison is made between the anisotropy decay curves obtained by time-averaged phosphorescence and steady-state fluorescence.