Maximum likelihood method for the analysis of time-resolved fluorescence decay curves

The usefulness of fluorescence techniques for the study of macromolecular structure and dynamics depends on the accuracy and sensitivity of the methods used for data analysis. Many methods for data analysis have been proposed and used, but little attention has been paid to the maximum likelihood method, generally known as the most powerful statistical method for parameter estimation. In this paper we study the properties and behavior of maximum likelihood estimates by using simulated fluorescence intensity decay data. We show that the maximum likelihood method provides generally more accurate estimates of lifetimes and fractions than does the standard least-squares approach especially when the lifetime ratios between individual components are small. Three novelties to the field of fluorescence decay analysis are also introduced and studied in this paper: a) discretization of the convolution integral based on the generalized integral mean value theorem: b) the likelihood ratio test as a tool to determine the number of exponential decay components in a given decay profile; and c) separability and detectability indices which provide measures on how accurately, a particular decay component can be detected. Based on the experience gained from this and from our previous study of the Padé-Laplace method, we make some recommendations on how the complex problem of deconvolution and parameter estimation of multiexponential functions might be approached in an experimental setting. Offprint requests to: F. G. Prendergast     

Real-time monitoring of antibody secretion from hybridomas on a microchip by time-resolved luminescence anisotropy analysis

This article presents a real-time monitoring system for cellular analysis using micro total analysis systems technology. Time-resolved luminescence anisotropy analysis was adopted for real-time detection of small amounts of a target protein produced by a small number of cells. The system was tested by real-time monitoring of the antibody secretion by hybridomas. The cells were successfully cultivated in a micro-incubation chamber (240 nl) fabricated on a microchip. The quantification of the antibody was achieved using the Ru(II) complex-labeled Staphylococcus aureus protein A probe, which can bind specifically to the Fc region of the antibody. Using this system, we detected as little as 24 fmol of immunoglobulin G under physiological conditions without the bound/free separation protocol. We successfully achieved real-time and quantitative monitoring of small amounts of antibody production by approximately 200 hybridoma cells. This method could be applied to various cellular analyses using small numbers of cells.     

Time-resolved fluorescence spectroscopy of lumazine protein from Photobacterium phosphoreum using synchrotron radiation

Time-resolved fluorescence on lumazine protein from Photobacterium phosphoreum was performed with synchrotron radiation as a source of continuously tunable excitation. The experiments yielded structural and dynamic details from which two aspects became apparent. From fluorescence anisotropy decay monitoring of lumazine fluorescence with different excitation wavelengths, the average correlation times were shown to change, which must indicate the presence of anisotropic motion of the protein. A similar study with 7-oxolumazine as the fluorescent ligand led to comparable results. The other remarkable observation dealt with the buildup of acceptor fluorescence, also observed with 7-oxolumazine although much less pronounced, which is caused by the finite energy transfer process between the single donor tryptophan and the energy accepting lumazine derivatives. Global analytical approaches in data analysis were used to yield realistic correlation times and reciprocal transfer rate constants. It was found that the tryptophan residue has a large motional freedom as also reported previously for this protein and for the related protein from P. leiognathi (Lee et al. 1985; Kulinski et al. 1987). The average distance between the tryptophan residue and the ligand donor-acceptor couple has been determined to be 2.7 nm for the same donor and two different acceptors.     

Development of a multipurpose time-resolved fluorescence immunoassay for rat insulin

We present a time-resolved fluorescence immunoassay (TR-FIA) for the measurement of rat insulin in cell extracts and culture media. This assay is based on the binding of two monoclonal antibodies to different parts of the insulin molecule in a 96-well microtiter plate. For the detection, europium-labeled streptavidin that interacts with the second biotinylated antibody is used. Samples of 25 μl could be analyzed in less than 2 days with a measuring range between 5 and 1250 pg (0.2-50 μg/L or 34.4-8600 pM). The inter- and intraassay percentage coefficients of variation were less than 8.3 and 5.1, respectively. Recoveries of 0.48 to 40 μg/L rat insulin, added to culture medium, ranged between 94 and 107%. Results were significantly correlated with those of an in-house radioimmunoassay (RIA) for rodent insulin (P < 0.0001, r² = 0.99). The TR-FIA method had a similar detection limit (0.16 μg/L), but its working range was at least 5-fold larger. Additional advantages include the lower cost, the applicability to measurements in tissue and serum, and the quantification of insulin from other species.     

Synchrotron-excited time-resolved fluorescence spectroscopy of adenosine,protonated adenosine and 6N, 6N-dimethyladenosine in aqueous solution at room temperature

The fluorescence behavior of adenosine in neutral solution has been studied by time-resolved spectroscopy using synchrotron excitation and timecorrelated single photon counting, and by decay time measurements. Three emissions have been identified and correlated with three excitation spectra. The assignment of these transitions has been made by comparison with similar measurements on ⁶N, ⁶N-dimethyladenosine (6 DMA), and on adenosine in acid solution (ADO H⁺). It is proposed that two of the transitions of adenosine which correlate with 6DMA originate from coplanar and orthogonal rotational conformers of the amino group. The other transition, correlating with ADO H⁺ may originate either from the ³H-imino tautomer, or from a differently solvated rotational conformer.A partial presentation of this work has been made at the Second Congress of the European Society for Photobiology Padova, Italy, 6–10 September 1987     

Design of peptide substrates for nanosecond time-resolved fluorescence assays of proteases: 2,3-diazabicyclo[2.2.2]oct-2-ene as a noninvasive fluorophore

Fluorescence protease assays were investigated with peptide substrates containing a 2,3-diazabicyclo[2.2.2]oct-2-ene-labeled asparagine (Dbo) as a fluorescent amino acid. The special characteristic of the fluorophore Dbo is its exceedingly long fluorescence lifetime (ca. 300 ns in water under air), which allows the use of nanosecond time-resolved fluorescence (Nano-TRF) detection to efficiently suppress shorter-lived background emission. In addition, the natural amino acids tryptophan and tyrosine can be employed as intramolecular fluorescence quenchers, which facilitates substrate design. Fourteen synthetic peptide substrates (composed of 2-19 amino acids) and five enzymes (trypsin, pepsin, carboxypeptidase A, leucine aminopeptidase, and chymotrypsin) were investigated and, in all 28 examined combinations, enzymatic activity was detected by monitoring the increase in steady state fluorescence with time and determining the reaction rates as kcat/Km values, which ranged from 0.2 to 80x10(6) M-1 min-1. The results suggest an excellent compatibility of the very small and hydrophilic fluorescent probe Dbo with solid-phase peptide synthesis and the investigated proteases. For all 14 peptides the fluorescence lifetimes before and after enzymatic cleavage were measured and Nano-TRF measurements were performed in 384-well microplates. The fluorescence lifetimes of the different peptides provide the basis for the rational design of Dbo-based fluorescent substrates for protease assays. Measurements in Nano-TRF mode revealed, in addition to efficient suppression of background fluorescence, an increased differentiation between cleaved and uncleaved substrate. The Dbo-based assays can be adapted for high-throughput screening.     

Probing the interactions of hemoglobin with antioxidant flavonoids via fluorescence spectroscopy and molecular modeling studies

Steady state and time resolved fluorescence spectroscopy, combined with molecular modeling computations, have been used to explore the interactions of two therapeutically important flavonoids, fisetin (3,7,3′,4′-OH-flavone) and 3-hydroxyflavone (3-HF), with normal human hemoglobin (HbA). Distinctive ‘two color’ fluorescence signatures and fairly high fluorescence anisotropy (r = 0.12-0.28) of fisetin and 3-HF reveal their specific interactions with HbA. Binding constants estimated from the fluorescence studies were ≈ 4.00 × 10⁴ M^− 1 and 9.83 × 10³ M^− 1 for fisetin and 3-HF respectively. Specific interactions with HbA were further confirmed from flavonoid-induced static quenching of the protein tryptophan fluorescence as indicated by: (a) bimolecular quenching constant K_q ? diffusion controlled limit (b) closely matched values of Stern-Volmer quenching constant and binding constant (c) τ_o/τ ≈ 1 (where τ_o and τ are the unquenched and quenched tryptophan fluorescence lifetimes respectively). Molecular docking and electrostatic surface potential calculations reveal contrasting binding modes of fisetin and 3-HF with HbA.     

The globule diameter and some electron and conformational properties of the flavoprotein fragment of mitochondrial NADH dehydrogenase studied by fluorescence spectroscopy

The globule dimensions and some electron and conformational properties of the flavoprotein (peripheral) fragment of the mitochondrial NADH dehydrogenase were determined by the time-resolved, phase-modulating, and polarization fluorescence spectroscopies, as well as correlated confocal microscopy. The rotational and the diffusion (translocation) diameters of the protein fragment were shown to be no less than 44 and ∼72 ?, respectively. The diameter of protomitochondrial particles from the bovine heart, which were used for the isolation of the fraction of peripheral fragments, was no less than 2300 ?. The fluorescence from tryptophan and flavin fluorophores in the fragment is strongly quenched by iron of the iron-sulfur clusters, which suggests that a strong electron-vibrational interaction of iron with Trp residues and flavin takes place. An overlapping of the electron clouds of iron-sulfur clusters, Trp residues, and flavin is likely to facilitate the electron transfer through the protein. The heat inactivation of the enzyme was accompanied by neither its substantial conformational changes, nor a considerable release of iron ions from the clusters located near the Trp residues.     

Time-dependent decay and anisotropy of fluorescence from diphenylhexatriene embedded in the chloroplast thylakoid membrane

The hydrophobic fluorescent probe 1,6-diphenyl-1,3,5-hexatriene has been incorporated into the membranes of isolated thylakoids, separated granal and stromal lamellae and aqueous dispersions of extracted thylakoid galactolipids. Time-resolved fluorescence decays have been recorded on a nanosecond scale using single-photon counting in order to assess the motional properties of the probe. All the experimental systems used showed biphasic decay kinetics and the anisotropies of the decays have been interpreted in terms of a model for wobbling diffusion confined to a cone. The analysis has given information about dynamic and structural restraints of the lipid acyl chains. In the intact thylakoid membrane the degree of order of the fatty acid acyl chains is higher and their rate of motion slower than for isolated lipids. Even so, the dynamic and structural parameters indicate that the thylakoids can be considered as a relatively fluid membrane system when compared with many other biological membranes, a property which is probably required to facilitate efficient long-range diffusion of lipophilic mobile electron-transport components. It is suggested that the optimization of thylakoid fluidity is linked to regulation of the membrane protein/lipid ratio which is also likely to be responsible for the higher fluidity of stromal membranes relative to those of the grana.     

Global analysis of fluorescence fluctuation data

Over the last decade the number of applications of fluorescence correlation spectroscopy (FCS) has grown rapidly. Here we describe the development and application of a software package, FCS Data Processor, to analyse the acquired correlation curves. The algorithms combine strong analytical power with flexibility in use. It is possible to generate initial guesses, link and constrain fit parameters to improve the accuracy and speed of analysis. A global analysis approach, which is most effective in analysing autocorrelation curves determined from fluorescence fluctuations of complex biophysical systems, can also be implemented. The software contains a library of frequently used models that can be easily extended to include user-defined models. The use of the software is illustrated by analysis of different experimental fluorescence fluctuation data sets obtained with Rhodamine Green in aqueous solution and enhanced green fluorescent protein in vitro and in vivo.An erratum to this article can be found at Victor V. Skakun, Mark A. Hink and Anatoli V. Digris contributed equally to this work.     

Construction and performance of a variable-frequency phase-modulation fluorometer

We describe the construction and performance of a variable-frequency phase-modulation fluorometer. This instrument, which provides modulation frequencies from 1 to 200 MHz, was constructed using commercially available components. To facilitate the introduction of these instruments into other laboratories we describe in detail the chosen components and the principles of operation. The present light source is a continuous-wave helium-cadmium laser, which provides convenient excitation wavelengths of 325 and 442 nm. Modulation of the incident light is provided by one of several electro-optic modulators. The extent of modulation ranges from 1.0 to 0.2 as the frequency increases from 1 to 200 MHz. Phase angles and demodulation factors are measured using the cross-correlation method. The closely spaced frequencies are provided by two direct frequency synthesizers. The phase and modulation measurements are accurate to 0.2 degrees and 0.002, respectively, from 1 to 200 MHz. This accuracy allows considerable resolution of complex decay laws. The usefulness of frequency-domain fluorometry for the resolution of multiexponential decays is illustrated by the analysis of several difficult mixtures. As examples, we resolved a two-component mixture of anthracene (4.1 ns) and 9,10-diphenylanthracene (6.3 ns), and confirmed that the intensity decay of NADH in aqueous buffer is at least a double exponential (0.2 and 0.86 ns). We also resolved an especially difficult mixture of anthracene (4.1 ns) and 9-methylanthracene (4.5 ns), and a three-component mixture with decay times of 1.3, 4.1 and 7.7 ns. Frequency-domain fluorometers appear to be particularly useful for determination of complex decays of fluorescence anisotropy. This capability is illustrated by the determination of rotational correlation times as short as 47 ps for p-bis[2-(5-phenyloxazolyl)]benzene (POPOP) in hexane at 40 degrees C, and by the resolution of the two correlation times of anisotropic rotators such as perylene and 9-aminoacridine. Resolution of two anisotropy decay times for 9-aminoacridine is a difficult test because these correlation times differ by less than 2-fold. The resolution of multiexponential decays of intensity and anisotropy possible with this instrument is at least equivalent to that obtained using state-of-the-art time-resolved instruments based on mode-locked laser sources. The ease and rapidity of frequency-domain measurements, the relative simplicity of the equipment, the accuracy of the measurements and the lack of significant systematic errors indicate that frequency-domain fluorometry will be widely useful in chemical and biochemical research.     

The recovery of dipolar relaxation times from fluorescence decays as a tool to probe local dynamics in single tryptophan proteins

The dipolar relaxation process induced by the excitation of the single tryptophan residue of four proteins (staphylococcal nuclease, ribonuclease-T1, phosphofructokinase, and superoxide dismutase) has been studied by dynamic fluorescence measurements. A new algorithm taking into account the relaxation effect has been applied to the fluorescence decay function obtained by phase-shift and demodulation data. This approach only requires that fluorescence be collected through the whole emission spectrum, avoiding the time-consuming determination of the data at different emission wavelengths, as usual with time-resolved emission spectroscopy. The results nicely match those reported in the literature for staphylococcal nuclease and ribonuclease-T1, demonstrating the validity of the model. Furthermore, this new methodology provides an alternative explanation for the complex decay of phosphofructokinase and human superoxide dismutase suggesting the presence of a relaxation process even in proteins that lack a lifetime-dependent spectral shift. These findings may have important implications on the analysis of small-scale protein dynamics, since dielectric relaxation directly probes a local structural change around the excited state of tryptophan.     

Refining membrane penetration by a combination of steady-state and time-resolved depth-dependent fluorescence quenching

Accurate determination of the depth of membrane penetration of a fluorescent probe, attached to a lipid, protein, or other macromolecule of interest, using depth-dependent quenching methodology is complicated by thermal motion in the lipid bilayer. Here, we suggest that a combination of steady-state and time-resolved measurements can be used to generate a static quenching profile that reduces the contribution from transverse diffusion occurring during the excited-state lifetime. This procedure results in narrower quenching profiles, compared with those obtained by traditional measurements, and thus improves precision in determination of the underlying depth distribution of the probe.     

A second generation global analysis program for the recovery of complex inhomogeneous fluorescence decay kinetics

A flourescence spectroscopy global data analysis environment is described. Within this analysis environment multidimensional fluoroscence decay data (time and frequency domains) can be analyzed in terms of a wide variety of photophysical models. A generalized compartmental analysis structure is utilized, where one can specify the functions used to link the various compartments together. All fitting parameters may be characterized by either discrete or distributed values. Applications of these new analysis programs to the examination of phase transitions in lipid/membrane systems are described.     

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)     

Binding characterization of the interleukin-13 signaling complex and development of a ternary time-resolved fluorescence resonance energy transfer assay

Interleukin-13 (IL-13) is a critical mediator of pulmonary pathology associated with asthma. Drugs that block the biological function of IL-13 may be an effective treatment for asthma. IL-13 signals by forming a ternary complex with IL-13Rα1 and IL-4R. Genetic variants of IL-13 and of its receptor components have been linked to asthma. One in particular, IL-13R110Q, is associated with increased IgE levels and asthma. We characterized the interactions of the binary complexes composed of IL-13 or IL-13R110Q with IL-13Rα1 and the ternary complexes composed of IL-13 or IL-13R110Q and IL-13Rα1 with IL-4R using surface plasmon resonance and time-resolved fluorescence resonance energy transfer (TR-FRET). By both biophysical methods, we found no differences between IL-13 and IL-13R110Q binding in either the binary or the ternary complex. IL-4R bound to the IL-13/IL-13Rα1 complex with slow on and off rates, resulting in a relatively weak affinity of about 100 nM. We developed a TR-FRET assay targeting the interaction between the IL-4R and the binary complex. Two antibodies with known binding epitopes to IL-13 that block binding to either IL-13Rα1 or IL-4R inhibited the TR-FRET signal formed by the ternary complex. This assay will be useful to identify and characterize inhibitory molecules of IL-13 function.     

Analysis of RNA-protein interactions by a microplate-based fluorescence anisotropy assay

Quantitative studies of RNA-protein interactions are quite cumbersome using traditional methods. We developed a rapid microplate-based fluorescence anisotropy (FA)/fluorescence polarization assay that works well, even with RNA probes >90 nucleotides long. We analyzed binding of RNA targets by vigilin/DDP1/SCP160p and by c-myc coding region instability determinant (CRD) binding protein, CRD-BP. Vigilin is essential for cell viability and functions in heterochromatin formation and mRNA decay. The CRD-BP stabilizes c-myc mRNA. Vigilin bound to a vitellogenin mRNA 3'-UTR probe with a two to three-fold lower affinity than to a Drosophila dodecasatellite ssDNA binding site and bound to the c-myc CRD with a two- to three-fold lower affinity than to the vitellogenin mRNA 3'-UTR. Competition between vigilin and CRD-BP for binding to the CRD may therefore play a role in regulating c-myc mRNA degradation. We analyzed suitability of the microplate-based FA assay for high-throughput screening for small-molecule regulators of RNA-protein interactions. The assay exhibits high reproducibility and precision and works well in 384-well plates and in 5 microl to 20 microl samples. To demonstrate the potential of this assay for screening libraries of small molecules to identify novel regulators of RNA-protein interactions, we identified neomycin and H33342 as inhibitors of binding of vigilin to the vitellogenin mRNA 3'-UTR.     

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 flourescent 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 components. Determination of the individual lifetime requires knowledge of the steady-state emission spectra of the components. Use of low-frequency (≈ 10 Hz) cross-correlated signals eliminates the need for high-frequency frequency (≈10⁶ 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 fluorescence emissions which frequently occur from proteins, membranes and other biological samples.