What causes the variation of polarization degree across the emission spectrum of proteins?

A gradual decrease in fluorescence polarization across the emission spectrum on increase in wavelength has been recorded for a number of proteins and also for tryptophan, N-acetyltryptophan and glycyltryptophan. Various factors responsible for this dependence have been analyzed. It is shown that if the emission originates from both the 1La and 1Lb states, the position and form of the fluorescence spectrum polarization components as well as the slope of the dependence of the degree of polarization upon emission wavelength must always vary with the excitation wavelength. However, this condition, although necessary, is not enough to prove the participation of 1Lb in emission. The dependence of the form of the emission polarization spectrum upon excitation wavelength obtained for some proteins is explained by tyrosine residues contributing to the emission. Consequently, there are no reasons for assuming that the 1Lb oscillator participates in emission. It has been observed that for individual emitting centres, the slope of the dependence of the degree of polarization upon emission wavelength is determined by alteration of the vibrational substates, between which the transition with radiation takes place. The heterogeneity in the microenvironment properties of separate tryptophan residues in multitryptophan proteins and the existence, under certain conditions, of a correlation between the radiative lifetime of the emitting centre (determining the degree of the emission polarization) and the completeness of the microenvironment orientational relaxation (determining the emitted quantum of energy) can also affect the slope of this dependence.     

What causes the depolarization of trypsin and trypsinogen fluorescence: Intramolecular mobility or non-radiative energy transfer?

Analysis of protein data bank information about the coordinates of definite atoms of protein macromolecules provides an opportunity to evaluate the efficiency of non-radiative resonance energy transfer within the model of fixed, strictly oriented oscillators. Such evaluations for trypsin and trypsinogen (and also for trypsin complex with a pancreatic inhibitor) show that the efficiency of energy transfer among each pair of tryptophan residues is negligibly small. It is also shown that a fairly effective energy transfer from tyrosine to tryptophan residues is possible. The conclusions have been made that the Tyr-Trp energy transfer is one of the factors determining the shape of the trypsin polarization spectrum, and that upon fluorescence excitation at the long-wavelength edge of the absorption spectrum, the depolarization of trypsin fluorescence in aqueous solution at ambient temperature - compared to model compounds (tryptophan, N-acetyltryptophan, glycyltryptophan, etc.), under the conditions of infinite viscosity - is due to the Brownian rotational motion of the macromolecules as a whole as well as the intramolecular mobility. The differences in the level and character of intramolecular mobility of trypsin and trypsinogen are discussed.     

Quenching-resolved emission anisotropy studies with single and multitryptophan-containing proteins

Measurements of the anisotropy of protein fluorescence as a function of an added collisional quencher, such as acrylamide, are used to construct Perrin plots. For single tryptophan containing proteins, such plots yield an apparent rotational correlation time for the depolarization process, which, in most cases, is approximately the value expected for Brownian rotation of the entire protein. Apparent limiting fluorescence anisotropy values, which range from 0.20 to 0.32 for the proteins studied, are also obtained from the Perrin plots. The lower values for the limiting anisotropy found for some proteins are interpreted as indicating the existence of relatively rapid, limited (within a cone of angle 0 degrees--30 degrees) motion of the tryptophan side chains that is independent of the overall rotation of the protein. Examples of the use of this fluorescence technique to study protein conformational changes are presented, including the monomer in equilibrium dimer equilibrium of beta-lactoglobulin, the monomer in equilibrium tetramer equilibrium of melittin, the N in equilibrium F transition of human serum albumin, and the induced change in the conformation of cod parvalbumin caused by the removal of Ca+2. Because multitryptophan-containing proteins have certain tryptophans that are accessible to solute quencher and others that are inaccessible, this method can be used to determine the steady state anisotropy of each class of tryptophan residues.     

Time-resolved fluorescence study of human recombinant interferon alpha 2. Association state of the protein, spatial proximity of the two tryptophan residues.

Human recombinant interferon alpha 2 belongs a to family of proteins active against a wide range of viruses. It contains two tryptophan residues located at positions 77 and 141 in the peptide sequence. The fluorescence emission spectrum of these tryptophan residues displays a maximum at 335 nm. The fluorescence intensity decay is described by one broad excited-state-lifetime population centered around a value of 1.7 ns (full width at half maximum, 1.5 ns). These observations suggest that in the native protein, both tryptophan residues emit from similar environments, not directly exposed to the surrounding solvent. The anisotropy decay is essentially biexponential. The correlation-time value characterizing the Brownian rotation of the protein varies linearly with the viscosity/temperature ratio. The calculated hydrodynamic volumes are compatible with the existence of a dimer and a tetramer, at pH 5.5 and 9.4, respectively. Addition of urea at pH 5.5 disrupts the dimer and modifies to some extent the excited-state-lifetime distribution which becomes more heterogeneous. Disulfide-bond reduction also dissociates the dimer and leads to a highly heterogeneous fluorescence-intensity decay with four excited-state-lifetime populations. An opening of the local structure in the Trp region of the protein is likely to occur in these conditions. The fast-anisotropy-decay components can be due to either fast rotation or energy transfer between the indoles. Close proximity of the two Trp residues (less than 1 nm) is suggested from steady-state and time-resolved fluorescence-anisotropy measurements in vitrified medium [95% (by mass) glycerol at -38 degrees C]. This suggestion is in agreement with the recently published three-dimensional structure of the homologous protein murine interferon beta [Senda, T., Shimazu, T., Matsuda, S. Kawano, G., Shimizu, H., Nakamura, K. T. & Mitsui, Y. (1992) EMBO J. 11, 3193-3201].     

A rare protein fluorescence behavior where the emission is dominated by tyrosine: case of the 33-kDa protein from spinach photosystem II

An abnormal fluorescence emission of protein was observed in the 33-kDa protein which is one component of the three extrinsic proteins in spinach photosystem II particle (PS II). This protein contains one tryptophan and eight tyrosine residues, belonging to a "B type protein". It was found that the 33-kDa protein fluorescence is very different from most B type proteins containing both tryptophan and tyrosine residues. For most B type proteins studied so far, the fluorescence emission is dominated by the tryptophan emission, with the tyrosine emission hardly being detected when excited at 280 nm. However, for the present 33-kDa protein, both tyrosine and tryptophan fluorescence emissions were observed, the fluorescence emission being dominated by the tyrosine residue emission upon a 280 nm excitation. The maximum emission wavelength of the 33-kDa protein tryptophan fluorescence was at 317 nm, indicating that the single tryptophan residue is buried in a very strong hydrophobic region. Such a strong hydrophobic environment is rarely observed in proteins when using tryptophan fluorescence experiments. All parameters of the protein tryptophan fluorescence such as quantum yield, fluorescence decay, and absorption spectrum including the fourth derivative spectrum were explored both in the native and pressure-denatured forms.     

Spectral properties and function of two lumazine proteins from Photobacterium

The spectral properties are compared for two 6,7-dimethyl-8-ribityllumazine proteins from marine bioluminescent bacteria, one from a psychrophile, Photobacterium phosphoreum, and the other from a thermophile, Photobacterium leiognathi. The visible spectral properties, which are the ones by which the protein performs its biological function of bioluminescence emission, are almost the same for the two proteins: at 2 degrees C and 50 mM Pi, pH 7, fluorescence quantum yield phi F = 0.59 and 0.54, respectively; fluorescence lifetime tau = 14.4 and 14.8 ns, respectively; fluorescence maxima, both 475 nm; absorption maximum, 417 and 420 nm, respectively; circular dichroism minima at around 420 nm, both -41 X 10(3) deg cm2 dmol-1. The ligand binding sites therefore must provide very similar environments, and arguments are presented that the bound ligand is relatively exposed to solvent. The dissociation equilibrium was studied by steady-state fluorescence polarization. The thermophilic protein binds the ligand with Kd (20 degrees C) = 0.016 microM, 10 times more tightly than the other protein [Kd (20 degrees C) = 0.16 microM]. The origin of the binding difference probably resides in differences in secondary structure. The tryptophan fluorescence spectra of the two proteins are different, but more significant is an observation of the decay of the tryptophan emission anisotropy. For the psychrophilic lumazine protein this anisotropy decays to zero in 1 ns, implying that its single tryptophan residue lies in a very "floppy" region of the protein. For the other protein, the anisotropy exhibits both a fast component and a slow one corresponding to rotation of the protein as a whole.(ABSTRACT TRUNCATED AT 250 WORDS)     

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.     

Electron spin polarization in photosynthesis and the mechanism of electron transfer in photosystem I. Experimental observations.

Transient electron paramagnetic resonance (EPR) methods are used to examine the spin populations of the light-induced radicals produced in spinach chloroplasts, photosystem I particles, and Chlorella pyrenoidosa. We observe both emission and enhanced absorption within the hyperfine structure of the EPR spectrum of P700+, the photooxidized reaction-center chlorophyll radical (Signal I). By using flow gradients or magnetic fields to orient the chloroplasts in the Zeeman field, we are able to influence both the magnitude and sign of the spin polarization. Identification of the polarized radical and P700+ is consistent with the effects of inhibitors, excitation light intensity and wavelength, redox potential, and fractionation of the membranes. The EPR signal of the polarized P700+ radical displays a 30% narrower line width than P700+ after spin relaxation. This suggests a magnetic interaction between P700+ and its reduced (paramagnetic) acceptor, which leads to a collapse of the P700+ hyperfine structure. Narrowing of the spectrum is evident only in the spectrum of polarized P700+, because prompt electron transfer rapidly separates the radical pair. Evidence of cross-relaxation between the adjacent radicals suggests the existence of an exchange interaction. The results indicate that polarization is produced by a radical pair mechanism between P700+ and the reduced primary acceptor of photosystem I. The orientation dependence of the spin polarization of P700+ is due to the g-tensor anisotropy of the acceptor radical to which it is exchange-coupled. The EPR spectrum of P700+ is virtually isotropic once the adjacent acceptor radical has passed the photoionized electron to a later, more remote acceptor molecule. This interpretation implies that the acceptor radical has g-tensor anisotropy significantly greater than the width of the hyperfine field on P700+ and that the acceptor is oriented with its smallest g-tensor axis along the normal to the thylakoid membranes. Both the ferredoxin-like iron-sulfur centers and the X- species observed directly by EPR at low temperatures have g-tensor anisotropy large enough to produce the observed spin polarization; however, studies on oriented chloroplasts show that the bound ferredoxin centers do not have this orientation of their g tensors. In contrast, X- is aligned with its smallest g-tensor axis predominantly normal to the plane of the thylakoid membranes. This is the same orientation predicted for the acceptor radical based on analysis of the spin polarization of P700+, and indicates that the species responsible for the anisotropy of the polarized P700+ spectrum is probably X-. The dark EPR Signal II is shown to possess anisotropic hyperfine structure (and possibly g-tensor anisotropy), which serves as a good indicator of the extent of membrane alignment.     

Nanosecond segmental mobilities of tryptophan residues in proteins observed by lifetime-resolved fluorescence anisotropies.

Steady-state and lifetime-resolved fluorescence anisotropy measurements of protein fluorescence were used to investigate the depolarizing motions of tryptophan residues in proteins. Lifetime resolution was achieved by oxygen quenching. The proteins investigated were carbonic anhydrase, carboxypeptidase A, alpha-chymotrypsin, trypsin, pepsin, and bovine and human serum albumin. When corrected for overall protein rotation, the steady state anisotropies indicate that, on the average, the tryptophan residues in these proteins rotate 29 degrees +/- 6 degrees during the unquenched excited state lifetimes of these proteins, which range from 1.7 to 6.1 ns. The lifetime-resolved anisotropies reveal correlation times for these displacements ranging from 1 to 12 ns. On the average these correlation times are tenfold shorter than that expected for overall protein rotation. We conclude that the tryptophan residues in these proteins display remarkable freedom of motion within the protein matrix, which implies that these matrices are highly flexible on the nanosecond time scale.     

Global analysis of steady-state polarized fluorescence spectra using trilinear curve resolution.

Global analysis using trilinear curve resolution is described and shown to be a powerful method for the resolution of polarized fluorescence data arrays, in which the measured fluorescence intensity is a separable function of polarization orientation, excitation wavelength, and emission wavelength. This methodology is applicable to mixtures the components of which have linearly independent excitation and emission spectra and distinct anisotropies. Normalized excitation and emission spectra of individual components can be uniquely determined without prior assumptions concerning spectral shapes (e.g., sum of Gaussians) and without the uncertainties inherent in bilinear techniques such as principal component analysis or factor analysis. The normalized excitation and emission vectors are combined with the total absorption spectrum of the multicomponent mixture to compute absolute absorption and emission spectra. The precision of this methodology is evaluated as a function of noise, overlap, relative intensity, and anisotropy difference between components using simulated mixtures of the DNA bases. The ability of this method to extract individual spectra from steady-state fluorescence data arrays is illustrated for mixtures containing two and three components.     

Time-resolved fluorescence of the single tryptophan residue in rat alpha-fetoprotein and rat serum albumin: analysis by the maximum-entropy method.

The time-resolved fluorescence emissions of the lone tryptophan residues in rat alpha-fetoprotein (RFP) and rat serum albumin (RSA) were studied. The total fluorescence intensity decays in both proteins were multiexponential. Analysis of the data by nonlinear least squares as a sum of discrete exponentials showed that four exponentials were needed for a satisfactory fit for both proteins. Analysis by the maximum entropy method using 150 logarithmically equally spaced exponentials yielded four well-resolved excited-state lifetime classes with barycenters and relative amplitudes values (ci) that corresponded to those obtained from the nonlinear least-squares method. Changing the temperature affected the relative amplitudes of the lifetime classes but had little effect on the lifetime values themselves. This suggests that the four classes reflect local conformational substates that exchange slowly with respect to the time window of observation defined by the longest lifetime. The internal rotational dynamics of the tryptophan in each protein was monitored by fluorescence anisotropy decay measurements. The mobility of the tryptophan appeared to be larger and faster in RFP than in RSA. The nonlinear least-squares analysis suggests the existence of three rotational correlation times of 0.1, 3, and 55 ns for this protein. As a function of temperature, the long correlation time did not follow the Perrin's law expected for a rigid rotating body. This suggests that this correlation time may reflect not only the Brownian rotation of the whole protein but also the flexibilities of domains in the protein. For RSA a two-component model with correlation times of 0.4 and 31 ns was sufficient to describe the data.(ABSTRACT TRUNCATED AT 250 WORDS)     

Motions studies of the human alpha 1-acid glycoprotein (orosomucoid) followed by red-edge excitation spectra and polarization of 2-p-toluidinylnaphthalene-6-sulfonate (TNS) and of tryptophan residues.

Dynamics studies on tryptophan residues of human alpha 1-acid glycoprotein (orosomucoid) and of 2-p-toluidinylnaphthalene-6-sulfonate bound to the protein are performed. Excitation at the red edge of the absorption spectrum of the tryptophan does not lead to a shift of the fluorescence emission maximum of the fluorophore. This reveals that Trp residues present motions with respect to their microenvironment. This is confirmed by polarization studies as a function of temperature. Excitation at the red edge of the absorption spectrum of TNS leads to an important shift (15 nm) of the fluorescence emission maximum of the probe. This reveals that emission of TNS occurs before relaxation of the amino-acids dipole occurs. Emission from a non-relaxed state means that TNS molecules are bound tightly to the protein, a result confirmed by polarization studies.     

An ultrafast time-resolved anisotropy study of bacteriochlorophyll a in pyridine

The transient absorption anisotropy spectrum of bacteriochlorophyll a (BChl a) in pyridine was measured in the wavelength interval 550-850 nm, 1 ps after optical excitation with a 792-nm femtosecond light pulse. In the wavelength region of Q(y) absorption and stimulated emission (775-825 nm), the anisotropy was found to be close to the theoretically expected value (0.4) for a two-level system. In the wavelength region 650-750 nm, where the transient absorption signal is dominated by excited state absorption, the anisotropy is reduced to approximately 0.18. Anisotropy kinetics were measured at several wavelengths and found to be constant within the time window 0-5 ps, showing that no internal dynamics of the BChl a molecule change the anisotropy on the time scale of tens of picoseconds.     

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.     

Transfer of singlet energy within trypsin.

Transfers of singlet energy within trypsin were investigated by measuring the fluorescence absorption anisotropy of its tryptophan residues. A ratio of the anisotropy of trypsin to that for N-acetyl-L-tryptophanamide was determined between 306 and 250 nm. The ratio had an average value of 0.7, whether the trypsin anisotropy was measured at 228 of 296 K. However, trypsin dissolved in 5 M guanidine hydrochloride showed little fluorescence depolarization at 228 K (the anisotropy ratio was approximately equal to 0.9). Thus, there is an extensive conformation-dependent energy transfer between tryptophans in trypsin. The ratio of anisotropies of tyrpsin at 304--270 nm was used to estimate energy transfer from tyrosine to tryptophan. Ratios of 1.8 and 1.7 were obtained at 296 K for the native and guanidinium-unfolded enzyme, respectively. The comparable value for N-acetyl-L-tryptophanamide was 1.7. This indicates that there is little transfer from tyrosine to tryptophan in trypsin at 296 K. As confirmation, the excitation wavelength dependencies of the indole fluorescence quantum yield were the same for native and unfolded trypsin. When experiments were performed at 228 K, the 304--270-nm anisotropy ratios were 2.6 for native and 2.1 for unfolded trypsin at pH2. This indicates that the efficiency of energy transfer from tyrosine to tryptophan increases at low temperatures. A photochemical source of error in the quantitation of the efficiency of energy transfer from tyrosine to tryptophan is also described.     

The effect of ATP on the cell membrane structure]

ATP influence on the structure of plasma membranes thymocytes of cattle was studied. Fluorescence anisotropy of tryptophan residues of membrane proteins, fluorescence anisotropy of 3-methoxybenzanetron and fluorescence intensity of 1-anilinonaphthalene-8-sulphonate were determined. Changes of tryptophan fluorescence anisotropy and of ANS fluorescence intensity were established. It is supposed that the observed changes are connected with the change of membrane proteins structure and plasma membrane charge.     

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.     

The effect of electrostatic intermolecular interactions on Brownian rotation of proteins in solution]

A qualitative model that takes into account the influence of electrostatic interactions on the form of correlation function of Brownian rotation of a protein as a whole is given. It is supposed that these interactions give rise to anisotropy of Brownian rotation and this leads to the nonexponentiality of the correlation function. To define experimentally the form of the correlation function nonselective measurements of relaxation times T1 and T2 of protein protons at different resonance frequencies in lysozyme solution were carried out. Literature data on frequency dependencies of relaxation time T1 of water in protein solutions were analysed. Analysis of experiments confirms the proposed model. Correlation times, activation energies and parameters of anisotropy were found.     

Correlation between internal motion and emission kinetics of tryptophan residues in proteins

Time-resolved fluorescence anisotropy measurements of tryptophan residues were carried out for 44 proteins. Internal rotational motion with a sub-nanosecond correlation time (0.9 +/- 0.6 ns at 10 degrees C) was seen in a large number of proteins, though its amplitude varied from protein to protein. It was found that tryptophan residues which were almost fixed within a protein had either a long (greater than 4 ns) or short (less than 2 ns) fluorescence lifetime, whereas a residue undergoing a large internal motion had an intermediate lifetime (1.5-3 ns). It is suggested that the emission kinetics of a tryptophan residue is coupled with its internal motion. In particular, an immobile tryptophan residue emitting at long wavelength was characterized by a long lifetime (greater than 4 ns). It appears that a tryptophan residue fixed in a polar region has little chance of being quenched by neighboring groups.     

Stark effect spectroscopy of tryptophan.

The change in permanent dipole moment (magnitude of delta mu) for the transition from the 1La state to the ground state of tryptophan is the key photophysical parameter for the interpretation of tryptophan fluorescence spectra in terms of static and dynamic dielectric properties of the surrounding medium. We report measurement of this parameter by means of electric field effect (Stark) spectroscopy for N-acetyl-L-tryptophanamide (NATA) in two solvents, the single tryptophan containing peptide melittin, and 5-methoxytryptophan. The values ranged from 5.9 to 6.2 +/- 0.4 Debye/f for NATA and melittin, where f represents the local field correction. The 1Lb magnitude of delta mu was much smaller. Application of Stark spectroscopy to these chromophores required decomposition of the near-UV absorption into the 1La and 1Lb bands by measurement of the fluorescence excitation anisotropy spectrum and represents an extension of the method to systems where band overlap would normally preclude quantitative analysis of the Stark spectrum. The results obtained for 5-methoxytryptophan point out limitations of this method of spectral decomposition. The relevance of these results to the interpretation of steady-state and time-resolved spectroscopy of tryptophan is discussed.