Homogeneous Spectrally - American Chemical Society

J. Phys. Chem. B 2001, 105, 2043-2055

2043

Homogeneous Spectrally- and Time-Resolved Fluorescence Emission from Single-Tryptophan Mutants of IIAGlc Protein Dmitri Toptygin,* Regina S. Savtchenko, Norman D. Meadow, and Ludwig Brand Department of Biology, Johns Hopkins UniVersity, 3400 N. Charles Street, Baltimore, Maryland 21218 ReceiVed: September 21, 2000; In Final Form: January 3, 2001

We report an experimental study of protein relaxation dynamics on the picosecond and nanosecond time scales. The protein equilibrium state is perturbed by the redistribution of electric charge density over the side chain of a tryptophan residue. Electronic excitation of the residue induces the charge shift and triggers a relaxation process, the dynamics of which is reflected in tryptophan fluorescence emission. In the case of homogeneous emission, the relaxation dynamics can be extracted from a time-dependent red shift in the emission spectrum. In the case of heterogeneous emission, the spectral shift may not represent relaxation dynamics. A criterion for distinguishing between homogeneous and heterogeneous fluorescence emission is suggested here. Emission from the mutants E21W and F3W of IIAGlc is found to be free from permanent or long-lived heterogeneity. In E21W, the only tryptophan residue is in a rigid globule, whereas in F3W it is on a flexible tail. The relaxation dynamics reported by the tryptophan residue in F3W is much faster than that in E21W. Addition of glycerol to the solvent slows down the relaxation dynamics for both tryptophan residues.

1. Introduction Biological functions of ion channels and pumps, chloroplast and mitochondrial electron transport proteins, ATP synthases, and many other enzymes and proteins are based on their ability to either transfer electric charges or bind charged or polar molecules. Equilibria and rates of the processes involving relocation of electric charges are defined by microscopic dielectric characteristics of the protein. These include polarity, which represents a microscopic analogue of the bulk static dielectric constant , and a response function, which represents a microscopic analogue of the bulk dielectric response (t). In liquid solvents both the polarity and the response function are commonly measured using polar aromatic solutes: several empirical polarity scales utilize their steady-state absorption1-3 or fluorescence4,5 spectra, whereas the response function is derived from their transient absorption spectra6-8 or timeresolved fluorescence spectra.9-12 Essentially the same methods have been applied to measure the microscopic dielectric characteristics of proteins.13-21 Some of these studies employed polar aromatic molecules (ANS,13,19 TNS,14-16 DANCA,17 eosin21) that were noncovalently bound to bovine serum albumin,13,14,19 apomyoglobin,15-17 lysozyme,13,21 and a number of other proteins.13 Other studies utilized covalently attached synthetic chromophores18,19 or the natural chromophore found in a light-harvesting protein.20 In the present work we make use of another natural chromophore, the side chain of a tryptophan residue, to measure microscopic dielectric relaxation in proteins. In contrast to liquid solvents, proteins are both heterogeneous and anisotropic on the microscopic scale, therefore the microscopic dielectric characteristics must vary with the location and orientation of the spectroscopic probe. Identical chromophores can produce disparate spectroscopic signals if they have different locations and/or orientations and if the difference is preserved for the duration that equals or exceeds experimental time * To whom correspondence should be addressed. E-mail address: [email protected]. FAX: 410-516-5213.

resolution (in time-resolved measurements) or the lifetime of the excited state (in steady-state fluorescence measurements). Multiple chromophore locations and/or orientations may result in a heterogeneous spectroscopic signal that sometimes creates an illusion of relaxation.22 Several possible origins of heterogeneous fluorescence emission from tryptophan residues in proteins have been discussed in the literature. Different tryptophan residues in the amino acid sequence never end up in exactly identical environments in a folded protein, and this difference is permanent. Thus, multiple tryptophan residues in the sequence of a protein represent the most common origin of permanent heterogeneity.23 Multiexponential time-resolved fluorescence emission from single-tryptophan proteins and tryptophan in solution is often interpreted in terms of heterogeneity associated with discrete rotational conformers (rotamers) of the tryptophan side chain.24,25 For some protein structures, several possible conformations of the tryptophan side chain were found in molecular dynamics simulations;26,27 however, the time scale of these simulations was too short and it is not clear whether the rotamers could interconvert during the lifetime of the excited state. If the rotamers do not interconvert during the excited-state lifetime, then this results in long-lived heterogeneity, which may also create a false illusion of relaxation. Besides heterogeneity, a relaxation process, such as microscopic dielectric relaxation, can be responsible for multiexponential time-resolved fluorescence emission. The first convincing evidence of a nanosecond-scale relaxation process in the fluorescence emission from tryptophan residues in a protein was presented by Grinvald and Steinberg.28 Relaxation was found in the fluorescence of other tryptophan-containing proteins29-31 and free tryptophan in solution.32 To the best of our knowledge, however, a possible contribution of heterogeneity has not been ruled out, even in those cases where there was a positive proof of relaxation. Chicken pepsinogen, in the fluorescence of which a negative exponential was first found,28 has multiple tryptophan residues in its sequence, and this inevitably results in permanent heterogeneity.

10.1021/jp003405e CCC: $20.00 © 2001 American Chemical Society Published on Web 02/07/2001

2044 J. Phys. Chem. B, Vol. 105, No. 10, 2001

Toptygin et al.

In the present work we suggest and experimentally test a criterion for distinguishing between homogeneous and heterogeneous time-resolved fluorescence emission of tryptophan residues in proteins and measure the microscopic dielectric response function in two proteins where we found no longlived or permanent heterogeneity. The two proteins are the mutants E21W and F3W of IIAGlc (formerly known as IIIGlc),33-37 a phospho-carrier protein of the bacterial phosphoenolpyruvate: glycose phosphotransferase system (PTS) from Escherichia coli. The native IIAGlc protein has neither tryptophan nor tyrosine residues;33 therefore, each mutant has just one tryptophan and no tyrosine, which helps to avoid permanent heterogeneity and precludes complications due to conceivable tyrosine-to-tryptophan energy transfer. The IIAGlc protein has a well-defined solution structure, which has been solved by NMR33-35 and by X-ray diffraction.36 The protein consists of a rigid globule of residues 19 through 168 and a flexible tail of the first 18 residues.34,36 The tail is invisible both by NMR34 and by X-ray diffraction,36 but it is vital for the biological activity of the protein.37 In the first mutant, E21W, a tryptophan residue was inserted in the rigid globule. In the second mutant, F3W, a tryptophan residue was inserted in the flexible tail. On the basis of the structural information, one could expect the environment of the tryptophan residue to be homogeneous in E21W and heterogeneous in F3W; however, no estimates about the time span of the heterogeneity could be made based on the X-ray and NMR data. The polarity and the dielectric response function were expected to be different in the environments of the tryptophan residues in E21W and F3W.

In the case of no relaxation, the parameters νj and µ are timeinvariant, therefore the factors S(ν - νj) and |µ|2 on the righthand side of eq 3 are also time-invariant, and the time variation of Fν(ν,t) at any constant ν repeats within a constant factor the decay function N(t). For this reason, the time variation of fluorescence intensity is commonly referred to as a decay curve. This term is confusing in the cases where νj and/or µ are timevariant and Fν(ν,t) does not reproduce the decay of the excited state. 2.3. Dielectric Relaxation. Electronic excitation of tryptophan alters electric charge distribution over the indole rings.39,40 This is followed by dielectric relaxation of the tryptophan environment. The relaxing environment generates a time-variant electric field that acts back on the tryptophan side chain and modulates the energy gap between its ground and excited electronic states. The energy gap is represented by the parameter νj in eq 3. This parameter is expected to vary considerably during dielectric relaxation. The shape of the function S(ν) is not expected to vary.38 The theoretical predictions regarding νj and S(ν) have been confirmed experimentally using a solution of indole in glycerol.38 No significant variation of |µ|2 was discovered in these experiments. 2.4. Expansion of Fν(ν,t) in Exponential Series. Assuming that the relaxation of the tryptophan environment is aperiodic (which is usually true for nano- and picosecond scale motions, but may be false for very fast “inertial” motions of small molecules9,11), the time variation of any parameter can be represented as a linear combination of exponential functions

νj(t) ) νj∞ +

2. Theory 2.1. Description of Spectrally- and Time-Resolved Fluorescence. Spectrally- and time-resolved fluorescence emission intensity will be represented as either Fλ(λ,t) or Fν(ν,t). The spectral variables are: λ, the emission wavelength, and ν, the emission wavenumber. Time, t, is counted from the δ-excitation. Fλ represents the number of photons per unit wavelength per unit time. Fν represents the number of photons per unit wavenumber per unit time. Using the conversion factors |dλ/ dν| ) ν-2 and |dν/dλ| ) λ-2, the quantities Fν and Fλ can be expressed in terms of one another:

Fν(ν, t) ) ν-2Fλ(ν-1, t)

(1)

Fλ(λ, t) ) λ-2Fν(λ-1, t)

(2)

2.2. Homogeneous Emission. Emission from a homogeneous ensemble of excited chromophores can be represented in the form38

Fν(ν, t) ) aν3S(ν - νj)|µ|2 N(t)

(3)

where a ) (64π4)/(3h), h is the Planck constant; ν3 takes care of the frequency dependence of the spontaneous emission probability; S(ν) represents the vibrational envelope of the electronic transition, by definition38 ∫S(ν)dν ) 1, ∫S(ν)νdν ) 0 (the integration is over the entire emission spectrum); νj represents the mean energy gap between the ground and excited singlet electronic states; µ is the transition dipole moment corresponding to the transition between these states, |µ|2 denotes the squared magnitude of the vector; N is the number of molecules in the excited state, N(t) describes the decay of the excited state.

∑i νji exp(-k reli t)

(4)

A similar expression can be written for |µ(t)|2. After substituting these expressions into eq 3 and expanding nonlinear functions of exponentials in the Taylor series, we have obtained38 the following expression: ∞

Fν(ν, t) )

∑ Rn(ν) exp(-t/τn)

(5)

n)1

It is convenient to number the time constants τn in descending order. The greatest time constant, τ1, is defined by the asymptotic behavior of N(t) at tf∞:

d ln[N(t)] 1 ) - lim tf∞ τ1 dt

(6)

This implies that the tail of the decay function, N(t), is approximately exponential and the time constant involved in this exponential equals τ1:

N(t) ≈ N0 exp(-t/τ1)

(7)

Because of its role in eq 7, the time constant τ1 will be also called the lifetime of the excited state. The inverses of the other time constants are some combinations of the inverse of the excited-state lifetime with one or more of the relaxation rate constants:

1 1 ) + m1k1rel + m2k2rel + ... τn τ1

(8)

where m1, m2, etc. are any nonnegative integers, and k1rel, k2rel, ... represent the relaxation rate constants. Equations similar to

Protein Relaxation Dynamics

J. Phys. Chem. B, Vol. 105, No. 10, 2001 2045

a combination of eq 8 with eq 5 have been published previously by other authors.41,42 2.5. Resolving Large Numbers of Exponentials. Although the theoretical eq 5 contains an infinite number of exponentials, the model function for fitting to experimental data does not need to include all of these exponentials. The exponentials with τn beyond the instrument’s time resolution can be omitted. The time constants corresponding to the remaining exponentials fall within the range τmineτneτmax where τmin is defined by the time resolution and τmax equals the lifetime of the excited state. Within this finite window of time constants there can be only a finite number (Nmax) of exponentials that are linearindependent to a finite accuracy level. If the number of exponentials is greater than Nmax, then some of the exponentials can be expressed as linear combinations of the others without exceeding a specified error margin. The maximum number of linear-independent exponentials can be estimated using the following empirical formula:

Nmax e a log10 (b τmax/τmin) log10 (c/)

(9)

where a ) 0.537, b ) 4.09, c ) 1.38, and represents the accuracy level (by definition equals the sum of squared errors divided by the sum of squared values). Equation 9 is accurate only when both τmax/τmin > 10 and < 0.01; it summarizes the results of an extensive computational study that will be published elsewhere. Substituting τmax/τmin ) 100 and ) 10-5 yields Nmax ) 7. This represents the number of exponentials with fixed τn that are needed to fit any time-correlated photon-counting data with the peak photon count about 105 when τmax is 100fold greater than the width of the instrument response. If τn are free fitting parameters, then an adequate fit is achieved with the number of exponentials equal to 1/2Nmax, rounded to the next larger integer when Nmax is odd. In the above example, four exponentials with free τn should be sufficient for an adequate fit. If five exponentials need to be resolved, then either the response time must be decreased 5 times or the photon count must be increased 25 times. On the basis of the above considerations, the fitting function for spectrally- and time-resolved experimental data should be

spectrum of the nth species.23,43 Since fluorescence emission intensity cannot be negative, no negative Rn(ν) values are tolerated in the absence of relaxation. Thus, a negative preexponential factor serves as a proof of relaxation, but it does not rule out heterogeneity. 2.7. Shape Conservation Criterion. In the case of homogeneous relaxation, Fν(ν,t) must satisfy eq 3. Multiplying both sides of this equation by ν-3 yields

ν-3 Fν(ν, t) ) a S[ν - νj(t)]|µ(t)|2N(t)

Of the four factors on the right-hand side of eq 11, only S[ν νj(t)] varies with ν. To cancel all of the ν-invariant factors, the spectra ν-3Fν(ν,t)|t)const can be normalized either to a constant integral or to a constant peak. The normalized spectra ν-3Fν(ν,t)|t)const corresponding to different values of t must be identical in shape; the only difference between them must be a parallel translation along the ν axis. This can serve as a criterion for distinguishing between homogeneous and heterogeneous relaxation. The criterion is insensitive to heterogeneity with the time span shorter than the width of the instrument response. The shortlived heterogeneity broadens all the normalized spectra equally, and leads to no shape variations. Permanent and long-lived heterogeneity is likely to result in shape variations. Application of this criterion requires accurate spectral correction, because uncorrected spectral variation of the instrument sensitivity distorts the spectral shapes. 2.8. Reconstructing Dielectric Response from Fitting Parameters. The time-variant energy gap νj(t) represents the microscopic dielectric response of the protein at the location of the tryptophan residue. It can be expressed as the ratio of two spectral moments:38

νj(t) )

∑ Rn(ν) exp(-t/τn)

M3(t)

(12)

∫0∞ λi Fλ (λ, t) dλ

(13)

∫0∞ ν-i Fν (ν, t) dν

(14)

Mi(t) ) (10)

Mi(t) )

n)1

where Rn and τn represent free fitting parameters, Rn are ν-variant and τn are ν-invariant, and Nexp ≈ 1/2Nmax. An adequate Nexp can be determined by using models with successively increasing Nexp and applying a reliable goodness-of-fit test. The fitting parameters in eq 10 do not necessarily have a direct physical meaning. If the number of exponential relaxation terms in eq 4 is finite and less than 1/2Nmax, then the greatest time constant (τ1) represents the lifetime of the excited state and the other time constants represent combinations according to eq 8 with small mi (usually Σmi ) 1). If the number of different kirel is equal to or greater than 1/2Nmax, then the fitting parameters have no direct physical meaning and it is not possible to determine the actual number of different kirel. 2.6. Significance of Negative Preexponential Factors. By coincidence, spectrally- and time-resolved emission from a heterogeneous ensemble of excited chromophores in nonrelaxing environments is also described by eq 10. In this case Nexp represents the number of different emitting species, while τn and τnRn(ν) represent the lifetime and the steady-state emission

M2(t)

The moments Mi(t) can be defined using either of the following equations:

Nexp

Fν(ν, t) )

(11)

If Fν(ν,t) is represented by the linear combinations of exponentials in eq 10, then the spectral moments are also linear combinations of exponentials: Nexp

Mi(t) )

∑ Jin exp(-t/τn)

(15)

n)1

where

J in )

∫0∞ ν-i Rn (ν) dν

(16)

In practical applications, the integration in eq 16 should be carried out over a finite spectral range that includes the entire emission spectrum. 2.9. Dielectric Response in Heterogeneous Ensembles. In the case of a homogeneous ensemble, νj(t) represented the timevariant energy gap for every excited chromophore. In the case of a heterogeneous ensemble, different homogeneous subensembles have different νj(t), and the νj(t) obtained from eq 12

2046 J. Phys. Chem. B, Vol. 105, No. 10, 2001 represents a weighted mean, where the weights are proportional to the subensemble populations. If the weights change due only to migration of chromophores between subensembles, which represents a form of relaxation, then νj(t) still represents the microscopic dielectric response function, but in the ensemble mean sense. In the presence of permanent (or long-lived) heterogeneity, the weights can also change because some noninterconverting subensembles (or subensembles interconverting very slowly) live longer than others. In this case νj(t) obtained from eq 12 does not represent the dielectric response function; it usually does not reach its tf∞ limit until the emission intensity becomes too low to be measured, and νj(∞) does not represent the mean polarity of environment for all tryptophan residues. Instead, it represents the polarity for the longest-lived subensemble, which can be a very small fraction of all the tryptophan residues. The longest-lived tryptophan residues can be located in chemically altered, unfolded or misfolded protein molecules. The longestlived chromophores can also be chemical products of tryptophan photobleaching.44 3. Experimental Section 3.1. Protein Mutagenesis, Expression, and Purification. E21W. A mutagenesis method based on two-step PCR was used to construct a plasmid containing mutant allele of the crr gene where glutamic acid in position 21 was replaced by tryptophan. The plasmid pDS 3545 has been used as a template. Mutagenesis of this triplet was performed in the first PCR step with four primers: two mutagenic primers, G21T-1 (5′-GGAACTATTTGGATCATTGCT-3′) and G21T-2 (5′-AGCAATGATCCAAATAGTTCC-3′); and two primers to attach restriction sites for cloning, SS112 (5′-GGCGCCATTTTTCACTGCCAGAATTCTTACTTCTTGATGCG-3′) for EcoRI site and SS110 (5′-ACTGCTTAGGAGAAGCATATGGGTTTGTTCGATAAACTG-3′) for NdeI site. The results of this reaction were two PCR products, which were used as template for the second PCR reaction with SS112 and SS110 primers to obtain the full size of the mutated crr gene. The PCR product was restricted with NdeI and EcoRI restriction enzymes and cloned into pET21a plasmid (Novagen). F3W. The mutation of phenylalanine in position 3 of the crr gene was previously described.46 Each of the mutated IIAGlc proteins were expressed in Escherichia coli BL21 (DE3) strain where the crr gene has been deleted47 and purified using a previously published technique.33 The purity of the proteins was tested using polyacrylamide gel shift assay both before and after the fluorescence measurements to ensure that no proteolysis occurred during the measurements. 3.2. Protein Fluorescent Samples. Fluorescence of each of the two mutated proteins was measured in three different aqueous solvents containing 0%, 3%, and 30% glycerol by volume. At the end of the purification, the proteins were obtained in a solvent containing 3% v/v glycerol, 50 mM TrisHCl buffer, pH ) 7.5, 1 mM EDTA, and 0.05% w/v NaN3; this was used as the 3% glycerol solvent. To prepare the 0% glycerol samples, the protein solutions were dialyzed for 24 h against a solvent of identical composition except for the glycerol. To obtain the 30% glycerol solutions, an appropriate amount of anhydrous glycerol was added to the 3% glycerol solution. This decreased the concentrations of Tris, EDTA, and NaN3 to approximately 36 mM, 0.72 mM, and 0.036% w/v. To reduce the effects of photobleaching,44 concentrated protein solutions were used for fluorescent measurements. Protein concentration varied between 30 µM and 44 µM in

Toptygin et al. different solvents. The high concentrations made it possible to work at low excitation intensities (2 µW or less), which reduced the fluorescence contamination from the products of tryptophan photobleaching to negligible levels. Due to the high concentrations, the absorbance at the excitation wavelength (289 nm) was close to 0.2. This resulted in some inner-filter effect that was corrected as described below. The absorbance at the peak of emission (345 nm for E21W, 355 nm for F3W) was below 0.001, therefore fluorescence reabsorption was not an issue. 3.3. Model Fluorescent Samples. Two fluorescent model systems were used in this work. The first model system was a solution of indole in glycerol prepared as described elsewhere.38 The second model system involved two solutions: a 30 µM solution of indole (99+%, Aldrich) in anhydrous ethyl ether (J. T. Baker) and a 40 µM solution of indole in water. The two solutions were placed in identical cuvettes. Steady-state emission spectra were measured with one cuvette at a time and then added. In time-correlated photon counting experiments, the two cuvettes were switched after every 15 s by the program that automatically ran the instrument and collected the data. The program was set to count photons from both cuvettes for exactly the same live time and to add the counts together. 3.4. Temperature. A temperature denaturation study over the temperature range from -10 °C to +90 °C has shown that neither mutant undergoes cold denaturation, whereas both mutants denature at hot temperatures, Tm ≈ 69 °C, similar to the native protein.35 A detailed account of this study will be published elsewhere. At temperatures below 55 °C, the fraction of the protein that is in the unfolded state is less than 1%. All protein fluorescence measurements were carried out at 5 ( 0.25 °C. At this temperature, the lifetime of the excited state is longer than at 20 °C. The increased lifetime results in a wider time window during which the time-resolved emission spectra can be reliably measured. Model system fluorescence was measured at 20 ( 0.25 °C (indole in glycerol)38 and 4 ( 0.25 °C (indole in ethyl ether and water). 3.5. Steady-State Fluorescence Measurements. All steadystate measurements were carried out on an SLM-48000 spectrofluorometer (SLM Instruments, Urbana, Illinois). The excitation monochromator slits were set to 2 nm spectral width in all of the measurements. The excitation intensity is proportional to the squared slit width; after 1 h excitation through the 4 nm slits, the fluorescence emission of photobleached tryptophan residues was barely detectable.44 All steady-state emission spectra were measured with the excitation polarizer set to the magic angle (55° from vertical) and the emission polarizer set to the vertical polarization. The latter eliminates Wood’s anomalies in the emission monochromator. In the studies of the emission spectrum variation with the excitation wavelength the emission, monochromator slits were set to 4 nm width. The steady-state emission spectra required for the renormalization of the time-resolved emission spectra were obtained with the emission monochromator slit width equal to that in the timecorrelated photon counting instrument (8 nm). The steady-state emission spectra were corrected for excitation intensity spectral variation, emission sensitivity spectral variation, and the inner filter effect:

Icor(λex, λem) )

101/2A(λex) + 1/2A(λem) I (λ , λ ) Iex(λex) Sem (λem) raw ex em

(17)

In eq 17, Iraw and Icor represent the raw and corrected intensity, λex and λem represent the excitation and emission wavelength, A(λ) represents the absorption spectrum of the same sample,



Iex(λ) represents the excitation intensity signal obtained from a triangular cuvette with 3 g/L solution of rhodamine B in ethylene glycol, and Sem(λ) is the emission sensitivity curve that was calculated from the emission spectrum of a quartz tungsten lamp T ) 2860 °K. Steady-state emission anisotropy was measured in the Lformat (90° angle between the excitation and emission beams) with a monochromator (8 nm slit width) in the emission channel. Glass filters were used neither instead of nor in combination with the emission monochromator because of their inherent UV luminescence and inefficiency in rejecting scattered light. With the monochromator in the emission channel, the background signal did not exceed 2 × 10-4 of the E21W fluorescence signal and 5 × 10-4 of the F3W fluorescence signal. Four intensity readings were taken with the excitation/emission polarizers in the following orientations: vertical/vertical, vertical/horizontal, horizontal/horizontal, and horizontal/vertical. The latter two readings were used to correct for unequal emission channel sensitivity to vertical and horizontal polarization. The steadystate anisotropy was calculated as follows:

rss )

IvvIhh - IvhIhv IvvIhh + 2IvhIhv

(18)

3.6. Time-Resolved Fluorescence Measurements. Timecorrelated single-photon counting data were obtained using the instrument built in the laboratory. Frequency-doubled output from a cavity-dumped dye laser synchronously pumped by a frequency-doubled output from a mode-locked YAG:Nd laser was used to excite fluorescence. The exciting radiation was a train of vertically polarized 15 ps laser pulses separated by 245 ns intervals. Fluorescence emission passed through a polarizer and a monochromator with 8 nm spectral resolution and was detected by a microchannel plate photomultiplier R1564U. The polarizer was oriented at 55° to the vertical in the intensity measurements and at either 0° or 90° in the anisotropy measurements. Photon counts were stored in 2048 channels (13.333 ps/channel). The excitation pulse recorded using a scatterer cell was about 5 channels or 65 ps fwhm; this represents the overall time resolution. The instrument was meticulously tested for systematic errors. After eliminating several sources of systematic errors (crosstalk between electronic devices, reflections in coaxial cables), the photon counts strictly followed Poissonian statistics up to approximately 106 photons per channel; at higher photon counts, the differential nonlinearity of the analog-to-digit converter could be detected. 4. Data Analysis 4.1. Singular Value Decomposition (SVD). The steady-state fluorescence intensity readings obtained at multiple excitation and emission wavelengths were not corrected using eq 17 prior to SVD, because such correction would significantly alter the error statistics. The raw data matrix covered the excitation wavelength range from 266 nm to 320 nm and the emission wavelength range from 279 nm to 450 nm. The overlaps between the excitation and emission wavelength resulted in 6 nm-wide spikes due to scatter. The scatter had to be subtracted from the spectra prior to SVD. For this purpose two emission scans were made at every excitation wavelength: one with the protein solution and one with the solvent. The scatter intensity was slightly lower in the absence of the protein, therefore a direct subtraction did not eliminate the spikes completely. For a complete elimination of the spikes, the solvent spectra were

multiplied by adjustable factors prior to subtraction. The factors were adjusted to minimize the integral of the squared second derivative of the spectrum after the subtraction. The data matrix after the scatter elimination was decomposed as usual.48 The singular spectral vectors obtained from SVD were corrected for the spectral variation of the excitation intensity and instrument sensitivity and for the inner-filter effect. This post-SVD correction makes the singular spectral vectors look like the corrected absorption and emission spectra of the corresponding chromophores, but the corrected spectra are no longer orthogonal. 4.2. Analysis of Time-Resolved Intensity Data. Timecorrelated single-photon counts were fit by numerical convolutions of the instrument response function (recorded using a scatterer cell) with linear combinations of discrete exponentials. In single-curve fitting, all of the time constants, τn, and preexponential factors, Rn, as well as the constant photomultiplier background, b, and the intensity of scattered light, s, were free fitting parameters. In simultaneous fitting of the curves measured at multiple emission wavelengths, one set of τn was used for all the curves, but an individual set of Rn, b, and s was used for every curve. For the single-curve fitting we used the program TCPHOTON. For the simultaneous fitting we used the previously described49 program L_GLOBAL. Both programs utilize weighted nonlinear least squares and the numerical convolution algorithm described elsewhere50 and calculate derivatives of the model function with respect to fitting parameters analytically rather than numerically. 4.3. Correction and Smoothing of Preexponential Factor Spectra. Due to spectral sensitivity variation, small uncontrolled variations in the exciting power and the dead time in the electronics that processes photoelectron pulses, the values of the preexponential factors obtained from the program L_GLOBAL are relative rather than absolute. The relative factors will be denoted R′in. The first index (i) counts the emission wavelengths, the second index (n) counts the exponentials, and the prime mark is used to distinguish the relative from the absolute factors. A conversion from the relative to the absolute factors is based on the relation

∫0∞Fν(ν, t) dt ) Fνss(ν)

(19)

where Fνss(ν) is the corrected steady-state emission spectrum in photons per unit wavenumber (to convert from photons per unit wavelength to photons per unit wavenumber the wavelength spectrum must be multiplied by ν-2). A combination of eqs 10 and 19 gives Nexp

τn Rn(ν) ) Fνss(ν) ∑ n)1

(20)

This results in a simple procedure23,43 for renormalizing the preexponential factors:

/( ) Nexp

fin ) τn R′in

∑ τm R′im

(21)

m)1

ss Rin ) τ-1 n fin Fν (νi)

(22)

where fin and Rin represent the intensity fraction and the absolute preexponential factor for the exponential exp(-t/τn) at the wavenumber νi. A conversion from the discrete factors Rin to the continuous factors Rn(ν) requires interpolation. Interpolation


Toptygin et al.

is commonly accomplished by fitting an analytical function to discrete data. A polynomial function would be the simplest choice, but it poorly represents the functions Rn(ν) because every Rn(ν) approaches zero at the extreme values of ν, whereas a polynomial approaches (∞ as its argument approaches (∞. Fractional intensities fn(ν) do not approach zero at the extreme values of ν, therefore we first fitted fin with the polynomial function Npol

fn(ν) )

Ckn νk ∑ k)0

(23)

and then calculated the continuous absolute preexponential factors

Rn(ν) ) τ-1 n fn(ν) Fν (ν) ss

(24)

The fitting based on weighted linear least squares was carried out for one value of n at a time. It was found that any Npol g 8 resulted in adequate fits. All of the results shown in this paper were produced with Npol ) 10. In plots of preexponential factor spectra, we show the discrete factors Rin (calculated without polynomial fitting) by dots and the continuous factors Rn(ν) (obtained from polynomial fitting) by solid lines. 4.4. Analysis of Time-Resolved Anisotropy Data. Vertical and horizontal polarization fluorescence data were fit by the model based on the following system of equations:

IV(t) ) g+1/2[1 + 2r(t)] I(t)

(25)

Ih(t) ) g-1/2[1 - r(t)] I(t)

(26)

Nani

∑ βm exp(-t/φm)

r(t) )

(27)

m)1 Nint

I(t) )

∑ Rn exp(-t/τm)

(28)

n)1

Numerical convolutions of Iv and Ih with the instrument response function were simultaneously fit to the vertical and horizontal fluorescence data. The ratio of the instrument sensitivity to vertical and horizontal polarization was represented by the free fitting parameter g. Traditionally the factor g is included in the model equation for Iv and not for Ih. We have included the factor g+1/2 in eq 25 and g-1/2 in eq 26. With these factors the ratio of Iv/Ih is still proportional to g, but there is less correlation between the fitting parameter g and the other fitting parameters, which results in improved convergence of the fitting algorithm. The fitting parameters Rn, βm, τn, φm were constrained by the relation Nint Nani

∑∑

Rn βm

-1 n)1 m)1 τ n

+ φ-1 m

Nint

) rss

∑ Rn τn

(29)

n)1

where rss represented the experimental value of the steady-state anisotropy measured as described above. The constrained fitting was carried out by the program POLARTCP. The program utilizes constrained weighted nonlinear least squares, the numerical convolution algorithm described elsewhere,50 and calculates the derivatives of the model function with respect to fitting parameters analytically rather than numerically. 5. Results and Discussion 5.1. Spectral Heterogeneity Test. The shape of the emission spectrum is independent of the excitation wavelength in

Figure 1. Fluorescence excitation and emission spectra that represent the first two singular vectors obtained in the SVD of the excitationemission matrix for E21W (solid lines) and F3W (broken lines) in the 0% glycerol solvent. The first and the second singular vectors are marked “1” and “2”. The emission spectra in the upper panel represent the column vectors; the excitation spectra in the lower panel represent the row vectors. The spectra have been corrected for lamp intensity and photomultiplier sensitivity variation. This post-SVD correction resulted in the loss of orthogonality between the singular vectors.

homogeneous ensembles. In a heterogeneous ensemble the emission spectrum may vary with the excitation wavelength. In the cases of indole or tryptophan, this results in the welldocumented red-edge excitation effect.51,52 Steady-state emission spectra of both E21W and F3W in the 0% glycerol solvent were measured at a series of excitation wavelengths from 266 nm to 320 nm. No emission spectral variation with the excitation wavelength was found by visual inspection for either mutant form. Singular value decomposition48 (SVD) is superior to visual inspection for detecting heterogeneity. The steady-state spectra measured with each mutant protein were organized in the form of a matrix of 28 columns and 172 rows, corresponding to 28 excitation and 172 emission wavelengths. SVD of each matrix gave 28 positive singular values arranged in descending order, 28 column vectors and, 28 row vectors. With either mutant protein, the singular values 3 through 28 were close in magnitude and the corresponding vectors resembled random noise. The first and second singular values were 500 and 1.8 (E21W) or 420 and 2.9 (F3W) times greater than the third singular value. The first two singular vectors are shown in Figure 1. The first column vectors for E21W (solid line) and F3W (broken line) represent typical emission spectra of tryptophan in different environments. Likewise, the first row vectors represent typical tryptophan absorption spectra. The second column vectors have their peaks at λem ≈ 280 nm, where tryptophan never emits. The emission peak of phenylalanine is close to λem ≈ 280 nm, and its absorption band is limited to λex < 274 nm; the latter is consistent with the second row vectors in Figure 1. E21W and F3W have 8 and 7 phenylalanine residues, respectively, and the second SVD components are due


J. Phys. Chem. B, Vol. 105, No. 10, 2001 2049 TABLE 1: Parameters Resulting in the Best Global Fit to Polarized Time-Correlated Photon Counts

Figure 2. Time-resolved fluorescence emission anisotropy for E21W (A) and F3W (B) in the 0% glycerol solvent. Dots and solid lines represent raw experimental data and multiexponential fits. Broken lines represent the time-resolved anisotropy that would be observed if the protein globule was not rotating as a whole. For details, see section 5.2.

to these residues. The third and subsequent SVD components represent random noise, the mean squared amplitude of which is less than 0.25% of the mean squared signal. For either mutant form, only one singular component corresponds to tryptophan fluorescence; therefore, the first column vector represents the shape of the tryptophan emission spectrum at any excitation wavelength. The excitation-wavelength-invariant emission spectrum proves that either all tryptophan residues have identical emission spectra or interconversion between conformations in which tryptophan has different emission spectra is faster than the lifetime of the excited state. We will not consider the case in which different conformations of the tryptophan environment result in different emission spectra but identical excitation spectra because any environmental parameter that perturbs the shape of the emission spectrum also perturbs the shape of the excitation spectrum. (Although the peak wavenumber in the low-energy absorption band of indole and its derivatives is less sensitive to environment than the peak wavenumber in the emission spectrum, one cannot disregard the profound effect of environment on the red slope of the absorption band.) 5.2. Time-Resolved Fluorescence Anisotropy. Interconversion between different conformations of the tryptophan environment is very likely to result in a reorientation of the tryptophan side chain. The model of tryptophan rotamers24,25 explicitly assumes that the orientation of the tryptophan side chain is different for different conformations. Reorientation of the tryptophan side chain during the excited-state lifetime is revealed by the time-resolved fluorescence anisotropy. This can be used to determine whether tryptophan conformers interconvert and how fast. Vertically and horizontally polarized time-resolved fluorescence data were obtained with both E21W and F3W in the 0% glycerol solvent using 296 nm excitation. The emission monochromators were set to 345 nm for E21W and 355 nm for F3W, which was close to the peak emission wavelength in each case. The time-resolved anisotropy is shown in Figure 2. The dots

mutant form

χ2

m

βm ( σβm

φm ( σφm [ns]

E21W

0.980

F3W

1.006

1 2 1 2 3

0.175 ( 0.008 0.040 ( 0.009 0.060 ( 0.003 0.072 ( 0.002 0.030 ( 0.007

39.8 ( 2.0 5.4 ( 0.9 44.8 ( 5.1 1.4 ( 0.1 0.25 ( 0.05

depict anisotropy values calculated on a channel-by-channel basis and plotted versus the delay relative to the center of the excitation pulse. The solid lines represent the multiexponential models that gave the best fits to the polarized time-correlated photon counts, see section 4.4. The fitting produced r(t) curves deconvoluted from the instrument response. An adequate fit to E21W data was achieved when r(t) and I(t) were approximated by 2 and 4 exponentials, respectively. For an adequate fit to F3W data, a minimum of 3 and 4 exponentials were required for r(t) and I(t). The best reduced χ2 values and corresponding values of the fitting parameters are shown in Table 1. Only the parameters associated with r(t) are shown; the parameters associated with I(t) will be described later. The r(t) curves represent the combined effect of the rotation of the tryptophan side chain relative to the protein globule and the rotation of the protein globule as a whole. Assuming that the protein globule represents a spherical rotator with the rotational correlation time equal to the greatest of φm from Table 1, we have factored out the rotation of the protein globule. The ratios r(t)/exp(-t/φmax) are shown by broken lines in Figure 2 and represent the rotational dynamics of the tryptophan side chains with respect to the protein globule. It is clear that the internal rotation of the tryptophan side chain in E21W (broken line A in Figure 2) is constrained to a much greater extent than in F3W (broken line B). This is consistent with the a priori information34,36 that in E21W the tryptophan residue is inserted in the rigid globule, whereas in F3W it is close to the end of a floppy tail of the residues 1 through 18. The magnitude of internal rotations in the case of F3W speaks against the existence of long-lived rotational conformers (rotamers) of tryptophan side chain. In the case of E21W, either the rotamer interconversion is slow or there is just one conformation of the tryptophan side chain. The latter is consistent with the X-ray diffraction data36 and with the results of SVD. 5.3. Time-Resolved Fluorescence Intensity: Single-Curve Analysis. Time-resolved fluorescence emission intensity data were collected at multiple emission wavelengths using 289 nm excitation. The data obtained with E21W in the 0% glycerol solvent at two selected emission wavelengths are shown in Figure 3. Neither the photon counts collected at λem ) 320 nm nor the counts collected at λem ) 400 nm can be fit adequately by a convolution of one exponential with the instrument response function. The best-fitting convolution of one exponential with the instrument response function is shown by a solid line; at λem ) 320 nm the peak of the convolution lies below the data, while at λem ) 400 nm the peak of the convolution lies above the data. The maximum magnitude of the difference between the data and the 1-exponential fit is about 6000 and 2000 photon counts per channel for λem ) 320 nm and λem ) 400 nm, respectively. The data in Figure 3 were fitted by linear combinations of up to five exponential terms convoluted with the instrument response function. The minimum reduced χ2 obtained with 1, 2, 3, 4, and 5 exponentials equals 39.327, 4.273, 1.340, 1.028, 1.017 for λem ) 320 nm and 3.138, 1.061, 1.039, 1.033, 1.033 for λem ) 400 nm. For a data array of 2000 channels with the


Toptygin et al.

Figure 3. Single-curve fitting of the time-resolved emission intensity of E21W in the 0% glycerol solvent. The emission wavelength is 320 nm for the left panel and 400 nm for the right panel. For details, see section 5.3.

probability of 95%, the reduced χ2 does not exceed 1.052 and with the probability of 99.5% it does not exceed 1.081.53 Thus, the minimum number of exponentials required for an adequate fit equals four at λem ) 320 nm and two at λem ) 400 nm. The same conclusion can be derived by inspecting weighted residuals and autocorrelations in Figure 3. In the case of λem ) 320 nm, the best fit is achieved with all positive preexponential factors for any Nexp. At λem ) 400 nm, both positive and negative preexponential factors are required: for Nexp ) 2, there is one positive and one negative factor; for Nexp ) 3, there is one positive factor and two negative factors, etc. By single-curve analysis, we found negative preexponentials not only for E21W in the 0% glycerol solvent (Figure 3) but also for E21W in the 3% and 30% glycerol solvents and for F3W in the 30% glycerol solvent (data not shown). 5.4. Time-Resolved Fluorescence Intensity: Global Analysis. Time-resolved fluorescence emission intensity data were collected at 31 emission wavelengths from 300 nm to 450 nm at 5 nm increments using 289 nm excitation. The data were fit simultaneously by convolutions of the instrument response function with linear combinations of exponentials. In accordance with eq 10, the time constants τn were held equal between all emission wavelengths and played the roles of global fitting parameters, whereas the preexponential factors at different emission wavelengths were completely independent and played the roles of local fitting parameters. Fitting the data obtained with E21W in the 0% glycerol solvent resulted in the global reduced χ2 values of 17.688, 2.160, 1.105, 1.016, and 1.006 for Nexp ) 1, 2, 3, 4, and 5, respectively. Global autocorrelations of unweighted residuals for these fits are shown in Figure 4. On the basis of the global reduced χ2 values and the autocorrelations, we have concluded that a minimum of four exponentials are required for an adequate fit. The same conclusion holds true for E21W in the other two solvents and for F3W in all

Figure 4. Global autocorrelations of unweighted residuals that characterize the quality the global fits with 1, 2, 3, 4, and 5 exponentials to the time-resolved fluorescence emission intensity of E21W in the 0% glycerol solvent.

three solvents. Autocorrelation plots and reduced χ2 values obtained with the five protein-solvent combinations are not shown for space economy, but they are similar to those obtained with E21W in the 0% glycerol solvent. The four-exponential global reduced χ2 values for all of the six data sets fall between 0.991 and 1.017. The preexponential factors obtained from the global fitting have been corrected using steady-state emission spectra (see section 4.3) and plotted versus the emission wavenumber (ν).



Figure 5. Corrected preexponential factor spectra obtained in the four-exponential global fitting of time-resolved fluorescence intensity. Panel A: E21W, 0% glycerol; panel B: F3W, 0% glycerol; panel C: E21W, 30% glycerol; panel D: F3W, 30% glycerol. The values of the corresponding time constants τn are used as the curve labels. Dots and continuous curves represent the discrete factors Rin and the continuous factors Rn(ν), see section 4.3. Error bars represent 95% confidence intervals and are shown only for the preexponential factor associated with the shortest exponential; the confidence intervals for longer exponentials are too narrow to be shown in the figure.

The plots are shown in Figure 5 for E21W and F3W in the solvents containing 0% and 30% glycerol (by volume). 5.5. Evidence of Relaxation. On the basis of the results of SVD, we have shown that either all tryptophan residues have identical emission spectra or interconversion between conformations in which tryptophan has different emission spectra is faster than the lifetime of the excited state. The interconversion represents a form of relaxation; therefore, if we assumed that there was no relaxation, then, on the basis of the results of SVD, we would have to conclude that all tryptophan residues would have identical emission spectra. Consider the preexponential factor spectra shown in panels A or B of Figure 5. The spectra differ in shape: the spectrum associated with a shorter τ always has its peak at a higher ν and vice versa. Thus, the spectra cannot be attributed to different subensembles of tryptophan residues,

and static heterogeneity cannot account for the multiexponential emission intensity. This represents an indirect proof of relaxation. The above proof is applicable to both E21W and F3W, but only in the 0% glycerol solvent, because SVD was done only with the data obtained in this solvent. Panels C and D of Figure 5 represent the data obtained in the 30% glycerol solvent. For these data, as well as for the data shown in panel A, the presence of negative preexponential factors that exceed in magnitude the random errors can serve as a proof of relaxation. In panel B, negative preexponential factors are of the magnitude of the random errors and cannot serve as a reliable proof of relaxation. Thus, for the data presented in panels B, C, and D we have only one proof of relaxation, and for the data in panel A there are two independent proofs of relaxation.


Figure 6. Peak-normalized instantaneous emission spectra ν-3Fν(ν,t). Panel I represents the case of a relaxing homogeneous model system (indole in glycerol). Panel II represents the case of a static heterogeneous model system (indole in ethyl ether and in water). Panel I is reprinted from Chemical Physics Letters 322, D. Toptygin, L. Brand, “Spectrallyand time-resolved fluorescence emission of indole during solvent relaxation: a quantitative model”, p 496-502, Copyright 2000, with permission from Elsevier Science.

5.6. Heterogeneity Test. For a homogeneous ensemble, the shapes of the normalized spectra ν-3Fν(ν,t) are expected to be conserved, see section 2.7. Figure 6 illustrates the case of a relaxing homogeneous ensemble (I), where the shape is conserved, and the case of a static heterogeneous ensemble (II), where the shape is not conserved. The spectral shapes in Figure 6 were generated from experimental data obtained with two model systems. A homogeneous solution of indole in anhydrous glycerol38 at T ) +20 °C was used as a model of a relaxing homogeneous ensemble (I). To imitate a static heterogeneous ensemble (II) indole was dissolved in ethyl ether and in water. Relaxation of these low-viscosity solvents is much faster than the time resolution of our instrument, therefore the emission of

Toptygin et al. indole in either solvent appears monoexponential with τ ) 3.47 ns in ethyl ether and τ ) 6.39 ns in water (T ) +4 °C). The emissions from the two solutions were combined as described in section 3.3. Normalized spectra ν-3Fν(ν,t) generated from the protein data are shown in Figure 7. The curves in each panel of Figure 7 were generated from the preexponential factor spectra and time constants in the corresponding panel of Figure 5. All spectra in Figure 7 and Figure 6 were generated by the same software from the data collected on the same instrument. In all cases except panel II of Figure 6, the shape of the spectrum ν-3Fν(ν,t) remains practically unchanged as the spectrum shifts to the red. The widths of the time-dependent spectra are plotted versus time in Figure 8. W(t) has been defined as the full width of the spectrum ν-3Fν(ν,t)|t)const at half-maximum. In the case of the static heterogeneous model system (II) the width decreases considerably at long times, and it keeps decreasing at times that are much longer than the longest lifetime. This behavior is expected in a heterogeneous system: a heterogeneous spectrum is wider than its homogeneous components. As one homogeneous component outlives the others, the spectrum narrows; however, it usually takes several lifetimes until the contributions of the short-lived components vanish. No long-time decrease in the spectral width is revealed by the curves A, B, C, D, and I in Figure 8 and in Figure 9, where the same curves are shown on expanded scales. For the systems B, D, and I, all of the width variations take place at short times, and these variations may be illusive. Estimated uncertainty in the spectral width at t < 0.5 ns is at least 100 cm-1, which exceeds the amplitude of the width variations for the systems B, D, and I. In the systems A and C, the slow increase in the spectral width at t > 1 ns is probably real, because the magnitude of the increase is about 50 cm-1 and the uncertainty in W(t) is less than 50 cm-1 at t > 2 ns. The relative increase in W(t) is quite small (about 1%), and its origin is not certain. According to one hypothesis, the long-time increase in W(t) could be due to a small fraction of the protein in the unfolded state. The emission spectrum of water-exposed tryptophan residues in the unfolded protein is usually wider than that of buried residues in the folded protein, and if the fluorescence of the unfolded protein lived longer than that of the folded protein, then this would explain the increase in the width at long times. Since the dominant lifetime is about 8.5 ns in the system A and 8.0 ns in the system B (see Figure 5), the lifetime of the tryptophan residues in the unfolded protein would have to be longer than that. In reality, the lifetimes of tryptophan residues in unfolded proteins rarely exceed 5ns. Thus, the heterogeneity associated with the conceivable unfolded protein cannot explain the width increase in the systems A and C. It is also highly unlikely that a permanent or long-lived heterogeneity of another origin could explain this result. 5.7. Dielectric Response and Polarity. The curves νj(t) for E21W and F3W in the solvents containing 0% and 30% glycerol (by volume) are shown by solid lines in Figure 10. Since there is no evidence of permanent or long-lived heterogeneity for either protein in either solvent, the curves represent the microscopic dielectric response function at least in the ensemble mean sense. Dielectric relaxation of liquid water at T ) 5 °C takes only about 15 ps (the slowest component),54 which is beyond the time resolution of our instrument; therefore, the experimental curves contain no contribution from the relaxation of the main solvent. The curves represent dielectric relaxation of the protein itself (which may include slow diffusion of water



Figure 7. Peak-normalized instantaneous emission spectra ν-3Fν(ν,t). Panel A: E21W, 0% glycerol; panel B: F3W, 0% glycerol; panel C: E21W, 30% glycerol; panel D: F3W, 30% glycerol.

molecules within the protein), and in glycerol-containing solvents it may also contain a contribution from the rotational relaxation of glycerol molecules. The time window during which νj(t) can be accurately recovered from experimental data is defined by the instrument’s time resolution (about 50 ps) on one hand and by the duration of fluorescence (about 20 ns for E21W and 10 ns for F3W) on the other hand. Thus, the range of observable relaxation rates covers over 2 orders of magnitude. To represent relaxation processes with the wide range of possible relaxation rates in one figure, a logarithmic time scale was chosen for Figure 10. The dielectric responses for E21W and F3W reflect individual characteristics of the tryptophan environment in these proteins. In the case of F3W in the 0% glycerol solvent (curve B), the plot of νj versus log(t) has the steepest slope at t < 0.2 ns; in the interval 0.2 ns < t < 3 ns the slope decreases, and at t > 3 ns the curve is almost flat, which shows that dielectric relaxation is practically complete by 3 ns. In the case of E21W

in the 0% glycerol solvent (curve A), the slope continues all the way to 20 ns, which is indicative of the presence of slow relaxation components. Since dielectric relaxation of the tryptophan environment in E21W is not complete when the fluorescence signal vanishes, it is not possible to get an accurate estimate of νj(∞) for this protein; however, considering that the entire curve A lies above curve B, it is most likely that the value of νj(∞) for curve A is higher than that for curve B. The value of νj(∞) represents the polarity of tryptophan environment; therefore, in E21W the tryptophan environment is less polar than in F3W, which is consistent with the apriori knowledge34,36 that in IIAGlc residue 21 is less solvent exposed than residue 3. 5.8. Glycerol Effect. Addition of 30% glycerol (by volume) to either the E21W (curve C) or F3W (curve D) shifts the relaxation curve up on the νj scale and also increases the slope. Curves C and D do not achieve their tf∞ limits by the end of the time window, therefore it is difficult to say how much the


Toptygin et al.

Figure 8. The widths at half-maximum of the instantaneous emission spectra shown in Figures 6 and 7. Curve labels correspond to the panel labels in Figures 6 and 7.

Figure 10. The dynamics of microscopic dielectric relaxation in the environment of tryptophan residues. Solid curves A and C represent the tryptophan residue in E21W. Solid curves B and D represent the tryptophan residue in F3W. Glycerol concentration is 0% for the solid curves A and B, 30% for the solid curves C and D, and 3% for the dotted curves.

TABLE 2: Experimental Values of R3/30 R3/30

Figure 9. Some of the W(t) data from Figure 8 charted on the expanded scales.

addition of glycerol alters the polarity of tryptophan environments in the two proteins. The increased slope reflects the changes in relaxation dynamics that can be due to direct contribution from rotating glycerol molecules and/or due to the effect of increased viscosity on the relaxation of the protein. To examine the linearity of the glycerol effect, we measured time-resolved emission spectra also at 3% glycerol concentration (by volume) and calculated νj(t) from these data. The results are shown by dotted lines in Figure 10. For a quantitative estimate of the linearity we used the ratio

R3/30 )

νj(t, 3%) - νj(t, 0%) νj(t, 30%) - νj(t, 0%)

Experimental values of R3/30 are shown in Table 2.

t [ns]

E21W

F3W

0.1 0.3 1.0 3.0 10.0

.091 .085 .080 .073 .061

.058 .078 .076 .072 .066

If the variations in νj(t) were linear with glycerol concentration, then R3/30 would equal 0.1. If the effect was due to bound glycerol, then it wound be saturable, and R3/30 would be greater than 0.1. If the saturation of glycerol binding sites took place at glycerol concentrations much greater than 30%, then R3/30 would be only slightly greater than 0.1, but it could not be less than 0.1. All experimental values of R3/30 are less than 0.1, which can be interpreted as evidence against the effect of bound glycerol on νj(t). It is possible that IIAGlc has no affinity to glycerol and/or that glycerol binding site(s) are not close to residues 21 and 3. It is likely that the variations in νj(t) reflect the changes in protein relaxation dynamics associated with the increase in solvent viscosity upon the addition of glycerol. Addition of 3% glycerol by volume to water increases the macroscopic viscosity η of the solution by 8.5%, whereas the addition of 30% glycerol by volume results in a 236% increase in viscosity.55 If the variations in νj(t) were linear with the macroscopic viscosity, then the ratio R3/30 would be equal to 0.036. This explains why the ratio R3/30 can be lower than 0.1; however, because macroscopic viscosity laws are not applicable on the molecular level, one cannot expect R3/30 to exactly follow the estimate based on the macroscopic viscosity values. 6. Conclusions

(30)

Fluorescence emission from the single-tryptophan mutants E21W and F3W of the IIAGlc protein is free from permanent and long-lived heterogeneity. A variation in the shape of the

Protein Relaxation Dynamics steady-state emission spectrum with the exciting wavelength or a decrease in the width of the time-resolved emission spectra ν-3Fν(ν,t)|t)const at long times would give a sufficient proof of permanent or long-lived heterogeneity, but neither of these symptoms are observed. Time-resolved emission spectra of E21W and F3W have been used to calculate the microscopic dielectric response of the environment of the tryptophan residues in these proteins. In F3W the environment is more polar than in E21W. The dielectric responses in both E21W and in F3W are multiexponential and cover a wide range of relaxation rates. In F3W the dielectric relaxation is practically complete at t ) 3 ns, whereas in E21W it is not complete even at t ) 20 ns. The difference in the relaxation dynamics reported by the tryptophan residues in E21W and F3W represents the difference between the structured protein globule (E21W) and the flexible tail (F3W). Addition of glycerol to the solvent results in a significant variation in the dielectric response. The glycerol effect is not saturable at high glycerol concentrations, therefore it cannot be due to bound glycerol. The changes in the dielectric response are most likely due to the effect of solvent viscosity on the relaxation dynamics of the protein. Acknowledgment. We thank Professor Saul Roseman for his support and Dr. Kavita A. Vyas for purifying the proteins. This work was supported by National Science Foundation grant MCB9810812 and National Institutes of Health grant GM38759. References and Notes (1) Kosower, E. M. J. Am. Chem. Soc. 1958, 80, 3253. (2) Dimroth, K.; Reichardt, C.; Siepmann, T.; Bohlmann, F. Liebigs Ann. Chem. 1963, 661, 1. (3) Mente, S. R.; Maroncelli, M. J. Phys. Chem. B 1999, 103, 7704. (4) Jacobson, A.; Petric, A.; Hogenkamp, D.; Sinur, A.; Barrio, J. R. J. Am. Chem. Soc. 1996, 118, 5572. (5) Ren, B.; Gao, F.; Tong, Z.; Yan, Y. Chem. Phys. Lett. 1999, 307, 55. (6) Oksanen, J. A. I.; Martinsson, P.; Åkesson, E.; Hynninen, P. H.; Sundstro¨m, V. J. Phys. Chem. A 1998, 102, 4328. (7) Gumy, J.-C.; Nicolet, O.; Vauthey, E. J. Phys. Chem. A 1999, 103, 10737. (8) Kovalenko, S. A.; Dobryakov, A. L.; Ruthmann, J.; Ernsting, N. P. Phys. ReV. A 1999, 59, 2369. (9) Maroncelli, M. J. Mol. Liq. 1993, 57, 1. (10) Horng, M. L.; Gardecki, J. A.; Papazyan, A.; Maroncelli, M. J. Phys. Chem. 1995, 99, 17311. (11) Stratt, R. M.; Maroncelli, M. J. Phys. Chem. 1996, 100, 12981. (12) Gardecki, J. A.; Maroncelli, M. J. Phys. Chem. A 1999, 103, 1187. (13) Turner, D. C.; Brand, L. Biochemistry 1968, 7, 3381. (14) Brand, L.; Gohlke, J. R. J. Biol. Chem. 1971, 246, 2317. (15) Gafni, A.; DeToma, R. P.; Manrow, R. E.; Brand, L. Biophys. J. 1977, 17, 155. (16) Lakowicz, J. R.; Gratton, E.; Cherek, H.; Maliwal, B. P.; Laczko, G. J. Biol. Chem. 1984, 259, 10967.

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