Decay time distribution analysis of Yt-base in benzene—methanol mixtures

Journal

ofPhotochemistry

and Photobiology,

B: Biology,

4 (1989)

DECAY TIME DISTRIBUTION ANALYSIS BENZENE-METHANOL MIXTURES IGNACY

GRYCZYNSKI,

WIESLAW

WICZK

and JOSEPH

159

OF Y,-BASE

IN

Chemistry,

L. JOHNSON

University of Virginia, Department Charlottesville, VA 22908 (U.S.A.) (Received

159

R. LAKOWICZt

University of Maryland, School of Medicine, Department of Biological 660 West Redwood Street, Baltimore, MD 21201 (U.S.A.) MICHAEL

- 170

August

4,1988;

of Pharmacology,

accepted

February

School

of Medicine,

10,1989)

Keywords. Frequency-domain fluorometry, nential analysis, Lorentzian distribution.

fluorescence decay, multiexpo-

Summary Frequency-domain fluorometry was used to measure intensity decays of synthetic Y,-base in mixtures of benzene-methanol at 20 “C. Multiexponential analysis shows that the decay of Y,-base fluorescence in benzene and methanol can be well fitted to a single-exponential model with r = 9.67 ns and 6.25 ns respectively. In mixtures of benzene-methanol the decays became heterogeneous, and the maximum of heterogeneity observed was in a mixture containing 6% methanol. Since we expected a distribution of Y,-base solvation states in the solvent mixtures, and because the decay times of Y,-base are sensitive to solvent, we analyzed the data in terms of decay time distributions. The goodness-of-fit for the unimodal distribution model which has two floating parameters was equivalent to that found using the double exponential model with three floating parameters. The Lorentzian distribution model appears to provide a slightly superior fit relative to the Gaussian distribution model. These results suggest that the intensity decays of solvent-sensitive fluorophores in mixed solvents are described by a distribution of decay times.

1. Introduction The application of fluorescence spectroscopic methods to biological samples often involves analysis of the intensity and anisotropy decay kinetics. The decay times are of interest because they can represent molecular features +Author

to whom

loll-1344/89/$3.50

correspondence

should

be addressed.

@ Elsevier Sequoia/Printed

in The Netherlands

160

of the sample and can give information about the existence of two or more conformations of the biomolecules. They are also usually sensitive to the polarity of the environment surrounding the fluorophore. The intensity decays are generally more complex than a single exponential, and are usually analyzed in terms of a sum of discrete exponential decays (multiexponential model) [l - 41. Recently, continuous distributions of decay times were proposed [5 - lo] as alternative models for the sum of discrete exponentials. To date relatively few systems have been described for which one can state with confidence that the decay is due to a distribution of decay times. These cases include transient effects in quenching, energy transfer [ll] and conformational heterogeneity of proteins [12], but it should be noted that there are alternative models that account for the data from such systems and that these models contain a molecular description of the system. Lifetime distributions have also been proposed to account for the complex decays of single tryptophan proteins [lo, 131, but to date there appears to be little statistical evidence to support acceptance of the distribution model. In the present paper we describe a system where one can predict a distribution of decay times, this being the decay of a solvent-sensitive fluorophore 4,9dihydro-4,6dimethyl-9-oxo-W-1-imidazo-[ 1,2a] -purine (Y,-base) (Scheme 1) in mixtures of benzene and methanol. Several papers have appeared [14 - 181 which describe the physicochemical properties of this modified nucleotide. It has been of special interest because of its strong fluorescence which offers a unique tool for probing the conformational properties of t-RNAphe [19, 201, as well as more simple synthetic compounds such as Y,-(CHz)n-adenine [ 21 - 231. Our data suggest that the intensity decay of Y,-base in benzenemethanol is in fact described by a distribution of decay times.

Scheme 1. Structure of Yt-base.

2. Theory Fluorescence intensity decays are usually described as the sum of individual exponentials. The intensity decay following a-function excitation is described by I(t)

=

C ai

e@‘i

(1)

i

where ri is the individual decay time and (Xiis the associated pre-exponential factor. The fractional contribution of the ith component to the total emission is

161

O!jTi fi =

c

(2)

(yiTi

i

where oi and fi are normalized values; X(Y~= 1 and Cfi = 1. We also used an alternative model in which the oi values are not discrete amplitudes at Ti, but are described by a continuous distribution o(r) around a central value ?. The intensity decay then contains components of each lifetime r with amplitude (X(T).The component with each individual r value is given by 1(7, t) = ar(t) eCtl’

(3)

The total decay law is the sum of the individual decays weighted by the amplitudes I(t)

= _f a(~) eet17 d7

(4)

0

where /a(r)dT = 1. The relationship between the two models (eqns. (1) and (4)) can be seen by noting that a Dirac distribution at.rO results in a single exponential decay I(t)

= 16(T

- To)

e-f’7 dT = eCt”O

(5)

0

One can expand Q!(T) to include several o-weighted &functions, which we refer to as bimodal, trimodal, etc., distributions. Then, application of eqn. (5) yields the multiexponential model. We selected Gaussian (G) and Lorentzian (L) functions to describe unimodal lifetime distributions. For these functions the Q(T) values are

(6)

016(T) =

1 Q(T)

=

r

r/2 (7

-

T)2

+

(r/2)2

where ? is the central value of distribution, CJis the standard deviation of the Gaussian and r is the full-width at half-maximum (hw) for the Lorentzian. For a Gaussian the full-width at half-maximum is given by 2.354~. For ease of interpretation we describe the width of both distributions by the fullwidth at half-maxima. The use of functional forms for a(~) minimizes the number of floating parameters in our fitting algorithms. In the frequencydomain, the frequency response of the emission consists of the frequencydependent values of the phase angle (4,) and the demodulation factor (m,), where o refers to the modulation frequency in rad s-l. These values can be calculated from the sine (N,) and cosine (D,) transforms of the impulse response function. Using eqn. (4) these transforms are

162

N,J=

7

o(r)ePtl’dTsin(ot)dt

1

(3)

t=o 7=0

7 f o(r)e-f/7drcos(tit) t=o 7=0

D,J=

dt

(9)

m

J=

_I-Q((T)Tdr

(10)

7=0

Reversal of the order of integration is possible for well-behaved functions with continuous derivatives, yielding

D,J=

1 7=.

Q[(T)7

dr

l+W2T2

(1%

For any form of the decay law the phase on modulation values are given by 4, = arctan(NJD,)

(13)

171, = (NU2 + D,2)1’2

(14)

The measured phase (4,) and modulation values (m,) were analyzed by the method of non-linear least squares [24, 251. Calculated values (c) were obtained using eqns. (8) - (14). The goodness-of-fit was judged by the value of reduced xn2 (15) where v is the number of degrees of freedom and S@ = 0.2” and 6m = 0.005 are the uncertainties in the measured phase and modulation values, respectively. These uncertainties are based on examination of single- and multicomponent mixtures [24 - 261 under a wide variety of experimental conditions.

3. Materials and methods The frequency-domain data were measured using a 2-GHz harmonic content fluorometer. The excitation wavelength was 310 nm from the frequency-doubled output of an R6G dye laser [26]. Magic angle polarizer orientations were used to eliminate the effects of rotational diffusion. The emission was observed through a Coming O-52 bandpass filter, which absorbs

163

all the emission and/or scattered light below 340 nm. The Y,-base was prepared by reacting 3-methylguanine with bromoacetone [27, 281 and was purified by HPLC before the measurements. Benzene and methanol were spectroscopic grade. All measurements were recorded at 20 “C. 4. Results and discussion Normalized absorption and fluorescence spectra of Y,-base in benzene and methanol are shown in Fig. 1. The dependence of these spectra on solvent is unusual in that the absorption spectrum shifts to shorter wavelengths (hypsochromic) in the more polar solvent, while the emission spectrum displays the more usual red shift (bathochromic) as the solvent is changed from benzene (non-polar) to methanol (polar). These shifts in Y,base spectra can be explained on the basis of solvatochromic theories [29 321. The dipole moment of the excited state of Yt-base has a direction which is nearly opposite that of the ground state [ 331. Also, the dipole moment changes from 3.5 D in the ground state to 4.3 D in the excited state. WAVELENGTH

tnm)

WAVENUMBER

(kK

I

Fig. 1. Normalized absorption and fluorescence methanol (- - -) at 20 “C (kK = lo3 cm-‘).

spectra

of Yt-base

in benzene

(-

) and

In benzene and methanol the intensity decays are well approximated by the single-exponential model. This is shown in Fig. 2, which shows that the calculated single-exponential curves overlap with the data (top panel). Also, the residuals are randomly distributed (lower panels). The double-exponential analysis (Table 1) shows no decrease in xa2 as compared with the singleexponential model, which indicates the single-exponential model is adequate to account for the data. We note that we can only estimate the standard errors in the data, so that the absolute values of xa’ are not necessarily unity [24]. The goodness-of-fit is best judged by the relative values of xa’ as the model is made more complex. For instance, the value of x$ for Y,-base in methanol did not decrease for the one- or two-exponential model (Table 1). Hence Xa 2 = 1.9 is the noise-limited value of xa” for this particular set of data.

164

2

5

10

50

20

FREQUENCY

100

200

(MHZ)

Fig. 2. Frequency-response data of Yt-base lines show the best single-exponential fit.

fluorescence

in benzene

and methanol.

Full

The intensity decay of Y,-base becomes more complex in mixtures of benzene and methanol. This is seen from the increase in xa” found for the single-exponential model (Table 1). The maximum heterogeneity is seen near 6% methanol, where ~a* is elevated about seven-fold relative to the double-exponential model. The changes in the emission of Y,-base are realized with only a few per cent of methanol in the mixture. By 10% methanol the lifetime and emission become characteristic of that found in 100% methanol (Fig. 3). To distinguish between ground and excited state processes we determined the decay times at various emission wavelengths (Fig. 4). In

IO

Yt-Base,

10

430 Y, - Base,

20°C

Benzene

t.

20°C

Benzene +6% MeOH

6

0

5

10

15

100

400

380

% Methanol

Fig. 3. Dependence centage of methanol Fig. 4. Dependence

of the mean in benzene.

lifetime

of mean lifetime

and emission

of Yt-base

420

460

WAVELENGTH

(nm)

maximum

upon the wavelength

Yt,-base

upon

of observation.

the per-

165 TABLE

1

Multiexponential tures at 20 “C Per cent methanol

analysis

of

the intensity

decays

of Yt-base

in benzene-methanol

mix-

Ti (ns)

%

fi

XI%*

0

9.67 9.18 9.82

1.0 0.093 0.907

1.0 0.079 0.921

1.3

2

9.23 0.74 9.30

1.0 0.023 0.977

1.0 0.002 0.998

4

8.80 3.67 9.10

1.0 0.061 0.939

1.0 0.026 0.974

3.2

6

8.36 3.50 8.92

1.0 0.113 0.887

1.0 0.048 0.952

8.9

7.84 3.26 8.29

1.0 0.102 0.898

1.0 0.043 0.957

7.5

10

7.23 2.99 7.56

1.0 0.082 0.918

1.0 0.034 0.966

4.9

15

6.75 3.39 7.00

1.0 0.076 0.924

1.0 0.038 0.962

3.0

6.25 5.72 6.61

1.0 0.408 0.592

1.0 0.374 0.626

1.9

8

100

1.3 2.0 1.1

1.2

1.2

1.3

1.0

1.3

1.9

100% benzene or 100% methanol the decay time are independent of wavelength. In the mixture the mean decay times increase somewhat with increasing emission wavelength. If the heterogeneity in the decay is due only to ground state interactions, then we expect the mean decay time to decrease with increasing observation wavelength, owing to an increasing contribution from the red-shifted methanol-like emission spectrum. The increase in decay time indicates that there is some detectable evolution of the emission during the lifetime of the excited state [ 32, 341. In the binary solvent there exists a distribution of environments for the fluorophore, owing to the heterogeneous solvent shell. The statistics of such systems have been discussed by other researchers [35 - 371. It seems probable that this shell changes dynamically during the lifetime of the excited state, with regard to the number, location and orientation of the methanol molecules. Since we expected a distribution of Y,-base solvation states we analyzed our data in terms of lifetime distributions. The results of this analysis, using

166 TABLE

2

Lifetime distribution tures at 20 “C

Per cent methanol 0

2 4 6 8 10 15 100

analysis

of Yt-base

fluorescence

Lorentzian

decays

in benzene-methanol

mix-

Gaussian

7 (ns)

hw (ns)

XR2

7(ns)

hw (ns)

XR2

9.67 9.27

0.07 0.64 1.05 1.92 1.52

1.3 1.3 1.1 1.2 1.2 1.1 1.5 1.9

9.67 9.24 8.81

1.23 2.76 3.56 4.68 4.13 3.33 2.46 1.05

1.3 1.4 1.3 1.6 1.5 1.3 1.5 1.9

8.83 8.38 7.81 7.19 6.71 6.24

1.00

0.54 0.11

8.36 7.83 7.23 6.74 6.25

unimodal Lorentzian and Gaussian distributions of o(r) are summarized in Table 2. Both models provide adequate fits to the data, but the Lorentzian model appears to be somewhat superior to the Gaussian model. The values of ~a* are about identical to those found for the double-exponential fit. It should be noted that the distribution model contains only’ two floating parameters (? and hw), whereas the double-exponential model has three variable parameters (two ri and oi, with o1 + o2 = 1.0). In general we should accept the simplest model which accounts for the data, which in this case is the Lorentzian lifetime distribution. The largest width in the distributions, and the largest heterogeneity, was found for the mixture containing 6% methanol. The phase and modulation data for this mixture are shown in Fig. 5. The full line shows the best Lorentzian fit and the broken line shows the fit when the half-width was held fixed at 0.01 ns, which corresponds to the single-exponential model. The lower panels show the residuals and it is clear that the data are well fitted by the distribution model, but not when the half-width is fixed at a small value. The distributions recovered from the analysis are summarized in Fig. 6. These distributions are narrow in the pure solvents, and show increased widths at 6% and 10% methanol. We believe these distributions reflect the heterogeneity of solvation states about the Y,-base molecules. Wider distributions were recovered from the Gaussian model than from the Lorentzian model. This result is characteristic of the models [ 111 and not of the samples. The Lorentzian model has significant amplitude at lifetime values distant from the mean lifetime. These amplitudes are suppressed by the fitting algorithm, resulting in apparently narrow distributions near the central value. In contrast, the Gaussian amplitudes decrease rapidly away from the mean, allowing a wider distribution near the center. As this time the data and our knowledge are not adequate to select either model as being a superior representation of the system.

0 FREQUENCY

2

4

6 Tau

(MHz)

8

10

1

(ns)

Fig. 5. Phase and modulation data for fluorescence of Yt-base in mixtures containing 6% methanol. The full line shows the best fit to the Lorentzian distribution model, and the broken line shows the fit with the hw fixed to 0.01 ns. Fig. 6. Distribution of lifetimes of Yt-base fluorescence top, Lorentzian unimodal; bottom, Gaussian unimodal. 2.0 Gy

R

in benzene-methanol

mixtures:

&_-Base t

in Benzene-MeCI-i 100

0

Mixtures, 8

20°C

6%MeOH

ll?4!u

1.5

2

_

1.0

0

1.0 thw) (ns)

2.0

Fig. 7. Dependence of X$ on the hw of the Lorentzian lifetime distribution for Yt-base in mixtures of benzene-methanol. The values of xn2 are normalized to unity (xw*) about the minimum values.

We questioned the uncertainties in the half-widths by examining the xR2 surfaces (Fig. 7). The half-widths were held constant at the value indicated in the X axis, while f was allowed to vary to minimize xR2. The broken line indicates the value of xR2 expected 33% of the time owing to random errors, and intersection of the ~a* surface with this line indicates the maximum range of hw values which are connected with the data. There is relatively little uncertainty in the half-widths, typically 0.3 ns. Clearly, the data

168

for Y,-base in the solvent mixtures are not consistent with a zero half-width. These half-widths appear to be characteristic of the solvent composition. 5. Conclusion Frequency-domain measurements of the time-dependent emission of Y,-base, in mixtures of benzene and methanol, demonstrated the existence of a distribution of decay times. The single-modal distribution models with two variable parameters provided fits to the mixture data which were equivalent to the double-exponential model with three variable parameters. Additional theory and analysis is necessary to link these data to molecular and statistical properties of the solvent-fluorophore interactions. Acknowledgments This work was supported by Grants GM 35154 and GM 39617 from the National Institutes of Health and Grants DMB 8804931 and 8502835 from the National Science Foundation. The authors wish to thank Professor Stefan Paszyc (Adam Michiewicz University, Poznan, Poland) for providing Y,-base. J.R.L. and W.W. acknowledge support from the University of Maryland Medical Biotechnology Center. This work was performed using facilities at the Center for Fluorescence Spectroscopy, University of Maryland. References 1 A. Grinvald and I. Z. Steinberg, On the analysis of fluorescence decay kinetics by the method of least-squares, Anal. Biochem., 59 (1974) 583 - 598. 2 D. V. O’Connor, W. R. Ware and J. C. Andre, Deconvolution of fluorescence decay curves: a critical comparison of techniques, J. Phys. Chem., 83 (1979) 1333 - 1343. 3 J. N. Demas, Excited State Lifetime Measurements, Academic Press, New York, 1983. 4 D. V. O’Connor and D. Phillips, Time-correlated Single Photon Counting, Academic Press, New York, 1984. 5 D. R. James and W. R. Ware, A fallacy in the interpretation of fluorescence deacay parameters, Chem. Phys. Lett., 120 (1985) 455 - 459. 6 D. R. James and W. R. Ware, Distributions of fluorescence lifetimes: consequences for the photophysics of molecules adsorbed on surfaces, Chem. Phys. Lett., 120 (1985)

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