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Enhanced resolution of anisotropic rotational diffusion by multi-wavelength frequency-domain fluorometry and global analysis
Volume 135, number 3
3 April 1987
CHEMICAL PHYSICS LETTERS
ENHANCED RESOLUTION OF ANISOTROPIC ROTATIONAL DIFFUSION BY MULTI-WAVELENGTH FREQUENCY-DOMAIN FLUOROMETRY AND GLOBAL ANALYSIS *
Ignacy GRYCZYNSIU, Henryk CHEREK, Gabor LACZKO and Joseph R. LAKOWICZ University of Maryland at Baltimore, School of Medicine, Department of Biological Chemistry 660 West Redwood Street, Baltimore, MD 21201. USA
Received 10 November 1986; in final form 9 January 1987
Frequency-dependent differential polarized phase and modulation data were used to measure time-dependent anisotropy decays of 9-aminoacridine and Y-base. The data were obtained at various excitation wavelengths, at which the fundamental anisotropies (ra) varied from - 0.17 to 0.373. The different values of r0 result in different contributions of the multiple correlation times to the anisotropy decay. The multi-wavelength data were analyzed globally, revealing both molecules to be anisotropic rotators. The rotational motions of Y-base are more anisotropic than those of 9-aminoacridine. In propylene glycol at - 5°C the two correlation times for Y-base were found to be 2.1 and 12.1 ns. For 9aminoacridine the correlation times were 9.5 and 14.1 ns.
1. Introduction
Fluorescence anisotropy decays can reveal the size and shape of the rotating molecule [ l-4 1. Ellipsoids of resolution and asymmetric molecules have two or three different rotational diffusion coefficients, resulting in multi-exponential decays of the anisotropy. The main difficulty in applying this method is obtaining data adequate to recover closely spaced rotational correlation times. In the present paper we report improved resolution by two means. First, anisotropy data were obtained in the frequency domain [ $61, which is now known to provide good resolution of complex anisotropy decays [ 6-8 1. Secondly, the data were obtained at several excitation wavelengths, at which the fundamental anisotropies (r,,) are distinct. It is known that for different values of r. the various correlation times contribute differently to the anisotropy decay [ 9, lo]. In particular, for a disk-like molecule with the transition moments within the plane, the in-plane and out-of-plane motions are expected to both contribute to the initial portion of the anisotropy decay. At r. values near 0.1 the slower out-of-plane motion dominates the initial portion of the anisotropy decay [ 9- 111. For a rod* Dedicated to Professor Stefan Paszyc on the occasion of his 65th birthday.
like molecule, with the emission dipole perpendicular to the long axis, the faster rotation about the thin axis contributes more to the overall anisotropy decay as r. decreases from 0.4 to 0.1. Hence, measurements performed at different excitation wavelengths provide a different weighting of the correlation times. Consequently, these different measurements may be of greater value in recovering the correlation times than are multiple measurements at a single excitation wavelength. The multi-wavelength data were analyzed globally, using methods analogous to those described by Brand and co-workers [ 12,131, and by this laboratory for frequency-domain data [ 141.
2. Theory and analysis The anisotropy decay at each excitation wavelength (2) can be described by r”(t)=Cr$g,
exp(--t/8,)
,
(1)
where r”,(t) is the limiting anisotropy at 1, and ei are the correlation times. The values of r$gj represent the amplitude of the anisotropy which decays via the ith correlation time. It should be noted that the correlation times are related to, but not equal to, the rota-
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tional diffusion coefficients of the fluorophore about the principle axes [ l-41. The values of rt depend upon the average angle between the absorption and emission transition moments at each excitation wavelength. This dependence in turn alters the relative contribution of each rotational motion to the anisotropy decay. Data were obtained at several excitation wavelengths, and were analyzed to recover one or two correlation time by the method of non-linear least squares [ 15,161. In the frequency domain the measured quantities are the phase angle difference between the parallel ( )I) and perpendicular ( I ) components of the emission (A”, = @I - @,,) and the ratio of the polarized and modulated components of the emission (A”, = m ,,lm I ) , each measured over a range of modulation frequencies (0). Calculated values are obtained using A$,, = arctan A” = cw
D;N:
-N?D:
N;N:
+D;iD:
(N”)2-(D1)2
(2)
“*
(N’)* + (D”)’ >
’
(3)
where m Nt=
s
Z:(t) sinwtdt,
(4)
Z;(t) cos wt dt
(5)
0
00
0;” =
s 0
and i represents parallel or perpendicular. The parallel and perpendicular components of the emission are given by Z#)=iZ:,(t)
[1+2r”(Ol
z~(t)=~z8(t)[l--r”(t)],
,
(6) (7)
where Zi( t) is the decay of the total emission. The goodness-of-fit is estimated from the value of reduced chi-squared,
(8) 194
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3 April 1987
where v is the number of degrees of freedom (number of data points minus the number of floating parameters), and 6 A, and &!, are the uncertainties in the measured quantities. If the data are obtained for several excitation wavelengths, the data can be analyzed simultaneously to obtain the anisotropy decay (eq. (1)). Alternatively, data at a single excitation wavelength can be used to determine r(t) . At each excitation wavelength the intensity decay (I$( t)) must be determined, as it is needed to calculate the values of A& and &. We now prefer a modified form for the modulation ratio A,. We define [ 81 the frequency-dependent or modulated anisotropy as rlw =(A2w -l)/(A” w +2) .
(9)
The values of r”, are comparable to those of the steady state anisotropy (rL) and the fundamental anisotropy r& At low modulation frequencies r”, is nearly equal to r’. At high modulation frequencies r”, approaches r$. The anisotropy data were fit to expressions like eq. (1). Two variations are possible. In some cases the fundamental anisotropy may be known, so the variable terms can be the 8, and g,, with Xg, = 1.O. If r. is accurately known, this additional constraint improves the resolution of the anisotropy decay [ 81. This is especially true for rapid anisotropy decays, for which limited time resolution results in a decrease in the apparent value of r,. In the present paper the total anisotropy was a floating parameter, so the variable terms in eq. (1) were the values of 0, and rig,.
3. Materials and methods
Frequency-domain data were obtained on the instrument described previously [ 61. To obtain suitable wavelengths for excitation at and below 300 nm this instrument was modified with a continuous ultraviolet laser light source. This source consisted of an argon ion laser (Coherent, Innova 15) , and a ringdye laser (model 699). The dye was rhodamine 6G. Continuous UV is obtained from an angle-tuned doubling crystal (potassium dihydrogen phosphate) within the dye laser cavity. The angle-tuned doubler provided l-3 mW of UV when pumped with 7 W of
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CHEMICAL PHYSICS LETTERS
514 nm light from the ion laser. Additional excitation wavelengths were obtained from a HeCd laser (325 and 442 nm) and from the direct 35 1 nm output from the argon laser. These sources were intensity modulated using an electro-optic modulator (Lasermetrics model 1042). Examination of solvent (propylene glycol) revealed no significant fluorescence due to the solvent at any of the excitation wavelengths. Fluorescence intensity decays were measured with polarizer oriented to yield rotation-free results. The emission from 9-aminoacridine (9-AA) emission was observed through a Coming 3-72 filter to eliminate scattered light. For Y-4,9-dihydro-4,6-dimethyl-9-oxo-lHimidazo 1,2-a purine (Y-base) the emission filter was Coming 3-75. The intensity decays measured at all the excitation wavelengths were analyzed globally to obtain a single decay law. For both molecules the intensity decays were mostly independent of excitation wavelength. The decay of 9-AA was adequately described by a single exponential with a decay time of 13.06 ns. The decay of Y-base was a double exponential with decay times of 1.61 and 9.95 ns, and preexponential factors of 0.108 and 0.892, respectively. Anisotropy spectra were obtained at - 60” C in propylene glycol, using a standard spectrofluorometer.
4. Results The absorption and anisotropy spectra of 9-AA and Y-base are shown in fig. 1. In each case data were obtained at the excitation wavelengths indicated by the arrows. In this way ri was varied from - 0.17 to 0.37 for 9-AA, and for Y-base from 0.02 to 0.33. Visual comparison of the differential phase data indicate that the rotational motions of the Y-base are more anisotropic than those of 9-AA. The rotational anisotropy is evident from the shifts in the frequency of the maximum differential phase angles. This shift is easily visible for Y-base (fig. 2). Close examination of the data for 9-AA also reveals shifts in the frequency of maximum phase angle (fig. 3). For rt values below zero the maximum shifts to lower frequencies. This shift is evident for 9-A& for which negative rt values were accessible (fig. 3). Unfortunately, negative values of rt for Y-base were not
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Fig. 1. Absorption and anisotropy spectra of 9-aminoacridine and Y-base. The arrows indicate the wavelengths used for excitation. The solid dots indicate the values of rk measured in the frequency-domain fluorometer ( - 60°C) under the experimental conditions used for the measurements. The complete anisotropy spectra (-) was measured in a different spectrofluorometer. Also shown are the approximate directions for the S,-S, transition, as reported by Barkley et al. [ 41 and by Gryczynski et al.
1171.
obtainable with our laser light sources. Additionally, for 9-AA the values of A$ are near zero when excited near ri = 0 ( 300 nm), whereas the At values for Ybase with rt near zero (280 nm) show a dependence on modulation frequency. This dependence on the value of rt is characteristic of a rod-like molecule for which the emission moment is nearly perpendicular to the long axis [ 10,181, which is the orientation thought to be correct for 9-AA [4] and for Y-base [171-
Least-squares analysis of the data prove the rotations of both 9-AA and Y-base are anisotropic, and reveals the individual correlation times. When the data for 9-AA are fit to a single correlation time model the values of & is unacceptable large. This value decreases 7-fold when the data are analyzed using a 195
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Volume 135, number 3
1 1 %Amlnoacrdlne c
-1
I
2
,
,
I/I,//
5
I
10
20
FREQUENCY
I
/111111
50
I
100
200
(MHz)
Fig. 2. Differential phase and moduIation data for Y-base in propylene glycol at - 5°C. The correlation times are 2.1 and 12.1 ns. From top to bottom the excitation wavelengths are 35 1,325,300, 288 and 280 nm. The arrows indicate the maximum values of the differential phase angles.
model with two correlation times. This large decrease in ,& is especiahy notewo~hy when one notices the correlation times are in the ratio 1.5 to 1 (table 1). In earlier studies of 9-AA using time-correlated photon counting there were practically no differences in x& for the fits with one or two correlation times [ 41. The anisotropy data of Y-base also required a model with two correlation times. In this case the value of xi decreased 54-fold, the greater decrease being the result of the greater difference between its two correlation times. These dramatic decreases in xi indicate that it should be possible to recover still more complex anisotropy decays using the frequencydomain method. In fact, preliminary data indicate that the anisotropy decay of perylene is described by three correlation times, but further experimentation and analysis are needed to unambiguously recover such a complex decay. In table 1 we also summarized the amplitude factors (rig,) for the anisotropy decay recovered from the analysis, as well as the measured values of r$. It is interesting to notice that both positive and negative components are present in the anisotropy decay, 196
FREQUENCY
(MHZ)
Fig. 3. Differential phase and modulation data for 9-aminoacridine in propylene glycol at - 5°C. The correlation times for the anisotropy decay are 9.5 and 14.1 ns. From top to bottom the excitation wavelengths are 442, 35 1, 325, 300, 298 and 28 I nm. The arrows indicate the rnax~~ values of the differential phase angles.
which is a characteristic of asymmetric rotators when r,, is near zero. We expect the sum of the amplitude factors (rgg,) to equal r$. This agreement is rather good for 9-AA and for Y-base. Some differences are apparent for 9-AA, such as the values at 325 and 300 nm. These differences may be the result of temperature-dependent shifts in its anisotropy spectrum. The absorption and anisotropy spectrum are changing rapidly at 300 nm, and there are probably overlapping transitions at 325 nm (fig. 1). The advantage of using data obtained at several excitation wavelengths is illustrated in fig. 4. This figure shows the values of xi when one of the correlation times is held at fixed values and all the other parameters are allowed to vary to minimize xi. This procedure reveals the resolution of the measurement in a manner which accounts for correlation between the parameters [ 19,201. Evidently, the values of & are more sensitive to the correlation times of 9-AA if the data for all six wavelengths are analyzed globally (-), as compared with analysis of the data for a
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CHEMICAL PHYSICS LETTERS
3 April 1987
Table 1 Global analysis of anisotropy decays of 9-aminoacridine and Y-base Excitation wavelength (nm)
8, (ns)
9-aminoacridine 442 351 325 300 298 281 442-28 1
0.341”’ 0.229 -0.167 -0.001 0.008 0.007
0.328 0.277 -0.102 0.023 0.004 0.008
0.068 0.073 0.080 -0.058 0.003 0.000
0.260 0.154 -0.182
9.5
6r (ns)
14.1
13.0
Y-base 351 325 300 288 280 351-280
0.323 0.235 0.104 0.047 0.020
0.298 0.255 0.082 0.035 0.010
0.041 0.032 0.038 0.034 0.026
0.257 0.193 0.044 0.001 -0.016
2.1
9.8
l.7Sb’
12.1 12.1
0.63
32.3
a) These values of ri are those measured in the frequency-domain fluorometer with laser excitation and the same optical conditions as the measurements. The temperature was - 60°C. b, The values of 6A and 8A in eq. (8) were 0.1’ and 0.005, respectively.
YtBASE T=-5°C
2 Xl3
IN PROPYLENE
GLYCOL
I
OLI 20 x;
9-AMINOACRIDINE IN PROPYLENE GLYCOL T=-5’C
15
0
5
IO 0 [nsl
15
1 20
Ftg. 4. Dependence of xi on the correlation times of 9-aminoacridine and Y-base. Top: Global analysis of the Y-base data (35 1 to 280 nm; -) and analysis of the data for 35 1 nm (---). Bottom: Values of & are shown for analysis of the 9-AA data obtained at 442 nm (- - -), and for analysis at all the data from 28 1 to 442 nm (-_).
single excitation wavelength at 442 nmn (- - -) . At a single excitation wavelength the value of XL is very insensitive to the correlation time. The xi surface for Y-base improves less dramatically for the global analysis, perhaps indicating the multi-wavelength analysis is most useful when the system is near the resolution limit of the measurements. It is also important to consider the amplitudes associated with each correlation time. For 9-AA the amplitudes we observed for excitation at 442 nm are not in agreement with those of Barkley et al. [ 41, for excitation at 430 nm, whereas the ratio of the correlation times (about 1.5 to 1) is in good agreement with the earlier results. For excitation at 442 nm we found values of r&, of 0.068 and 0.260 for the shorter and longer correlation times, respectively. Barkley et al. [4] reported values of 0.27 and 0.07, respectively, the reverse of our results. For excitation at 325 nm our results are in good agreement with their results for 3 I7 nm. At present we do not understand the reason for the differences at 442 nm. We observed these same r”dz values for 9-AA in preliminary studies in glycerol at several temperatures [ 61. Additionally, we attempted to tit our data with the amplitudes 197
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reversed. These attempts resulted in elevated values of xi if the values of rig, were fixed. If these values were variable then the program returned the values listed in table 1. Since the previous measurements [ 41 showed no difference in xi for the one- and twocorrelation-time fits we regard the amplitudes in table 1 as having the higher probability of being correct. It should be recalled that resolution of such closely spaced correlation times is a difficult task. We questioned the origin of the different results and whether the anisotropy decay could be predicted from the available data and theory. The direction of the transition moment shown in fig. 1 is that suggested by Barkley et al. [ 41. The anisotropy decay for 442 nm reported in table 1 is not consistent with this orientation. It seems unlikely but not impossible that the difference is due to the small difference in excitation wavelengths (442 versus 430 nm) . In simulations based on the theoretical expressions by Belford et al. [ 1 ] we found that the large amplitude can be associated with the larger correlation time if the transition moments form an angle of 40-50” with the N-N axis of 9-AA, and also if the moments are 20” from the long axis. For these simulations we assumed that rotation about the long axis was IO-fold faster than the in-plane rotation or rotation about the N-N bond. The precise value of this ratio does not affect the simulations, as we were only looking for the association of correlation times with amplitudes. We note that the values of r&, are rather sensitive to the orientation of the transition moments, so that a small difference in excitation wavelength could have a substantial effect. Additionally, this sensitivity makes it difficult to predict the expected rgZ values, even if the structure of the fluorophore is known and the direction of the transition moments can be estimated.
5. Conclusions Multi-wavelength frequency-domain data provide good resolution of complex anisotropy decays. Anisotropic rotations were revealed by frequency shifts in the maximum value of the differential phase angles, and by non-zero values of the phase angle when the fundamental anisotropy is near zero. The ease of recovering correlation times which differs by less than 2-fold indicates that more closely spaced 198
3 April 1987
correlation times may be recovered. Since the axial ratios of globular proteins are often in the range of 2to- 1, we expect this method to be valuable in studies of the shapes of proteins.
Acknowledgement Supported by grants PCM-8210872 and DMB08502835 from the National Science Foundation and GM-293 18 and GM-35 154 from the National Institutes of Health. JRL offers his special thanks to the National Science Foundation for supporting development of the frequency-domain method. HC was on leave from Nicholas Copernicus University, Torun, Poland with partial support from CPBP 01.06.2.03 (Poland). IG was on leave from University of Gdansk, Institute of Experimental Physics, Gdansk, Poland, with partial support from CPBP 01.06.2.01 (Poland).
References [ 1] G.G. Belford, R.L. Belford and G. Weber, Proc. Natl. Acad. Sci. US 69 (1972) 1392. [2] E.W. Small and I. Isenberg, Biopolymers 16 (1977) 1907. [ 31 T.J. Chuang and K.B. Eisenthal, J. Chem. Phys. 57 (1972) 5094. [ 41 M.D. Barkley, A. Kowalczyk and L. Brand, J. Chem. Phys. 75 (1981) 3581. [5] E. Gratton and M. Limkeman, Biophys. J. 44 (1983) 315. [ 61 J.R. Lakowicz and B.P. Maliwal, Biophys. Chem. 21 (1985) 61. [ 71 J.R. Lakowicz, I. Gryczynski and H. Cherek, J. Biol. Chem. 261 (1986) 2240. [ 8 ] B.P. Maliwal and J.R. Lakowicz, Biochim. Biophys. Acta, to be published. [9] G. Weber, J. Chem. Phys. 55 (1971) 2399. [lo] G. Weber, J. Chem. Phys. 66 (1977) 4081. [ 111 L. Brand, J.M. Beechem, R.E. Date, D.G. Wallbrdige and A.A. Kowalczyk, in: Spectroscopy and the dynamics of molecular biological systems, eds. P.M. Bayley and R.E. Date (Academic Press, New York, 1985) pp. 259-305. [ 121 J.M. Beechem, J.R. Knutson, J.A.B. Ross, B.J. Turner and L. Brand, Biochemistry 22 (1983) 6054. [ 13 ] J.R. Knutson, J.M. Beechem and L. Brand, Chem. Phys. Letters 102 (1983) 501. [ 141 J.R. Lakowicz, E. Gratton, G. Laczko, H. Cherek and M. Limkeman, Biophys. J. 46 (1984) 463. [ 151 P.R. Bevington, Data reduction and error analysis for the physical sciences (McGraw-Hill, New York, 1969).
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[ 161 J.R. Lakowicz, H. Cherek, B.P. Maliwal and E. Gratton, Biochemistry 24 (1985) 376. [ 171 I. Gryczynski, Z. Gryczynski, A. Kawski and S. Paszys, Photochem. Photobiol. 39 ( 1984) 3 19. [ 181 J.R. Lakowicz, I. Gryczynski and H. Cherek, in preparation.
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[ 191 B.P. Maliwal and J.R. Lakowicz, Biochim. Biophys. Acta, to be published. [ 201 J.R. Lakowicz, H. Cherek, I. Gryczynski and N. Joshi, submitted for publication.
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ENHANCED RESOLUTION OF ANISOTROPIC ROTATIONAL DIFFUSION BY MULTI-WAVELENGTH FREQUENCY-DOMAIN FLUOROMETRY AND GLOBAL ANALYSIS *
Ignacy GRYCZYNSIU, Henryk CHEREK, Gabor LACZKO and Joseph R. LAKOWICZ University of Maryland at Baltimore, School of Medicine, Department of Biological Chemistry 660 West Redwood Street, Baltimore, MD 21201. USA
Received 10 November 1986; in final form 9 January 1987
Frequency-dependent differential polarized phase and modulation data were used to measure time-dependent anisotropy decays of 9-aminoacridine and Y-base. The data were obtained at various excitation wavelengths, at which the fundamental anisotropies (ra) varied from - 0.17 to 0.373. The different values of r0 result in different contributions of the multiple correlation times to the anisotropy decay. The multi-wavelength data were analyzed globally, revealing both molecules to be anisotropic rotators. The rotational motions of Y-base are more anisotropic than those of 9-aminoacridine. In propylene glycol at - 5°C the two correlation times for Y-base were found to be 2.1 and 12.1 ns. For 9aminoacridine the correlation times were 9.5 and 14.1 ns.
1. Introduction
Fluorescence anisotropy decays can reveal the size and shape of the rotating molecule [ l-4 1. Ellipsoids of resolution and asymmetric molecules have two or three different rotational diffusion coefficients, resulting in multi-exponential decays of the anisotropy. The main difficulty in applying this method is obtaining data adequate to recover closely spaced rotational correlation times. In the present paper we report improved resolution by two means. First, anisotropy data were obtained in the frequency domain [ $61, which is now known to provide good resolution of complex anisotropy decays [ 6-8 1. Secondly, the data were obtained at several excitation wavelengths, at which the fundamental anisotropies (r,,) are distinct. It is known that for different values of r. the various correlation times contribute differently to the anisotropy decay [ 9, lo]. In particular, for a disk-like molecule with the transition moments within the plane, the in-plane and out-of-plane motions are expected to both contribute to the initial portion of the anisotropy decay. At r. values near 0.1 the slower out-of-plane motion dominates the initial portion of the anisotropy decay [ 9- 111. For a rod* Dedicated to Professor Stefan Paszyc on the occasion of his 65th birthday.
like molecule, with the emission dipole perpendicular to the long axis, the faster rotation about the thin axis contributes more to the overall anisotropy decay as r. decreases from 0.4 to 0.1. Hence, measurements performed at different excitation wavelengths provide a different weighting of the correlation times. Consequently, these different measurements may be of greater value in recovering the correlation times than are multiple measurements at a single excitation wavelength. The multi-wavelength data were analyzed globally, using methods analogous to those described by Brand and co-workers [ 12,131, and by this laboratory for frequency-domain data [ 141.
2. Theory and analysis The anisotropy decay at each excitation wavelength (2) can be described by r”(t)=Cr$g,
exp(--t/8,)
,
(1)
where r”,(t) is the limiting anisotropy at 1, and ei are the correlation times. The values of r$gj represent the amplitude of the anisotropy which decays via the ith correlation time. It should be noted that the correlation times are related to, but not equal to, the rota-
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tional diffusion coefficients of the fluorophore about the principle axes [ l-41. The values of rt depend upon the average angle between the absorption and emission transition moments at each excitation wavelength. This dependence in turn alters the relative contribution of each rotational motion to the anisotropy decay. Data were obtained at several excitation wavelengths, and were analyzed to recover one or two correlation time by the method of non-linear least squares [ 15,161. In the frequency domain the measured quantities are the phase angle difference between the parallel ( )I) and perpendicular ( I ) components of the emission (A”, = @I - @,,) and the ratio of the polarized and modulated components of the emission (A”, = m ,,lm I ) , each measured over a range of modulation frequencies (0). Calculated values are obtained using A$,, = arctan A” = cw
D;N:
-N?D:
N;N:
+D;iD:
(N”)2-(D1)2
(2)
“*
(N’)* + (D”)’ >
’
(3)
where m Nt=
s
Z:(t) sinwtdt,
(4)
Z;(t) cos wt dt
(5)
0
00
0;” =
s 0
and i represents parallel or perpendicular. The parallel and perpendicular components of the emission are given by Z#)=iZ:,(t)
[1+2r”(Ol
z~(t)=~z8(t)[l--r”(t)],
,
(6) (7)
where Zi( t) is the decay of the total emission. The goodness-of-fit is estimated from the value of reduced chi-squared,
(8) 194
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where v is the number of degrees of freedom (number of data points minus the number of floating parameters), and 6 A, and &!, are the uncertainties in the measured quantities. If the data are obtained for several excitation wavelengths, the data can be analyzed simultaneously to obtain the anisotropy decay (eq. (1)). Alternatively, data at a single excitation wavelength can be used to determine r(t) . At each excitation wavelength the intensity decay (I$( t)) must be determined, as it is needed to calculate the values of A& and &. We now prefer a modified form for the modulation ratio A,. We define [ 81 the frequency-dependent or modulated anisotropy as rlw =(A2w -l)/(A” w +2) .
(9)
The values of r”, are comparable to those of the steady state anisotropy (rL) and the fundamental anisotropy r& At low modulation frequencies r”, is nearly equal to r’. At high modulation frequencies r”, approaches r$. The anisotropy data were fit to expressions like eq. (1). Two variations are possible. In some cases the fundamental anisotropy may be known, so the variable terms can be the 8, and g,, with Xg, = 1.O. If r. is accurately known, this additional constraint improves the resolution of the anisotropy decay [ 81. This is especially true for rapid anisotropy decays, for which limited time resolution results in a decrease in the apparent value of r,. In the present paper the total anisotropy was a floating parameter, so the variable terms in eq. (1) were the values of 0, and rig,.
3. Materials and methods
Frequency-domain data were obtained on the instrument described previously [ 61. To obtain suitable wavelengths for excitation at and below 300 nm this instrument was modified with a continuous ultraviolet laser light source. This source consisted of an argon ion laser (Coherent, Innova 15) , and a ringdye laser (model 699). The dye was rhodamine 6G. Continuous UV is obtained from an angle-tuned doubling crystal (potassium dihydrogen phosphate) within the dye laser cavity. The angle-tuned doubler provided l-3 mW of UV when pumped with 7 W of
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514 nm light from the ion laser. Additional excitation wavelengths were obtained from a HeCd laser (325 and 442 nm) and from the direct 35 1 nm output from the argon laser. These sources were intensity modulated using an electro-optic modulator (Lasermetrics model 1042). Examination of solvent (propylene glycol) revealed no significant fluorescence due to the solvent at any of the excitation wavelengths. Fluorescence intensity decays were measured with polarizer oriented to yield rotation-free results. The emission from 9-aminoacridine (9-AA) emission was observed through a Coming 3-72 filter to eliminate scattered light. For Y-4,9-dihydro-4,6-dimethyl-9-oxo-lHimidazo 1,2-a purine (Y-base) the emission filter was Coming 3-75. The intensity decays measured at all the excitation wavelengths were analyzed globally to obtain a single decay law. For both molecules the intensity decays were mostly independent of excitation wavelength. The decay of 9-AA was adequately described by a single exponential with a decay time of 13.06 ns. The decay of Y-base was a double exponential with decay times of 1.61 and 9.95 ns, and preexponential factors of 0.108 and 0.892, respectively. Anisotropy spectra were obtained at - 60” C in propylene glycol, using a standard spectrofluorometer.
4. Results The absorption and anisotropy spectra of 9-AA and Y-base are shown in fig. 1. In each case data were obtained at the excitation wavelengths indicated by the arrows. In this way ri was varied from - 0.17 to 0.37 for 9-AA, and for Y-base from 0.02 to 0.33. Visual comparison of the differential phase data indicate that the rotational motions of the Y-base are more anisotropic than those of 9-AA. The rotational anisotropy is evident from the shifts in the frequency of the maximum differential phase angles. This shift is easily visible for Y-base (fig. 2). Close examination of the data for 9-AA also reveals shifts in the frequency of maximum phase angle (fig. 3). For rt values below zero the maximum shifts to lower frequencies. This shift is evident for 9-A& for which negative rt values were accessible (fig. 3). Unfortunately, negative values of rt for Y-base were not
04r 03.
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400
450
(“ml
Fig. 1. Absorption and anisotropy spectra of 9-aminoacridine and Y-base. The arrows indicate the wavelengths used for excitation. The solid dots indicate the values of rk measured in the frequency-domain fluorometer ( - 60°C) under the experimental conditions used for the measurements. The complete anisotropy spectra (-) was measured in a different spectrofluorometer. Also shown are the approximate directions for the S,-S, transition, as reported by Barkley et al. [ 41 and by Gryczynski et al.
1171.
obtainable with our laser light sources. Additionally, for 9-AA the values of A$ are near zero when excited near ri = 0 ( 300 nm), whereas the At values for Ybase with rt near zero (280 nm) show a dependence on modulation frequency. This dependence on the value of rt is characteristic of a rod-like molecule for which the emission moment is nearly perpendicular to the long axis [ 10,181, which is the orientation thought to be correct for 9-AA [4] and for Y-base [171-
Least-squares analysis of the data prove the rotations of both 9-AA and Y-base are anisotropic, and reveals the individual correlation times. When the data for 9-AA are fit to a single correlation time model the values of & is unacceptable large. This value decreases 7-fold when the data are analyzed using a 195
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Volume 135, number 3
1 1 %Amlnoacrdlne c
-1
I
2
,
,
I/I,//
5
I
10
20
FREQUENCY
I
/111111
50
I
100
200
(MHz)
Fig. 2. Differential phase and moduIation data for Y-base in propylene glycol at - 5°C. The correlation times are 2.1 and 12.1 ns. From top to bottom the excitation wavelengths are 35 1,325,300, 288 and 280 nm. The arrows indicate the maximum values of the differential phase angles.
model with two correlation times. This large decrease in ,& is especiahy notewo~hy when one notices the correlation times are in the ratio 1.5 to 1 (table 1). In earlier studies of 9-AA using time-correlated photon counting there were practically no differences in x& for the fits with one or two correlation times [ 41. The anisotropy data of Y-base also required a model with two correlation times. In this case the value of xi decreased 54-fold, the greater decrease being the result of the greater difference between its two correlation times. These dramatic decreases in xi indicate that it should be possible to recover still more complex anisotropy decays using the frequencydomain method. In fact, preliminary data indicate that the anisotropy decay of perylene is described by three correlation times, but further experimentation and analysis are needed to unambiguously recover such a complex decay. In table 1 we also summarized the amplitude factors (rig,) for the anisotropy decay recovered from the analysis, as well as the measured values of r$. It is interesting to notice that both positive and negative components are present in the anisotropy decay, 196
FREQUENCY
(MHZ)
Fig. 3. Differential phase and modulation data for 9-aminoacridine in propylene glycol at - 5°C. The correlation times for the anisotropy decay are 9.5 and 14.1 ns. From top to bottom the excitation wavelengths are 442, 35 1, 325, 300, 298 and 28 I nm. The arrows indicate the rnax~~ values of the differential phase angles.
which is a characteristic of asymmetric rotators when r,, is near zero. We expect the sum of the amplitude factors (rgg,) to equal r$. This agreement is rather good for 9-AA and for Y-base. Some differences are apparent for 9-AA, such as the values at 325 and 300 nm. These differences may be the result of temperature-dependent shifts in its anisotropy spectrum. The absorption and anisotropy spectrum are changing rapidly at 300 nm, and there are probably overlapping transitions at 325 nm (fig. 1). The advantage of using data obtained at several excitation wavelengths is illustrated in fig. 4. This figure shows the values of xi when one of the correlation times is held at fixed values and all the other parameters are allowed to vary to minimize xi. This procedure reveals the resolution of the measurement in a manner which accounts for correlation between the parameters [ 19,201. Evidently, the values of & are more sensitive to the correlation times of 9-AA if the data for all six wavelengths are analyzed globally (-), as compared with analysis of the data for a
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Table 1 Global analysis of anisotropy decays of 9-aminoacridine and Y-base Excitation wavelength (nm)
8, (ns)
9-aminoacridine 442 351 325 300 298 281 442-28 1
0.341”’ 0.229 -0.167 -0.001 0.008 0.007
0.328 0.277 -0.102 0.023 0.004 0.008
0.068 0.073 0.080 -0.058 0.003 0.000
0.260 0.154 -0.182
9.5
6r (ns)
14.1
13.0
Y-base 351 325 300 288 280 351-280
0.323 0.235 0.104 0.047 0.020
0.298 0.255 0.082 0.035 0.010
0.041 0.032 0.038 0.034 0.026
0.257 0.193 0.044 0.001 -0.016
2.1
9.8
l.7Sb’
12.1 12.1
0.63
32.3
a) These values of ri are those measured in the frequency-domain fluorometer with laser excitation and the same optical conditions as the measurements. The temperature was - 60°C. b, The values of 6A and 8A in eq. (8) were 0.1’ and 0.005, respectively.
YtBASE T=-5°C
2 Xl3
IN PROPYLENE
GLYCOL
I
OLI 20 x;
9-AMINOACRIDINE IN PROPYLENE GLYCOL T=-5’C
15
0
5
IO 0 [nsl
15
1 20
Ftg. 4. Dependence of xi on the correlation times of 9-aminoacridine and Y-base. Top: Global analysis of the Y-base data (35 1 to 280 nm; -) and analysis of the data for 35 1 nm (---). Bottom: Values of & are shown for analysis of the 9-AA data obtained at 442 nm (- - -), and for analysis at all the data from 28 1 to 442 nm (-_).
single excitation wavelength at 442 nmn (- - -) . At a single excitation wavelength the value of XL is very insensitive to the correlation time. The xi surface for Y-base improves less dramatically for the global analysis, perhaps indicating the multi-wavelength analysis is most useful when the system is near the resolution limit of the measurements. It is also important to consider the amplitudes associated with each correlation time. For 9-AA the amplitudes we observed for excitation at 442 nm are not in agreement with those of Barkley et al. [ 41, for excitation at 430 nm, whereas the ratio of the correlation times (about 1.5 to 1) is in good agreement with the earlier results. For excitation at 442 nm we found values of r&, of 0.068 and 0.260 for the shorter and longer correlation times, respectively. Barkley et al. [4] reported values of 0.27 and 0.07, respectively, the reverse of our results. For excitation at 325 nm our results are in good agreement with their results for 3 I7 nm. At present we do not understand the reason for the differences at 442 nm. We observed these same r”dz values for 9-AA in preliminary studies in glycerol at several temperatures [ 61. Additionally, we attempted to tit our data with the amplitudes 197
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reversed. These attempts resulted in elevated values of xi if the values of rig, were fixed. If these values were variable then the program returned the values listed in table 1. Since the previous measurements [ 41 showed no difference in xi for the one- and twocorrelation-time fits we regard the amplitudes in table 1 as having the higher probability of being correct. It should be recalled that resolution of such closely spaced correlation times is a difficult task. We questioned the origin of the different results and whether the anisotropy decay could be predicted from the available data and theory. The direction of the transition moment shown in fig. 1 is that suggested by Barkley et al. [ 41. The anisotropy decay for 442 nm reported in table 1 is not consistent with this orientation. It seems unlikely but not impossible that the difference is due to the small difference in excitation wavelengths (442 versus 430 nm) . In simulations based on the theoretical expressions by Belford et al. [ 1 ] we found that the large amplitude can be associated with the larger correlation time if the transition moments form an angle of 40-50” with the N-N axis of 9-AA, and also if the moments are 20” from the long axis. For these simulations we assumed that rotation about the long axis was IO-fold faster than the in-plane rotation or rotation about the N-N bond. The precise value of this ratio does not affect the simulations, as we were only looking for the association of correlation times with amplitudes. We note that the values of r&, are rather sensitive to the orientation of the transition moments, so that a small difference in excitation wavelength could have a substantial effect. Additionally, this sensitivity makes it difficult to predict the expected rgZ values, even if the structure of the fluorophore is known and the direction of the transition moments can be estimated.
5. Conclusions Multi-wavelength frequency-domain data provide good resolution of complex anisotropy decays. Anisotropic rotations were revealed by frequency shifts in the maximum value of the differential phase angles, and by non-zero values of the phase angle when the fundamental anisotropy is near zero. The ease of recovering correlation times which differs by less than 2-fold indicates that more closely spaced 198
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correlation times may be recovered. Since the axial ratios of globular proteins are often in the range of 2to- 1, we expect this method to be valuable in studies of the shapes of proteins.
Acknowledgement Supported by grants PCM-8210872 and DMB08502835 from the National Science Foundation and GM-293 18 and GM-35 154 from the National Institutes of Health. JRL offers his special thanks to the National Science Foundation for supporting development of the frequency-domain method. HC was on leave from Nicholas Copernicus University, Torun, Poland with partial support from CPBP 01.06.2.03 (Poland). IG was on leave from University of Gdansk, Institute of Experimental Physics, Gdansk, Poland, with partial support from CPBP 01.06.2.01 (Poland).
References [ 1] G.G. Belford, R.L. Belford and G. Weber, Proc. Natl. Acad. Sci. US 69 (1972) 1392. [2] E.W. Small and I. Isenberg, Biopolymers 16 (1977) 1907. [ 31 T.J. Chuang and K.B. Eisenthal, J. Chem. Phys. 57 (1972) 5094. [ 41 M.D. Barkley, A. Kowalczyk and L. Brand, J. Chem. Phys. 75 (1981) 3581. [5] E. Gratton and M. Limkeman, Biophys. J. 44 (1983) 315. [ 61 J.R. Lakowicz and B.P. Maliwal, Biophys. Chem. 21 (1985) 61. [ 71 J.R. Lakowicz, I. Gryczynski and H. Cherek, J. Biol. Chem. 261 (1986) 2240. [ 8 ] B.P. Maliwal and J.R. Lakowicz, Biochim. Biophys. Acta, to be published. [9] G. Weber, J. Chem. Phys. 55 (1971) 2399. [lo] G. Weber, J. Chem. Phys. 66 (1977) 4081. [ 111 L. Brand, J.M. Beechem, R.E. Date, D.G. Wallbrdige and A.A. Kowalczyk, in: Spectroscopy and the dynamics of molecular biological systems, eds. P.M. Bayley and R.E. Date (Academic Press, New York, 1985) pp. 259-305. [ 121 J.M. Beechem, J.R. Knutson, J.A.B. Ross, B.J. Turner and L. Brand, Biochemistry 22 (1983) 6054. [ 13 ] J.R. Knutson, J.M. Beechem and L. Brand, Chem. Phys. Letters 102 (1983) 501. [ 141 J.R. Lakowicz, E. Gratton, G. Laczko, H. Cherek and M. Limkeman, Biophys. J. 46 (1984) 463. [ 151 P.R. Bevington, Data reduction and error analysis for the physical sciences (McGraw-Hill, New York, 1969).
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[ 161 J.R. Lakowicz, H. Cherek, B.P. Maliwal and E. Gratton, Biochemistry 24 (1985) 376. [ 171 I. Gryczynski, Z. Gryczynski, A. Kawski and S. Paszys, Photochem. Photobiol. 39 ( 1984) 3 19. [ 181 J.R. Lakowicz, I. Gryczynski and H. Cherek, in preparation.
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[ 191 B.P. Maliwal and J.R. Lakowicz, Biochim. Biophys. Acta, to be published. [ 201 J.R. Lakowicz, H. Cherek, I. Gryczynski and N. Joshi, submitted for publication.
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