- Email: [email protected]
Anisotropic rotational diffusion of indole in cyclohexane studied by 2 GHz frequency-domain fluorometry
Volume 149, number 2
CHEMICAL PHYSICS LETTERS
12August 1988
ANISOTROPIC ROTATIONAL DIFFUSION OF INDOLE IN CYCLOHEXANE STUDIED BY 2 GHz FREQUENCY-DOMAIN FLUOROMETRY Joseph R. LAKOWICZ, Ignacy GRYCZYNSIU and Wieslaw M. WICZK Department of Biological Chemistry, University of Maryland at Baltimore, School of Medicine, 660 West RedwoodStreet, Baltimore, MD 21201, USA Received 13 May 1988
We measured the frequency response of the polarized emission of non-quenched and quenched indole in cyclohexane at 2O”C, up to 2 GHz. Non-radiative energy transfer from indole to 1-stilbene was used to decrease indole decay time. Quenching increases the fraction of the total emission, which occurs on a picosecond timescale, and thereby provides increased information on rapid rotational motions. The measurement of quenched sample allowed resolution of the anisotropic rotation of indole with correlation times of 17 and 73 ps. The longer correlation time is consistent with that expected for a sphere with stick boundary conditions, the shorter with the slip boundary condition for an oblate ellipsoid.
1. Introduction Measurement of fluorescence anisotropy is often used to probe the orientational motions of simple and complex molecules. The time-dependent anisotropy decays depend upon the shape, size and optical properties of the rotating molecules, as well as the dynamical properties of their surroundings [ l-41. Depending on their geometrical symmetry, molecules can have one, two or three different rotational diffusion coefficients, resulting in multiexponential anisotropy decays. It is a difficult task to obtain data adequate to recover closely spaced rotational correlation times, especially when these values are in the picosecond time range. This is because of the limited time resolution and signal-to-noise of most fluorescence measurements, and because the picosecond motions only contribute during the early portion of the intensity decay process. One approach to improving the resolution at early times is the use of collisional quenching, which preferentially removes the molecules emitting at long times. As the fluorescence lifetime is decreased by quenching the early time portion of the anisotropy decay contributes increasingly to the data. Measurement of the anisotropy decays under these condi134
tions provides increased resolution of complex and/ or rapid rotational processes [ 5-71. Acrylamide is an efficient quencher of indole fluorescence [ 8,9]. However, acrylamide is a highly polar substance, and is not sufficiently soluble in cyclohexane, which is the solvent we selected to allow measurement of rotational diffusion in the absence of hydrogen bonding. We could have used chlorinated hydrocarbons, which are also effective quenchers of indole, but such quenching is often accompanied by undesirable photochemical processes. Hence, we used non-radiative energy transfer [ lo] from indole to stilbene, which is soluble in cyclohexane. An additional advantage of this method is that energy transfer occurs at loo-fold lower acceptor concentrations than does collisional quenching, which minimizes perturbations of the solvent by the acceptor (quencher). Also, quenching by energy transfer can be used in both high and low viscosity solvents.
2. Theory Information about rotational diffusion is contained in the anisotropy decay law, which can be described as a sum of exponentials
0 009-2614/88/$ 03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Volume149,number2
cI rag,exp( -t/e,)
J-(f)=
CHEMICALPHYSICSLETTERS
,
(1)
where Biare the rotational correlation times and values rag, represent the amplitude of the anisotropy which decays via ith correlation time. The value v. is the total amplitude of the anisotropy decay, or equivalently the value of the anisotropy which would be observed in the absence of rotational diffusion. In our analyses the individual values of rogj were variable parameters, which is equivalent to considering r, to be unknown. Alternatively, we used known value of r,, in which case the g, values were variable with the restriction that C,g,= 1.0. It should be noted that the correlation times are related, but not equal, to the rotational diffusion coefficients of the fluorophore about the principle axes [ l-41. In the frequency domain, the measured quantities are the phase angle difference between the parallel ( 11) and perpendicular ( 1) components of the emission (& =@I -4, ) and the ratio of the polarized modulated components of the emission (/i$ = m ,,/m I ), each measured over a range of modulation frequencies (a). The superscript q indicates the acceptor (quencher) concentration. For the non-linear least-squares analysis the calculated values (denoted by c) were obtained using A& = arctan
12August1988
where Za(t) is the decay of the total emission. The goodness-of-fit to the anisotropy decay law (eq. ( 1) ) is estimated from the value of the reduced chi-square,
where 2 is the number of degrees of freedom (number of data points minus the number of floating parameters), and 6A and &4 are the uncertainties in the measured values. The modulation data are presented as the modulated anisotropy ‘4-l yq =w OJ fl2,+2’
(9)
The values of r:, can be compared with those of the steady-state anisotropy ( rq) and the fundamental anisotropy r,. At low modulation frequencies rz is nearby equal to rq. At high modulation frequencies r: approaches r. [ 11,12 1. It should be noted that the intensity decays of indole become heterogeneous in the presence of acceptor (quencher) due to nature of non-radiative energy transfer and diffusion of the donor and acceptor. The intensity decays were obtained from the frequency response of the emission with magic angle polarization. The data were fit to the multi-exponential model [ 13,141
c a: exp( -tl?p)
(2)
zgt)=
(3)
The parameters from the double exponential fit were used in eqs. (4) and (5).
.
(10)
l/2 ’
where m
NP =
s
3. Materials and methods Z?(t) sin(W) dt ,
(4)
0
m
0: =
s
Z:(t)cos(ot) dt
(5)
0
and i represents the parallel or perpendicular components of the emission. These components are given by
19(t)=fZ8(t)[lf2r(t)l,
(6)
Z"1(1)=4Z8(t)[l-'(t)l,
(7)
Frequency-domain measurements were performed using 2 GHz fluorometer described previously [ 15 1. The laser beam was expanded to about 5 mm in diameter to decrease its local intensity. Indole was excited at 297 nm, and the emission was observed through 313 nm interference filter using frontface geometry. No fluorescence of t-stilbene was observed at 3 13 nm. Intensity decays were measured using magic angle polarization conditions. Indole was purified by HPLC, t-stilbene was from Kodak, scintillation grade. All solutions were in cy135
I2 August 1988
CHEMICAL PHYSICS LETTERS
Volume 149. number 2
clohexane at 20°C. The solutions were not purged by nitrogen. 4. Results The fluorescence spectrum of indole and the absorption spectrum of t-stilbene are shown in fig. 1. High spectral overlap provides a FGrster distance of R,,= 31.6 A. This value indicates that quenching of indole fluorescence will occur for quencher (t-stilbene) concentrations in the range of 1fP2 M. The frequency-domain intensity data are shown in fig. 2, in the absence ( l ) and presence ( o ) of 10e2 M tstilbene. In the absence of t-stilbene the intensity decay of indole is single exponential (xi = 1.4). This is seen from the overlap of these measured phase and modulation data ( l ) with the curves calculated for the single exponential model with a decay time of 5.6 ns (---). In the presence of t-stilbene the decay becomes strongly heterogeneous, and cannot even be approximated by the single exponential model (xi = 1769). The intensity decay was parameterized using a double exponential model (table I), but it should be remembered that the actual form of the decay is not a sum of exponential components. In the presence of 10B2 M t-stilbene the mean decay time is decreased about fivefold, to 1.07 ns. The frequency-domain anisotropy data are shown in fig. 3 (top). In the absence of acceptor the data could only be measured to 220 MHz due to extensive demodulation of the emission, which is the result of the 5.6 ns decay time of indole. In the presence of acceptor the differential phase and modulation data could be measured up to the 2 GHz limit of the instrumentation. These sets of data (with and with-
-
FREQUENCY
out acceptor) were analyzed globally to recover the anisotropy decay law. The recovered correlation times are 17 and 73 ps, with amplitudes 0.093 and 0.192, respectively. The sum of recovered amplitudes is in good agreement with measured r. of indole in propylene glycol at -60°C ro=0.275 [ 161. The single exponential model gives only slightly higher xi, but with a smaller value for the total anisotropy (table 2). This result is typical of that found when a complex anisotropy decay is fit to a single
Table I Multi-exponential analysis of indole fluorescence in cyclohexane at 20°C [ t-stilbene]
5, (ns)
tx,
1;“’
0
5.60
1
1
1.4
5.56 5.61
0.636 0.364
0.631 0.369 /’
1.4
0.76
I
1
300
0.09 1.25
0.7!9 0.28 1
0.159 0.841
~t~uorescence~ - I8 f
350 WAVELENGTH
400
1769 1.9
(nn-11
Fig. 1. Emission spectrum of indole (-) and absorption trum of t-stilbene (---) in cyclohexane at 20°C.
136
x6
Indole
0.01 ”
(MHz1
Fig. 2. Frequency response of the emission of indole with ( 0 ) and without ( l ) 0.01 M t-stilbene. The solid lines show the best single decay time fits to the data.
a) The fractional intensities f; arc given by 1; = (Y,T,/1 (Y,T, . The mean decay times can be calculated from k Ej;r,
Volume 149, number 2
CHEMICAL PHYSICS LETTERS
Table 2 Analysis of anisotropy decay of indole in cyclohexane at 20°C in presence of 0.01 M of t-stilbene
0,
N”2 l2 - INDOLEin Cyclohexane,20% HI =L 3 p gE
9 _
0 l
iy E$
0 M O.OlM
t-Stilbene ”
Model
6-
z*
Experiment a’ p r&s,
10 28
18 28
-.o&
I
20
I
I
50
I I III
100
I
200
FREQUENCY
1
12 August 1988
I
r, floating 0.244 63 0.093 0.192
17 13
xi
stick
slip
1.0
57
19
0.9
52 60
17 20
r,fixed(0.275 [16]) 0.275 52
8.9
0.095 0.180
0.8
22 75
I
I11111
500
I 2000
6, (PS)
Calculations b, 6, (ps)
1000
(MHZ)
Fig. 3. Frequency-domain anisotropy data for indole (top) up to 2 GHz and simulated data (bottom) up to 20 GHz.
exponential model with a variable value for ro. Calculations with a fixed value for r. give a more significant difference in xi between single and double exponential model, but the correlation times and amplitudes are essentially equivalent to that found with a variable value for r,. This agreement supports our acceptance of the two-correlation-time model for indole in cyclohexane.
‘) The values of 6A and 6A in eq. (8) were 0.1’ and 0.005, respectively. b, Calculated for an oblate spheroid with long and short dimensions of 8.2 and 3.7 A, respectively. One component ( I 0) was calculated as 0= (3D,, + 30, )-I, two components (2 0) were calculated as e,=(60,)-‘-8,=5(0,+D,,)-’ and &= (20, + 40, ) - ’ according to Tao [ 17,181. Calculations for slip conditions were provided according to Hu and Zwanzig [ 191.
The bottom of fig. 3 shows simulated anisotropy data using the correlation times and amplitudes recovered for indole in cyclohexane. The simulations were extended to 20 GHz. One notices that the 17 ps correlation time shows a differential phase maximum near 10 GHz. Hence, still more rapid correlation times could be measured if the frequency range of the measurements could be extended above 2 GHz. Surprisingly, the 73 ps component shows a non&rentzian shape. This is not due to anisotropic rotation, but rather to the multi-exponential form of the intensity decay in the presence of quenching. We questioned the uncertainties in the correlation times. An estimation of the uncertainty is provided by the least-squares analysis, in particular by the diagonal elements of the covariance matrix [ 201. This estimation is correct only if there is no correlation between the fitted parameters. These estimated uncertainties are near 10 and 5 ps for ro-floating and rofixed models, respectively. We also performed a more rigorous analysis of the uncertainties. The values of xi were examined when one of the correlation times was kept constant at different values near to its value 137
CHEMICAL PHYSICS LETTERS
Volume 149, number 2 1.2 t
t
5. Discussion Indole
in Cyclohexane
20°C ---
(0)
0 M t-st,lbene O.OlM ”
(ps)
Fig. 4. xi surfaces for two correlation times of indole in cyclohexane at 20°C. Top - calculations with r, as floating parameter. Bottom - calculations with r. held constant at the measured value 0.275 [ 161.
corresponding to the minimum &, while the other parameters were floating. The least-squares analysis was performed again, allowing the floating parameters to vary, yielding the minimum value of xi consistent with the fixed-parameter value. Since all the other parameters were floating during this re-analysis, this procedure should account for all the correlations between the parameters. For the correlation times, the result of this procedure is shown in fig. 4 (top for r,-floating model, bottom for r&ixed model). The dotted lines indicate the values of ,Y& expected 33% of the time due to random errors. We believe that this method overestimates the uncertainties in the correlation times by about a factor of two. The dashed lines show J& dependence for nonquenched samples. In the absence of quenching the two correlation times cannot be recovered from the data, at least not on the basis of the xi values for the single correlation time tit. In the presence of quenching the xi surfaces for the two correlation times do not overlap within the xi values expected for random errors. This non-overlap, and the relative steepness of the xi surfaces, provides strong evidence for two indole correlation times near 20 and 75 ps. 138
12 August 1988
We now consider our results in terms of hydrodynamics models for indole, with the stick and slip boundary conditions. For clarity we note that the term spheroid refers to ellipsoids of resolution or equivalently to symmetrical ellipsoids. An ellipsoid can, in general, have three different axial dimensions. The term ablate refers to flattened disc-shaped molecules. The indole molecule can be aproximated by ablate spheroid with diameters 8.2 and 3.7 A corresponding to longer and shorter axis, respectively. The smaller value corresponds to the thickness of aromatic rings. The volume of this ablate spheroid ( 130 A3) is close to that obtained from the density and molecular weight of indole ( 160 k3), The rotational diffusion coefficients of the ablate spheroid may be obtained from the solution of the Navier-Stokes equation subject to certain boundary condition. With the stick boundary condition (Stokes-Einstein theory) 8;=1/6Di=~~3L1VlkT=~C,,
(11)
where V is the volume of the molecule, k is the Boltzmann constant, T is the temperature in K, Dj and C, are diffusion and friction coefficients, respectively. The li depend only on the shape of the molecule, and the values are tabulated in refs. [ 17,18 1, Hydrodynamics with stick boundary conditions requires that the velocity of the solute molecule surface relative to the nearest solvent molecules is zero. In systems where the solvent and solute molecules are both of molecular dimensions and no strong interactions occurs, it is more appropriate to employ slip (i.e. no tangential stress) boundary conditions. Here, the resistance to the motion arises from the fact that, for non-symmetrical molecules, some solvent must be displaced as the molecule rotates. The friction coefficient for a spheroid with slip is zero about the symmetry axis. In the case of slip boundary conditions the correlaton times are given by e,=1/6D,=r/c:+z(0’,
(12)
with C;d.;VfkT.
(13)
Volume 149,number 2
CHEMICALPHYSICSLETTERS
This equation was proposed by Pecora and co-workers [ 21,221 from depolarized light scattering measurements and A: have been computed numerically by Hu and Zwanzig [ 191 for spheroids and by Youngren and Acrivos for ellipsoids [ 231. The value of 7,‘“’corresponds to the inertial limit, generally out of reach of fluorescence anisotropy decay. For example, in DODCI case, at least twice bigger than indole, 71(O) has been found 4 ps [ 18,241. Calculated correlation times for indole, as a spheroid and as an oblate rotor, are given in table 2. For stick boundary conditions the calculated correlation time near 60 ps corresponds to longer measured correlation time in our experiment. The correlation time calculated for slip boundary conditions ( 17-20 ps) is in good agreement with shorter correlation time recovered from our anisotropy decay. At first glance it is surprising that we did not observe a correlation time near the inertial limit, that is near 2 ps. The transition moment of indole is expected to be within the plane of the aromatic ring, and the molecule might be expected to be symmetric with regard to rotations within this plane. However, the data appear to account for all of the expected anisotropy, that is C rogi was found equal to the fundamental anisotropy Y,,.This result implies that either
indole is not symmetric with regard to in-plane rotation, or that the 17 ps correlation time is the result of rotations which are not directed about one of its symmetry axes. In conclusion, the above results demonstrate that indole rotation in cyclohexane represent an intermediate situation between stick and slip boundary conditions. Similar intermediate situations have been found for rhodamine 6G and DODCI by Fleming and co-workers [ 25 1. In a future publication we will describe the effects of hydrogen bonding on stick versus stick rotations of indole in non-polar solvents [ 261.
12August 1988
References [ I ] G.G. Belford,R.L. Belfordand G. Weber,Proc. Natl. Acad. Sci. US 69 (1972) 1392.
[ 2 ] E.W. Small and I. Isenberg, Biopolymers 16 ( 1977) 1907. [3] T.J. Chuang and K.B. Eisenthal, J. Chem. Phys. 57 (1972) 5094. [4] M.D. Barkley, A. Kowalczyk and L. Brand, J. Chem. Phys. 75 (1981) 3581. [ 5 ] J.R. Lakowicz, H. Cherek, I. Gryczynski. N. Joshi and M.L. Johnson, Biophys. J. 5 1 (1987) 755. [6] J.R. Lakowicz. H. Szmacinski and I. Gryczynski, Photothem. Photobiol. 47 ( 1988) 3 I. [ 71 J.R. Lakowicz, G. Laczko and I. Gryczynski, Biochemistry 26 (1987) 82. [ 8 ] M.R. Eftink and CA. Ghiron, Anal. Biochem. 1I4 ( 1981) 199. [9] M.R. Eftink and CA. Ghiron, J. Phys. Chem. 80 ( 1976) 486. [IO] Th. FBrster, Ann. Phys. (Leipzig) 2 ( 1948) 55. [ 111 B.P. Maliwal and J.R. Lakowicz, Biochim. Biophys. Acta 873 (1986) 161. [ 121 B.P. Maliwal, A. Hermeter and J.R. Lakowicz, Biochim. Biophys. Acta 873 (1986) 173. [ 131J.R. Lakowicz, G. Laczko, H. Cherek, E. Gratton and M. Limkeman, Biophys. J. 46 ( 1984) 193. [ 141 E. Gratton, J.R. Lakowicz, B. Maliwal, H. Cherek, G. Laczko and M. Limkeman, Biophys. J. 46 ( 1984) 479. [ 151J.R. Lakowicz, G. Laczko and I. Gryczynski, Rev. Sci. Instr. 57 (1986) 2499, [ 161 J.R. Lakowicz and I. Gryczynski, in preparation. [ 171 T. Tao, Biopolymers 8 ( 1969) 609. [ 18 ] G.R. Fleming, Chemical applications of ultrafast spectroscopy (Oxford Univ. Press, Oxford, 1986) ch. 6. [ 191 CM. Hu and R. Zwanzig, J. Chem. Phys. 60 (1974) 4354. [20] P.R. Bevington, Data reduction and error analysis for the physical sciences (McGraw Hill, New York, 1969) pp. 248, 313. [2I ] G.R. Alms, D.R. Bauer, J.I. Brauman and R. Pecora, J. Chem. Phys. 59 (1973) 5321. [22] D.R. Bauer, G.R. Alms, J.I. Brauman and R. Pecora, J. Chem. Phys. 61 (1974) 2255. [23] G.K. Youngren and A. Acrivos, J, Chem. Phys. 63 (1975) 3846. [24]G.R. Fleming, A.E.W. Knight, J.M. Morris, R.J. Robbins and G.W. Robinson, Chem. Phys. Letters 49 (1977) 1. L25lG.R. Fleming, A.E.W. Knight, J.M. Morris, R.J. Robbins and G.W. Robinson, Chem. Phys. Letters s I ( I 977) 399. [26] J.R. Lakowicz, I. Gryczynski and W. Wink, in preparation.
Acknowledgement Supported by Grants DMB-85 11065 and DMB8502835 from the National Science Foundation and Grant GM-3961 7 from the National Institutes of Health. 139
CHEMICAL PHYSICS LETTERS
12August 1988
ANISOTROPIC ROTATIONAL DIFFUSION OF INDOLE IN CYCLOHEXANE STUDIED BY 2 GHz FREQUENCY-DOMAIN FLUOROMETRY Joseph R. LAKOWICZ, Ignacy GRYCZYNSIU and Wieslaw M. WICZK Department of Biological Chemistry, University of Maryland at Baltimore, School of Medicine, 660 West RedwoodStreet, Baltimore, MD 21201, USA Received 13 May 1988
We measured the frequency response of the polarized emission of non-quenched and quenched indole in cyclohexane at 2O”C, up to 2 GHz. Non-radiative energy transfer from indole to 1-stilbene was used to decrease indole decay time. Quenching increases the fraction of the total emission, which occurs on a picosecond timescale, and thereby provides increased information on rapid rotational motions. The measurement of quenched sample allowed resolution of the anisotropic rotation of indole with correlation times of 17 and 73 ps. The longer correlation time is consistent with that expected for a sphere with stick boundary conditions, the shorter with the slip boundary condition for an oblate ellipsoid.
1. Introduction Measurement of fluorescence anisotropy is often used to probe the orientational motions of simple and complex molecules. The time-dependent anisotropy decays depend upon the shape, size and optical properties of the rotating molecules, as well as the dynamical properties of their surroundings [ l-41. Depending on their geometrical symmetry, molecules can have one, two or three different rotational diffusion coefficients, resulting in multiexponential anisotropy decays. It is a difficult task to obtain data adequate to recover closely spaced rotational correlation times, especially when these values are in the picosecond time range. This is because of the limited time resolution and signal-to-noise of most fluorescence measurements, and because the picosecond motions only contribute during the early portion of the intensity decay process. One approach to improving the resolution at early times is the use of collisional quenching, which preferentially removes the molecules emitting at long times. As the fluorescence lifetime is decreased by quenching the early time portion of the anisotropy decay contributes increasingly to the data. Measurement of the anisotropy decays under these condi134
tions provides increased resolution of complex and/ or rapid rotational processes [ 5-71. Acrylamide is an efficient quencher of indole fluorescence [ 8,9]. However, acrylamide is a highly polar substance, and is not sufficiently soluble in cyclohexane, which is the solvent we selected to allow measurement of rotational diffusion in the absence of hydrogen bonding. We could have used chlorinated hydrocarbons, which are also effective quenchers of indole, but such quenching is often accompanied by undesirable photochemical processes. Hence, we used non-radiative energy transfer [ lo] from indole to stilbene, which is soluble in cyclohexane. An additional advantage of this method is that energy transfer occurs at loo-fold lower acceptor concentrations than does collisional quenching, which minimizes perturbations of the solvent by the acceptor (quencher). Also, quenching by energy transfer can be used in both high and low viscosity solvents.
2. Theory Information about rotational diffusion is contained in the anisotropy decay law, which can be described as a sum of exponentials
0 009-2614/88/$ 03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Volume149,number2
cI rag,exp( -t/e,)
J-(f)=
CHEMICALPHYSICSLETTERS
,
(1)
where Biare the rotational correlation times and values rag, represent the amplitude of the anisotropy which decays via ith correlation time. The value v. is the total amplitude of the anisotropy decay, or equivalently the value of the anisotropy which would be observed in the absence of rotational diffusion. In our analyses the individual values of rogj were variable parameters, which is equivalent to considering r, to be unknown. Alternatively, we used known value of r,, in which case the g, values were variable with the restriction that C,g,= 1.0. It should be noted that the correlation times are related, but not equal, to the rotational diffusion coefficients of the fluorophore about the principle axes [ l-41. In the frequency domain, the measured quantities are the phase angle difference between the parallel ( 11) and perpendicular ( 1) components of the emission (& =@I -4, ) and the ratio of the polarized modulated components of the emission (/i$ = m ,,/m I ), each measured over a range of modulation frequencies (a). The superscript q indicates the acceptor (quencher) concentration. For the non-linear least-squares analysis the calculated values (denoted by c) were obtained using A& = arctan
12August1988
where Za(t) is the decay of the total emission. The goodness-of-fit to the anisotropy decay law (eq. ( 1) ) is estimated from the value of the reduced chi-square,
where 2 is the number of degrees of freedom (number of data points minus the number of floating parameters), and 6A and &4 are the uncertainties in the measured values. The modulation data are presented as the modulated anisotropy ‘4-l yq =w OJ fl2,+2’
(9)
The values of r:, can be compared with those of the steady-state anisotropy ( rq) and the fundamental anisotropy r,. At low modulation frequencies rz is nearby equal to rq. At high modulation frequencies r: approaches r. [ 11,12 1. It should be noted that the intensity decays of indole become heterogeneous in the presence of acceptor (quencher) due to nature of non-radiative energy transfer and diffusion of the donor and acceptor. The intensity decays were obtained from the frequency response of the emission with magic angle polarization. The data were fit to the multi-exponential model [ 13,141
c a: exp( -tl?p)
(2)
zgt)=
(3)
The parameters from the double exponential fit were used in eqs. (4) and (5).
.
(10)
l/2 ’
where m
NP =
s
3. Materials and methods Z?(t) sin(W) dt ,
(4)
0
m
0: =
s
Z:(t)cos(ot) dt
(5)
0
and i represents the parallel or perpendicular components of the emission. These components are given by
19(t)=fZ8(t)[lf2r(t)l,
(6)
Z"1(1)=4Z8(t)[l-'(t)l,
(7)
Frequency-domain measurements were performed using 2 GHz fluorometer described previously [ 15 1. The laser beam was expanded to about 5 mm in diameter to decrease its local intensity. Indole was excited at 297 nm, and the emission was observed through 313 nm interference filter using frontface geometry. No fluorescence of t-stilbene was observed at 3 13 nm. Intensity decays were measured using magic angle polarization conditions. Indole was purified by HPLC, t-stilbene was from Kodak, scintillation grade. All solutions were in cy135
I2 August 1988
CHEMICAL PHYSICS LETTERS
Volume 149. number 2
clohexane at 20°C. The solutions were not purged by nitrogen. 4. Results The fluorescence spectrum of indole and the absorption spectrum of t-stilbene are shown in fig. 1. High spectral overlap provides a FGrster distance of R,,= 31.6 A. This value indicates that quenching of indole fluorescence will occur for quencher (t-stilbene) concentrations in the range of 1fP2 M. The frequency-domain intensity data are shown in fig. 2, in the absence ( l ) and presence ( o ) of 10e2 M tstilbene. In the absence of t-stilbene the intensity decay of indole is single exponential (xi = 1.4). This is seen from the overlap of these measured phase and modulation data ( l ) with the curves calculated for the single exponential model with a decay time of 5.6 ns (---). In the presence of t-stilbene the decay becomes strongly heterogeneous, and cannot even be approximated by the single exponential model (xi = 1769). The intensity decay was parameterized using a double exponential model (table I), but it should be remembered that the actual form of the decay is not a sum of exponential components. In the presence of 10B2 M t-stilbene the mean decay time is decreased about fivefold, to 1.07 ns. The frequency-domain anisotropy data are shown in fig. 3 (top). In the absence of acceptor the data could only be measured to 220 MHz due to extensive demodulation of the emission, which is the result of the 5.6 ns decay time of indole. In the presence of acceptor the differential phase and modulation data could be measured up to the 2 GHz limit of the instrumentation. These sets of data (with and with-
-
FREQUENCY
out acceptor) were analyzed globally to recover the anisotropy decay law. The recovered correlation times are 17 and 73 ps, with amplitudes 0.093 and 0.192, respectively. The sum of recovered amplitudes is in good agreement with measured r. of indole in propylene glycol at -60°C ro=0.275 [ 161. The single exponential model gives only slightly higher xi, but with a smaller value for the total anisotropy (table 2). This result is typical of that found when a complex anisotropy decay is fit to a single
Table I Multi-exponential analysis of indole fluorescence in cyclohexane at 20°C [ t-stilbene]
5, (ns)
tx,
1;“’
0
5.60
1
1
1.4
5.56 5.61
0.636 0.364
0.631 0.369 /’
1.4
0.76
I
1
300
0.09 1.25
0.7!9 0.28 1
0.159 0.841
~t~uorescence~ - I8 f
350 WAVELENGTH
400
1769 1.9
(nn-11
Fig. 1. Emission spectrum of indole (-) and absorption trum of t-stilbene (---) in cyclohexane at 20°C.
136
x6
Indole
0.01 ”
(MHz1
Fig. 2. Frequency response of the emission of indole with ( 0 ) and without ( l ) 0.01 M t-stilbene. The solid lines show the best single decay time fits to the data.
a) The fractional intensities f; arc given by 1; = (Y,T,/1 (Y,T, . The mean decay times can be calculated from k Ej;r,
Volume 149, number 2
CHEMICAL PHYSICS LETTERS
Table 2 Analysis of anisotropy decay of indole in cyclohexane at 20°C in presence of 0.01 M of t-stilbene
0,
N”2 l2 - INDOLEin Cyclohexane,20% HI =L 3 p gE
9 _
0 l
iy E$
0 M O.OlM
t-Stilbene ”
Model
6-
z*
Experiment a’ p r&s,
10 28
18 28
-.o&
I
20
I
I
50
I I III
100
I
200
FREQUENCY
1
12 August 1988
I
r, floating 0.244 63 0.093 0.192
17 13
xi
stick
slip
1.0
57
19
0.9
52 60
17 20
r,fixed(0.275 [16]) 0.275 52
8.9
0.095 0.180
0.8
22 75
I
I11111
500
I 2000
6, (PS)
Calculations b, 6, (ps)
1000
(MHZ)
Fig. 3. Frequency-domain anisotropy data for indole (top) up to 2 GHz and simulated data (bottom) up to 20 GHz.
exponential model with a variable value for ro. Calculations with a fixed value for r. give a more significant difference in xi between single and double exponential model, but the correlation times and amplitudes are essentially equivalent to that found with a variable value for r,. This agreement supports our acceptance of the two-correlation-time model for indole in cyclohexane.
‘) The values of 6A and 6A in eq. (8) were 0.1’ and 0.005, respectively. b, Calculated for an oblate spheroid with long and short dimensions of 8.2 and 3.7 A, respectively. One component ( I 0) was calculated as 0= (3D,, + 30, )-I, two components (2 0) were calculated as e,=(60,)-‘-8,=5(0,+D,,)-’ and &= (20, + 40, ) - ’ according to Tao [ 17,181. Calculations for slip conditions were provided according to Hu and Zwanzig [ 191.
The bottom of fig. 3 shows simulated anisotropy data using the correlation times and amplitudes recovered for indole in cyclohexane. The simulations were extended to 20 GHz. One notices that the 17 ps correlation time shows a differential phase maximum near 10 GHz. Hence, still more rapid correlation times could be measured if the frequency range of the measurements could be extended above 2 GHz. Surprisingly, the 73 ps component shows a non&rentzian shape. This is not due to anisotropic rotation, but rather to the multi-exponential form of the intensity decay in the presence of quenching. We questioned the uncertainties in the correlation times. An estimation of the uncertainty is provided by the least-squares analysis, in particular by the diagonal elements of the covariance matrix [ 201. This estimation is correct only if there is no correlation between the fitted parameters. These estimated uncertainties are near 10 and 5 ps for ro-floating and rofixed models, respectively. We also performed a more rigorous analysis of the uncertainties. The values of xi were examined when one of the correlation times was kept constant at different values near to its value 137
CHEMICAL PHYSICS LETTERS
Volume 149, number 2 1.2 t
t
5. Discussion Indole
in Cyclohexane
20°C ---
(0)
0 M t-st,lbene O.OlM ”
(ps)
Fig. 4. xi surfaces for two correlation times of indole in cyclohexane at 20°C. Top - calculations with r, as floating parameter. Bottom - calculations with r. held constant at the measured value 0.275 [ 161.
corresponding to the minimum &, while the other parameters were floating. The least-squares analysis was performed again, allowing the floating parameters to vary, yielding the minimum value of xi consistent with the fixed-parameter value. Since all the other parameters were floating during this re-analysis, this procedure should account for all the correlations between the parameters. For the correlation times, the result of this procedure is shown in fig. 4 (top for r,-floating model, bottom for r&ixed model). The dotted lines indicate the values of ,Y& expected 33% of the time due to random errors. We believe that this method overestimates the uncertainties in the correlation times by about a factor of two. The dashed lines show J& dependence for nonquenched samples. In the absence of quenching the two correlation times cannot be recovered from the data, at least not on the basis of the xi values for the single correlation time tit. In the presence of quenching the xi surfaces for the two correlation times do not overlap within the xi values expected for random errors. This non-overlap, and the relative steepness of the xi surfaces, provides strong evidence for two indole correlation times near 20 and 75 ps. 138
12 August 1988
We now consider our results in terms of hydrodynamics models for indole, with the stick and slip boundary conditions. For clarity we note that the term spheroid refers to ellipsoids of resolution or equivalently to symmetrical ellipsoids. An ellipsoid can, in general, have three different axial dimensions. The term ablate refers to flattened disc-shaped molecules. The indole molecule can be aproximated by ablate spheroid with diameters 8.2 and 3.7 A corresponding to longer and shorter axis, respectively. The smaller value corresponds to the thickness of aromatic rings. The volume of this ablate spheroid ( 130 A3) is close to that obtained from the density and molecular weight of indole ( 160 k3), The rotational diffusion coefficients of the ablate spheroid may be obtained from the solution of the Navier-Stokes equation subject to certain boundary condition. With the stick boundary condition (Stokes-Einstein theory) 8;=1/6Di=~~3L1VlkT=~C,,
(11)
where V is the volume of the molecule, k is the Boltzmann constant, T is the temperature in K, Dj and C, are diffusion and friction coefficients, respectively. The li depend only on the shape of the molecule, and the values are tabulated in refs. [ 17,18 1, Hydrodynamics with stick boundary conditions requires that the velocity of the solute molecule surface relative to the nearest solvent molecules is zero. In systems where the solvent and solute molecules are both of molecular dimensions and no strong interactions occurs, it is more appropriate to employ slip (i.e. no tangential stress) boundary conditions. Here, the resistance to the motion arises from the fact that, for non-symmetrical molecules, some solvent must be displaced as the molecule rotates. The friction coefficient for a spheroid with slip is zero about the symmetry axis. In the case of slip boundary conditions the correlaton times are given by e,=1/6D,=r/c:+z(0’,
(12)
with C;d.;VfkT.
(13)
Volume 149,number 2
CHEMICALPHYSICSLETTERS
This equation was proposed by Pecora and co-workers [ 21,221 from depolarized light scattering measurements and A: have been computed numerically by Hu and Zwanzig [ 191 for spheroids and by Youngren and Acrivos for ellipsoids [ 231. The value of 7,‘“’corresponds to the inertial limit, generally out of reach of fluorescence anisotropy decay. For example, in DODCI case, at least twice bigger than indole, 71(O) has been found 4 ps [ 18,241. Calculated correlation times for indole, as a spheroid and as an oblate rotor, are given in table 2. For stick boundary conditions the calculated correlation time near 60 ps corresponds to longer measured correlation time in our experiment. The correlation time calculated for slip boundary conditions ( 17-20 ps) is in good agreement with shorter correlation time recovered from our anisotropy decay. At first glance it is surprising that we did not observe a correlation time near the inertial limit, that is near 2 ps. The transition moment of indole is expected to be within the plane of the aromatic ring, and the molecule might be expected to be symmetric with regard to rotations within this plane. However, the data appear to account for all of the expected anisotropy, that is C rogi was found equal to the fundamental anisotropy Y,,.This result implies that either
indole is not symmetric with regard to in-plane rotation, or that the 17 ps correlation time is the result of rotations which are not directed about one of its symmetry axes. In conclusion, the above results demonstrate that indole rotation in cyclohexane represent an intermediate situation between stick and slip boundary conditions. Similar intermediate situations have been found for rhodamine 6G and DODCI by Fleming and co-workers [ 25 1. In a future publication we will describe the effects of hydrogen bonding on stick versus stick rotations of indole in non-polar solvents [ 261.
12August 1988
References [ I ] G.G. Belford,R.L. Belfordand G. Weber,Proc. Natl. Acad. Sci. US 69 (1972) 1392.
[ 2 ] E.W. Small and I. Isenberg, Biopolymers 16 ( 1977) 1907. [3] T.J. Chuang and K.B. Eisenthal, J. Chem. Phys. 57 (1972) 5094. [4] M.D. Barkley, A. Kowalczyk and L. Brand, J. Chem. Phys. 75 (1981) 3581. [ 5 ] J.R. Lakowicz, H. Cherek, I. Gryczynski. N. Joshi and M.L. Johnson, Biophys. J. 5 1 (1987) 755. [6] J.R. Lakowicz. H. Szmacinski and I. Gryczynski, Photothem. Photobiol. 47 ( 1988) 3 I. [ 71 J.R. Lakowicz, G. Laczko and I. Gryczynski, Biochemistry 26 (1987) 82. [ 8 ] M.R. Eftink and CA. Ghiron, Anal. Biochem. 1I4 ( 1981) 199. [9] M.R. Eftink and CA. Ghiron, J. Phys. Chem. 80 ( 1976) 486. [IO] Th. FBrster, Ann. Phys. (Leipzig) 2 ( 1948) 55. [ 111 B.P. Maliwal and J.R. Lakowicz, Biochim. Biophys. Acta 873 (1986) 161. [ 121 B.P. Maliwal, A. Hermeter and J.R. Lakowicz, Biochim. Biophys. Acta 873 (1986) 173. [ 131J.R. Lakowicz, G. Laczko, H. Cherek, E. Gratton and M. Limkeman, Biophys. J. 46 ( 1984) 193. [ 141 E. Gratton, J.R. Lakowicz, B. Maliwal, H. Cherek, G. Laczko and M. Limkeman, Biophys. J. 46 ( 1984) 479. [ 151J.R. Lakowicz, G. Laczko and I. Gryczynski, Rev. Sci. Instr. 57 (1986) 2499, [ 161 J.R. Lakowicz and I. Gryczynski, in preparation. [ 171 T. Tao, Biopolymers 8 ( 1969) 609. [ 18 ] G.R. Fleming, Chemical applications of ultrafast spectroscopy (Oxford Univ. Press, Oxford, 1986) ch. 6. [ 191 CM. Hu and R. Zwanzig, J. Chem. Phys. 60 (1974) 4354. [20] P.R. Bevington, Data reduction and error analysis for the physical sciences (McGraw Hill, New York, 1969) pp. 248, 313. [2I ] G.R. Alms, D.R. Bauer, J.I. Brauman and R. Pecora, J. Chem. Phys. 59 (1973) 5321. [22] D.R. Bauer, G.R. Alms, J.I. Brauman and R. Pecora, J. Chem. Phys. 61 (1974) 2255. [23] G.K. Youngren and A. Acrivos, J, Chem. Phys. 63 (1975) 3846. [24]G.R. Fleming, A.E.W. Knight, J.M. Morris, R.J. Robbins and G.W. Robinson, Chem. Phys. Letters 49 (1977) 1. L25lG.R. Fleming, A.E.W. Knight, J.M. Morris, R.J. Robbins and G.W. Robinson, Chem. Phys. Letters s I ( I 977) 399. [26] J.R. Lakowicz, I. Gryczynski and W. Wink, in preparation.
Acknowledgement Supported by Grants DMB-85 11065 and DMB8502835 from the National Science Foundation and Grant GM-3961 7 from the National Institutes of Health. 139