J. Phys. Chem. 1987, 91, 6344-6346
6344
Analyses of Nonexponential Fluorescence Decay Functions of a Single Tryptophan Residue in Erabutoxin b Fumio Tanaka, Mie Nursing College, 100 Torii-cho, Tsu. Mie 514, Japan
Norio Kaneda, Department of Biochemistry, Nagoya University School of Medicine, Nagoya 466, Japan
Noboru Mataga,* Department of Chemistry, Faculty of Engineering Science, Osaka University, Toyonaka, Osaka 560, Japan
Naoto Tamai, Iwao Yamazaki, Institute for Molecular Science, Okazaki 444, Japan
and Kyozo Hayashi Department of Biology, Gifu Pharmaceutical University, Mitahora, Gifu 502, Japan (Received: March 27, 1987; In Final Form: July 29, 1987)
Fluorescence of a single tryptophan (Trp-29) in erabutoxin b exhibited nonexponential decay curves at 6, 20, and 40 OC. The decay curves were analyzed by a best-fit procedure with a theoretical decay function based on a model where internal rotations of tryptophan in the protein are described with a rotational analogue of the Smoluchowski equation containing an angular-dependentquenching constant. Diffusion coefficientsof Trp-29 relating to the internal rotation around the covalent bond connecting the indole ring and peptide were greater than the other ones, and most of them were nearly proportional to temperature. These results suggest that Trp-29 has appreciable freedom of internal rotation around the covalent bond in the time region of subnanoseconds to nanoseconds.
Introduction
A number of works have revealed that protein structure is inherently dynamic.'s2 It has been reported that in many proteins tryptophan residue has appreciable freedom of internal rotation, even if they are buried in the protein matrices, according to the measurements of time-resolved fluorescence ani~otropy,~ and at the same time the fluorescence of a single tryptophan in proteins shows a nonexponential decay.3 To elucidate the mechanism of the nonexponential decay of tryptophan fluorescence, theoretical expressions for the decay function as well as time-resolved anisotropy have been derived in the previous work.4 This work is based on the model that the tryptophan as a completely asymmetric rotor has a motional freedom of the internal rotations, which is described by a rotational analogue of the Smoluchowski equation, and the quenching constant is dependent on the rotational angles. Erabutoxin b is a neurotoxic protein from the venom of the sea snake Laticauda semifasciata5j6 and consists of 62 amino acid residues, belonging to the class of the short-chain neurotoxin. The primary structure of erabutoxin b has been determined by Sato and Tamiya.6 The three-dimensional structure of erabutoxin b has been determined by Low et al.' and also by Tsernoglou and Petsk0.*9~ It contains a single tryptophan (Trp-29), which has been considered to play an important role in the binding of era(1) Gurd, F. R. N.; Rothgeb, T. M. Adv. Protein Chem. 1979, 33, 73. (2) Karplus, M.; McCammon, J. A. Annu. Rev. Biochem. 1983, 52, 263. (3) Beechem, J. M.; Brand, L. Annu. Rev. Biochem. 1985, 54, 43. (4) Tanaka, F.;Mataga, N. Biophys. J. 1987, 51, 487. (5) Tamiya, N.; Arai, H. Biochem. J. 1966, 99, 624. (6) Sato, S.; Tamiya, N. Biochem. J. 1971, 122, 453.
(7) Low,B. W.; Preston, H. S.; Sato, A,; Rosen, L. S.;Searl, J. E.; Rudko, A. D.; Richardson, J. A. Proc. Natl. Acad. Sci. U.S.A. 1976, 73, 2991. (8) Tsernoglou, D.; Petsko, G. A. FEBS Lett. 1976, 68, 1. (9) Tsernoglou, D.; Petsko, G. A. Proc. Natl. Acad. Sci. U.S.A. 1977, 74, 971.
0022-3654/87/2091-6344$01 SO10
butoxin b to the acetylcholine In the present work we have analyzed the fluorescence decay curves of erabutoxin b with the theoretical decay function as described in the following and have obtained information on the motional mode of the internal rotation of the tryptophan in erabutoxin b. Experimental Section
Erabutoxin b was purchased from Sigma (St. Louis, MO) and purified by column chromatography on CM-cellulose, according to Tamiya and Abe.I2 Fluorescence spectra were measured with a calibrated Shimazu spectrofluorometer (RF502). Fluorescence decay curves of the tryptophan of erabutoxin b were measured with a time-correlated, single-photon-counting method using a synchronously pumped, cavity-pumped dye laser for the excitation at 295 nm (pulse width, 6 ps). The polarizer was adjusted to a magic angle (54.7') so that the influence of the fluorescence depolarization due to rotational Brownian motion of the protein should be eliminated. Details of the experimental arrangement were described e1~ewhere.l~ Observed decay curves were analyzed both with a theoretical decay function based on the model described below and with multiexponential decay functions. Parameters were adjusted until the values of x2 became the minimum
x2 =
ni=1
xfi
d t ' E ( t 3 F(ti - t ' ) - Z o ( t i ) ] 2 / Z o ( t i )
(1)
where E(r) is the exciting pulse and F ( t ) is the theoretical decay (10) Chang, C. C.; Hayashi, K. Biochem. Biophys. Res. Commun. 1969, 37, 841. ( 1 1 ) Chang, C. C.; Yang, C. C. Biochim. Biophys. Acta 1973, 295, 595. (12) Tamiya, N.; Abe, H. Biochem. J. 1972, 130, 547. (13) Yamazaki, I.; Tamai, N.; Kume, H.; Tsuchiya, H.; Oba, K. Rev. Sci. Instrum. 1985, 56, 1187.
0 1987 American Chemical Society
The Journal of Physical Chemistry, Vol. 91, No. 25, 1987 6345
Letters
TABLE I: Constants Used for the Analysis location of location of energy quencherb minimum
kl,O ns-’ 0.1163
aq,deg -24.8
a,. deg
aprdeg
Bp, deg
79.6
41.8
66.7
“The value was obtained from the longest lifetime of free Trp observed in alkaline solution.20 bCoordinations of the N atom of the -NH3+ group of Lys-27 were obtained from X-ray data.*s9 Location of the potential energy minimum was assumed to be one of Trp-29 obtained by X-ray However, the potential energy for the rotation around z axis was neglected. TABLE II: Parameters Obtained by Best-Fit Procedure between Observed and Calculated Decay Curves diffusion coefficients, ns-I T , k.”, P, “C n? k-i T’ D,, = Dyy D,, Ox, = Dyz x 2 D, 2.29 1.46 0.474 1.70 0.036 6 0.668 1.30 2.53 1.54 0.506 1.88 0.16 20 0.935 1.30 40
Figure 1. Geometrical arrangement of tryptophan residue in proteins. Coordinate systems of a spherical protein and tryptophan residue are shown by (x’y’z? and (xyz), respectively. The origin of (x’y’z’) was chosen at the CHI group connecting the peptide bond and indole ring. Internal rotation of the tryptophan residue from the (x’y’z’) system to the (xyz) system is expressed with Euler’s angles (a&). The location of the quencher, -NH3+ of Lys-27, is also illustrated in the figure. Polar coordinates of the N atom of the quencher in the system (x’y’z’) are indicated by cyq and 0,.
function or a multiexponential decay function. Decay parameters of two-exponential and three-exponential decay functions were determinedl43l5by the method of moments according to Isenberg et a1.16J7
Theoretical Model In our present model, the tryptophan residue, which is a completely asymmetric rotor, covalently binds to a spherical protein. The geometrical arrangement of the molecular systems is illustrated in Figure 1. Tryptophan residue possesses a motional freedom of internal rotations described by Euler’s angles (aPy) from the spherical macromolecular system (x’y’z’) to the tryptophan system ( x y z ) . Rotational motions of tryptophan residue were described by a diffusion equation of the rotational analogue of the Smoluchowski e q u a t i ~ n ~and * ’ ~ described by Green’s function, G(ww’t) 1 a -G(ww’t) = -(kl kq(w))G(ww’t)- J,*D*J,G(ww’t)- -Jus 2kT at
+
where k , is the decay constant of the excited fluorophore in the absence of the quencher and D the second rank tensor of the rotational diffusion coefficient of the internal motion of the fluorophore. k is the Boltzmann constant and T the temperature. The angular momentum operator for a completely asymmetric rotor is represented by J,. In the present model we assumed that the fluorescence quenching constant and the potential energy were expanded with spherical harmonics as eq 3 and 4, respectively,
(14) Kaneda, N.; Tanaka, F.; Kido, N.; Yagi, K. Photochem. Photobiol. 1985, 41, 519. (15) Tanaka, F.; Kaneda, N.; Mataga, N. J . Phys. Chem. 1986,90,3167. (16) Isenberg, I.; Dyson, R. D.; Hanson, R. Biophys. J . 1973, 13, 1090. (17) Isenberg, I. J . Chem. Phys. 1973, 59, 5696. (18) Favro, L. D. In Fluctuation Phenomena in Solids; Burgess, R. D., Ed.; Academic: New York, 1958; p 79.
1.24
1.20
0.529
2.00
0.15
2.70
2.03
where a4and Pq are polar coordinates of the fluorescence quencher expressed in the macromolecular system (x’y 5’). We assumed that the efficient quencher of fluorescence of Trp-29 is the -NH3+ group of Lys-27, since Lys-27 is closest to Trp-29 in the threedimensional structure of erabutoxin b,7-9and it is known that the dissociable proton of the lysine residue quenches the indole fluorescence in free tryptophan in aqueous solution? We can show that the second term of eq 3 is equal to cos x, where x represents a solid angle between the z axis and a vector of the N atom of the -NH3+ group formed in the system (x’y’z’). The relative position of the N atom of the -NH3+ group is illustrated in Figure 1 . We also assumed that the potential energy for the internal rotation of Trp-29 with respect to a and P has a minimum at the location obtained by X-ray crystallography,’-9 while the rotational motion around the z axis is free. In eq 4 apand flP indicate polar coordinates of the z axis on the basis of the system (x’y’z’). The second term of eq 4 is equal to cos x, where x is a solid angle between the movable z axis and the z axis obtained by X-ray crystallography. The fluorescence decay function of Trp-29 was expanded in a power series of p , where p is represented in units of k T . We have used an approximate equation which takes into account the expansion terms up to the second order.
Results and Discussion The fluorescence spectrum of Trp-29 of erabutoxin b exhibited a broad structureless band with a maximum at 350 nm. The wavelength of the maximum did not change when the excitation wavelength was changed. The fluorescence should be from the La state.19 Fluorescence decay curves of Trp-29 of erabutoxin b were measured at 6, 20, and 40 O C . The observed decay curves were all nonexponential. Figure 2 shows the decay curves at 20 “C. Observed intensities are indicated with dots in Figure 2C. The excitation pulse is shown by curve c in Figure 2C. The observed decay curves were simulated with the following four models concerning the rotational diffusion tensor, D, which consists of diagonal elements, D,, Dyy,and D,,, and off-diagonal elements, D,, Dyz,and D,,;in the framework of the theoretical decay function stated above, (i) D,, = Dyy = D,,, Oxy= Dyz = D,,, (ii) D,, = Dyy # Dzz,D , = Dyz = D,, = 0 , (iii) D,, = Dyy Z D,,, D , = Dyz = D,,, and ( 1 ~ ) D,, = Dyy f Df,, D , Z Dyz = D,,. The parameters kqo,p , and independent diffusion coefficients in the above cases were varied systematically until the value of x2 attained in the minimum. Constants used for the calculation are shown in Table I. It has been found that the observed results were reproduced only poorly in the cases of (i), (ii), and (iii). When D , was varied independently from the other off-diagonal (19) Mataga, N.; Torihashi, Y.; Ezumi, K. Theor. Chim. Acta 1964, 2, 158.
6346 The Journal of Physical Chemistry, Vol. 91, No. 25, 1987 1
+ 4 L
Letters TABLE III: Multiexponential Decay Analyses" T, 'C T ~ ns , ai T ~ ns . a2 73, ns 6 1.32 0.927 4.08 0.073 1.32 0.928 4.09 0.072 47.1 20 1.11 0.959 4.30 0.041 1.12 0.960 4.33 0.040 27.5 0.048 40 0.836 0.952 3.35 0.841 0.954 3.41 0.046 7.71
aj
-0.000
-0.000 -0.000
x2 4.17 4.17 3.36 3.38 2.60 2.58
'The decay function was expressed by the equation F ( t ) = X j a , exp(-t/r,), where a!is the component fraction and T~ the lifetime of the ith component. These parameters were determined by the method of moment~.l~-~'
4
.i* I
, IC ,
I
I
I
I
diffusion coefficients as in the case of (iv), the agreement between the observed and calculated results became much improved. It should be noted here that diffusion coefficients related to the z axis were always greater than the others. It implies that rotational motion of Trp-29 is fastest around the z axis in the time region of subnanoseconds where the quenching process is taking place. Various parameters as the best fit and the values of x2 are listed in Tble 11. The theoretical decay curve at 20 OC is shown in Figure 2C, curve a, of which the deviation from the observed decay curve is indicated in Figure 2A. The value of k,' increased as the temperature was elevated (see Table 11), indicating the overall e n h a n c e m e n t of t h e q u e n c h i n g at t h e higher temperature. Most
than 10% of the fractions. The agreements between the observed and calculated decay curves in this case were rather poor. We have also attempted to analyze them with three-exponential decay functions but could not improve the fittings (see Table 111). However, the fitting with three-exponential decay functions could be much improved, if we utilize other method of analysis such as the nonlinear least-squares method. A number of works have revealed that the fluorescence from tryptophan in aqueous solution shows multiexponential decay f ~ n c t i o n s .This ~ feature has been explained by the presence of ~~~ rotamer configurations of =CO and -NH3+ g r o ~ p s . *This interpretation has been extended to the interpretation for nonexponential fluorescence decay of the single tryptophan in prot e i n ~ : which ~ ~ ~ is, however, based on the rather static model for protein structure. On the other hand, our model is based on an inherently dynamic picture, where an angular-dependent quenching constant was introduced into the motional equation for the tryptophan residue in proteins. This seems reasonable because the quenching constant should always depend on the mutual orientation between the fluorophore and a quencher whatever the quenching mechanism is. In relation to the above arguments, the following points should be emphasized here. Namely, the main purpose of the present paper is to demonstrate that not only the multiexponential analysis of the fluorescence decay curve, for which the rather rigid and heterogeneous model of protein structure must be assumed, but also the analysis in terms of our theory4 based on the clear-cut model of the inherently dynamic protein structure can reproduce satisfactorily the observed nonexponential decay of the tryptophan fluorescence of the protein. The results of the present study will be very important from a biological point of view. Namely, Trp-29 is considered to play an important role in the binding of erabutoxin b to the acetylcholine Motional freedom of Trp-29 could be essential for the binding, since the location of Trp-29 should be adjustable for the most stable binding between erabutoxin b and the receptor.
Acknowledgment. We are indebted to Prof. Katsube of Osaka University, Institute for Protein Research, for a helpful discussion on the three-dimensional structure of erabutoxin b and for providing us with three-dimensional coordinates of atoms of erabutoxin 6. We also thank the Computer Center, Institute for Molecular Science, Okazaki National Research Institutes, for the use of the HITAC M-680. ~~
of the diffusion coefficients were nearly proportional to temperature, which is reasonable since a diffusion coefficient should be proportional to T in general. The height of potential energy or strength of torque, p , which contains kT in the denominator, decreased a little as the temperature was elevated. This is also reasonable because the value of p should decrease upon increasing the temperature. The observed decay curves were also analyzed with multiexponential decay functions, according to the method of mom e n t ~ . ' ~ -It~ 'was ,possible to reproduce approximately the observed decay curves by the superposition of two exponential functions. The obtained decay parameters are shown in Table 111. The shorter lifetimes were about 1 ns w i t h more than 90% of the fractions, and the longer lifetimes were a b u t 4 ns with less
(20) Jameson, D. M.; Weber, G. 1. Phys. Chem. 1981, 85, 953. (21) Rayner, D. M.; Szabo, A. G. Can. J . Chem. 1978, 569743. (22) Szabo, A. G.; Rayner, D. M. J . Am. Chem. Sac. 1980, 102, 554. (23) Robbins, R. J.; Fleming, G. R.; Beddard, G. S.; Robinson, G. W.; Thistlethwaite, P. J.; Woolfe, G. J. J . Am. Chem. SOC.1980, 102, 6271. (24) Chang, M. C.; Petrich, J. W.; McDonald, D. B.; Fleming, G. R. J . A m . Chem. SOC.1983, 105, 3819. (25) Petrich, J. W.; Chang, M. C.; McDonald, D. B.; Fleming, G. R. J . Am. Chem. SOC.1983, 105, 3824. (26) Ross, J . B. A,; Rousslang, K. W.; Brand, L. Biochemistry 1981, 20, 4361. (27) Szabo, A. G.; Krajcarski, D.; Zuker, M. Chem. Phys. Leu. 1984,108, 145. (28) Alcala, J. R.; Gratton, E.; Prendergast, F. G . Biophys. J . 1987, 5 1 , 587. (29) Alcala, J. R.; Gratton, E.; Prendergast, F. G . Biophys. J . 1987, 51, 597.
