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Transference of triplet state excitation energy from tyrosine to tryptophan
ARCHIVES
OF
BIOCHEMISTRY
Transference
AND
BIOPHYSICS
of Triplet
258-270 (1968)
124,
State
Excitation
Energy
from
Tyrosine
to Tryptophan I. Amino Acids in Simple
and Mixed
Solutions’
B. RABINOVITCH2 Biophysics
Laboratory,
Stanford
University,
Stanford,
Received
August 1,1967
California
S&OS
Quantitative measurements have been made of the electron spin resonance energy absorption (signal height) of tyrosine and tryptophan triplet states, in simple and in mixed solutions. Calculations were also made for the relative signal heights of these amino acids in mixed solutions. Results were satisfactorily explained on the basis of a transfer of excitation energy from tyrosine to tryptophan, but only to nearest neighbors. The much larger distances over which this energy is transferred has suggested a different mechanism from the dipole-dipole interaction of Fiirster’s. The dependence of the energy transfer probability on the inverse third power rather than the sixth power led to good agreement with experiment, and suggested a possible exciton mechanism.
A considerable amount of work has been done on the fluorescence spectroscopy (1) and fluorescence depolarization (2) of amino acids and proteins, and has been well summarized by Beaver (3) and Weber and Teale (4). Other work on peptides (5) has tended to support the evidence that there is an interaction between the tyrosine and tryptophan moieties of these natural and synthetic peptides. This interaction, it has been suggested, leads to the transfer of singlet state excitation energy from the first to the second of these aromatic amino acids. However, although Weber (6) and Weber and Teale (7) draw the conclusion that such transfer of energy leads to quenching and does not contribute to the fluorescence of 1 This research was supported in part by AIW contract AT(W3)326-14 and in part by the PHS Special Fellowship l-F3-GM-32, 898-01 awarded by the National Institute of General Medical Sciences. 2 Present address : Department of Biochemistry, Medical School, University of Oklahoma, 866 Northeast Thirteenth Street, Oklahoma City, Oklahoma 73194. 258
the acceptor, Burshtein (8) has calculated that both processes occur with a greater or lesser efficiency among the proteins, while Vladimirov (9) concludes that essentially no such transfer of energy occurs in proteins. On the other hand, Konev et al. (10) have shown that in concentrated tryptophan solutions energy migration without quenching can occur. Phosphorescence of aromatic amino acids and proteins has also undergone some study (1 l-13), and a similar transfer of excitation energy from the triplet state of tyrosine to tryptophan has been suggested. From observations of the decay times of the phosphorescence emanating from serum albumin, on the short and long wavelength sides of the emission band, Longworth (14) concludes that both tyrosine and tryptophan are phosphorescing. However, considering the molar ratio of tyrosine to tryptophan in this protein (17: l), it is certain that a considerable part of the energy transferred is quenched. The first direct observation of the excited tripIet state of these amino acids was made
TRIPLET
STATE
ENERGY
by Douzou and Ptak (15) by electron spin resonance spectrometry (ESR) and corresponds to the Am = f2 transition. They showed what appeared to be a relation between the rate of increase of the triplet state population and the rate of free radical formation. This was later confirmed by Azizova and co-workers (16), who suggested t,hat the path of the free radical formation goes through the triplet state of the molecule. The first triplet state observation 011 proteins was made by Shiga and Piette (17), who observed the clear suppression of the tyrosine ESR absorption band leaving the tryptophan band intact. However, it could not be demonstrated that the tryptophan ESR absorption band was enhanced together with the loss of the tyrosine band; hence energy transfer could not be demonstrated. On the other hand, these authors claimed to have demonstrated this transfer in the case of a mixture of tyrosine and tryptophan in solution. An unequivocal resolution of this question would be of importance in understanding the energy transfer problem in macromolecules. We have undertaken to attempt an exploration of the relative changes in equilibrium concentration of triplet state species in mixtures of t,yrosine and tryptophan. MATERIALS
AND
METHODS
The L-tyrosine and L-tryptophan analytical grade, chromatographically ous, and characterized in the following $X0Sitrogen Determined Calculated L-Tyrosine rJ-Tryptophan
8.02 13.66
7.73 13.72
used were homogeneway: [a1116 N HCl -7.0” -31.4”
Solutions were made up in 6 N HCl prepared by dilution from reagent-grade HCl (sp. gr., 1.19). This solvent has the virtue of ensuring just one ionic species per amino acid in solution, the ammonium ion, and at the same time giving a clear glass at liquid nitrogen temperature withollt the complication of the presence of organic liquids. No precautions were taken to exclude oxygen. Samples were placed in fused silica tubing of orItside diameters 0.155 + 0.004 inch and frozen in liquid nitrogen before being placed in the spectrometer cavity. 9 baseline for each sample was obtained aft,er establishing the spectrometer
TRANSFERENCE
2.50
parameters to be used, e.g., 100 KHz modulation amplitude and d-c magnetic field sweep rate, but before ultraviolet irradiation. The source of ultraviolet radiation was a Hanovia 200-W Hg-Xe discharge lamp focused with quartz optics at the center of the cavity. After ultraviolet irradiation was begun, a resonance absorption band was observed in all cases, falling in the g - 4 region of the spectrum, which decayed over a period of seconds on removal of the irradiation. A marked phosphorescence could be observed visually when the samples were removed from the cavity and from the irradiation. These bands were readily identifiable as due to triplet state species and easily assignable to either tyrosine or tryptophan. These amino acids also gave large free radical absorption bands in the g - 2 region of the spectrum. Because of the subsequent reactions of these free radicals, even at liquid nitrogen temperature, a colored product appeared at the surface of the sample where the ultraviolet radiation was incident. It was also noted that the height of the triplet st,ate bands decreased slowly with continued exposure of the sample to the ultraviolet radiation. We have assumed that this attenuation of the triplet state signal was a direct result of the formation of the colored product which, although it absorbs in the ultraviolet, did not prodlIce a triplet state. In any event, in all quantitative determinations of signal height, in equilibrium systems the signal was observed as a function of time of irradiation, and the signal height was extrapolated to zero time of irradiation. Determination of the exact field location of each triplet state signal, for ideutification purposes, was carried out with a proton probe placed in the field adjacent to the cavity. Simultaneous determinations of the frequencies at which the protons gave a nuclear magnetic resonance absorption while the d-c field was sweeping through the ESR signal gave a very accurate determination of the midpoint, field for each amino acid triplet state sigllal. Control of the incident, light intensity was obtained with the use of copper wire gauges of different mesh size, nsed singly or in combination, as neutral filt,ers. These filters were characterized by means of the Cary recording spectrophotometer. RESULTS
Figure 1 shows a typical scan of the triplet state signals for tyrosine and tryptophan with the concomitant’ field determination with the proton probe. Table I shows the characteristics of these lines. The midfield
260
RABINOVITCH
(a)
(b)
FIG. 1. Typical ESR differential signals with field resonance frequencies). (a) Tryptophan, 3.25 X lo-%;
determination (b) tyrosine,
data (proion 6.54 X 10-2~.
probe
TRIPLET TABLE CHARACTERISTICS SalIlpl‘2
gauss)
L-Tyrosine L-Tryptophan
ENERGY
TRANSFERENCE
261
I
OF TRIPLET
Fifdw$jf
STATE
Line width hwuss)
1281.0 31.5 1441.2 24.0
STATE Rise constant (Kr %x-l)
0.529 0.255
LINES Decay Constant (Kd m-1)
7.0
0.419 0.177
point is the point of zero slope in the absorption line, and the line width is taken from the points of inflection (peak to peak in the differential signal). These values agree well with those given by Shiga and Piette (17). Equilibrium measurements were made on tyrosine, tryptophan, and mixed solutions. In these cases the signal heights were always measured as a function of the time of exposure to the incident ultraviolet radiation and extrapolated to zero time of exposure. Figures 2 and 3 show the variation in signal height (So) as a function of intensity, and as a function of concentration, respectively, for tryptophan at low concentrations. Figures 4 and 5 show the signal heights for tyrosine and hryptophan, respectively, over a much wider concentration range, obtained with circuit, parameters identical to each other but different from those in Figs. 2 and 3. In all of t*hese results, it is worth noting that the signal height is neither linear in concentration nor in intensity of incident ultraviolet radiation. Moreover, it would appear that, in the case of tyrosine, the concentration of triplet state species falls off at very high concentrations after passing through a maximum, but in the case of Oryptophan this does not appear to be the case. The nonlinearity in concentration leading to a saturation in triplet state concentration is readily understood since total extinction of the incident intensity must correspond t’o a limit, and indeed the nonlinearity will be quantitatively explained below. For an explanat’ion of the nonlinearity in incident intensity as well as for the fall off in triplet state concentration at higher concentrations, we must look to the details of the paths leading from the ground state singlet species to the triplet state and back again. This we will do in Part II of this article.
2.0
1.0
-I
0 0
0.2
0.4
0.6
RELATIVE
0.8
1.0
INTENSITY
FIG. 2. Signal height of tryptophan as a function of incident ultraviolet intensity. Concentration, 8.59 X 10e4M.
Figures 6 and 7 show the results obtained with mixed systems. In Fig. 6 we have plotted the signal heights of tryptophan and tyrosine directly, for a system in which the tyrosine concentration is fixed at 5 X lo-” M and the tryptophan concentration is varied up to 5 X lop4 M. In Fig. 7, this same data is plotted as a ratio of signal heights since this eliminates the effects due to variation and attenuation in ultraviolet light intensity and in spectrometer stability and sensitivity. In this same figure further data is given on a system in which the tryptophan concentration is maintained constant at 5 X 10e4 M and the tyrosine concentration is varied up to 2 x lo-’ M. ANALYSIS
OF DATA
We will first attempt to calculate the relative signal heights of tyrosine and tryptophan triplet states purely on the basis of a division of the incident energy between the two species according to their extinction coefficients with DO subsequent transfer of
RABINOVITCH
262 9
18 16 14
2 0 0
2
I TRYPTOPHAN
3
4
CONCENTRATION
5
(10-4M)
FIG. 3. Signal height of tryptophan as a function of concentration. data; (- - -) calculated curve witdL = 0.287
(0) Experimental
1.0
1
IO 0
2
I
TYROSINE
3
4
CONCENTRATION
5
6
7
llO-2M~
FIG. 4. Signal height of tyrosine as a function of concentration. (0) Experimental data; (- - -) calculated curve with L = 0.287 cm.
energy. Let F = the luminous flux per unit area (arbitrary units) Fh = the flux per unit area per unit band width (arbitrary units) Fh.dX = flux per unit area reaching the sample in a band width lying between X f dx/2.
! I
0 0
I
,
I
I
I
6 (10‘3M1
7
I
2 3 4 5 TRYPTOPHAN CONCENTR*TlON
FIG. 5. Signal height of tryptophan tion of concentration.
8
as a func-
the luminous energy absorbed in this band is I& = Fx (1 - evehAL) dX,
Thus
where Q = the extinction coefficient (liter .moles-l . cm-l), d
at X
= the concentration of absorbing species (moles/liter), and
L = the pat,h length sample (cm).
t,hrough
the
The total luminous energy absorbed by a
TRIPLET
STATE ENERGY
single species in solution between X2 and XI is given by El:(l)
=J,:?FJl
- exp -(E~(~)A~L)IcZX.
(1)
FL can be identified as the spectral energy distribution of the lamp used for irradiating the sample, and EL is obtained from the ult,raviolet absorption spectrum of the species under consideration. Thus Z&“(l) and Ei”(3) for tryptophan and tyrosine, respectively, where the superscript 0 refers to t’he pure component’ solu8 7-
TRYPTOPHAN
S;l
L=O.287-
25
.
i/-_-i;
52
L=O.287
5
I
l
0
TYROSINE
S;
*
0 I
and
m s-cr.
. l
tions, can readily be obtained in arbitrary units (since Fh is given in arbitrary units) by a graphical integration of Ey. (l), We will assume the general case of an asymmetric resonance energy absorption band of Gaussian form v = D exp - (c?H2), the two halves of which are characterized by constants CI’ and CY”and a common height D. The applied field is H (see Pig. 8). Thus, it is easy t,o show that
Moreover, the total of energy absorbed (IS,) in the resonance band is
. LL=O.SOO
5 04 5 =3 2
L = 0.800 I 3
I 2 TRYPTOPHAN
CONCENTRATION
so that we may write I 4
-!
TYROSINE
a
\
0.4
But B, is proportional to t’he excess population of triplet state of a given species in the lower energy state of the split level, ER m N+ - N- . Also Eh is proportional to the total triplet state population of a given
CONCENTRATION
0.8
\ ’ \
S = 4/(-\/27re) a’ an E, .
5 (l6%,
FIG. 6. Signal heights of tryptophan and tyrosine in mixed solutions as a function of tryptophan concentration with tyrosine concentration fixed at 5 X lW4 .M. Experimental points with curves calculated by using I, = 0.287 and 0.800 cm.
0
263
S = S’ + 8” = (J + a”) -\/2.D.@2.
Gi
$6 s
TRANSFERENCE
I
1.2
I
(10-2M11)t---j
1.6
I
2.0 1.6
\
6
0
I TRYPTOPHAN
2
3 CONCENTRATION
4
5
(10-4M)
FIQ. 7. Ratios of tryptophan to tyrosine signal heights. Experimental points: (0) fixed tyrosine, 5 X W4~, lower and left scales; (A) fixed tryptophan, 5 X IOVM, upper and right scales. Curves are calculated with L as indicated.
264
RABINOVITCH
species, Eh = N+ + N- , from which, we can write x N+--N++N?2=’ Eh
N-
E
N+ - N- is very small, since E, the energy difference between the two energy states, is very small. Thus, we may write
SI” = K1 Eh” (1) and
Sz” = K, Eh” (2),
FIG. 8. Schematic representation of a differen tial ESR signal and its relation to the integraf resonance band. TABLE CALCULATED DATA FOR MIXED
Pathlength
1.0
4.15 7.87
10.98 13.77 16.30
5.0 5.0 5.0 5.0 5.0
3.15 3.15 3.15 3.15 3.15
II
SOLUTION; TYRO~INE
3.94 7.45 10.50 13.22 15.68
TABLE CALCULATED DATA FOR MIXED
(M XA’lO’)
where K1 and Kz are proportionality constants. These last expressions are valid so long as we are far removed from saturation where all the rf energy is absorbed and populations in the triplet state are not high. In the case of a mixture of these amino acids the total energy absorbed is distributed between the two species proportionately to Q .A. Thus the energy absorbed by tryptophan in a mixture of concentration Al and AZ and extinction coefficients ~(1) and ~(2)
FIXED
AT 5 X 1W4 M
L = 0.287 cm.
2.0 3.0 4.0 5.0
Pathlength
(14
2.955 2.760 2.582 2.422 2.283
.851 .824
.950 .947
,937 .875
.811
,956
319
.761 ,714
.960 .962
.769 .724
1.138 2.225 3.295 4.155 4.905
III
SOLUTION; TYROSINE FIXED
AT 5 X 10d4 M
L = 0.800 cm.
Eh” (1) (w.F)
1.0
10.22
2.0 3.0 4.0 5.0
17.38 22.60 26.32
29.12
(M ?IO’)
EAQ(2) (w.F)
EAm(1) (Wl~F)
(““,“. m $’
5.0 5.0 5.0 5.0 5.0
7.76 7.76 7.76 7.76 7.76
9.08 15.62 20.38 24.02 26.72
6.508 5.536 4.776 4.144 3.656
.849
2.30
.839
1.187
.917
4.21
.714
2.595
.966 .982 .985
5.79 6.82 7.57
.616 .535 .471
4.125 5.695
7.190
TRIPLET
STATE
ENERGY TABLE
CALCULATED DATA FOR MIXED Pathlength L = 0.287 cm. (I&W) 5.0 5.0 5.0 5.0 5.0
(1) (w.F)
(M $10")
EAO(2) (mrr.F)
16.30 16.30 16.30 16.30 16.30
0.4 0.8 1.2 1.6 2.0
16.56 23.09 26.31 28.23 29.59
E.xo
265
TRANSFERENCE IV
SOLUTION; TRYPTOPHAN FIXED
@wF)
Ehm (2) (w F)
12.08 9.66 8.16 7.18 6.45
12.90 18.74 22.20 24.35 25.93
Ehm (1)
AT 5 X 10m4 M
Kl/& 1.484 1.859 2.000 2.060 2.125
(a,,,. 1.393 0.958 0.736 0.607 0.528
where ET(l) Slrn -zxS1° and
XI” -zz-. SP
aIld
EGO K, Kz
&” -= s20
&“(l) m =-. 6’; S,”
Ei=,“(2) . E’x”(1) Ek’(l) bm ’
(3)
Tables II-IV summarize all the calculated quant’ities obtained from Eqs. (l)-(3) that are subsequently used in our discussion. In Figs. 3 and 4 we have included the values of t’he signal heights calculated from Eqs. (1) and (la) in arbitrary units, as a function of the concentration of tryptophan and tyrosine in simple solution up to con0 0 I 2 3 4 5 6 cent’rations of 5 X 10e4 M and 2 X 10d2 M, CONCENTRITION (lo-4M, respectively. The parameters used in these FIG. 9. Calculated tryptophan and tyrosine calculations were: an opt’ical path length L signal heights as functions of concentration, with of 0.287 cm as a measured mean of the L as indicated. quartz sample tubes used; the ultraviolet absorption spectra (between the limits X1 = is given by 245 rnp and Xz = 300 mM) of tyrosine and trypt,ophan (E:t,yrosine at 274.5 rnp = Q(l)& 1.438 X 103,tryptophan at 279 rnp = 5.75 X Exm(l) = s,l’ Eh(l)A1 + EX(2)& 103) as measured with a Cary recording (2) .Fx{l - exp [-- Q(I)& spectrophotometer, model 14M; the spectral energy distribution of the Hanovia mercury- Q(2)AzILJ dX, xenon arc lamp (901 B-l, 200 W) as published (1s). and a similar expression mill apply to JZxm(2), Figure 9 compares calculated signal where the superscript 112refers to the comheights at, low concentrations obtained from ponents in the mixture. An evaluation of EAm(l) and Exn(2) is readily obt,ained by a Eqs. (1) and (la) with two values for the path length. It, is clear from these calculagraphical int’egration of Eq. (2). Cons that, while we can qualitatively acOnce again we may writ,e count for the nonlinearity in concentration, quant’itatively t,he calculated values do not Slm = K1 Exm(l) and SP = Kz EL”(~),
266
RAESINOVITCH
fall off rapidly enough. We can account for this fact, however, by considering the effect of the attenuation of the incident ultraviolet radiation on the production of triplet state species. Even in the simplest possible reaction path leading to triplet state formation, we find (see Appendix A) that the equilibrium concentration of triplet species T, (moles/liter) is not a linear function of incident intensity. Thus, as the incident radiation is attenuated in its passage through the sample cell, the local concentration T, will vary in a complex way. We have derived, in Appendix A, the following relationship between the total amount 3 in moles of triplet state species in the irradiated volume to the various parameters of the system: b+C = exp ~(ka + k4)3/&, beerAL + c
CONCENTRATION 0
0.5
1.0
1.5
W3M) 2.0
2.5
3.0
\
(4)
where b = (k3 + k4)kl n and c = (k, + k3)k4 . The k’s are the velocity constants of the several steps in the reaction path, and n is the number of photons falling on the sample cell per unit area per second. To see how this function varies with A, we have put kin = kz = kS = 10 k4 , L = 0.3, and E = 5 X 103, and calculated the quantity s/AL, the fraction of all species present that are in the triplet state, as a function of A. In the limit of a disappearingly small C, this fraction becomes T,/A and, with the above velocity constants, is equal to 0.769. In Fig. 10 we have plotted the quotient (s/AL)/(T,/A), which is a correction factor to be applied to any calculations of So, arising from attenuation of the incident beam. As k4 decreases relative to k, , this correction factor approaches 1.0 at all values of A, and it is therefore clear that by appropriate choice of these velocity constants, the corrected calculated values of So may be brought into conformity with the observed values, even to passing through a maximum. However, in a mixed solution, a calculation of the ratio of signal heights of the two amino acids will be independent of this attenuation of the incident beam, if it is taken that the path leading to triplet state formation is the same for the two species. Thus, in Fig. 6 we have included the values calculated from Eqs. (2) and (2a) for the
03 0
0.5
1.0
1.5
CONCENTRATION
2.0
2.5
3.0
(10-2Mn)
Fro. 10. Dependence of a correction factor, arising out of attenuation of the incident radiation, on concentration. With an assumed reaction path in which kl = kz = ka = 10 k4.
tryptophan and the tyrosine signal heights as a function of concentration of tryptophan with two values L = 0.287 and 0.800. The calculated value of Slm is obtained from the calculated value of &“/&O multiplied by the experimental value of &O; similarly for Szm. It is clear that the better fit is obtained with the completely fictitious pathlength of 0.800 cm rather than the experimental value of 0.287. This is brought out perhaps more clearly in Fig. 7, where the values of LS~“/S~~, calculated from Eq. (3) with the experimental values of S1°/Szo, are plotted. The curve corresponding to L = 0.287 deviates widely from the experimental points. In this same figure, the calculated values for the case of constant tryp-of &“/Sz” tophan concentration and higher tyrosine concentrations are plotted, and it aan be
TRIPLET
STATE
ENERGY
seen that in this case very good agreement is obtained when the experimental value of the pathlength L = 0.287 is used. We are forced to conclude that there is no transfer of energy at these relatively high concentrat#ions of tyrosine, while the deviation of the calculated curve from experiment at, the lower relative concentration is real and must, correspond to a transfer of energy from tyrosine to tryptophan. DISCUSSION
It is not easy to see immediately why a transfer of energy only takes place at, low relative tyrosine to tryptophan concentrations (AZ/Al), unless it is that. aside from parameters such as phosphorescence distribution and overlap for the donor and acceptor and lifetime of the respective excited triplet st’ates, intermolecular distance alone will not determine the probability of transfer. It is noteworthy that the distances over which this triplet state excitation energy is capable of being transferred are much greater than those calculated and found for the similar transfer of singlet &ate excitation energy in similar systems and as observed by fluorescence measurement,s (19). By extrapolation of our dat,a, it may be estimated that, R. , the distance at which transfer of excitation energy and its extin$on are equally probable, lies close to 160 A. This $ompares to yalues in t’he vicinity of 50 A and even 14 A for a t,riplettriplet transfer (20). However, these calcu&ions are based upon the assumption of a dipole-dipole interaction mechanism for t,he transfer process which gives rise to nn inverse sixth-power dependence of the transfer probability. However, because of the much larger distances, we have assumed that a different mechanism is operative, and insofar as we are dealing n-ith solid glassy systems, this might’ well be t’ransfer by excitons. Such a mechanism would result in transfer over much larger dist’ances as Simpson (21) has found. I,et us consider that a given tyrosine species in the t,riplet stat’c is capable of transmitting its energy in any direction, but only to one of its nearest, neighbors which must be a trypt#ophan species in other than
267
TRANSFERENCE
the triplet, state. Then, clearly, at relatively high A2/L41 values, a given tyrosine triplet species will be surrounded by nearest neighbors, most of which, on the average, will be tyrosine, and the transfer process will be that much the less likely. Indeed, if all of its nearest, neighbors are tyrosine species, then transfer of energy will be impossible no matter how close t,hey may be, unless it be to a next, to nearest neighbor, a far less likely process. Quantitatively, we may say that t’he total energy transferred (ET) will be proportional t’o the fraction of nearest neighbors that are (a) tryptophan (2’) ; (b) inversely proportional to the cube of the most probable distance between nearest neighbors (P); (c) proportional to the fraction of tyrosine molecules that are in the triplet, st,at,e before transfer, which may be taken as a first approximation as proportional to Eh”(2)/A, ; and (d) proportional to the fraction of tryptophan molecules that, are not in the t’riplet st)ate which may be taken to a second approximation as inversely proportional to EArn(l)l~41 . This can be t’herefore written as
The rat,io of pairs of nearest neighbors stands as l--1:1-2:2--2 = A12:2AJz:A22. Thus for a given tyrosine molecule the fraction of its nearest neighbors that is tryptophan must. be 2’ =
2AIAz 2A1A2 + AJ-’
(6)
To calculate I, we have asked what is the probability that, in a spherical volume of radius I*, only one molecule each of tyrosine and tryptophan of n2 and nl molecules, respectively, in a total volume J’, will be found. This is given by the expression
From t’his we can readily obtain the radius rp of that sphere which will most probably encompass only one of each molecular species, and we can equabe 2r, to the most,
RABINOVITCH TABLE
V
CALCULATED DATA FOR OBTAINING FRACTION OF ENERGY ABSORBED BY TYROSINE TEAT Is TRANSFERRED TO TRYPTOPHAN; TYROSINE-FIXED AT 5 X lW* M
Pathlength
L = 0.287 cm.
(Ia$lW)
(la%O~)
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
EA”
(2) /EA”’
5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0
0
1
ET/.%’
8 (A,
2’
(1)
.749
.285
220
.370
.444
208
.246
.546
199
.183
.615
192
.146
.667
185
Observed
(2)
Calculated
.102 - .046 .133 .060 .163 .169 .241 .307 .254 .281
.062 -121 .182 .242 .311
0.3
0.2 5 E,” . s 0. I
0 TRYPTOPHAN
FIG. 11. Values of the fraction
transferred to tryptophan.
probable intermolecular (f/a3
=-
CONCENTRATION
of energy
absorbed
Points are experimental;
;
(&Vv)
3 1000 27rN A1 + Az ’
4
5
(10-4M)
by tyrosine
in a mixed solution
that is
the curve is calculated.
constant of assuming a proportionality 4.6 X 10’ (I in Angstroms). Included also are the values of (ET&s obtained from experimental data and expression (9) :
distance 1. Thus
= f”,3 = g (nI,V)
3
2
(8)
Table V summarizes all the calculated quantities required for the calculation of (Ep)eslc obtained from expression (5) and
&Ex”(l) + ET (fJImlfhm>obs = K, Ex”(2) _ E * (9) T
The proportionality constant 4.6 X 10’ was chosen for the best fit (Fig. 11). If the errors in the experimental data and the
TRIPLET
STATE
ENERGY
sensitivity of ET to these errors are considered, the agreement is perhaps better than should be expected. We have shown, therefore, that there is indeed a transfer of triplet state energy from tyrosine to tryptophan determined not only by intermolecular distances but also by the number of appropriate nearest neighbor pairs. Moreover, the suggestion is that a mechanism of transfer different from the inductive resonance mechanism of FBrster is operating such that a lower power of inverse dependence on intermolecular distance maintains. APPENDIX
A
So + hv + X1 kl
TI --f So h where SI = concentration of first excited singlet species SO = concentration of ground state species T1 = concentration of triplet state species and Icl , k2 , k3 , and kq are the velocity constants for each successive step. We will assume a steady state concentration in S1, so that
A = So + X1 + T1.
where, from eqs. (Al), obtain
= 0,
(A3)
(A2) and (A3), we
Tm = (ka + k,)k;i?$k, Now consider an incident
L
-----------
+
tx
4
ax Then, the equilibrium concentration of triplet state species in a section of thickness dx and distance x from the incident surface is given by
5=
beam of unit
oL (Tm)z+dx, s
from which b+C = exp E(ka + khlk3, be-e*= + c
(A6)
where b = (ka + k,)km and c = (k2 + k3)k4 . REFERENCES 1. 2. 3. 4.
5. 6. 7. 8. 9.
+ ks)kr ’ (A4)
(-45)
where E = the extinction coefficient and the total amount of triplet state species in the irradiated volume, given by
L42)
If the system is irradiated long enough, T1 reaches its asymptotic limit T, , so that, at this time = k,& - k,T,
---
n
(k, + k&S1 = 0, (Al)
where n = number of photons per second per unit area incident on the solution. We also have that the total concentration
dTJdt
+
klksAne-‘Ax = (k, + k4)klnemLAz+ (kz + kJk4 ’
SI+ TI ks
= km% -
cross section
(Tn,>z
XI + So k,
d&/dt
269
TRANSFERENCE
10.
TEALE, F. W. J., Biochem. J. 76, 381 (1960). WEBER, G., Trans. Faraday Sot. 60,552 (1954). BEAVEN, G. H., Advan. Spectry. 2, 331 (1961). WEBER, G., AND TEALE, F. W. J., in “The
Proteins” (H. Neurath, ed.), 2nd edition, Vol. 3, Chapt. 17. Academic Press, New York (1965). COWGILL, R. W., Biochim. Biophys. Acta 76, 272 (1963). WEBER, G., Biochem. J. 76, 48 (1969). WEBER, G. AND TEALE, F. W. J., Biochem. J. 72, 150 (1959). BURSHTEIN, E. A., Biophysics (USSR) (English Transl.) 6, 848 (1961). VLADIMIROV, Y. A., Photochem. Photobiol. 4, 369 (1965). KONEV, S. V., KATIBNIBOV, M. A., AND LYSKOVA, T., Biophysics (USSR) (English Transl.) 9, 125 (1964).
270
RABINOVITCH
G. O., Science 116, 11. DEBYE, P., AND ED~.\RDS, 143 (1952). 12. STEELE, R. H., AND SZENT-GY~GYI, A. L., Proc. Null. Acad. Sci. U.S. 44, 540 (1958). 13. VL.~~IMIROV, Y. A., AND LITVIN, F. F., Biophysics (USSR) (English l’ransl.) 6, 151 (1960). 14. LONGWORTH, J. W., Hiochem. b. 81, 23P (1961). 15. Douzou, P., AND PTAK, M., J. Chim. Phys. 61, 1681 (1964) ; Suture 199, 1092 (19ci3) ; also, PT.4K, M., ANn ~~ouzou, l’., Compt. Rend. 267, 438 (1963).
16. Az~zova, 0. A., GRIBOVA, Z. P., K.~YUSHIN, L. P., .~ND PULATOVA, M. K., Photochem. Photobiol. 6, 763 (1966). 17. SHIGA, T., AND PIETTE, L. H., Photochem. Photobiol. 3, 223 (1964). 18. Lamp Division, Englehard, Hanovia Inc., Newark, New Jersey. 19. FBRSTER, TH., Discussions Faraday Sot. 27, 7 (1959). 20. TERENIN, A., AND ERMOLBEV, V., Trans. Faraday Sot. 62, 1042 (1956). 21. SIMPSON, O., Proc. Roy. Sot. (London), Ser. A 238, 402 (1956).
OF
BIOCHEMISTRY
Transference
AND
BIOPHYSICS
of Triplet
258-270 (1968)
124,
State
Excitation
Energy
from
Tyrosine
to Tryptophan I. Amino Acids in Simple
and Mixed
Solutions’
B. RABINOVITCH2 Biophysics
Laboratory,
Stanford
University,
Stanford,
Received
August 1,1967
California
S&OS
Quantitative measurements have been made of the electron spin resonance energy absorption (signal height) of tyrosine and tryptophan triplet states, in simple and in mixed solutions. Calculations were also made for the relative signal heights of these amino acids in mixed solutions. Results were satisfactorily explained on the basis of a transfer of excitation energy from tyrosine to tryptophan, but only to nearest neighbors. The much larger distances over which this energy is transferred has suggested a different mechanism from the dipole-dipole interaction of Fiirster’s. The dependence of the energy transfer probability on the inverse third power rather than the sixth power led to good agreement with experiment, and suggested a possible exciton mechanism.
A considerable amount of work has been done on the fluorescence spectroscopy (1) and fluorescence depolarization (2) of amino acids and proteins, and has been well summarized by Beaver (3) and Weber and Teale (4). Other work on peptides (5) has tended to support the evidence that there is an interaction between the tyrosine and tryptophan moieties of these natural and synthetic peptides. This interaction, it has been suggested, leads to the transfer of singlet state excitation energy from the first to the second of these aromatic amino acids. However, although Weber (6) and Weber and Teale (7) draw the conclusion that such transfer of energy leads to quenching and does not contribute to the fluorescence of 1 This research was supported in part by AIW contract AT(W3)326-14 and in part by the PHS Special Fellowship l-F3-GM-32, 898-01 awarded by the National Institute of General Medical Sciences. 2 Present address : Department of Biochemistry, Medical School, University of Oklahoma, 866 Northeast Thirteenth Street, Oklahoma City, Oklahoma 73194. 258
the acceptor, Burshtein (8) has calculated that both processes occur with a greater or lesser efficiency among the proteins, while Vladimirov (9) concludes that essentially no such transfer of energy occurs in proteins. On the other hand, Konev et al. (10) have shown that in concentrated tryptophan solutions energy migration without quenching can occur. Phosphorescence of aromatic amino acids and proteins has also undergone some study (1 l-13), and a similar transfer of excitation energy from the triplet state of tyrosine to tryptophan has been suggested. From observations of the decay times of the phosphorescence emanating from serum albumin, on the short and long wavelength sides of the emission band, Longworth (14) concludes that both tyrosine and tryptophan are phosphorescing. However, considering the molar ratio of tyrosine to tryptophan in this protein (17: l), it is certain that a considerable part of the energy transferred is quenched. The first direct observation of the excited tripIet state of these amino acids was made
TRIPLET
STATE
ENERGY
by Douzou and Ptak (15) by electron spin resonance spectrometry (ESR) and corresponds to the Am = f2 transition. They showed what appeared to be a relation between the rate of increase of the triplet state population and the rate of free radical formation. This was later confirmed by Azizova and co-workers (16), who suggested t,hat the path of the free radical formation goes through the triplet state of the molecule. The first triplet state observation 011 proteins was made by Shiga and Piette (17), who observed the clear suppression of the tyrosine ESR absorption band leaving the tryptophan band intact. However, it could not be demonstrated that the tryptophan ESR absorption band was enhanced together with the loss of the tyrosine band; hence energy transfer could not be demonstrated. On the other hand, these authors claimed to have demonstrated this transfer in the case of a mixture of tyrosine and tryptophan in solution. An unequivocal resolution of this question would be of importance in understanding the energy transfer problem in macromolecules. We have undertaken to attempt an exploration of the relative changes in equilibrium concentration of triplet state species in mixtures of t,yrosine and tryptophan. MATERIALS
AND
METHODS
The L-tyrosine and L-tryptophan analytical grade, chromatographically ous, and characterized in the following $X0Sitrogen Determined Calculated L-Tyrosine rJ-Tryptophan
8.02 13.66
7.73 13.72
used were homogeneway: [a1116 N HCl -7.0” -31.4”
Solutions were made up in 6 N HCl prepared by dilution from reagent-grade HCl (sp. gr., 1.19). This solvent has the virtue of ensuring just one ionic species per amino acid in solution, the ammonium ion, and at the same time giving a clear glass at liquid nitrogen temperature withollt the complication of the presence of organic liquids. No precautions were taken to exclude oxygen. Samples were placed in fused silica tubing of orItside diameters 0.155 + 0.004 inch and frozen in liquid nitrogen before being placed in the spectrometer cavity. 9 baseline for each sample was obtained aft,er establishing the spectrometer
TRANSFERENCE
2.50
parameters to be used, e.g., 100 KHz modulation amplitude and d-c magnetic field sweep rate, but before ultraviolet irradiation. The source of ultraviolet radiation was a Hanovia 200-W Hg-Xe discharge lamp focused with quartz optics at the center of the cavity. After ultraviolet irradiation was begun, a resonance absorption band was observed in all cases, falling in the g - 4 region of the spectrum, which decayed over a period of seconds on removal of the irradiation. A marked phosphorescence could be observed visually when the samples were removed from the cavity and from the irradiation. These bands were readily identifiable as due to triplet state species and easily assignable to either tyrosine or tryptophan. These amino acids also gave large free radical absorption bands in the g - 2 region of the spectrum. Because of the subsequent reactions of these free radicals, even at liquid nitrogen temperature, a colored product appeared at the surface of the sample where the ultraviolet radiation was incident. It was also noted that the height of the triplet st,ate bands decreased slowly with continued exposure of the sample to the ultraviolet radiation. We have assumed that this attenuation of the triplet state signal was a direct result of the formation of the colored product which, although it absorbs in the ultraviolet, did not prodlIce a triplet state. In any event, in all quantitative determinations of signal height, in equilibrium systems the signal was observed as a function of time of irradiation, and the signal height was extrapolated to zero time of irradiation. Determination of the exact field location of each triplet state signal, for ideutification purposes, was carried out with a proton probe placed in the field adjacent to the cavity. Simultaneous determinations of the frequencies at which the protons gave a nuclear magnetic resonance absorption while the d-c field was sweeping through the ESR signal gave a very accurate determination of the midpoint, field for each amino acid triplet state sigllal. Control of the incident, light intensity was obtained with the use of copper wire gauges of different mesh size, nsed singly or in combination, as neutral filt,ers. These filters were characterized by means of the Cary recording spectrophotometer. RESULTS
Figure 1 shows a typical scan of the triplet state signals for tyrosine and tryptophan with the concomitant’ field determination with the proton probe. Table I shows the characteristics of these lines. The midfield
260
RABINOVITCH
(a)
(b)
FIG. 1. Typical ESR differential signals with field resonance frequencies). (a) Tryptophan, 3.25 X lo-%;
determination (b) tyrosine,
data (proion 6.54 X 10-2~.
probe
TRIPLET TABLE CHARACTERISTICS SalIlpl‘2
gauss)
L-Tyrosine L-Tryptophan
ENERGY
TRANSFERENCE
261
I
OF TRIPLET
Fifdw$jf
STATE
Line width hwuss)
1281.0 31.5 1441.2 24.0
STATE Rise constant (Kr %x-l)
0.529 0.255
LINES Decay Constant (Kd m-1)
7.0
0.419 0.177
point is the point of zero slope in the absorption line, and the line width is taken from the points of inflection (peak to peak in the differential signal). These values agree well with those given by Shiga and Piette (17). Equilibrium measurements were made on tyrosine, tryptophan, and mixed solutions. In these cases the signal heights were always measured as a function of the time of exposure to the incident ultraviolet radiation and extrapolated to zero time of exposure. Figures 2 and 3 show the variation in signal height (So) as a function of intensity, and as a function of concentration, respectively, for tryptophan at low concentrations. Figures 4 and 5 show the signal heights for tyrosine and hryptophan, respectively, over a much wider concentration range, obtained with circuit, parameters identical to each other but different from those in Figs. 2 and 3. In all of t*hese results, it is worth noting that the signal height is neither linear in concentration nor in intensity of incident ultraviolet radiation. Moreover, it would appear that, in the case of tyrosine, the concentration of triplet state species falls off at very high concentrations after passing through a maximum, but in the case of Oryptophan this does not appear to be the case. The nonlinearity in concentration leading to a saturation in triplet state concentration is readily understood since total extinction of the incident intensity must correspond t’o a limit, and indeed the nonlinearity will be quantitatively explained below. For an explanat’ion of the nonlinearity in incident intensity as well as for the fall off in triplet state concentration at higher concentrations, we must look to the details of the paths leading from the ground state singlet species to the triplet state and back again. This we will do in Part II of this article.
2.0
1.0
-I
0 0
0.2
0.4
0.6
RELATIVE
0.8
1.0
INTENSITY
FIG. 2. Signal height of tryptophan as a function of incident ultraviolet intensity. Concentration, 8.59 X 10e4M.
Figures 6 and 7 show the results obtained with mixed systems. In Fig. 6 we have plotted the signal heights of tryptophan and tyrosine directly, for a system in which the tyrosine concentration is fixed at 5 X lo-” M and the tryptophan concentration is varied up to 5 X lop4 M. In Fig. 7, this same data is plotted as a ratio of signal heights since this eliminates the effects due to variation and attenuation in ultraviolet light intensity and in spectrometer stability and sensitivity. In this same figure further data is given on a system in which the tryptophan concentration is maintained constant at 5 X 10e4 M and the tyrosine concentration is varied up to 2 x lo-’ M. ANALYSIS
OF DATA
We will first attempt to calculate the relative signal heights of tyrosine and tryptophan triplet states purely on the basis of a division of the incident energy between the two species according to their extinction coefficients with DO subsequent transfer of
RABINOVITCH
262 9
18 16 14
2 0 0
2
I TRYPTOPHAN
3
4
CONCENTRATION
5
(10-4M)
FIG. 3. Signal height of tryptophan as a function of concentration. data; (- - -) calculated curve witdL = 0.287
(0) Experimental
1.0
1
IO 0
2
I
TYROSINE
3
4
CONCENTRATION
5
6
7
llO-2M~
FIG. 4. Signal height of tyrosine as a function of concentration. (0) Experimental data; (- - -) calculated curve with L = 0.287 cm.
energy. Let F = the luminous flux per unit area (arbitrary units) Fh = the flux per unit area per unit band width (arbitrary units) Fh.dX = flux per unit area reaching the sample in a band width lying between X f dx/2.
! I
0 0
I
,
I
I
I
6 (10‘3M1
7
I
2 3 4 5 TRYPTOPHAN CONCENTR*TlON
FIG. 5. Signal height of tryptophan tion of concentration.
8
as a func-
the luminous energy absorbed in this band is I& = Fx (1 - evehAL) dX,
Thus
where Q = the extinction coefficient (liter .moles-l . cm-l), d
at X
= the concentration of absorbing species (moles/liter), and
L = the pat,h length sample (cm).
t,hrough
the
The total luminous energy absorbed by a
TRIPLET
STATE ENERGY
single species in solution between X2 and XI is given by El:(l)
=J,:?FJl
- exp -(E~(~)A~L)IcZX.
(1)
FL can be identified as the spectral energy distribution of the lamp used for irradiating the sample, and EL is obtained from the ult,raviolet absorption spectrum of the species under consideration. Thus Z&“(l) and Ei”(3) for tryptophan and tyrosine, respectively, where the superscript 0 refers to t’he pure component’ solu8 7-
TRYPTOPHAN
S;l
L=O.287-
25
.
i/-_-i;
52
L=O.287
5
I
l
0
TYROSINE
S;
*
0 I
and
m s-cr.
. l
tions, can readily be obtained in arbitrary units (since Fh is given in arbitrary units) by a graphical integration of Ey. (l), We will assume the general case of an asymmetric resonance energy absorption band of Gaussian form v = D exp - (c?H2), the two halves of which are characterized by constants CI’ and CY”and a common height D. The applied field is H (see Pig. 8). Thus, it is easy t,o show that
Moreover, the total of energy absorbed (IS,) in the resonance band is
. LL=O.SOO
5 04 5 =3 2
L = 0.800 I 3
I 2 TRYPTOPHAN
CONCENTRATION
so that we may write I 4
-!
TYROSINE
a
\
0.4
But B, is proportional to t’he excess population of triplet state of a given species in the lower energy state of the split level, ER m N+ - N- . Also Eh is proportional to the total triplet state population of a given
CONCENTRATION
0.8
\ ’ \
S = 4/(-\/27re) a’ an E, .
5 (l6%,
FIG. 6. Signal heights of tryptophan and tyrosine in mixed solutions as a function of tryptophan concentration with tyrosine concentration fixed at 5 X lW4 .M. Experimental points with curves calculated by using I, = 0.287 and 0.800 cm.
0
263
S = S’ + 8” = (J + a”) -\/2.D.@2.
Gi
$6 s
TRANSFERENCE
I
1.2
I
(10-2M11)t---j
1.6
I
2.0 1.6
\
6
0
I TRYPTOPHAN
2
3 CONCENTRATION
4
5
(10-4M)
FIQ. 7. Ratios of tryptophan to tyrosine signal heights. Experimental points: (0) fixed tyrosine, 5 X W4~, lower and left scales; (A) fixed tryptophan, 5 X IOVM, upper and right scales. Curves are calculated with L as indicated.
264
RABINOVITCH
species, Eh = N+ + N- , from which, we can write x N+--N++N?2=’ Eh
N-
E
N+ - N- is very small, since E, the energy difference between the two energy states, is very small. Thus, we may write
SI” = K1 Eh” (1) and
Sz” = K, Eh” (2),
FIG. 8. Schematic representation of a differen tial ESR signal and its relation to the integraf resonance band. TABLE CALCULATED DATA FOR MIXED
Pathlength
1.0
4.15 7.87
10.98 13.77 16.30
5.0 5.0 5.0 5.0 5.0
3.15 3.15 3.15 3.15 3.15
II
SOLUTION; TYRO~INE
3.94 7.45 10.50 13.22 15.68
TABLE CALCULATED DATA FOR MIXED
(M XA’lO’)
where K1 and Kz are proportionality constants. These last expressions are valid so long as we are far removed from saturation where all the rf energy is absorbed and populations in the triplet state are not high. In the case of a mixture of these amino acids the total energy absorbed is distributed between the two species proportionately to Q .A. Thus the energy absorbed by tryptophan in a mixture of concentration Al and AZ and extinction coefficients ~(1) and ~(2)
FIXED
AT 5 X 1W4 M
L = 0.287 cm.
2.0 3.0 4.0 5.0
Pathlength
(14
2.955 2.760 2.582 2.422 2.283
.851 .824
.950 .947
,937 .875
.811
,956
319
.761 ,714
.960 .962
.769 .724
1.138 2.225 3.295 4.155 4.905
III
SOLUTION; TYROSINE FIXED
AT 5 X 10d4 M
L = 0.800 cm.
Eh” (1) (w.F)
1.0
10.22
2.0 3.0 4.0 5.0
17.38 22.60 26.32
29.12
(M ?IO’)
EAQ(2) (w.F)
EAm(1) (Wl~F)
(““,“. m $’
5.0 5.0 5.0 5.0 5.0
7.76 7.76 7.76 7.76 7.76
9.08 15.62 20.38 24.02 26.72
6.508 5.536 4.776 4.144 3.656
.849
2.30
.839
1.187
.917
4.21
.714
2.595
.966 .982 .985
5.79 6.82 7.57
.616 .535 .471
4.125 5.695
7.190
TRIPLET
STATE
ENERGY TABLE
CALCULATED DATA FOR MIXED Pathlength L = 0.287 cm. (I&W) 5.0 5.0 5.0 5.0 5.0
(1) (w.F)
(M $10")
EAO(2) (mrr.F)
16.30 16.30 16.30 16.30 16.30
0.4 0.8 1.2 1.6 2.0
16.56 23.09 26.31 28.23 29.59
E.xo
265
TRANSFERENCE IV
SOLUTION; TRYPTOPHAN FIXED
@wF)
Ehm (2) (w F)
12.08 9.66 8.16 7.18 6.45
12.90 18.74 22.20 24.35 25.93
Ehm (1)
AT 5 X 10m4 M
Kl/& 1.484 1.859 2.000 2.060 2.125
(a,,,. 1.393 0.958 0.736 0.607 0.528
where ET(l) Slrn -zxS1° and
XI” -zz-. SP
aIld
EGO K, Kz
&” -= s20
&“(l) m =-. 6’; S,”
Ei=,“(2) . E’x”(1) Ek’(l) bm ’
(3)
Tables II-IV summarize all the calculated quant’ities obtained from Eqs. (l)-(3) that are subsequently used in our discussion. In Figs. 3 and 4 we have included the values of t’he signal heights calculated from Eqs. (1) and (la) in arbitrary units, as a function of the concentration of tryptophan and tyrosine in simple solution up to con0 0 I 2 3 4 5 6 cent’rations of 5 X 10e4 M and 2 X 10d2 M, CONCENTRITION (lo-4M, respectively. The parameters used in these FIG. 9. Calculated tryptophan and tyrosine calculations were: an opt’ical path length L signal heights as functions of concentration, with of 0.287 cm as a measured mean of the L as indicated. quartz sample tubes used; the ultraviolet absorption spectra (between the limits X1 = is given by 245 rnp and Xz = 300 mM) of tyrosine and trypt,ophan (E:t,yrosine at 274.5 rnp = Q(l)& 1.438 X 103,tryptophan at 279 rnp = 5.75 X Exm(l) = s,l’ Eh(l)A1 + EX(2)& 103) as measured with a Cary recording (2) .Fx{l - exp [-- Q(I)& spectrophotometer, model 14M; the spectral energy distribution of the Hanovia mercury- Q(2)AzILJ dX, xenon arc lamp (901 B-l, 200 W) as published (1s). and a similar expression mill apply to JZxm(2), Figure 9 compares calculated signal where the superscript 112refers to the comheights at, low concentrations obtained from ponents in the mixture. An evaluation of EAm(l) and Exn(2) is readily obt,ained by a Eqs. (1) and (la) with two values for the path length. It, is clear from these calculagraphical int’egration of Eq. (2). Cons that, while we can qualitatively acOnce again we may writ,e count for the nonlinearity in concentration, quant’itatively t,he calculated values do not Slm = K1 Exm(l) and SP = Kz EL”(~),
266
RAESINOVITCH
fall off rapidly enough. We can account for this fact, however, by considering the effect of the attenuation of the incident ultraviolet radiation on the production of triplet state species. Even in the simplest possible reaction path leading to triplet state formation, we find (see Appendix A) that the equilibrium concentration of triplet species T, (moles/liter) is not a linear function of incident intensity. Thus, as the incident radiation is attenuated in its passage through the sample cell, the local concentration T, will vary in a complex way. We have derived, in Appendix A, the following relationship between the total amount 3 in moles of triplet state species in the irradiated volume to the various parameters of the system: b+C = exp ~(ka + k4)3/&, beerAL + c
CONCENTRATION 0
0.5
1.0
1.5
W3M) 2.0
2.5
3.0
\
(4)
where b = (k3 + k4)kl n and c = (k, + k3)k4 . The k’s are the velocity constants of the several steps in the reaction path, and n is the number of photons falling on the sample cell per unit area per second. To see how this function varies with A, we have put kin = kz = kS = 10 k4 , L = 0.3, and E = 5 X 103, and calculated the quantity s/AL, the fraction of all species present that are in the triplet state, as a function of A. In the limit of a disappearingly small C, this fraction becomes T,/A and, with the above velocity constants, is equal to 0.769. In Fig. 10 we have plotted the quotient (s/AL)/(T,/A), which is a correction factor to be applied to any calculations of So, arising from attenuation of the incident beam. As k4 decreases relative to k, , this correction factor approaches 1.0 at all values of A, and it is therefore clear that by appropriate choice of these velocity constants, the corrected calculated values of So may be brought into conformity with the observed values, even to passing through a maximum. However, in a mixed solution, a calculation of the ratio of signal heights of the two amino acids will be independent of this attenuation of the incident beam, if it is taken that the path leading to triplet state formation is the same for the two species. Thus, in Fig. 6 we have included the values calculated from Eqs. (2) and (2a) for the
03 0
0.5
1.0
1.5
CONCENTRATION
2.0
2.5
3.0
(10-2Mn)
Fro. 10. Dependence of a correction factor, arising out of attenuation of the incident radiation, on concentration. With an assumed reaction path in which kl = kz = ka = 10 k4.
tryptophan and the tyrosine signal heights as a function of concentration of tryptophan with two values L = 0.287 and 0.800. The calculated value of Slm is obtained from the calculated value of &“/&O multiplied by the experimental value of &O; similarly for Szm. It is clear that the better fit is obtained with the completely fictitious pathlength of 0.800 cm rather than the experimental value of 0.287. This is brought out perhaps more clearly in Fig. 7, where the values of LS~“/S~~, calculated from Eq. (3) with the experimental values of S1°/Szo, are plotted. The curve corresponding to L = 0.287 deviates widely from the experimental points. In this same figure, the calculated values for the case of constant tryp-of &“/Sz” tophan concentration and higher tyrosine concentrations are plotted, and it aan be
TRIPLET
STATE
ENERGY
seen that in this case very good agreement is obtained when the experimental value of the pathlength L = 0.287 is used. We are forced to conclude that there is no transfer of energy at these relatively high concentrat#ions of tyrosine, while the deviation of the calculated curve from experiment at, the lower relative concentration is real and must, correspond to a transfer of energy from tyrosine to tryptophan. DISCUSSION
It is not easy to see immediately why a transfer of energy only takes place at, low relative tyrosine to tryptophan concentrations (AZ/Al), unless it is that. aside from parameters such as phosphorescence distribution and overlap for the donor and acceptor and lifetime of the respective excited triplet st’ates, intermolecular distance alone will not determine the probability of transfer. It is noteworthy that the distances over which this triplet state excitation energy is capable of being transferred are much greater than those calculated and found for the similar transfer of singlet &ate excitation energy in similar systems and as observed by fluorescence measurement,s (19). By extrapolation of our dat,a, it may be estimated that, R. , the distance at which transfer of excitation energy and its extin$on are equally probable, lies close to 160 A. This $ompares to yalues in t’he vicinity of 50 A and even 14 A for a t,riplettriplet transfer (20). However, these calcu&ions are based upon the assumption of a dipole-dipole interaction mechanism for t,he transfer process which gives rise to nn inverse sixth-power dependence of the transfer probability. However, because of the much larger distances, we have assumed that a different mechanism is operative, and insofar as we are dealing n-ith solid glassy systems, this might’ well be t’ransfer by excitons. Such a mechanism would result in transfer over much larger dist’ances as Simpson (21) has found. I,et us consider that a given tyrosine species in the t,riplet stat’c is capable of transmitting its energy in any direction, but only to one of its nearest, neighbors which must be a trypt#ophan species in other than
267
TRANSFERENCE
the triplet, state. Then, clearly, at relatively high A2/L41 values, a given tyrosine triplet species will be surrounded by nearest neighbors, most of which, on the average, will be tyrosine, and the transfer process will be that much the less likely. Indeed, if all of its nearest, neighbors are tyrosine species, then transfer of energy will be impossible no matter how close t,hey may be, unless it be to a next, to nearest neighbor, a far less likely process. Quantitatively, we may say that t’he total energy transferred (ET) will be proportional t’o the fraction of nearest neighbors that are (a) tryptophan (2’) ; (b) inversely proportional to the cube of the most probable distance between nearest neighbors (P); (c) proportional to the fraction of tyrosine molecules that are in the triplet, st,at,e before transfer, which may be taken as a first approximation as proportional to Eh”(2)/A, ; and (d) proportional to the fraction of tryptophan molecules that, are not in the t’riplet st)ate which may be taken to a second approximation as inversely proportional to EArn(l)l~41 . This can be t’herefore written as
The rat,io of pairs of nearest neighbors stands as l--1:1-2:2--2 = A12:2AJz:A22. Thus for a given tyrosine molecule the fraction of its nearest neighbors that is tryptophan must. be 2’ =
2AIAz 2A1A2 + AJ-’
(6)
To calculate I, we have asked what is the probability that, in a spherical volume of radius I*, only one molecule each of tyrosine and tryptophan of n2 and nl molecules, respectively, in a total volume J’, will be found. This is given by the expression
From t’his we can readily obtain the radius rp of that sphere which will most probably encompass only one of each molecular species, and we can equabe 2r, to the most,
RABINOVITCH TABLE
V
CALCULATED DATA FOR OBTAINING FRACTION OF ENERGY ABSORBED BY TYROSINE TEAT Is TRANSFERRED TO TRYPTOPHAN; TYROSINE-FIXED AT 5 X lW* M
Pathlength
L = 0.287 cm.
(Ia$lW)
(la%O~)
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
EA”
(2) /EA”’
5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0
0
1
ET/.%’
8 (A,
2’
(1)
.749
.285
220
.370
.444
208
.246
.546
199
.183
.615
192
.146
.667
185
Observed
(2)
Calculated
.102 - .046 .133 .060 .163 .169 .241 .307 .254 .281
.062 -121 .182 .242 .311
0.3
0.2 5 E,” . s 0. I
0 TRYPTOPHAN
FIG. 11. Values of the fraction
transferred to tryptophan.
probable intermolecular (f/a3
=-
CONCENTRATION
of energy
absorbed
Points are experimental;
;
(&Vv)
3 1000 27rN A1 + Az ’
4
5
(10-4M)
by tyrosine
in a mixed solution
that is
the curve is calculated.
constant of assuming a proportionality 4.6 X 10’ (I in Angstroms). Included also are the values of (ET&s obtained from experimental data and expression (9) :
distance 1. Thus
= f”,3 = g (nI,V)
3
2
(8)
Table V summarizes all the calculated quantities required for the calculation of (Ep)eslc obtained from expression (5) and
&Ex”(l) + ET (fJImlfhm>obs = K, Ex”(2) _ E * (9) T
The proportionality constant 4.6 X 10’ was chosen for the best fit (Fig. 11). If the errors in the experimental data and the
TRIPLET
STATE
ENERGY
sensitivity of ET to these errors are considered, the agreement is perhaps better than should be expected. We have shown, therefore, that there is indeed a transfer of triplet state energy from tyrosine to tryptophan determined not only by intermolecular distances but also by the number of appropriate nearest neighbor pairs. Moreover, the suggestion is that a mechanism of transfer different from the inductive resonance mechanism of FBrster is operating such that a lower power of inverse dependence on intermolecular distance maintains. APPENDIX
A
So + hv + X1 kl
TI --f So h where SI = concentration of first excited singlet species SO = concentration of ground state species T1 = concentration of triplet state species and Icl , k2 , k3 , and kq are the velocity constants for each successive step. We will assume a steady state concentration in S1, so that
A = So + X1 + T1.
where, from eqs. (Al), obtain
= 0,
(A3)
(A2) and (A3), we
Tm = (ka + k,)k;i?$k, Now consider an incident
L
-----------
+
tx
4
ax Then, the equilibrium concentration of triplet state species in a section of thickness dx and distance x from the incident surface is given by
5=
beam of unit
oL (Tm)z+dx, s
from which b+C = exp E(ka + khlk3, be-e*= + c
(A6)
where b = (ka + k,)km and c = (k2 + k3)k4 . REFERENCES 1. 2. 3. 4.
5. 6. 7. 8. 9.
+ ks)kr ’ (A4)
(-45)
where E = the extinction coefficient and the total amount of triplet state species in the irradiated volume, given by
L42)
If the system is irradiated long enough, T1 reaches its asymptotic limit T, , so that, at this time = k,& - k,T,
---
n
(k, + k&S1 = 0, (Al)
where n = number of photons per second per unit area incident on the solution. We also have that the total concentration
dTJdt
+
klksAne-‘Ax = (k, + k4)klnemLAz+ (kz + kJk4 ’
SI+ TI ks
= km% -
cross section
(Tn,>z
XI + So k,
d&/dt
269
TRANSFERENCE
10.
TEALE, F. W. J., Biochem. J. 76, 381 (1960). WEBER, G., Trans. Faraday Sot. 60,552 (1954). BEAVEN, G. H., Advan. Spectry. 2, 331 (1961). WEBER, G., AND TEALE, F. W. J., in “The
Proteins” (H. Neurath, ed.), 2nd edition, Vol. 3, Chapt. 17. Academic Press, New York (1965). COWGILL, R. W., Biochim. Biophys. Acta 76, 272 (1963). WEBER, G., Biochem. J. 76, 48 (1969). WEBER, G. AND TEALE, F. W. J., Biochem. J. 72, 150 (1959). BURSHTEIN, E. A., Biophysics (USSR) (English Transl.) 6, 848 (1961). VLADIMIROV, Y. A., Photochem. Photobiol. 4, 369 (1965). KONEV, S. V., KATIBNIBOV, M. A., AND LYSKOVA, T., Biophysics (USSR) (English Transl.) 9, 125 (1964).
270
RABINOVITCH
G. O., Science 116, 11. DEBYE, P., AND ED~.\RDS, 143 (1952). 12. STEELE, R. H., AND SZENT-GY~GYI, A. L., Proc. Null. Acad. Sci. U.S. 44, 540 (1958). 13. VL.~~IMIROV, Y. A., AND LITVIN, F. F., Biophysics (USSR) (English l’ransl.) 6, 151 (1960). 14. LONGWORTH, J. W., Hiochem. b. 81, 23P (1961). 15. Douzou, P., AND PTAK, M., J. Chim. Phys. 61, 1681 (1964) ; Suture 199, 1092 (19ci3) ; also, PT.4K, M., ANn ~~ouzou, l’., Compt. Rend. 267, 438 (1963).
16. Az~zova, 0. A., GRIBOVA, Z. P., K.~YUSHIN, L. P., .~ND PULATOVA, M. K., Photochem. Photobiol. 6, 763 (1966). 17. SHIGA, T., AND PIETTE, L. H., Photochem. Photobiol. 3, 223 (1964). 18. Lamp Division, Englehard, Hanovia Inc., Newark, New Jersey. 19. FBRSTER, TH., Discussions Faraday Sot. 27, 7 (1959). 20. TERENIN, A., AND ERMOLBEV, V., Trans. Faraday Sot. 62, 1042 (1956). 21. SIMPSON, O., Proc. Roy. Sot. (London), Ser. A 238, 402 (1956).