Lanthanide-dependent perturbations of luminescence in

J. Phys. Chem. 1993,97, 10326-10340

10326

Lanthanide-Dependent Perturbations of Luminescence in Indolylethylenediaminetetraacetic Acid-Lanthanide Chelate W. R. Kirk, W. S. Wessels, and F. G. Prendergast’ Department of Biochemistry and Molecular Biology, Mayo Foundation, Rochester, Minnesota 55905 Received: June 14. 1993’

Using a synthetic EDTA analog built out of tryptophan, we have investigated the photophysics of the interaction of indole with various lanthanides chelated in close enough proximity to the indole to permit dramatic quenching and energy transfer to the metals. We investigate the strength of a number of interactions and determine means to separate the most significant contributions (dipole4ipole energy transfer, intersystem crossing) to the overall quenching rate. This allows morequantitative agreement in molecular parameters between the various lanthanides than might otherwise be obtained. In those lanthanides which are readily reduced in aqueous solution, electron transfer apparently dominates other quenching processes. The electron-transfer process, which is treated by Marcus’ theory, shares some features in common with an additional energy-transfer process observable in the indolyl-EDTA-Ln complex (especially for Tb3+), involving an electronic state of the indole distinct from its first excited singlet. Metal luminescence consequent upon this energy transfer is quenched by added acrylamide or oxygen in a manner distinct from the effect of iodide, which suggests the involvement of the indole triplet in the additional transfer process. The overall analysis reveals a number of pitfalls to the facile generalization of results from this or any other particular single system to the interpretation of results of similar studies on tryptophyl residues in proteins.

Introduction The preparation of an EDTA-like chelator from L-tryptophan, (S)-N-[2- [bis(carboxymethyl)amino] -3- [3-indolyl]propyl] -N-(2carboxymethyl)glycine, by Abusaleh and Meares,’ indolyl-EDTA (hereafter referred to also as WEDTA), provided an exceptional model for the spectroscopicstudy of the effects of metal ions on indole photophysics. Additionally, there is a clear analogy between chelation of metal ions by such a model compound and their binding to proteins. As a consequence of the similarity in ionic size to Ca2+, lanthanides have been especially popular3-5 as “isomorphous” replacements for CaZ+in studies of metal ion induced conformational changes in proteins, particularly when the fluorescence of tryptophan in the protein provides the primary signal measured. A thorough understanding of the effects of lanthanides on indole luminescence is thus clearly important. Further, it has been frequently observed that Tb3+binding to proteins results in sensitized Tb l~minescence,5-~ presumably by energy transfer from tyr and trp residues. Martin and coworker~’~ originally suggested that the excitation spectrum of such sensitized Tb luminescencehas a specific signature (at 295 nm) proposed to be diagnostic for t r p T b resonant energy transfer. The excitationprofile was subsequentlyshown to closely resemble that of tryptophan itself, with a shoulder at -290 nm.’b-c Horrocks and co-workers,4a~bwho have done the most extensive optical studies to date of indole-Tb energy transfer, concluded that Tb did not markedly quench the fluorescenceof trp residues. Several years ago, we reported that sensitizedTb luminescence in several proteins was quenched at markedly higher rates by acrylamide and oxygen than expected if energy transfer were solely from the excited singlet state of trp.2 The preliminary conclusion was that the majority of the sensitized transfer to Tb occurring from trp must originate from an excited state of the indole with a significantly longer lifetime than the trp fluorescence. At that time, no specific evidence was adduced to substantiate that inference. Abusaleh and Meares1 reported that several lanthanides, including Tb, effectively quenched the fluorescence of the indole in indolylEDTA metal ion complexes. The To whom correspondence should be addressed. *Abstract published in Adounce ACS Abstracts, September 15, 1993.

0022-3654/93/2097- 10326$04.00/0

effectiveness of quenching varied with the lanthanide studied but appeared to follow the reduction potential of the aqua metal ion. Other investigators*working with free tryptophan complexes have inferred that direct coordination to the indole pyrrolo nitrogen was the basis for fluorescence quenching. In all of the above-mentioned studies, however, there was surprisingly little detailed data allowing evaluation of the mechanisms responsible for metal ion effects on indole luminescence. Thus, we do not know whether there are both throughspace and through-bond indole/lanthanide interactions, nor do we fully understand the differential effects of the various lanthanides on indole luminescence. Recent NMR investigations2show the complexity of magnetic interactionsbetween lanthanide ions and indole nuclei, apparently operating through space (dipolar) and through bond (“contact”like terms), and there is no reason not to expect an analogously complex situation for their electronic interactions. There are three issues we wish to investigate in this paper: (1) the roles of both singlet and triplet excited states of indole (in WEDTA) in mediating energy transfer to the lanthanides, (2) the possible role of paramagnetic properties of the chelated lanthanides in quenching indole luminescenceand (3) the role of electron transfer to the lanthanide as a sourceof indole quenching. We have measured and analyzed the indole-sensitized Tb luminescence through direct measurements of fluorescence lifetimes and detailed studies of acrylamide, iodide, and oxygen quenching of indole and Tb and other (Dy, Sm) lanthanide luminescence. In all instances,we assumed that we werestudying 1:1 complexes of chelator and metal ion; this inference was well substantiated by results from metal ion titrations. We were able to verify that Tb and other Ln’s can indeed quench indole fluorescence. It seems clear from comparison of the acrylamide and oxygen quenching of the indole fluorescence, vis-h-uis the Tb luminescence,that the majority of the sensitized transfer between indole and Tb in this system derives from other than the excited singlet state of the donor. Establishing this point required comparison with the transfer and quenching efficiencies for the luminescence of the Dy and Sm complexes as well. However, the effectivness of Eu and Yb as quenchers of indole fluorescence seems to correlate best with the ease with 0 1993 American Chemical Society

The Journal of Physical Chemistry, Vol. 97, No. 40, 1993 10327

Lanthanide Perturbation Indole which they undergo one-electron reduction. Sm shares this characteristic with Yb and Eu and helps to specify the model for electron transfer we employ. It is not our primary intention to give a detailed account of the photophysics of the indole itself, for which an extensive literature exists (e.g., refs 50-55). Rather, we are concernedwith the modes of quenching induced by the lanthanide in the complex and utilize data from the indole only insofar as it provides parameters from which to extract lanthanide-dependent values, as far as possible keeping the indole data model-independent.

Theory Since there are probably a variety of quenching processes at work in lanthanide complexes of indolyl-EDTA, we present a number of physical mechanisms which could be used to explain the experimental results. Specifically,weconsider energy transfer, intersystem crossing, and electron-transfer quenching, respectively, and subsequently examine these processes within thecontext of our experimental data. Theoretical details of these treatments are presented in Appendixes A and B. Energy Transfer. There are two general mechanisms of resonanceenergy transfer: the dipole-dipole mechanism and thc so-called exchange mechanism. An appropriate starting point for considering both mechanisms is the general treatment of electronicexcitation transfer in the tight binding schemeprovided by Dexter.9 Since the lanthanide electronicorbitals are relatively compact,one can employ the familiar point-dipole approximation for the interaction of centers 1and 2 in the dipoledipole Coulomb Hamiltonian, %dd:

(the p’s are the dipole moment vectors and u is a unit vector along the vector separating the two point-dipoles, R). Dexter considers then wave functions normalized on an energy scale (because of the continuous spectrum of the energylo). This allows one to perform the trick of averaging the squared matrix element ((1,2’)%~tdd12,1’)~) over energy insteadof averaging,i.e., integrating (%dd)firSt and then squaring, as one would usually expect. The density of states is subsumed thereby into a normalized spectral overlapintegral, involving the overlap of the normalized emission spectrumf(X) of the donor and the absorption spectrum of the acceptor, €(A). The (p2) are written separately as oscillator strengths: integrated absorptivity for the acceptor on the one hand and as an Einstein A coefficient for the donor on the other. The relative orientation of the two dipoles in space becomes a factor: (K * ) (cos Om - 3 cos eARcos 6SR)Z). In addition, since %dd is electromagnetic in character, a high-frequency dielectric constant, equal to the squared index of refraction, n2, is used as a screening factor on the energy, (%dd). For this FoersterDexter11 formalism, we have employed the final formula for the dipoledipole transfer rate kdd:

JX4e(X)f(X) dX in cm6 (2) We have indulged in some detail here to point out the nature and extent of the approximationswhich are usually made. If, for instance, the acceptor is admitted to have a discrete spectrum, its wave function normalization on an energy scale is not valid, and its dipole moment would be evaluated separately by, e.g., Judd-Ofelt theory,12 and dotted into the moment for the donor (presumably still using energy normalization). The orientation factor, K , for example, would be obtained first by summing over the three unit tensor operators appearing in that theory, U@), U(4),and U(6),19 and then squaring that result, so values of ( K ) ~ could occur which tend to be much closer to zero than, as we have assumed the transition dipoleof the lanthanide effectively behaves as an isotropic acceptor, ( ~ 2 )lying in the range between l / 3 and 4/3. Another possibility might occur if the donor/acceptor

separation is too small to support the validity of the point-dipole approximation (i.e., direct overlapof the donor and acceptor wave functions)? a possibility we do not consider further here. The dominant non-dipole-dipole energy-transfer mechanism is probablythat describedas electron exchange. For the exchange interaction, d

describes the spatial part of the interaction. In addition, a factor ( ud(l)ua(2)lud(1)us(2)) for the spin functions appear^.^ As Matsen and Klein” point out, as long as the electronpermutation symmetry irreducible representations (irreps) about the lanthanide and about the indole centers are “good” quantum numbers, which should be the case as long as there is no large perturbation of the eigenvalues of either the lanthanide or the indole, then the total spin, SI,,, before and after the interaction must be the same. St,, can be given by any number obeying the Wigner-Pauli rule: St,, Sa + S,,Sa + S,- 1, S a + S,- 2, ... p, - S,l. Thus, for an indole excited singlet and nearly all lanthanide configurations, the exchange integral vanishes. But the indole triplet-lanthanide (for Tb, Sm, Dy, Er, Eu, Ho) interaction is spin allowed for many of the excited terms of 4fk which are in resonance with the triplet. In the exchange case, the wave function normalization is over space, but the density of states is still subsumed into an overlap integral of emission and absorptiondistribution functions,f(E) and F(E),each normalized to unity: JAE) F(E) dE. We desire an explicit, even if approximate, formula for the expected values of k,,, the exchange-transfer rate; we find that k,, is

k,, z (1/hgag,)(2reZ/c)ZY2{Jdrl dr, R4‘(rl)RZp(lr, -

where we assume hydrogenic radical functions 93, ga is the degeneracy factor for the acceptor (lanthanide) = 25, + 1 for the si+’L,, ground state (”in = initial) term, g, is the degeneracy of the donor (=3, for triplet state), and e is the effective dielectric constant. The function R2P for the indole is roughly -( 1/ 2 d 6 ) (plr)2e-Plr/2, while the 734f for lanthanides is -( 1/768d35)(4pzr)4e-p2re In these formulas, p2 is obtained by means of a fit to the values of ( r z ) ~in , Table I for the lanthanides to the augmented hydrogenic equation for (r2)4f, namely,

The best fit (assuming that the core should represent a complete noble-gas shell, Z = 2, 10, 18, 36, 54, etc.) for the lanthanides listed is Z,, = 18, and a ’ = 2.16 A. Thus, p2 is ( Z - 18)/(4 X 2.16), which is given in Table I. The value for p1 for the indole is more difficult to assign. For numerical purposes, we have assumed a value of 1.OA. We also assume hydrogenic orbital functions, Le., spherical harmonics for the donor and acceptor, Yl,,, and Y,*,,,*, which combine together to form wave functions for the electron center-of-mass and relative-displacement coordinates with a composite YLMwhich must be the same in the initial Is’a) and final [sa’) states, due to the orthogonality of the spherical harmonics. Thus, “Y“ is equal to angular momentum coupling coefficients (Wigner 3 j symbols) for states Ilm) which combine to give a definite allowed L. As Condon and Shortley14 show, these are independent of m. So each Y is

-

(11 L

12)

0 0 0 For 4f electrons and 2p electrons, L must be either 2 or 4. The whole k,,is calculated for all possiblevaluesof L. Using Gray’sl5 multipolar expansion for 1/r12, and keeping only the major term, allows, instead of the term l/rlz, a substitution to ( r 2 ~ n ) d ( 3 / 35)e2rind/R,4. For the integral above, the term in curly brackets

Kirk et al.

10328 The Journal of Physical Chemistry, Vol. 97,No. 40, 1993

TABLE I: Electronic Parameters for Lanthanides Ln

term(cn~rgy)~

346

33c

6d

De

6-f

98

9h

Sm

W7/z(20 010) ‘Ig/2(20 550) 5Dz(21 492) 5D4(20500) 4F9/2(21 100) 41~s/z(22100) %11/z(23400) 5~421370) ~ ~ ~ 100) ( 2 2 2H~1/z(19150) 4 ~ , ~ 450) 2 0

4.74

0.883

5.09

-0.534

1180

3.79 1.73 6.37

0.834 0.755 0.726

5.21 5.44 5.56

1.328 1.746 -1.180

1360 1620 1820

5.04

0.696

5.67

1.258

2080

5.67

0.666

5.79

-0.691

2470

-0,1211 0.0364 -0.1332 -0.2516 -0.0331 -0,0335 -0.0183 -0.5422 -0.5057 0.07

0.096 0.045 0.075 0.01 0 0.197 0.0463 0.425 1.078 11.4 0 0

Eu

Tb

DY Ho

Er

0.0885 0.2149 0.067 4 Energy in cm-* for each term, from ref 19. b Spectral overlap integrals 9 calculated according to (2) for each lanthanide in lW9 cm6. C Average values in AZ, from ref 39, Hartree-Fock wave functions. Effective hydrogenic wave function radial coefficient square electron displacement (9)Ln in A-1, calculatedas described in text. e Group theoretical parameter for spin-orbital coupling for ground electronic state for each lanthanide,calculated as described in appendix B. f Scalar spin-orbitcoupling coefficients [ taken from Abragam & Bleaney.22. 8 Group theoretical parameters for ligandinduced configuration interaction,calculated as described in Appendix A. Reduced matrix elements (S4dz)PL9are calculated from those given in

ref 19.

is approximately equal to {(3,,)1/(3/35)e2/Rm4 7 X [720/(7681/35 X 220

8

4

21/61] 2 P2 P1 /(PZ + Pl)131 ( 5 ) In addition, F is 3/35 for L = 2,ll = 1,12 = 3. The result for Tb, for example, is (distances in A): k t r , ~ x 1.86 X 1020(rz)Lnz/ t2gSguR,8Jf(E) F(E) dE s-cm-1 (i.e., wavenumber interval normalized spectral overlap) or -2.1 X 108/e2 s-1 at a distance of 6 A (see Results and Discussion). An explicit result allowing numerical values of ktr,hto be calculatedand comparedfor various lanthanides has not, to our knowledge, been given before. In situations where the effective dielectric constant is like that in water (-80), this rate is only -3.3 X 105 s-1, compared with kd, of tryptophan of -4 X lo7 s-l (i.e., 2 orders of magnitude smaller). But if the effectivedielectricwere actuallymuch smaller, say in proteins or in crystalline solids, this transfer rate could become quite significant. This would also be the case if the effect were to propagate through bonds and not through space as we consider above; Le., the “effectivedielectric constant” in covalent bonds is much smaller than 80. In such cases, the effective exchange matrix element is “transferred” from bond to bond, at each bond picking up another “order of perturbation”, Le., another energy denominator for the mismatch of bond energy from the previous to the current site along the chain in a product of siteto-site transfer matrix elements. As long as the energy levels are in near resonance,these catenated matrix elements do not greatly diminish the strengthoftheinteraction. Thestrength is supposedz3 to fall off by a factor a e-nt, where “n” is the number of bonds and e is between 0.3 and 0.7. This interaction has been labeled “superexchange”.24 “Superexchange”, or through-bond interaction, is similar in nature to a ligand field-inducedconfiguration interaction (JuddI6 has discussed very similar physical concepts under the heading “inhomogeneous dielectric” effects). If \k(SLJ)is the lanthanide wave function for a given term and xenv is a product wave function for indole plus EDTA ligands, Le., xcnv= XindXCHXNXCH2XCOO‘ .., etc., then a general form for the interaction we have been discussing would be

-

where thejth electron of any ji pair is associated with the ligand (x’) center or lanthanide W(S’L’J?, while the ith electron is associatedwith thelanthanide *(SLJ), or ligand x. The detailed analysis is presented in Appendix A. From methods discussed there, we determine the factors E(6j@3jmSO3>O>DX), representing the group-theoretical dependencies of the Coulomb

interactionof thevarious lanthanideswith the ligand environment. They are listed in Table I under the column labeled 9. These quantities, together with those listed under 0 in the same table, can be used to determine the lanthanide dependence of 6 in the above equation (6). Comparisons between various lanthanides in terms of the relative efficiency of the superexchangemechanism can then be made. The various other factors in (6) are lumped together into a single coupling coefficient which should be specific for the ligands, not the lanthanide. The spectral overlaps of excited singlet to lanthanide, and of triplet to lanthanide, are very different for different lanthanides. It therefore will be necessary to observe luminescence from a variety of lanthanides to disentangle the various possible mechanisms of energy transfer. Similarly, since nonluminescent lanthanides have also been employed as fluorescencequenchers in a variety of protein environments,5-7 we employ several of these as well in an attempt to develop a consistent picture of lanthanide quenching processes. Only the dipole-dipole process has a clear distance dependence(in the approximationused above with the through-spaceexchange mechanism, using only the lowest order term gives a Rm4 dependence) which should be consistent between the lanthanides. The other major modes, through-bond exchange and through-space exchange, are supported only by the triplet state of indole (from the Wigner-Pauli rule) and so should be limited by the intersystem crossing rate. But they differ in that ligand geometry affects through-bond exchange coupling between mixed indole-ligand-lanthanide configurations, while through-space exchange is dependent on the dielectric constant of the intervening space. Intersystem Crossing. Quenching of WEDTA induced by lanthanides may have as much to do with their paramagnetic propertiesas with their spectral properties.* Quenchinginvolving the so-calledexternal heavy atom effect reflects efficient singlettriplet intersystem crossing in the indole brought about by an increase in spin-orbit coupling. This is caused by the spin of the lanthanide projecting on the nonzero orbital angular momentum of the indole SLn’lhd. Admittedly, the indole triplet could have a nonzero spin projection on a “borrowed” orbital angular momentum from the lanthanide as well, i.e., ILn’shd. In this paper, we consider only the first contribution, since the spatial extent of lanthanide wave functions is so limited, whereas similar restrictions do not ncessarily apply to their spin functions. We consider the relative size of this effect through the lanthanides series. Theoretical considerations applying to the lanthanide/indole spin-other orbit interaction are presented in Appendix B. The net effect on the intersystem crossing rate ki, can be expressed in terms of the product of the squares of two

The Journal of Physical Chemistry, Vol. 97, No. 40, 1993 10329

Lanthanide Perturbation Indole quantities:

Materials and Methods WEDTA (structure shown in Figure l a was synthesized by Dr. Werner Tueckmantel at Mayo Clinic, Jacksonville, FL, and the purity assayed by TLC on silica gel as described in ref 44 (RJ = 0.48), as well as on PEI-cellulose eluted with 2 M HCOOH, 0.1 M LiCl (RJ= 0.15). In all cases, only one spot was found. The structure was also confirmed by lH and 13C NMR (data not shown). Initial experiments had been done also on samples of WEDTA very kindly supplied by C. F. Meares, Dept. of Chemistry, University of California, Davis. For the studies reported here, solutions were buffered at pH = 7.2 (pD = 7.7) with 0.0375 M MOPS-H/0.0375 M M O P S K U (Fluka, Hauppagge, NY) for the high-concentration buffer (or IIMOPS) and 0.00188 M MPOS-H/O.O0188 M MOPS-K for the dilute (I-

which are presented in Table I separately under the columns labeled &-for f s , the lanthanide electrostatic spin-orbit scalar coupling coefficients-and a, which are group theoretical quantities for the spin-orbit interaction, similar in nature to those introduced above for the ligand field-induced configuration interaction and proportionalto ZS,( aSL&qaS‘LJ). The values as given in that table are literature values for the lanthanide spin-orbit interaction. But the relevant 4 in our case may be determined by WEDTA, not the lanthanide, since the spin of an electron associated with the lanthanide can range much further than its “orbit”. MOPS)buffer,oratpH=6.15(pD=6.6)withO.O375MMESElectron Transfer. Electron transfer from tryptophyl residues H/0.0375 M MES-K. The oxides of Sm, Eu, Tb, Dy, Ho, Er, has often been implicated in the quenching of protein fluorescence. and Yb (99.999%, Johnston Matthey, Ward Hill, MA) were The Marcus25126theory of electron transfer should be applicable dissolved in water or 2H20 (99.9%, MSD Isotopes, Montreal, in the systematic investigation of this possible quenching mechCanada) with addition of 3.5X mol/mol of Ln of HCl (or 2HC1 anism relevant to WEDTA-metal complexes. We shall support in 2H20 from MSD); in the case of Tb, this was done with gentle the hypothesis that this phenomenon explains the dramatic heating from the stream of an air dryer. For DzO solutions, the quenching of indole fluorescence by the more easily reduced glass vessel was sealed. Glassware was repeatedly acid washed lanthanides, though this quenching mechanism is rather more (3X) and rinsed 14X with distilled deionized water (Barnstead/ common in the transition metal series (Kirk and Prendergast, in Thermolyne, Dubuque, IA) and dried by a warm air stream preparation). (external, so that no metal from the dryer would be deposited on The Marcus parameters for AFo’ depend on the difference in the inner surface). Otherwise, similarly treated plasticware was the work done by the solution to bring the reactants together employed as often as possible to minimize metal contamination from infinity and on that to remove the products to infinity. This of WEDTA samples, found from early experimentation to be a difference should be given approximately by the difference in problem. Samples to be purged were cycled repeatedly (3X) in free energies of formation of the EDTA-Ln3+ and EDTA-Ln2+ a wetted Ar (UN1006 Union Carbide-Linde) stream for 15min/2 complexes in water. Fuoss2’ theory suggests a value of 10-15 mL of sample followed by venting on a vacuum line for 5 min/2 kJ/mol over the lanthanide series for this difference. The mL. remaining terms in the total free energy change in the reaction, Absorption spectra were collected on a Cary 2200 UV-VIS AF4, are the sum of the one-electron reduction potential of the spectrophotometer and fluorescence spectra on a Spex 1680 lanthanide and the oxidation potential of the indole. We further spectrofluorimeter. A thin (0.02-mm) sample of a concentrated assume that (as seems true for neutral pHs) the electron transfer WEDTA solution in 80% glycerol was imbedded in solid Ar to is proton assisted, in the sense that a proton leaves as or before obtain a triplet emission spectrum.33 Quantum yields of lanthe electron leaves. thanides in DzO solutions were obtained by comparison with Tb3+ in D2O at concentrations below 5 mM. Corrections were made For the ground state of indole, the oxidation potential is 1.1 eV.28 For the excited state, the difference between this positive for the finite slit width of fluorescence excitation relative to the narrow absorption peaks, using the averaging formula over a slit 1.1 eV and the excited state’s energy relative to the ground state width P about a peak at Ao: would be the now negative chemical redox potential. The reorganization energy A, employed in Marcus’ theory, can Jc(X) dX/JdA = d ( r / l n 2)hw/6 X (€(A)) be estimated by the difference between Stokes shifts of WEDTA with divalent cation bound, uersus trivalent cation bound, plus erf(d(1n 2 ) 6 / 2 w ) for €(A) he-”2(A-h)2’”2 the half-width of the singlet or triplet spectrum (which represents Fluorescence lifetime decays were collected on a multifrequency one-half of the reaction) at 30 kJ/mol. Alternatively, Marcus29 phaseand modulation fluorometerusing an ISS Koala automated estimates A for excited-state charge transfer between aromatic sample compartment (ISS, Champaign, IL)3‘ and a DRA A2Dchromophores, Le., both halves of the reaction are aromatics, to 160 digital acquisition card with synchronous acquisition module be -5000 cm-1, or 60 kJ/mol. The Flemir1g3~group offers a at 20 ‘C. We employed interference filters with 5-nm-bandwidth value of 90 kJ/mol for X for the trp of azurin, however. The rate constant for electron transfer is then essentially u ~ ~ - ( ~ o ’ - ~ transmittance ) ~ / ~ ~ ~ for ~ ,the 350-, 360-, and 390-nmemission wavelengths listed in Table 11; at 340 nm, we employed a 10-nm filter. These where uo can be given by a nonadiabatic potential energy surface data were analyzed using the Globals Unlimited package.35 hopping frequency such as that given in Marcussoor Newton and Sutin31 (ca. 1010 to 1014 s-’-the large difference in “slopes” of Results and Discussion electronic energy surfaces between indole and the lanthanides probably favors the smaller values). In Figure l a is displayed a “solution structure” for WEDTA, With the above formulas in hand, we now have all the tools consistent with the previous NMR measurements2 but built from necessary to construct a clearer picture of lanthanide-induced an X-ray structure of EDTA-Ln.36 The other panels of Figure quenching of indolylEDTA. Our intention is to be as compre1 catalog the general spectral properties of WEDTA and its hensive as possible in analyzing the experimental data, which complexes. Figure 1b shows an absorption spectrum for WEDTA, follow according to the foregoing considerations. There is no both in the presence and absence of 1:l Eu3+. Similar data are reason a priori to expect any one of these mechanisms to be obtained with Lu, Tb, Gd, etc. The concentration of solution obtained from weighing a known amount (-25 mg) of solid dominant throughout the lanthanide series, and probably more ammonium WEDTA salt, and comparing this also with fluothan one such mechanism comes into play in some particular rescence titrations against stock solutions of lanthanides (vide WEDTA-Ln cases. Inasmuch as what is true of WEDTA-Ln infra), yields values for molar extinction coefficients, EA, of 5930 complexes could also be true of protein-Ln systems, these at 288 nm, 6600 at 280 nm, and 2780 at 295 nm for the free complexities may be relevant more generally to tryptophyl WEDTA and values of 6270 at 290 nm and 3 180 at 295 nm for quenching by lanthanides.

-

Kirk et al.

10330 The Journal of Physical Chemistry, Vol. 97, No. 40, 1993 CHpCOO’

a

I

N-CH2COO‘

I

I

H

CH2COO-

I

I

I

I

I

I

300

350

400

450

500

I

550

Wavelength (nm)

I I

I

k U

0.15

1

I

I

320

I

I

I

340

360 Wavelength (nm)

380

0.0 4 l

260

~

l

280

~

300

Wavelength (nm)

l

~

l

*

~

~

320 300

400

500

600

Wavelength (nm)

Wavelength (nm)

Figure 1. (a) Structure of WEDTA, (inset) stereographic view of “best” fitted structure of WEDTA via a distance-gcometry algorithm from the data

in ref 2. (b) Absorption spectra of WEDTA at 25 pM concerning: (thin line) WEDTA, noadditions; (thick line) WEDTA + 25 pM Eu3+. (c) Excitation spectra of WEDTA-Tb complex, 25 pM in DzO and 0.075 M MOPS, 1-nm excitation, 4-nm emission slits: (thick line) emission at 546 nm, Tb luminescence excitation; (thin line) emission at 360 nm, indole fluorescence excitation. (d) Emission spectrum of WEDTA in 85% glycerol, 15% 0.075 M HzO and MOPS buffer a t 10 K with 295-nm excitation, 0.17-nm emission, and 8-nm excitation slits. (e) Excitation spectrum of Tb luminescence of 250 pM WEDTA-Tb (D20 with 0.075 M MOPS)at 546 nm, slits at 2 nm for excitation and 5 nm for emission. ( f ) Upper curve (- -), 25 pM WEDTA emission in 0.0375 M MOPS buffer in HzO a t 295-nm excitation with 4-nm excitation and 1-nm emission slits; lower curve (- -), emission of WEDTA-Y complex in the same conditions; (-) curve, emission of WEDTA-Tb complex, same conditions as upper curve.

-

-

~

Lanthanide Perturbation Indole

The Journal of Physical Chemistry, Vol. 97, No. 40, 1993 10331

TABLE II: WEDTA Fluorescence Decay Parameters*

x

71

a1

(12

72

x2

x

a1

71

340 350 390

4.05 4.10 4.19

1.o 1.o 1.o

1.2 2.84 2.13

(B) I'MES; H20 340 350 360 360 390 390

4.13 4.0 4.27 4.20 4.21 4.20

0.833 0.987 1.oo 0.997 1.oo 0.998

0.77 12.8 170.0 213.0

0.167 0.013 0.003 0.002

1.95 2.14 5.00 5.05 4.33 4.52

(C) IIMOPS; DzO 340 340 360 360 390

4.29 4.20 4.34 4.24 4.24

0.997 1.o 0.992 1.o

14.9

0.003

9.5

0.008

a2

72

X2

WEDTA-HOE"MOPS; Hz0

WEDTA-Tb: (A) 'MOPS; H2O

1.69 1*34 1.53 1.52 1.38

1.o

360

1.90

2.4

340 350 350 390

8.61 8.21 8.32 8.49

0.888 1.o 0.954 1.o

35O

9.82

0.93

360

8.38

(C) "MES; H20 1.o

WEDTA-Y: (A) "MOPS; H2O 1.68

0.112

0.694

0.056

1.54 1.64 1.03 1.51

(B) 'MOPS; H20 0.25

0.07

1.70 4.04

WEDTA (free): (A) IIMOPS; H20 340 350 390

11.0 12.3 12.8

0.76 0.7 0.525

2.42 3.0 4.0

0.24 0.3 0.475

4.2 3.9 3.9

(B) "MES; H2O

350

8.83

1.o

2.0

a Emission wavelengths A, lifetimes 7 (in nsec), associated amplitudesa, and x2statistic for various experiments. 'MOPS is 0.001 875 M = MOPS-H = MOPS-K buffer, IIMOPS is 0.0375 M MOPS-H MOPS-K. "MES is 0.0375 M MESH = M E S K . All samples are purged with Ar as described in text. All experiments recorded here were obtained with phase-modulation data and fit from the ISS/Globals software package?' Alternativefittings at a given wavelength are presented only where these are of similar x2 to the best fit.

Eu-WEDTA complex, which we taken to be consistent for all Ln-WEDTA complexes. At higher concentrations (0.3 mM), however, approximately20% hypochromicityoccurs upon addition of 1:l lanthanide (data not shown), indicating possible highercomplex formation or complexation at the pyrrolo nitrogen. Subsequent experiments were conducted at 1 2 5 pM WEDTA. Measurements of quantum yields were conducted at a concentration of 5 pM WEDTA. An important point in Figure l b is that the shape of the absorption spectrum is minimally changed upon interaction with Eu; i.e., there are only second-order changes observed in the difference spectrum (not shown, but compare the much stronger second-order effect in a protein trp absorption upon CaZ+ binding37). These changes involve increased intensities of certain contributory modes but no changes in the energy eigenvalues of the indole. Figure IC gives the excitation spectrum for indole and Tb emission in WEDTA-Tb, respectively. The Tb spectrum in Figure ICthus represents the transfer-of-excitation spectrum, and we see that it conforms to the absorption/excitation spectra (Figure l b and IC) of indole itself. In Figure Id, the singlet + triplet emission spectrum obtained in a thin glass at 10 K is shown. The emission maximum in fluorescence is shifted ca. 30 nm to the bluein the low-temperatureglass relative to room temperature aqueous solutions (cf. Figure If). Figure l e establishes that the energy eigenvalues of Tb are also essentially unchanged within the WEDTA-Tb complex. The characteristic Tb lines apparent before the onset of the huge indole excitationshoulder are precisely those observed for the aqua ion20. In Figure lf, the extent of energy transfer involved when Tb binds to WEDTA is evident. The fluorescence quenching observed is far greater than occurs for most Tb-protein systems reportedS7 yet. In part, it is this very degree of effectiveness of transfer which we seek to explain in this paper. Certain inferences concerning the nature of the complex can be drawn simply from steady-state Tb luminescenceand solvent isotope effects. The nonradiative decay rate of Tb is linear with the number of 0-H 0scillators~7bound to it. We can compare the quantum yield of Tb in WEDTA-Tb in DzO us HzO (ratio = 4.5) with that of aqueous Tb. Assuming 9 waters about the Tb in the aqua complex, we find a value of 3 waters about Tb in WEDTA (cf. ref 44). The same HzO/D20 ratio is obtained with Tb-EDTA us aqua Tb, and it is known that the Tb-EDTA complex has -3 waters!' Therefore, the EDTA portion does not have octahedral coordination to the Ln. Indeed, the highest local (approximate) symmetry is Cb. It may be significant that

one ligand (N) is directly bonded to the single asymmetric carbon in the system;thus, the highest local symmetry is probably merely Cz. This fact becomes relevant in generating our specific group chain factors (Appendix A). The fluorescencelifetime parameters for the best fitting to the decay of indole in free WEDTA and in WEDTA-Tb, WEDTAY,and WEDTA-Ho complexes are given in Table 11. Three experiments and their fits are also shown in Figure 2. Although these data are not the primary focus of this investigation, they do provide key parameters for our subsequentanalysiswith respect to modes of lanthanide-dependentquenching. Nonetheless,some word of comment on these lifetime results is in order, particularly with regard to the apparent heterogeneity in lifetimes and hence the quality of the fits to the data. In indoles and tryptophan analogs,multiple-exponentialdecays are often ob~erved.~",~ These have been ascribed in some cases to conformational heterogeneityof the molecules in solution. The indole C.-Co bond is substantially free to rotate in these analogs, one conformer bringing the charged amino group of tryptophan close to the ring near C4-H, another conformer bringing the carboxylate near. It has been proposed that these conformations, which presumably interconvert on or slower than the time scale of the excited-state lifetime, are responsible for two slightly different quenching rates which appear as two lifetimes. We do not believe this explanation suffices in our instance. The average lifetime and quantum yield of WEDTA are very large for indoles in aqueous media and especially for tryptophan derivatives. Its emission spectrum is shifted very much to the red for tryptophan analogs (cf. Figure 1f ) . These facts suggest that the major putative quenching mechanisms for tryptophan are not operating as efficiently in WEDTA. It has been suggested that the major quenching pathway for indoles is electron transfer to s0lvent,5l*~~ ETTS. It is interesting that one carboxylate actually comes quite close to the position of the 4-C-H proton (cf. Figure la) which becomes "acidic" in the excited state53~s4 and possibly by proton transfer assists the ETTS. The presence of the carboxylate may inhibit the ETTS (by stabilizing the proton at 4-C), while complexation by metals may partially offset this "dequenching" (cf. Table I1 and Figure 10.

The EDTA portion of WEDTA with chelated metal is likely to be relatively rigid, and Cp is an integral part of this chelate. In addition, the moment of inertia about the C.4, is much larger than that in most tryptophan analogs, so the assumed interconversion is probably very slow in WEDTA-Ln. Thus, if

Kirk et al.

10332 The Journal of Physical Chemistry, Vol. 97, No. 40, 1993

a 5j

1

5

1.o

-5 5

-

5

L loo

loo

k 0.g

0.4

0

1

2

3

[Ln]/[W EDTA]

Fgue 3. Stoichiometrictitration of WEDTAfluorescenceby lanthanides.

0

10

1

Ratios of the total fluorescence (295-nmexcitation)at a given lanthanide concentration to the fluorescenceat zero added lanthanideconcentration, 9/9(0), Ln,plotted against the concentration of added lanthanide as a ratio of the original WEDTA concentration (25 rM), [Ln]/[WEDTA]: (0)9/9(0)forSm;(o) 9/3(0)forTb;(+)9/9(0)forHo;(.)9/9(0) for Er.

160

Frequency (MHz)

b

5

’j

-5 > - 5

into a particular conformation, then it becomes problematic why WEDTA-Y is not similarly “frozen” (cf. Table 11). At pH 7.2, lanthanide-chelated WEDTA is not protonated at the amines (unlike tryptophan), whereas there might be some residual protonation of the amines at pH 6.15. Protonation of an amine probably does not in this case affect the rotameric equilibrium in the complex, but rather it could affect the rate of the ETTS. This might explain the increased dispersion of the fits in MES buffer; Le., hydrogen-bond rearrangements in the excited state can give negative preexponential factors (cf. ref 55) which have not been very well fit by our analysis so far. Clearly, further analysis of these small components will be required. Adding (positive) components to the analysis in MES buffer does not improve the x2 values. Heterogeneity in lifetime values might have resulted, as we mentioned in connection with the values in DzO, from trace metal ion contamination generating a variety of chelated species. Yet these trace contaminants would have to represent very weakly bound species to explain the noisiness (dispersion) in the data, in those cases where more than two lifetime components are not obtained. Impurity of the WEDTA itself does not appear to be involved, since some complexes yield excellent data. We note lastly that the values of x2, while not perhaps very impressive, do not become much better (-0.0543) by fitting to a Gaussian distribution-of-lifetimes model of the decay (data not shown). There is significant improvement, however, after purging samples of 02 (data not shown). Oxygen quenching is considered to be an additional quenching process with a rate of -3 X lO7/s a t standard partial pressure, so a lifetime of 4.1 ns becomes nearly 3.7 ns. Data from Figure 3 can be used to support the predominantly 1:1 stoichiometry of WEDTA:Ln complexes at the concentrations (24.5 pM) employed in MOPS buffer at pH 7.2, pD = 7.72. It is important for the analyses which follow to establish by means of this data both the 1:l stoichiometry of the WEDTA-Ln complexes and the steady-state quenching induced by the lanthanide in these complexes. If we consider the WEDTA-Tb complex as a physical-chemical system to be interrogated by time-resolved and steady-state fluorescence spectroscopy, then it would seem that WEDTA-Y should be an ideal “internal model” system for a +3 charged ion bound to WEDTA, because the diamagnetic Y should neither increment intersystem crossing for the indole nor be subject to energy transfer as the lanthanides would. We propose that all quenching processes which arise for WEDTA-Ln complexes are dynamical in character; i.e., they can be described in terms of rate constants which add to form an overall fluorescence decay rateconstant. Dynamic quenching implies that the ratioof steadystate fluorescent intensities must equal the ratio of decay times,

1

loo

loo

i

io

100

Frequency ( M H Z )

c

5

5i

-5 5

100

1

-

5

‘ V ,

i

io

100

100

Frequency (MHz)

Figure 2. (a) Phase and modulation decay of 340-nm fluorescence from

WEDTA-Tbcomplex (295excitation)in purged H20,0.00375M MOPS buffer, fit to a single exponential by means of the global^^^ program, as displayed in Table 11. Inset: residuals in phase and modulation from fit. The x2 statistic for this fit is 1.2 (b) Phase and modulation data for WEDTA-Y complex emission at 350 nm in purged 0.00375 M MOPS buffer. These data are fit to two exponentials with a x2statistic of 1.7. (c) Data for emission at 350 nm for WEDTA (free) in 0.075 M MES buffer. These data are fit with a single exponential with ~ Z e q u ato l 2.0.

there were distinct conformers these should be manifest in more than one component of decay, probably with different speciesassociated spectra. Uncomplexed WEDTA does indeed seem to have a significant contribution to its decay from two or more components, as we might expect on the basis of the preceding hypothesis. Just as significantly, Tb-complexed WEDTA (cf. Table 11) in samples purged of oxygen presents single-exponential decays at a variety of emission wavelengths (whether in ‘MOPS buffer or in higher concentration “MOPS buffer in D2O-the small amplitude components in D20 being very likely due to trace contaminants, such as Zn, in the D20). However, if this agreement with the “rotamer model” were due solely to increased rigidity of the side chains in the complex, which could “freeze”

The Journal of Physical Chemistry, Vola97, No. 40, 1993 10333

Lanthanide Perturbation Indole

TABLE III: Rates for hocesses of Lanthanides (in 9-1) in WEDTA Complex

Ln

kex-

Sm

3.9 x 108

Tb

1.6 f 0.2/1.4 X lo8

EU

7.7 x 109 1.5 i 0.2 X lo8

Dy

Ho

Er Yb

3.7/3.9 X 108 5.9 X lo8 6.6 X lo9

k a (method) (9 0.4) x 107 (11) 0.54/1.0 X 108 (1)d (3.0& 0.3) X lo7 (11) 2.9 x 107 (I) (0.14-2.8) X lo8 (calc) (0.64-1.3) X lo8 (11) (7.9 0.4) x 107 (I) (0.214.1) x 108 (calc) (0.224.3) X lo8 (calc) 0

R’s(consistent)b 4.8 < R < 5.7 A 4.5 < R < 6.3 A 5.8 < R < 7.7 A 5.5 < R 6.2 < R

< 8.0 A < 7.6 A

remaindef

k’tot

3.0 X lo8

(1.0

1.15 X lo8

(8.4

7.5 x 109 (0-7) X lo7 (6 f 1) X lo7 (0-3.6) X lo8 (1.6-5.7) X lo8 6.6 X lo9

a-vc

* 0.3)

X

lo8

0.3) X lo7

(7.4 f 0.5) X lo7

1.2 X 108 (0.59-1.2) X lo8

a k,= from (7b) in the text. For Tb and Ho, this value is also comparable to that obtained from 1 / q n - 1/7y, so both values are reported here, the first value from (7b). b R’s (consistent) are values from the Foerster equation, (2), consistent with the derived values from method I or method I1 (as described in Appendix C) calculated using values for K* between I / j and 4/3. Remainder is defined as k,,, - kdd. Discussed in text, lower value if the quantum yield for Sm is 0.0053, and higher if it is 0.0029. If we take 1.0 X lo8 s-* to be the actual kdd, we obtain R < 5.4 A.

SCHEME I

i.e.:

9(W EDTA-Y)/9( WEDTA-Ln) = (7a) For Tb and Ho, data presented in Figure 3 and in Table I1 demonstrate that this equality is indeed closely obeyed; e.g., the intensity ratio for WEDTA-Tb relative to that for WEDTA-Y is 2.2 (for WEDTA-Y relative to free WEDTA the intensity ratio is 0.93, while from Figure 3, we find the ratioof fluorescence intensity of free WEDTA us fully bound WEDTA-Tb is 0.422, hence 0.93/0.422 = 2.2), and the ratio of 7’s in ‘MOPS buffer is 2.23. If all the steady-state quenching we observe upon binding the lanthanide is thus taken to be dynamical in nature, then it can be expressed as a rate, k,,, found from the relation which results from rewriting (7a) to solve for ~ / ~ W E D T A - Land ~ subtracting away the decay rate constants pertaining to the “model”, 1 / ( T)WEDTA-Y (this equation is useful in the general case where we have data only for steady-state quenching efficiencies, and no lifetime data for a particular complex):

Ind*

( 7 )WEDTA-Y/~WEDTA-L~

k,,,,

k non

ky

= [3(WEDTA-Y)/g(WEDTA-Ln,l:l) X

(7)WEDTA-Yl - 1/(7)WEDTA-Y (7b) In (7b), ( 7 ) is the average decay time of the model = Z C L Y I ~ ~ , which is proportional to its fluorescence quantum yield. The 9 ’ s Dy, we found, by comparison with Tb, a value in D20 of 0.025 (fluorescenceintensities) are determined from the graph in Figure at 361 nm-cf. the reported value of 0.07 from Stein and 3. It is this “excess” k which we must account for with a variety Wurzburg.”’ Similarly, their value of 0.035 for Sm in DzO we of processes such as intersystem crossing, energy transfer, or found to be too large, and we measured instead 0.0053. The excited-state electron transfer. yield in D20 for the Sm-EDTA complex is even lower, namely, These k,,, values are given in Table 111. In that table, we 0.0029 (at 401-nmexcitation), but this particular transition, which have also given, for the lanthanide, the amount of energy transfer is the major contributor to the Sm3+-indole dipoledipole 9 value, as a rate, ktotcmirsivc, which must be taking place to account for seems to be highly sensitive to the nature of the Sm ligands. the observed lanthanide luminescence. What one does is compare Therefore, both quantum yield values were used in analyzing the the lanthanide luminescence relative to its quantum yield with Sm data as presented in Table 111. the original fluorescenceof the indole donor relative to its quantum Analysis of Luminescence-Quenching Results. We have calyield. That is, the original WEDTA fluorescenceintensity divided culated formulas for disentanglingvarious quenching mechanisms by its quantum yield gives a quantity proportional to the effective for both the “single-exponential” and “multiexponential” cases. krad of WEDTA (see below). The ratio of this quantity to the Fortunately, for WEDTA-Tb the multiexponential formula is observed lanthanideluminescenceintensity dividedby its (smaller) not necessary because of the essentially monoexponential decay. quantum yield is the ratio krad/ktot c-ivc. We have determined These formulas are presented in Appendix C. A general treatment the quantum yield of WEDTA in ‘MOPS buffer concentrations similar to what is developed there has been presenteda4* (see Materials and Methods) in H20 as 0.58, and 0.50 at [IIf all the transfer from indole to Tb were due to dipole-dipole MOPS buffer concentrations (degassed samples) or 0.44 in interaction, Le., from the excited singlet sta’te of indole, then MOPS and not degassed, from comparison with the value of experiments involving quenching of both lanthanide and indole tryptophan in water (not degassed) at 0.12.44 From these data luminescence would lead to identical Stern-Volmer slopes. This and the lifetime table, one can find the radiative rate constant may be seen in Scheme I. From Scheme I for WEDTA-Ln complex as krad = (6.3 f 0.1) X lo7 s-I. The quantum yield of Tb in DzO we have found (exciting at 9(WEDTA,Q) Akra,/(knon + krad + ktr + Qkq) 365 nm) is 0.42. This is obtained by comparison of the value of and Dawson, Kropp, and Windsofis at 376 nm of 0.032 in H20, or Kirk‘s46value at 341 nm of 0.029 (HzO), considering an observed Y(Tb,Q) = A&ad,Tb/(knon,Tb + kad,Tb) solvent isotope effect of 13.2. The value for the solvent isotope where the efficiency of transfer, q, is equal to ktr/(knon + krad effect compares well with Heller’s47 value of 12.2 (f1.5). For

10334 The Journal of Physical Chemistry, Vol. 97,No. 40, 1993

Kirk et al.

+

ktr Qk,); k,, is the transfer rate; kmd is the radiative rate; knon is the nonradiative rate; and k, is the bimolecular quenching constant. Constructing S(WEDTA,O)/S(WEDTA,Q) and S(Tb,O)/S(Tb,Q), we obtain S(WEDTA,O)/S(WEDTA,Q) = 1 + Qkq7 = The same equality results if there is a multiexponential decay, with the sole distinction that T is replaced by the average decay time ( 7 ) . Here we have assumed the following: (1) There is no direct quenching by acrylamide of Tb luminescence. This assumption was checked independently and shown to be valid by studying the acrylamide quenching of Tb-EDTA complex upon direct excitation of the T b a t 365 nm (data not shown). (2) Acrylamide quenching competes, but does not interfere, with the transfer to Tb-Le., no modifications to k,,, nor for that matter to knon or krad,are observed upon additions of acrylamide. We see, however, in Figures 4 and 5 that the two quenching curves (Tb luminescence and WEDTA fluorescence as functions of quencher concentration) do not have the same slope. Additionally, a marked curvature is present in the lanthanideluminescence quenching which is not present in the indolefluorescence quenching. We infer from this that we are not dealing with transfer from a single excited indole state. If instead we consider the process shown in Scheme 11, for which

-

s2 $ Q k

61

41

21

1 0, (psi) -.1

b

1.8

I

1.6

Tb*

where kdd is the (Foerster-type) dipoledipole resonance energy transfer from the singlet of the indole (as discussed in the Theory section), k2 is some process of energy transfer allowed for the intermediate electronic state I’ (e.g., exchange transfer from a triplet), and k2’ is the (possibly lumped) rate constant for any other processes responsible for deexcitation of I’ to the ground state. The new feature is the presence of two acrylamidedependent quenching processes represented by k, and k:. The decay of WEDTA-Tb fluorescence a t low and high buffer concentrations is monoexponential, so we do not need to employ the formulas derived in Appendix C for the multiexponential case. Certain additional assumptions can now be made. The data shown in Figure 4 concerning both iodide and 0 2 quenching support the hypothesis that the second transfer process (from I’ to Tb) is from a triplet state. Oxygen a t high concentrations degrades I’ by a k,‘ process that is not unlike the effects of acrylamide; hence 0 2 decreases the effective energy transfer to Tb (which occurs via k2) but does not to such a great extent quench either WEDTA emission or the singlet dipoledipole transfer process to Tb. Oxygen probably degrades the indole triplet by a collisions1 ”spin-flip” process, generating singlet oxygen, while electron transfer to acrylamide is likely to be the major pathway for quenching by acrylamide.5’ Oxygen, however, has too negative a reduction potential for it to rapidly oxidize WEDTA triplet. On the other hand, while iodide probably increases intersystem crossing (hence decreasing WEDTA singlet emission, Le., fluorescence), presumably because of the enhanced formation of the indole triplet, it does not substantially change the overall extent of transfer to Tb. Thus, we associate kl with the intersystem crossing, ki,, while for purged samples we can take k2/(k2 + k2’) to be =1. We illustrate the use of the methods developed in Appendix c to obtain k k and kdd for WEDTA-Tb by carrying out the explicit calculation here by “method 11” for Tb. For the luminescent lanthanides used in this study, the two methods give comparablevalues except in the Dy case, which is discussed below. The agreement between the two methods-which, although similar in their basic design, employ very different and unrelated parameters-is gratifying (see Table 111).

-

b

b

1.4

ka + ku

Tb

-

1.2

-

s

1 0

20

60

40

80

INa (mM)

a 10

a

a

m I

****.***** 0

10

10

40

30

[aaylamidel mM

Figure 4. (a) Quenching, as the ratio of fluorescence without quencher to fluorescence at a given concentration of quencher, S(O)/S(Q),of indole fluorescence, A,and Tb luminescence,m, in WEDTA-Tb complex at 20 pM concentration by 02.All solutions in this figure are H20/ 0.075 M MOPS. (b) Quenching of indole fluorescence, and Tb luminescence, by NaI in 25 pM WEDTA-Tb complex; quenching of

+,

indole fluorescenceby NaI in WEDTA, m. (c) Quenching by acrylamide of indole fluorescence, m, and Tb luminescence, in 25 pM WEDTA-

+,

Tb. This sample was purged. From the lifetimes in Table 11, we obtain TWEDTA-Tb = (4.1 f 0.05) X s, while the Stern-Volmer slope ratio (method 11) iS + (kk/kdd) = 5.24. IfWe take ~ / T W E D T A - T ~ -~/TWEDTA-Y (i.e., the sum of the rate constants k,. + kmd + kdd + kl minus k,,, + kradfor a WEDTAcomplex with a trivalent, nonabsorbing, diamagnetic rare earth) to be equal to ki, + kdd, we obtain the simultaneous equations (1.6 f 0.2) X lo8 s-l = ki, + kdd and 1 + (kh/kdd) = 5.24. The solutions are (1.3 f 0.2) X 108 s-1 for k k and (3.0 f 0.3) X lo7s-I for kdd. Almost the same slope ratio

Lanthanide Perturbation Indole

The Journal of Physical Chemistry, Vol. 97, No. 40, 1993

~.

40

-

30

-

20

-

10335

SCHEME I1

Y

El

Ind*

El El

0

100

0

[Acrylamidel (mM)

10 0

- Ind” 0:

I

0

200

100

[Acrylamidel (mM) -”

1

I

8

6

El

El

4

0

e 0

2

I

I

100

200

0 1

0

[Acrylamide] (mM) Figure 5. (a) Quenchingof indolefluorescence, ,and Tb luminescence, 0,at a higher concentration range of acrylamide than in Figure 4c, DzO solution. All samples in this figure are unpurged. (b) Quenching by acrylamide of indole fluorescence, and Dy luminescence, 0,for WEDTA-Dy in D ~ 0 , 2 5pM. (c) Quenching by acrylamide of indole fluorescence, and Sm luminescence, 0,for 25 pM WEDTASm in DzO.

+

+,

+,

is involved in the 0 2 quenching case, which also shows curvature (Figure 4b). In fact, in the WEDTA-Tb acrylamide quenching experiments, k21 must be small relative to k2 even in nonpurged, atmospheric pressure samples, and hence it can be ignored. That is, in Figure 5a, an unpurged sample has a slope ratio that is still 5.2, which from method I1 should be 1 + (k2/k2 + k21)kh/kdd, nearly the same as when purged. Since the lumped rate constant k2~in the unpurged case contains an extra contribution from oxygen quenching not present in the purged sample, all k+ contributions must be relatively small, and the slope ratio is, even in this case, approximately 1 + kk/kdd. Foerster Energy-Transfer Analysis. Results for Dy and Sm from methods I and I1 are also displayed in Table 111. For the other lanthanides, we have calculated values for kdd consistent with the spectral overlap integrals (Table I) and the distances determined from the previous lanthanides (Tb, Dy, and Sm), namely, those consistent with distances between 5.5 and 7.2 A. We present results and discussion for the Dy and Sm cases under separate subheadings.

-Tb

( I ) Dysprosium(II2) Quenching and Energy Transfer. It is apparent that one needs to find a reasonable estimate of k l = ki, to employ “method 11”. For the particular case of Dy, we can begin by assuming that ki, is the same as that for Tb and calculating kdd from the Stern-Volmer slope ratio, 1.92, to obtain a “zeroth order” estimate of 1.4 X lo8 s-l for kdd. However, in principle the strength of the spin-orbit interaction (assumed to dominate theintersystemcrossing rate) isobtainedfrom theentries under 2) in Table I. These can be multiplied by the spin-orbit interaction constant E E ( h / m ~ )1/2r)dU/dr17,20,21 ~( to obtain a value for the relative strength of spin-orbit coupling between two lanthanides. The square of this value should be proportional to the intersystem crossing rate. For the Tb, Dy pair, the ratio k&,Tb/ki,,Dy would then equal 1.74. It is possible, however, that the radial scalar 5 for the whole WEDTA-Ln complex is nor dominated by EL”, since this number refers in any case to the electrostatic force exerted on an electron in the vicinity of the lanthanide by its own angular momentum. If so, we can diminish our estimate for kl,Dy by (1.7457)2/(1.1795)2 = 2.19, instead of by 2.19 X (1620/1820)2, and the estimated value of kl,Dywould be 5.9 X lo7 s-l instead of 7.5 X 107 s-1 (or the above “zeroth order estimate”, 1.2 X lo*). These new values give estimates for kdd of 6.4 x 107 and 8.15 X 107 s-1, respectively. These latter values accord well with the value of ktoremissive given in Table 111. Further, the sum of our newer estimates for kdd and kl,Dy,namely, 6.4 + 5.9 x IO7 s-l or 8.15 7.5 X lo7s-l, respectively, gives a total “k,,” of 1.23 X lo8 or 1.56 X 108 s-1, respectively. The latter value accords with our estimate from the steady-state quenchingof WEDTA fluorescence induced by Dy (the first column of Table 111) of (1.5 f 0.2) X 108 s-l. We stress the agreement reached here obtained between values derived from very different kinds of measurements (and applied theoretical considerations). ( 2 )Samarium(1ZI). Though in some ways similar to the other lanthanides, Sm must be treated separately, if for no other reason than that of its links to the dominant putative quenching mechanism for Yb and Eu, namely, electron transfer. We should point out that the actual ratio of emission intensity between WEDTA and Sm is 270:l before any addition of acrylamidethere is only a very small Sm signal in any event. Thus, errors in integrating the emission envelopes (“background” subtraction errors, for example), as well as the uncertainty in the relevant Sm quantum yield value, contribute to the lack of precision in the ktOGc-ivcvalue. Close agreement between thedifferent “methods” of finding kdd is obtained if we employ the quantum yield for Sm-EDTA of 0.0029 in D 2 0rather than that obtained for aqueous

+

10336 The Journal of Physical Chemistry, Vol. 97, No. 40, 1993 Sm3+in D2O. Moreover, because electron transfer by Sm could apply to the triplet state as much as to the singlet state, k2’ may not be inconsequential;thus, the assumption that k2/(k2 + k2.) 1 may no longer be so accurate. Nonetheless, the value for kdd of 9 X lo7 s-1 is consistent with the ktot,emisiveof 1 X lo8 s-l. The “indole” to metal distance prediction for Sm is 5.5 A. In general terms, this distance is certainly in the range found by Kemple et al.2 by NMR (cf. also Figure l a geometry). ( 3 )Other Foerster Dipole-Dipole Considerations. The dipole dipole transfer rate is proportional to 3,Rd, and (d). If Rd in the complex between the Ln center and the indole center is nearly the same in every case and somewhere between 5.5 and 6.3 A“, as seems likely, then differences in the value of kdd between the lanthanides should reflect their differences in either 3 values or ( K ~ values. ) For Sm, kdd is -3.3 times that for Tb, while the ratio of 3 values, 3sm/3m,is 2.7. The ratios of 3 values for Dy, Ho, and Er to that of Tb are 3.7,2.9, and 3.3, respectively. But kdd for Dy is -2-3 times the kdd of Tb-Le., much smaller than the 3 ratio. Er and Ho would seem to have much higher ratios of their kdd)Sto kd4mon the basis of their total dynamic quenching (assuming that k k for either Er or Ho is not likely to be greater than -2 X lo* s-l) rate, k,,, i.e., ratios of greater than 7 : l . We can try to rationalize these values from the ( K ~ )factors. The orientation factor in the dipoldipole expression is assumed to be between l / 3 and 4/3 (cf. Theory). Lanthanides have rank 2,4, and 6 unit tensors (U(z),U(4),U(6))describing the degree of spherical harmonic contribution to the strength of their dipole transitions. If most of the intensity could be assigned to lower rank tensor character, the absorption might be presumed to be less isotropic. From this point of view, both Sm and Tb would seem to be quite isotropic. Since ku,mis consistent with a distance of -6 A only if the value of ( ~ 2 ) mis close to l/3, then if we take kdd,Sm to be 9 X lo7s-l (Table III), we find ( K ~ ) would s ~ be -0.4. Dy and Er should be less isotropic than Tb-they have more U(2) character in the near UV (cf. ref 19a,b,c). But their “corrections” to ( K ~ ) T would ~ need to go in opposite directions. The Dy orientation factor would be low (-0.2) and the Er orientation factor high (- 1.9), if we estimate ki, in the same manner as we did above with Dy, though it is possible there are some extra contributions to the intersystem crossing rate induced by the heavier lanthanides from “orbit-spin” coupling (cf. Theory). H o ~ + absorption should also be relatively isotropic,lg and indeed, a (K~)H,, 1.1, with a ki, 1.1 X lo8 s-l, would agree with its observed quenching. It is gratifying that there thus seems to be a 1:1 correspondence between those lanthanides which can possess nonisotropic absorptionsand those lanthanides that requirevalues of ( K ~ )to make their kdd’s consistent with their 3’s (Table I) which are not “isotropic” ( ~ 2 ) values. Furthermore, those lanthanides which should possess isotropic absorptions require ( K ~ values ) in the “isotropic” l / 3 to 4/3 range.

Kirk et al.

TABLE Iv: Electron-Transfer Parameters’

=

-

-

Electron-Transfer Analysis Ejection of an electron from the excited singlet as an effective nonradiative decay pathway for indoles is a widely supported concept.5”52~57 Those readily reduced lanthanides for which a relatively stable aqueous Ln2+species can be observed (Eu, Yb, and Sm) are also more efficient quenchers of WEDTA fluorescence (Table 111) than can be explained by energy transfer and intersystem crossing alone. Eu and Yb, the two most easily reduced lanthanides, quench the indole fluorescence >10 times faster than any other lanthanide. This rate is far too fast to represent enhanced intersystem crossing or dipoldipole energy transfer. For that matter, Eu shows only minor sensitized emission from resonance energy transfer from WEDTA, despite its large quantum yield in D2O. Thus, Eu emission would in fact be very extensive if the WEDTA singlet were solely quenched by either intersystem crossing (because of subsequent effective tripletdependent energy transfer-see discussion below) or dipoledipole

Sm Eu

150 33.7 356 250.1 280 300 111

Tb DY Ho

Er Yb

2.4 X 108 7.56 x 109

2 h 30 -111 h 30 21 1 102 125 145 -34 h 30

-0 -0 -0 -1.1 x l08b 6.6 X lo9

Standard reduction potentials, Fo’,are given from ref 20. AFo’ is calculatedas described in the text. Remainder is defined as koxooll(Table 111) minus kir (1.2 X 1O*/s X [(~)~~/(~)Tb12 (Table I) minus ka (from Table 111-with ‘isotropic” ( K ~ values). ) In

the case of Eu, kdd for Sm is multiplied by the ratio o f f values (Table I) to obtain 7.2 X lo7 s-l for the expected & for Eu. This is the value for Er if we use an ‘isotropic” & and k h as in the above formula. A contribution from lanthanide-orbit/indole-spin coupling which might increase the value of kk, scaling as Z& (see Theory and ref 14) could be significant for the heavier lanthanides; if ( r 2 ) were 1.9 as discussed for Er would be zero. in the text, energy transfer. Yb has no absorptions in the near UV or visible, so energy transfer is automatically out of the question. Apparently, electron transfer to the lanthanide can be responsible for the fastest quenching processes observed in WEDTA. The Marcus formula gives a quadratic dependence of In k vs A&’, and indeed Sm, which differs in redox potential from Yb less than Eu does from Yb (see Table IV), has an appreciably slower rate. This “invertedparabolic” relationshipconfirmswhat one expects in the Marcus theory. Marcus’ formalism should then be appropriate to the WEDTA-Ln system. When we apply the formalism, however, we obtain evidence for the existence of an electron donor state of the indole which is not identical with the excited singlet of the indole (and is unlikely to be the triplet, either). Given the energy of the excited singlet state, “(ind), the electrical potential energy available upon oxidation of the indole, should be -396 kJ/mol (Le., 33 000 cm-l) + 96 kJ/mol, or -300 kJ/mol. But then, many of the other lanthanides, e.g., Dy (+250 kJ) or Er (+300 kJ) should actually quench more strongly than either Eu or Yb since the Marcus Gaussian factor (see Theory), {hEd(ind) + hEd(Ln3+) -11.5 + X)2/4X, is then much smaller for them than for Eu or Yb. We can invert the argument to gain a better idea. If Yb and Eu quench most strongly, they should appear near to and most probably on either side of the “top” of the Marcus rate parabola. Thus, since the reorganization energy X is by all estimates between 30 and 90 kJ/mol, one can find for which values of Eo(ind) the quantity {Eo(ind) 96 kJ hEd(Ln3+) 11.5 A) is equal to zero for some hEo’(Ln3+) between 111 and 33.7 kJ. One can see that Eo(ind) should be between 25 700 and 14 300 cm-l. Eu is slightly more efficient than Yb in quenching, so 33 kJ/mol should be closer to the value needed to make the Marcus factor vanish than 111 kJ/mol. Further, the value for X of -90 kJ/mol may be indicative of more extensive bond rearrangements required of a protein matrix32 accompanying electron transfer than what one might expect to be necessary for a small molecule. Hence, the rather indefinite parameter h may lie closer to 30 kJ than 90 kJ. One would then be able to estimate that &(I”), the energy of the actual electron-donorstate of the indole, which we label I”, must be between 14 500 and 20 500 cm-*. In Table IV, we have explicitly calculated Mo’assuming the value of 20 000 cm-1 for &(I”). We note also how extreme the assumptions must be in order to obtain an energy for I“ which matches even the level of the triplet (24 500 cm-1). The question arises as to whether or not one need explicitly prepare I” via intersystem crossing, etc., from the indole excited singlet state. The answer would appear to be “no”, since the rate constants for electron transfer for Eu and Yb, k e ~are , >30 times the ki, rates of the other lanthanides. The electron transfer does not wait for the triplet state to develop. That is, the rate of

-

-

+

+

+

+

+

The Journal of Physical Chemistry, Vol. 97,No. 40, 1993 10337

Lanthanide Perturbation Indole electron transfer from the “triplet” (which should be the state from which single-electron transfers6 originates), for I”, seems not to be limited by the intersystem crossing rate. What may be happening is that theconnection to thedonor 1”may beestablished through a number of bond-centered “j3” 23*9b.24 integrals from the excited singlet Is’) which perturbatively mix into the zeroth-order state, Is’)O, by

where a is d ( 2 m ( E - B,))/h and B, is the binding energy of an electron at overall energy E, to the vth bond. This interaction is exactly similar to what we considered in the Theory section under the concept of “superexchange”,except that here it applies to electron transfer, while in that section it was applied to energy transfer.s* In this way, the superexchange can break the spin restriction for a single-electron transfer without destroying the singlet status of the donor. Although the exact rate of superexchange electron transfer is hard to estimate, as long as the total number of bonds through which the electron propagates is not too large and the energy denominators stay relatively small, the rate at the top of the parabola (at zero drivingforce) can easily approach that observed in the WEDTA-Eu and WEDTA-Ybcases, Le., -8 X 109s-l.23 Superexchange Configuration Interaction Mechanism. The triplet state has a broad emission, which should give significant spectral overlap to several differing states for most lanthanides (except, notably, Tb). Each of these could conceivably act as pump states for lanthanide emission. As mentioned in the Introduction, the differing spectral and other properties of the various lanthanides allow some distinctions to be made among the efficiencies of differing mechanisms of energy transfer and quenching. For example, their spectral overlaps in the indole triplet emission region give, using the formulas discussed under Theory above, expected values of 1.8 X 109/ez for Dy and 5.4 X lO9/e2 for Sm (assuming R, is -6 A) for their triple-lanthanide through-spaceexchangetransfer rate. The normal through-space exchange mechanism is probably too slow in water (t 80) to accomplish the observed “extra”, non-dipoledipole, emissive transfer. Further, the above values would give Sm the largest, Dy the next largest, and Tb the least additional energy transfer. In fact, the observed relation is Tb = 5.0 X 107, Sm = 1.0 X 107, and Dy = 5 X 106s-l. In the through-bond exchangemechanism, which we have also called configuration interaction, we are no longer strictly bound by the spectral distribution of the original indole triple itself, sincewe are now concerned with ligand orbitals mixed into the triplet. That would mean, for instance, that the distribution would be shifted to lower energies, if the ligand orbital energies were lower lying. The rate of the superexchangemechanism with lanthanides is, however, still bounded by the rate of preparing the triplet state, since the Wigner-Pauli spin rules still operate. Hence, the effective rate of this superexchange transfer, ktr,s~, would be ksekh/(kss + k k ) , ~ S being E a rate similar in form to (4) (containing an additional term like e-“€,cf. Theory), except that the distance would be some nearest distance to the ligand (-2 A) and the value of e2 would probably be much smaller than 80. If responsible for the extra excitation transfer observed, the through-bond exchange mechanism would seem to be highly efficient in Tb SD4. Yet, this mechanism probably vanishes for Dy 4F9/z ( U 2 )= 0) and is also small for Sm 4 1 9 p (Le., it is -‘/4 of the squared product of the U(2) matrix element and the factor 9 of Table I for Tb 5D4) which is, like the latter terms,s9 4F9/2 of Dy and 5D4 of Tb, near 21 000 cm-l. For the other terms listed in Table I, e.g., 4G7/~and 4F5/~for Sm, or 4115/2 and 4G11/~for Dy, though they possess nonzero U(2) matrix elements, the superexchangemechanism nonethelessappears not to contribute much to the overall emissivetransfer rate-the k d d rate dominates the transfer.

-

An important point, which could explain the relative inefficiency of the superexchange mechanism to generate extra (non-dipoledipole) energy transfer in the Dy and Sm cases, is that the Xka coupling coefficients (see Appendix A) to C1 symmetry are much smaller than those to Cz. This could be the case if the ligand site was very strongly of C2 symmetry; i.e., the environmental interaction, ( 6 ) and (Al), has to be weak to a symmetry which is not well represented in the density of states. Our branching to 10) (the scalar irrep) of C2, SO3 3 0 3 D4 3 C4 3 CZ, vanishes for all odd-electron configurations with k = 2. These configurations can only connect via 11) of C2 to the scalar irrep of C1; consequently, the values in Table I for the odd-electron lanthanides represent this branching. Since matrix elements are identically zero unless the product of symmetry irreps of the states involved connect to the irrep of the operator, which in this case is IO), we have something in the nature of a “selectionrule” for lanthanides in a strong C2 ligand field. Since there is evidently some emissive transfer to Dy and Sm beyond pure dipoldipole transfer from the indole singlet (manifested in, e.g., nonidentical slopes of the Stern-Volmer plots), this transfer pathway is not exclusively to C2, and indeed, the local symmetry is not exact. It is an interesting question as to whether or not the energytransfer donor state 1’, involved in this mechanism and which is supposed to be established by through-bond superexchange, is not somehow related to the hypothetical electron-transfer donor state I”, established as we argue, by a similar process from the excited singlet.

Summary and Conclusions We observed extensive quenching and excitation transfer upon lanthanide binding in WEDTA-Ln complexes. There was a distinction in the nature of the metal luminescence quenching observed with oxygen and acrylamide on the one hand and iodide on the other. This differencewas not apparent in the fluorescence quenching of the indole in the WEDTA-Ln complex. We presented an analytic framework which permitted us to separate various contributions to the WEDTA quenching induced by the various lanthanides, as well as accounting for the different modes of metal luminescence quenching we observed. This analytic framework enables us to draw certain conclusions concerning the nature of iodole-lanthanide interactions, at least in WEDTALn: 1. Energy transfer to lanthanides is not limited to the dipoledipole process. The additional process seems to originate from other than the excited singlet of indole and, because of its oxygen sensitivity, we suppose that this other excited state has a nonzero spin multiplicity (e.g., triplet). We analyzed the efficiency of this second process from the point of view of both a throughspace exchange and through-bond superexchange mechanism. The new contributioncannot be ordinary through-spaceexchange transfer, since (1) the efficiency of the transfer was too large to be explained by through-space exchange and (2) the observed efficiency for luminescentlanthanides was in the order Tb >> Sm > Dy, whereas, because of much better spectral overlaps of Sm and Dy absorption with the emission of the indole triplet, the ordering for the through-space mechanism would be Sm > Dy >> Tb. 2. There are distinctions between the lanthanides in the extent to which the dipoledipole-transfer pathway dominates the superexchange transfer rate. For Dy, dipoldipole transfer accounts for -90% of the whole transfer, and similarly for Sm, Tb, on the other hand, obtains more than 60% of its observed transfer efficiency from this second process. The “forbiddenness” of this pathway for Sm and Dy may lie in a selection rule against odd-electron configurationsparticipating in exchangeinteractions with ligands occurring in “even”, Dz, Cz, etc., symmetry environments. 3. The best fit for electron-transfer parameters suggested the occurrenceof some energeticallylower-lying state than the indole

10338 The Journal of Physical Chemistry, Vol. 97,No. 40, 1993 triplet. Such a state would function hereas theeffective electrondonor state. The original excited singlet state is not as effective as the electron donor. The lower-lying electron-donor state did not need to be “prepared” from a manifest triplet species. Hence, the through-bond superexchange energy-transfer rate is limited by the intersystem crossing rate, whereas the electron transfer is evidently not. The exact rate of the energy transfer depends strongly on the actual bonds and bond paths through which the transferring state is prepared,which determinesthe region of donor/acceptor energy overlap that can critically affect which lanthanides are susceptible to the transfer. The rate of superexchange-mediated electrontransfer quenchingis partially determined by the electrochemical free energy AFo’ and the reorganization energy, which similarly depend on the relevant bond paths through which the electron transfer develops. Where bonds differ greatly in their electron binding energies, the energy denominators in (8) become considerable, and the superexchange less readily “propagates”. Since very different, and usually longer, bond paths are involved in protein systems, where occupancy of a cation-binding site by a lanthanide usually affords weaker sensitized luminescence from, and quenchingof, trp fluorescence than we observe with WEDTA, results on WEDTA may not be easily generalized to results with particular tryptophyl residues of protein. It is interesting to note that if the distance had been a bit closer than the -6A we obtained, the other terms in the Hamiltonian for an extended dipole-dipole interaction, unlike the point-dipole approximation of (l), would have been operative. It is conceivable that in some protein systems such very short distances are indeed involved and that a substantially different extended dipole formalism9 might need to be invoked in these cases.

Acknowledgment. We thank Prof. C. Meares for our initial samples of WEDTA. Mr. Peter Callahan of our laboratory was most helpful in the preparation of figures and performing oxygen quenching experiments. We thank Drs. P. Illich, S.Sedarous, and 3. Hedstrom for help in several measurements. Supported by NIH Grant GM 34847-07. Appendix A We consider here the superexchange/configurationinteraction, namely, that in (6):

d = ( H e n ” ) = Z,,te2(xen~\k(SU)11/r,~xe”v9(S’L’J3) (6) as the effect of ligands in immediate contact with the lanthanide (i.e., carboxylate) upon the lanthanide in terms of allowed vs forbidden angular momentum couplingsfor its given ground and excited states. Since we are mixing a state carried by an “f“ electron with that carried by a “p” electron, the expansion of the Coulombinteraction for each electron in terms of spherical tensor operators (cf. Butler17) requires the nonvanishing of the 3j symbol

(; 0“ ;) for a p electron and

(:

0“ 3

for an f electron. Hence k (the rank of the surviving tensor operators in the expansion) is either 2 or 4. But for k = 4, the ligand “induced”polarizationis small-that is, “hypersensitivity” is limited to cases where AJ S 2 (see Juddls), where the Uk unit tensor operator16with rank k = 2 is nonzero. In addition, the local symmetry of the lanthanide in the EDTA-like moiety with 3 waters bound has at most C%symmetry. If we look at all the group theoretical parameters which depend only on the particular lanthanide term, and lump the others parameters which either are constant for all lanthanides or depend only on WEDTA and

Kirk et al. hence are nearly constant over a series of 1anthanideWEDTA complexes, into Xka coupling coefficients, we find

He, = Zk,(2k

+ 1)’/’UkaP

(All where now the matrix element is shown in Butler17 (astands for all extra quantum numbers, representing e.g. configurational quantum numbers that can be mixed by the ligand field): (aSLJlUkla’S’L’J’) = (aSL)Ukla’SL’)x

where the reduced matrix elements (dLJUkla’SZ’)might be expected to be on the order of those tabulated by Carnal1 et al.’”.b.cfor aqueous lanthanidessince they change little in differing environments (ionic crystals, solution, etc.). We employ a vector-couplingschemefor the interactingangular momenta of the lanthanide and ligand electrons. That is, the acceptable values of S,, are given by the Wigner-Pauli rule for SLn + sligand + &at = sln + slipnd, SLn + sligand - 1, bln - Sligandl. Since a ligand singlet state interacts with the excited lanthanide, and excited bands of interest in the near UV spectral region of the lanthanide have A S = 1 from the ground state, whereas a ligand triplet interacts with the lanthanide ground state, while a nonvanishing exchange interaction requires Sbt for the two interacting (product) states to be the same, it so happens that there is only one allowed value of Statfor each lanthanide. Continuing in the same fashion, we construct the possible values Jtat = bat+ Stat, with the restriction that in the two-electron operator case such as in (Al), L can take only odd values for integral Statvalues, while taking only even values for half-integral spins (see ref 10). We have invoked the groupbranching chain SO3 3 0 3 D4 3 Cq 3 C2,whose irrep labels are J, A, 1,Y, and t, respectively, and the sum includes branching multiplicities which are implicitly contained in the term a. We calculated the coupling of the U(2) operator to the scalar irrep 0 of C2 (eventually Cl),Le., that of the Coulombic_H_amiltonian,by means of the branchings 122000), 122220),and (21220)for even-electron lanthanideconfigurations and by 1211110) for odd-electronconfigurations. The Xh depend on the branchings and the ligand field as parameters, and inasmuch as the differing lanthanides induce slightly different ligand field responses, they may also be weakly lanthanide dependent.

Appendix B We consider the spin-other orbit interaction for lanthanides onto the indole. The spin of the lanthanide is constant in this process, as well as the orbital angular momenta, but the indole “borrows”the excess spin of the lanthanide and is “flipped”thereby into a triplet state. We write the compound (spin) state as Sto, = SLn + Shdr ,..b~~- sidl, as above, and sum the following (squared) matrix elements over all allowed S, terms, to obtain a term proportional to the intersystem crossing rate constants for the lanthanide series:21

(aSLJls*I~aS’U) =

and thus

where tabulated values of the lanthanidespin-orbit coupling scalar

The Journal of Physical Chemistry, Vol. 97, No. 40, 1993 10339

Lanthanide Perturbation Indole coefficient 5 also appear in Table This coefficient may or may not be determining for the value o f t which should be used in the WEDTA-Ln complex.

Appendix C We present here the analytical framework we employed in our treatment of both lanthanide and indole luminescencequenching data. Our own experimental results motivated both the form of the analysisitself and the derivationsgiven. We take a description of quenching and energy transfer based on the solution of rate equations, instead of efficiencies,because we believe the quenching we observed is dynamical. If we solve the differential equations for the loss of I* and production and decay of I’

dZ’/dt = [k2

+ k,, + Qk‘,]Z’+

klZ*

(Clb)

the steady-state “yield” of excited metal ions (M*) is

Accordingly, the steady-stateintensities of I* and M* are kl,JZ*( 1 ) dr and qM(M*), respectively, with qM the quantum yield of metal ion luminescence. This formalismassumes that the creation of the state I* (from the radiation field) and of state M* (from transfer processes) is much faster than the decay of these states. We follow a pulse of light entering the system and watch the instantaneous production of I* (i,e., the t = 0 concentration of I* is I*O) and its exponential decay, the buildup and decay of 1’, and the buildup of M*, which only slowly decays. With the assumptions made above, we obtain ~ * ( t =) I*Oe-(k“+kmi+kdd+Q@

(C2a)

Thus, the steady-state luminescence of the metal as a function of acrylamide concentration, 9(M,Q), of a Stern-Volmer plot is given by 1/3(M,Q) = ( 1 / q M z * o ) ( ~ 2 ( Q ) ~ l ( Q ) / (k1k2 kddY,(Q))) ( c 3 ) Wenote here thequadraticdependence at small Q which becomes a linear dependence when kddYZ(Q) is large relative to klkz. Similarly for the fluorescence quenching l/S(WEDTA,Q) = (l/z*o)Y1(Q)/kmd (C4) We derived two methods for this type of analysisto recover values for kdd, the rate constant of greatest interest in typical energytransfer measurements because of its R-6 dependence. Method I. The ratio of slopes of [1/9(M,Q) us Q] to [l/S(WEDTA,Q) us Q], at high Q (linear range for the metal luminescence), yields [slope ratio] = krad/q&d

(ref 61)

MethodII. The ratioof Stern-Volmer slopes [3(WEDTA,O)/ S(WEDTA,Q) us Q] to [3(M,0)/9(M,Q) us Q], at high Q, yields [slope ratio] = 1 + [klk,/kdd(k,

+ k2,)]

(ref 62)

Method 11, based on the Stern-Volmer slope ratio, offers internal

normalization of fluorescenceintensities, whereas method I uses “total” intensities, which can be subject to backgroundsubtraction errors when, as is the case with Sm, the metal and WEDTA have very different luminescence intensities. Hence, method I1 is probably more reliable than method I. Note Added in Proof. Recently, Martini et al.,63 investigating protein phosphorescence and Tb luminescence quenching by 0 2 in elastase, concluded that most of the energy transfer to Tb in this system originates from the lowest triplet of a tryptophan by a non-dipoledipole process.

References and Notes (1) Abusaleh, A.; Meares, C. F. Photochem. Photobiol. 1984,39 (a), 763-769. (2) Kemple, M. D.; Ray, B. D.; Lipkowitz, K. B.; Prendergast, F.; Nageswara Rao, B. D. J. Am. Chem. SOC.1988,110, 8275-8282. (3) Richardson, F. Chem. Reu. 1982,82,541-552. (4) (a) Horrocks,W. Dew. Adu. Inorg. Biochem. 1982,4,201-261.(b) Horrocks, W. Dew.; Sudnick, D. R. Acc. Chem. Res. 1981,24, 384392. ( 5 ) Luk. C. K. Biochemistrv 1971. 10. 2838-2843. (6) Birnbaum, E. R.; Gom&, J. E.; Darnall, D. W. J. Am. Chem. Soc. 1970,92,5287-5288. (7) (a) Martin, R. B.; Richardson, F. S . Q. Rev. Biophys. 1979,12(2), 181-209. (bl DeJersev. J.: Jeffers Morlev. P.: Martin. R. B. Bioohvs. Chem. 1981,23, 233-243. (E) Martin, R. B. 1; Calcium in-Biology;Spko, T. G., Ed.; Wiley: New York, 1983. (8) Chen, R. In Biochemical Fluorescence Concepts; Chen, R. F., Ed.; Marcel Dekker: New York, 1976;pp 573606. (9) Dexter, D. L. J . Chem. Phys. 1953, 21 (9,836850. (10) Landau, L. D.; Lifschitz, E. M. Quantum Mechanics, 2nd revised ed.;Pergamon: Oxford, 1954. (1 1) Foerster, T. In Modern Quantum Chemistry; Sinanoglu, O., Ed.; Academic: New York, 1964. (12) Judd, B. R. Phys. Reu. 1962,227 (3), 750-761. (13) Matsen, F. A.; Klein, D. J. Adu. Photochem. 1969, 1-55. (14) Condon, E.U.; Shortley, G. H. Theory of Atomic Spectra, 2nd ed.; Cambridge University Press: Cambridge, 1951. (15) Gray, C. G. Can. J. Phys. 1968,46,135-139. (16) Judd, B. R. J . Chem. Phys. 1979,70 (ll),4830-4833. (17) Butler, P. H.Point Group Symmetry Applications; Plenum: New York, 1981. (18) Judd, B. R. J . Chem. Phys. 1966,44 (2),839-840. (19) (a) Carnall, W. T.; Fields, P. R.; Wybourne, B. G. J. Chern. Phys. 1965,42,1797-1803. (b) Carnall, W. T.; Fields, P. R.; Rajnak, K.J. Chem. Phys. 1968,49,4412-4424. (c) Ibid. 4424,4443,4447 (set of three). (20) Carnall, W. T.In Handbook on the Physics and Chemistry of the Rare Earths; Gschneider, K. A., Eyring, L., Eds.;North Holland: Amsterdam, 1979;Vol. 3. (21) Judd, B. R. Operator Techniques in Atomic Spectroscopy; McGraw-Hill: New York, 1963. (22) Abragam, A.; Bleaney, B. Electron Paramagnetic Resonance of Transition Ions; Oxford University: Oxford, 1970. (23) (a) Beratan, D.; Hopfield, J. J. Am. Chem. SOC.1984,104,1584 1594. (b) Onuchic, J.; Beratan, D. J . Am. Chem.Soc. 1987,109,6771-6778. (24) Jortner, J.; Bixon, M. In ProteinStructure, Molecular and Electronic Reactivity; Austin, R., Buhks, E., DeVault, D., Dutton, P., Frauenfelder, H., Gol’danski, V., Eds.; Springer-Verlag: Berlin, 1987,pp 277-308;cJ other articles therein. (25) Marcus, R. A. J. Chem. Phys. 1965,43,679-701. (26) Marcus, R. A. J . Chem. Phys. 1965,43, 1261-1274. (27) Bockris, J. OM.; Reddy, A. K. Modern Electrochemistry; Plenum: New York, 1970; pp 263-266. (28) DiFelippis, M. R.;Murthy, C. P.; Broitman, F.; Weintraub, D.; Faraggi, M.; Klappen, M. H. J . Phys. Chem. 1991, 95, 3416-3419. (29) Marcus, R. A. J . Phys. Chem. 1989, 93 (8),3078-3086. (30) Marcus, R. A. J . Chem. Phys. 1984,82 (lo), 4494-4499. (31) Newton,M. D.;Sutin,N. Ann. Reu.Phys. Chem. 1984,35,437-480. (32) Petrich, J. W.; Longworth, J. W.; Fleming, G. R. Biochemistry 1987, 26, 271 1-2722. (33) Ilich, P.; Prendergast, F. Photochem. Phorobiol. 1991,53,445453. (34) Fedderson, B.; Piston, D.; Gratton, E. Reu. Sci. Instrum. 1989,60, 9-13. (35) Beechem, J.; Gratton, E.; Mantulin, W. GLOBALS UNLIMITED Laboratory for Fluorescence Dynamics, Dept. of Physics, Univ. of Illinois, 1990. (36) Lee, B. Ph.D. Thesis, Cornell University, Ithaca, New York, 1967. (37) Marriott, G.; Kirk, W. R.; Johnson, N.; Weber, K. Biochemistry 1990,29,70047011. (38) Hogue, C.; Macmanus, J.; Banville, D.; Szabo, A. J . Biol. Chem. 1992, 267, 13340-13347. (39) Freeman, A. J.; Watson, R. Phys. Reu. 1962,127,2058-2073. (40) Stein, G.; Wuerzburg, A. J . Chem. Phys. 1978,62 (1). 208-213. (41) Horrocks, W. Dew.; Sudnick, D. R. J . Am. Chem. SOC.1979,101 (2), 334340. (42) Freeman, J. J.; Crosby, G. A.; Lawson, R. E. J. Mol. Specrrosc. 1964,13, 399406.

Kirk et al.

10340 The Journal of Physical Chemistry, Vol. 97, No. 40, 1993 (43) Fong, F. K.In Handbook on the Physics and Chemistry of the Rare Earths; Gschneider, K.A., Eyring, . - L., Eds.; North Holland: Amsterdam, 1979; Vol. 4, pp 317-339. (44) Kirk, W. R.; Amzel, L. M. Biochem. Biophys. Acta 1987,916,304312. (45) Dawson, W. R.; Kropp, J. L.; Windsor, M. W. J . Chem. Phys. 1966, 45, 2410-2418. (46) Kirk, W. R. Ph.D. Thesis, Johns Hopkins University, Sch. Med., Baltimore, MD, 1986. (47) Heller, A. J. Am. Chem. SOC.1966, 2058-2059. (48) Ware, W. In Time Resolved Fluorescence Spectroscopy in Biochemistry and Biology; Cundall, R., Dale, R., Eds.; NATO AS1 Series A; Plenum: New York, 1983; Vol. 69, pp 341-362. (49) Brand, L.; Witholt, P. Method in Enzymology 1967, XI,807-813. (50) (a) Szabo,A,; Rayner, D. J . Am. Chem. SOC.1980,102, 554-561. (b) Beddard, G. S. In Time Resolved Fluorescence Spectroscopy in Biochemistry & Biology; Cundall, R., Dale, R., Eds.; NATO AS1 Series A; Plenum: New York, 1983; Vol. 69. Compare also articles by Lopez-Delgado and by Ross and Brand therein. (51) Meech, S.; Lee, 5.;Brant, G. Chem. Phys. 1983,80, 317-325. (52) Gudgin-Templeton, E.; Ware, W. J . Phys. Chem. 1984, 88, 46264632. (53) Saito, I.; Sugiyama, H.; Yamamato, A.; Muramatsu, S.; Matsuura, T. J . Am. Chem. SOC.1984, 106, 4286-4287. (54) Colucci, W.; Tilstra, L.; Sattler, M.; Fronczek, F.; Barkley, M. J . Am. Chem. SOC.1990,112, 9182-9190.

(55) Vekshin,N.;Vincent,M.;Gallay, J. Chem.Phys.Lett. 1992,199(3), 459-464. (56) Michl, J. Acc. Chem. Res. 1990, 23 (5), 127-128. (57) Eftink, M.; Jia, Y.-W.; Graves, D.; Wiczk, W.; Gryczynski, I.; Lakowicz, J. Photochem. Photobiol. 1989, 49 (a), 725-729. (58) Specifically, the mixing of states described by (9) would represent long-range tunneling of a single electron to the "i" ligand sites (e.g. carboxylates), generating in the process a 'biradicaloid" configuration. (59) The word "term* used here (as under Theory) refers to spectroscopic nomenclature: W+lL,. (60) If P ( t ) = Pozaflcll while I' decays monoexponentially, then we have instead (M*)-I = (1/I*0)[Zal(kan2 klfk2)/~1,(Q)~~(Q)l-~. (61) In the case of multiexponential deca of I*, the same ratio is ( ~ ~ I ~ ~ ~ ~ / ~ H ) [ ~ ~ I ~ ~ ~ Y I ~ ~ - ~ ~ ~ ~ ~ ~ J This ~ ~ J / Y I ( I / ( [ simplifies considerably if the various decay components have the same spectral distribution, implying there is no manifest physical-chemical distinction between them. Then it is reasonable to assume that all the k ~ the. kw,and the k , are ~ equal, and the slope ratio formula reduces to k d / q y k a as above. (62) For the case of multiexponential decays, one obtains for the Stem, A= Volmer slo ratio at high Q the following: ( A B / G ) / ( D E / E ? ) where Zadk d i y 2 0) + kiikz)/(Yii o)Yz(o), B h k q j k w / 112, c h k d d J Y f r , D &$+jkqj/Yir(O), E = a&jkq,i/Yi?t and F = zkrpf/Yif. Under the same assumptions as madeunder the last footnote, oneobtains 1 &x,Tf'kIfk2/ kd(k2 + k z , ) / ( ~ ) I" 1 + (~ki)Ok2/(ka(k2+ k z , ) ( ~ ) O ) . (63) Martini, J.-L.; Tetreau, C.; Pochon, F.; Tourbez, H.; Lentz, J.-M.; Lavalette, D. Eur. J. Biochem. 1993, 211, 461-13.

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