A new NMR probe for intermolecular interactions: Relaxation-allowed multiple-quantum transitions in methyl groups

JOLJRNALOFMAGNETICRESONANCE81,520-529

(1989)

A New NMR Probe for Intermolecular Interactions: RelaxationAllowed Multiple-Quantum Transitions in Methyl Groups NORBERT

MILLER

Institut fir Chemie, Johannes Kepler Universitiit, Altenbergerstrasse 69, A-4040 Linz, Austria Received April 18,1988 Coherence-transfer pathways involving multiplequantum coherences in systems of degenerate spins are accessible through multiexponential relaxation. This behavior, for which nonextreme narrowing conditions are a prerequisite, is used to monitor intermolecular interactions. While it is possible in principle to extract mobility information from lineshapes in one- and two-dimensional multiplequantum-filtered and multiplequanturn spectra, it is sufficient to record the initial slopes of the buildup curves of forbidden methyl signals in these spectra to gain semiquantitative insights into the motional restrio tions involved with intermolecular complex formation. This is demonstrated by way of two experimental examples: the interaction of lysozyme and its inhibitor N-acetylglucosamine and the homoassociation of bilirubin-IXa-dimethylester. o 1989 Academic Press, Inc.

In a number of recent papers (l-8), new phenomena in multiple-quantum and multiple-quantum-filtered NMR were described and analyzed that find their manifestation in the occurrence of additional signals which had been considered forbidden according to earlier theoretical approaches ( 9). Originally apparent violations of the multiple-quantum filter selection rules have been found for AX3 spin systems in large molecules ( I, 2). Detailed theoretical analysis ( 7) and practical examples (4, 5, IO), however, indicate that this behavior is a general property of all spin systems with degenerate transitions, if the extreme narrowing condition is not fulfilled. It has been shown that the multi-Lorentzian peak shape of these signals is determined by eigenvalues of the Redfield relaxation matrix and can in principle be used to determine rotational correlation times (5- 7). The spectral density experienced by a particular group in a molecular complex differs from that present in the unbound form. This is caused not only by the change in molecular weight and shape slowing down overall tumbling but also through a reduction of the internal mobility of the group; i.e., the wobbling motion of the methyl group may be slowed down and restricted to a smaller cone. Based on this reasoning, the use of “forbidden” multiple-quantum methyl peaks as indicators for intermolecular interactions is advanced in the present paper. METHODS

Multiexponential relaxation effects in multiplequantum-filtered spectra were first observed in three- and four-quantum-filtered two-dimensional homonuclear correlation spectroscopy ( 3QF-COSY and 4QF-COSY) ( I ) . More detailed insight into the 0022-2364189 $3.00 Copyright Q 1989 by Academic Fress, Inc. All rigbt.3 of reproduction in any form nzserved.

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relaxationbehaviorof methyl signalscanbe obtainedthroughthe recentlydeveloped MERCY method (multiexponential relaxation spectroscopy) (4). In this twwdimensional experiment the characteristic multi-Lorentzian peak shapes along the o1 and wz axes are the Fourier transforms of the multiexponential longitudinal and transverse relaxation functions, respectively. For methyl singlets, which are the primary objects of interest here, only diagonal peaks are observed in proton 2D spectra. Therefore frequency separation in the wl dimension is not necessary and one-dimensional spectra are sufficient for a qualitative proof of the existence of “forbidden” multiple-quantum excitation pathways and-as will be shown below-also for a semiquantitative estimate of motional restrictions. Therefore experiments without net chemical-shift precession during the evolution time (sequences a and b in Fig. 1) are used. As usual, cycles of the phase 8 of the excitation pulses are applied while alternating the receiver phase to select a particular order of multiple-quantum coherence during the A period ( II ). The coherence-transfer pathways shown in Eq. [l] and Eq. [ 21 for the pulse sequences a and b in Fig. 1, respectively,

T,,oTLO-

xl2

7r

Tt,,, - Tt ,o -

7

Tw -

7 7-3.0

-

r/2

-

T3.+3

xl2 7’3.23

-

*I2

Tx,+I

42 T3.k

1,

Ill 14

serve to isolate particular ranks of the tensor terms via conversion into multiplequantum coherence. Thereby one makes use of the fact that the rank of a particular tensor term can never be lower than the absolute value of its coherence level. Choosing threequantum coherence by phase cycling therefore allows only third-rank terms to survive the multiplequantum filter, while a two-quantum filter allows second- and third-rank tensor terms to pass.

a

FIG. 1. Pulse sequences for multiplequantum-filtered cycled as explained in the text.

T2 (a) and r, (b) experiments. The phase Cpis

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The pulse sequences of these experiments are similar to those used by Jaccard et al. (5) for multiple-quantum spectroscopy of quadrupolar nuclei. However, while in Ref. (5) the wr dimension is used to separate different orders of multiple-quantum coherences by applying time-proportional phase incrementation, we select only threequantum coherence and use the evolution period to monitor the buildup and decay of third-rank tensor terms in the one-quantum density matrix. Sequence a in Fig. 1 serves to investigate multiexponential transverse relaxation and may be regarded as a multiplequantum-filtered T2-experiment. Kay and Prestegard (6) have used a similar two-quantum-filtered variant of the Carr-Purcell pulse sequence to measure cross-correlation effects in micellar solutions. Three-quantum-filtered experiments, however, offer some advantage as will be explained below. Sequence b in Fig. 1, a one-dimensional version of MERCY (4), may likewise be regarded as a multiple-quantum-filtered variant of the inversion-recovery T, experiment. For an isolated methyl group the time dependence of the three-quantum-titered T2 and T, experiments can be calculated using the formalism and notation of Ref. (7)tobe

and =I

Sp=3(7,

t2)

=

5v-z - 16 AMf~p,‘( 7)f$(

t,)e-‘*l2.

The numerical factors stem from the Wigner matrix rotation elements for pulse angles of rr/ 2. SOand AiU denote the amplitude of the initial transverse magnetization and longitudinal polarization, respectively. The relaxation functions f 2; describe the conversion of tensor operators of different ranks r and r’ into each other while the coherence order p is conserved. The other symbols have their usual meanings. Applying a two-quantum filter instead of a three-quantum filter results in superposition of second- and third-rank tensor terms in the T2 experiment:

As this introduces additional complexity, the three-quantum-filtered version of this experiment is preferred. In the two-quantum-filtered Tl experiment, however, the relevant third-rank Wigner rotation element for the first coherence transfer f& vanishes for a flip angle of z/2. So only the second-rank term is conserved:

S&(7, t2) = aM[~f~P~(~)fl’l(t,)]e-‘*‘2.

WI

It has been shown ( 4- 7) that the relaxation functions fif2p/ and fc2:: vanish when only dipolar cross relaxation of the methyl protons and external random field interactions are present. So the 2QF T, experiment can serve as an important test for the justifica-

MULTIPLE-QUANTUM

tion of the assumption described by

TRANSlTIONS

of biexponential

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relaxation. These relaxation functions are

and

The (negative) decay constants Rz’ are the eigenvalues of the RedGeld relaxation matrix for coherence order p . As they depend on the spectral density functions correlation times can in principle be determined, in cases where an adequate model for the molecular motions is available (see Refs. (5,6). Two-dimensional Fourier transformations of the right-hand sides of Eqs. [ 31 to [ 61, using T as the evolution period, yield spectra with signals located at (0, = 0, w2 = Q) exhibiting multi-Lorentzian lineshapes in both dimensions. The line&ape functions in the wI dimension depend on the longitudinal and transverse r&u&on functions in the Ti and T2 experiments, respectively. Of course only transverse relaxation functions determine the lineshapes along the 02 dimension in both experiments. In practice, however, a full two-dimensional experiment is often too time consuming. Fewer experiments together with simplified data evaluation in the time domain r after Fourier transforming along the t2 axis yield adequate results for comparative studies. The multiexponential relaxation functions can also be directly anatyzed in the time domain after Fourier transforming only in the w2 dimension. This offers some advantages: Erroneous data points can easily be recognized and eliminated before a curve fit; curve-fitting programs for multiexponential functions are more readily available than for multi-Lorentzian, ones. As will be shown below, a simplified evaluation using the initial slopes only is possible. Usually a smaller number ofdata points are needed for this kind of analysis. The initial slopes of the relaxation functions as calculated by a Taylor expansion

t101 and

represent differences of eigenvalues of the Redfield relaxation matrix, which vanish under extreme narrowing conditions. If slow isotropic overall tumbling of the observed species and fast rotation about the methyl CJ axis are assumed, these di@erences are proportional to differences of spectral-density functions, R4

(‘) - Rio’ oc J(w) - J(2w)

1121

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and R!” -R:”

or J(2w) - J(0).

[I31 Using J(n) = 27,( 1 + (~$)*)-’ the differences [J(W) - 4 ~w)]/T~ and [J( 2~) - J(0)]/rc are plotted as functions of war, in Fig. 2. From this it is evident that in the 3QF T, experiment one always gets weaker signals than in the 3QF T2 experiment. The longitudinal relaxation method is only useful in a range between the extreme narrowing and wo7, - 1. Its signal amplitudes vanish as wo7, approaches infinity. For the general case of anisotropic motions this dependence is not very different. The only advantage of the 3QF T, experiment is the fact that no three-quantum coherence can be excited by conventional (i.e., coupling) pathways, thus eliminating unwanted background signals. This, however, cannot compensate for the low signal-to-noise ratio in the cases so far investigated. Generally, without simplifying assumptions about the motional behavior, slower overall tumbling and restriction of the wobbling motion of the methyl C3 axis (as expressed by a larger anisotropy factor) always result in steeper initial slopes of the buildup curves of forbidden multiple-quantum peaks. For comparative studies of intermolecular interactions, these slopes, which can be obtained from a relatively small number of different 7 values, are a valuable source of information on overall and local mobility. A similar goal (although not restricted to methyl groups) can be achieved by a more time-consuming procedure involving measuring the temperature dependence of 13C longitudinal relaxation times, as, for example, in Ref. (12). For different methyl groups attached to the same molecular complex even the intensities of forbidden peaks recorded at a single sufficiently short excitation time (i.e., shorter than the relaxation time of the broadest peak component) can serve as a first check on relative mobilities. EXPERIMENTAL

EXAMPLES

To demonstrate the application of methods based on multiexponential relaxation for studying intermolecular interactions the complex formation of lysozyme with its inhibitor N-acetylglucosamine (NAG) and the homoassociation of bilirubin-IXadimethylester (BRE) were chosen. In all cases investigated, no methyl singlets apart a

FIG. 2. Dependence of peak intensities in multiplequantum-filtered T, experiments { [ 4 2~) - J( 0 ) ] / 7, } (a) and in multiplcquantum-liltered T, experiments { [J(w) - .J( 20)] /T= } (b ) on wr, .

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from subtraction artifacts were observed in the 2QF TI experiments. So the assumption of biexponential behavior is valid throughout, even for the RRE solutiuns, which fall into the intermediate range between the extreme narrowing and slow motion limits. Upon addition of one equivalent of NAG to a solution of lysozyme in ‘Hz0 at a p*H of 3.8 at a temperature of 3 13 K, one observes the appearance of two methyl peaks upfield from that found for unbound NAG, which as a small molecule is in the extreme narrowing limit (Fig. 3). They stem from the IV-acetyl groups of the CYand B forms of NAG which compete for the same enzyme site. Earlier investigations have

I

d

2.4

2.2

2.0 PPm

1.8

1.6

FIG. 3. Part of the conventional NMR spectrum of lysozyme ( 8 mmol liter-‘) (a); same region of the conventional NMR spectrum of N-acetylglucosamine (b); same region of the conventional NMR apectrum of an equimolar mixture of lysozyme and N-acet&l ucosamine(32scans)(c);sam;erelkiaada31;tF ~,spectrum(~ = 35 ms, 144Oscans, 10srepe&tioninterval)ofthismixture(d).NowimdowkmWns have been applied to any spectrum shown in this paper. All samples were degassed by bubbling argoa for 90 min.

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shown that the two forms have different binding constants ( 13). The methyl signals of bound NAG can be observed in 3QF Tz experiments (Fig. 3d) with typical biLorentzian lineshapes. Under identical conditions the methyl singlet of free NAG is strongly suppressed. In Fig. 4 the peak heights of the Q!and /I methyl signals are plotted as functions of the excitation time T in the 3QF T2 experiment. The initial slope of the curve obtained for the peak at lower frequency is approximately only half of that for the other peak. This clearly indicates that the cy-anomer is not only more tightly bound in terms of a thermodynamic binding constant, but that it also undergoes a more rigorous mobility restriction in its interaction with lysozyme. As a second example solutions of BRE in polar and nonpolar solvents were investigated at different concentrations. Dilute solutions in the nonpolar solvent C2HC13 as well as solutions in the polar solvent C2H302H are monomolecular. At higher concentrations, however, strong association occurs in nonpolar solvents ( 14). This process can be investigated by the methods discussed here, because at the observation frequency of 360 MHz the molecular weight change from 6 12 to 1224 associated with dimerization implies leaving the extreme narrowing limit. No methyl multiplequantum peaks are observed for the monomeric solutions, while the presence of dimers and possibly higher oligomers (IS) in concentrated C2HC13 solution causes the occurrence of these characteristic signals. A representative one-dimensional threequantum-filtered spectrum of a concentrated solution (0.30 mol liter-‘) of BRE in this solvent is shown in Fig. 5 together with a conventional spectrum of the methyl region. The initial slopes of the buildup curves in the 3QF T2experiments of the four peaks stemming from the methyl groups directly attached to the pyrrolic rings do not exhibit significant differences. From this fact one may conclude that in the homoassociate all four methyl groups have similar mobility. The concentration dependence of the averages over the initial slopes of the four methyl-group signals is shown in Fig. 6. In spite of the inaccuracies stemming from instrumental instabilities, the slopes

l3c. 4. Dependence of the (Yand @Aketylglucosamine methyl signals of Fig. 3d on the excitation time ‘Tof the 3QF T2 experiment. The peak heights are measured relative to those obtained in a conventional NMR spectrum. The straight lines represent the initial slopes obtained by a linear least-squares fit to the data.

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I

2.8

2.6

I)

t

2.4

i

2.2

IN METHYL

fi

I

2.0

I

I

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527

I

1.8

r-m 5. Region of the conventional spectrum of bilk&in-IX~dimetbykster ( CZHCls ,0.30 mol liter-‘, 305 K, 8 scans) containing signals of methyl groups and propionic acid side chains (a). Same region in a 3QF Tz spectrum (7 = 42 msec, 196 scans, 20 s repetition interval) (b). The methyl signals exhibit typical bi-Lorentzian lineshapes. FIG.

are roughly proportional to the dimer concentration (full curve in Fig. 6) which has been calculated from the estimated equilibrium constant of lo3 liters mol-’ ( 14). At the highest concentrations, however, the slopes increase disproportion&ely. Two reasons may account for this finding: the increased viscosity of the concentrated solutions as well as the formation of higher oligomers, which both may cause longer average correlation times for rotational tumbling. In both examples shown, the experimentally determined peak heights are subject to several systematic and random errors. In particular it would be difkult to fkt the data reliably to the theoretical biexponential functions because of large deviations observed in repeated measurements. This is in part caused by instabilities of the instrument used and becomes a more difficult problem with narrower lines. For this reason the methyl ester signals in BRE could not be evaluated. More stable measzrring conditions would probably allow the determination of the eigenvalues of the Red&&d relaxation matrix by biexponential curve fitting in many cases as has been done for quadrupolar nuclei by Jaccard et al. (5). A further source of error can be identified

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calculated dimer cont. a

;j 0.2-

0.0

0.1

0.2 BRE

0.3

0.4

(mou1)

FIG. 6. Concentration dependence of the average initial slopes of the four pyrrolic methyl signals in BRE. The full curve represents the calculated dimer concentration (see text).

in the lysozyme example. The methyl peaks are superimposed on protein signals, which show a time modulation due to coupling precession during the multiple-quantum excitation period. Although this can be accounted for by subtraction of lysozyme spectra recorded under identical conditions this still is a source of systematic errors as the protein signals are also affected by complex formation. In spite of these limitations the initial slope approach shown here has the advantage of giving semiquantitative mobility information in a relatively short experiment time even under unfavorable conditions. More accurate data evaluation may be achieved in spectra where the forbidden coherence is transferred to a coherence that can be observed at a frequency different from the methyl proton chemical shift, i.e., in two-dimensional or heteronuclear spectra, as will be reported at a later date. CONCLUSION

Forbidden methyl peaks in multiple-quantum-titered Tz experiments as well as in twodimensional multiplequantum spectra, MERCY spectra, and multiplequanturn-filtered spectra may be used to extract information about mobility changes caused by intermolecular interactions. This has been demonstrated here for an enzyme-inhibitor interaction and a homoassociation equilibrium. A fast route to the interpretation of these data has been presented, based on the initial slopes of the excitation time dependence of forbidden peaks. Further extensions of the method are conceivable. For example, forbidden signals can be used to identify the interaction sites. These possibilities are currently under investigation in our laboratory. ACKNOWLEDGMENT This work has been supported by the Fends zur Fiirderung der wissenschaftlichen Forschung (Project No. 6213).

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REFERENCES 1. N. MOLLER,

G. BODENHAUSEN, K. W-RICH, AND R. R. ERNST, J. Magn. Reson. 65,531(1985). 2. M. RANCEANDP. E. WRIGHT, Chem. Phys. Lett. 124,572 (1986). 3. N. MOLLER, K. W~~THRICH, ANDR. R. ERNST, J. Am. Chem. Sot. It&6482 (1986). 4. N. M-R, Chem. Phys. Lett. 131,218 (1986). 5. G. JACXARD, S. WIMPERB, AND G. EODENHAUSEN, .I. Chem. Phys. 85,6268 (I 986). 6. L. E. KAY AND J. H. PRESTEGARD, J. Am. Chem. Sot. 109,3829 (1987). 7. N. MILLER, G. BODENHAUSEN, AND R. R. ERNST, J. Mu@ Resort. 75,297 (1987). 8. L. E. KAY, T. A. HOLAK, AND J. H. PRFSTEGARD, J. Magn. Reson. 76,30 ( 1988). 9. U. PIANTMI, 0. W. SORENSEN, AND R. R. ERNST, J. Am. Chem. Sac. 104,680O (I 982). IO. S. WIMPERB AND G. BODENHAUSEN, Chem. Phys. Lett. Ml,41 ( 1987). Il. G. BODENHAUSEN, H. KOGLER, AND R. R. ERNST, J. Mum. Reson. 58,370 (1984). 12. 0. W. HOWARTH AND L. YUN LIAN, J. Chem. Sot. Chem. Commun. 434 (I 983). 13. F. W. DAHLQUISTANDM. A. VERY, Biochemistry7,3277 (1968). 14. H. FALK, T. SCHLEDERER, ANDP. WOLXHANN,~~~~~~~. Chm. 112,199 (1981). IS. H. FALKANDN. Mti~~~,Monutsh. Chem. 113,111(1982).