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Journal of Magnetic Resonance138,330–333 (1999)Article ID jmre.1999.1736, available online at http://www.idealibrary.com on

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Identification of Spin Diffusion Pathways in IsotopicallyLabeled Biomolecules

Thomas R. Eykyn,* Dominique Fru¨h,* and Geoffrey Bodenhausen*,†,1

*Section de Chimie, Universite´ de Lausanne, BCH, 1015 Lausanne, Switzerland; and†Departement de chimie, associe´ au CNRS,Ecole Normale Supe´rieure, 24 rue Lhomond, 75231 Paris cedex 05, France

Received December 22, 1998

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One-dimensional NOE experiments applicable to labeled mac-omolecules are presented which allow the manipulation of spe-ific spin diffusion pathways and thus unambiguously identifylandestine spins through which the direct NOE is mediated. Areatment of spin diffusion using average Liouvillian theory ishown to describe adequately these phenomena. Experiments arearried out on an 15N-labeled sample of human ubiquitin. © 1999

cademic Press

Key Words: selective NOE; spin diffusion; average Liouvillianheory; protein NMR.

The observation of NOEs between noncontiguous strucnits can yield knowledge about the global fold of proteinsbout their tertiary solution-state structures (1). In the two-spinpproximation the initial buildup of the NOE is proportiona26, wherer is the distance between source and target prorovided the motion can be described by a single correl

ime. However, one must exercise caution when calculaistances from NOEs since the flow of magnetization ma

ransferred via intermediate “clandestine” spins, thus introng large errors into these measurements. Consequently aeal of work has emerged within the past 10 years to rem

he effects of spin diffusion and thus obtain more reliaistances (2–9). In general the flow of magnetization mustonfined within subnetworks of the complete spin systemltimate goal being the complete removal of all spin diffusontributions. However, the observation of an NOE betwwo protons, in the absence of further information, will oield a distance constraint that positions the target promewhere on a sphere centered on the source proton. Itherefore be advantageous if one could not only distinguisource and target spins but also the clandestine spins thhich the indirect NOE is mediated. This can be achie

hrough a combination of single and triple inversion expents, as will be shown below. This adds an additional def directionality to the NOE that may assist in conformatiotudies. A recent investigation (10) of amide–amide NOEs in

1 To whom correspondence should be addressed. Geoffrey.Bodenhauser. Fax: 133 1 44 32 33 97.

330090-7807/99 $30.00opyright © 1999 by Academic Pressll rights of reproduction in any form reserved.

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15N-labeled protein has shown that one may selectivelyriminate between spin diffusion pathways mediated via bone CH or CH2 groups. In this Communication we proposedaptation of a recent 1D NOE experiment (11), applicable to

sotopically labeled macromolecules, which allows the idecation of a specific spin diffusion pathway within a protehese effects are discussed within an average Liouv

ramework (12–14).Consider an arbitrary system of three spins I1, I2, and I3,

here I1 is the source spin, I3 the target, and I2 an intermediatpin through which the NOE is mediated. The relaxationrix for this three-spin subspace may be written as

G 5 F r1 s12 s13

s12 r2 s23

s13 s23 r3

G , [1]

herer i ands ij are the familiar auto- and cross-relaxationonstants, respectively. We may then consider the effenverting spin I2 at time tm/2 in terms of average Liouvilliaheory. The density operator at the end of the mixing timiven by

s~tm! 5 expS2G92tm

2 DexpS2G91tm

2 Ds9~0!, [2]

here s9(0) is a transformed initial density matrix. If thnversion of the magnetization of I2 in the middle oftm isescribed by a matrixU, we have

G92 5 G

G91 5 UGU 21 5 F r1 2s12 s13

2s12 r2 2s23

s13 2s23 r3

G , [3]

here

U 5 F 1 0 00 21 00 0 1

G . [4]ens.

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331COMMUNICATIONS

he zero-order average Liouvillian is therefore given by

G ~0! 51

2@G92 1 G91# 5 F r1 0 s13

0 r2 0s13 0 r3

G . [5]

t is evident that the cross-relaxation via spin I2 has beeliminated to zero order. The average Liouvillian also contigher order terms that describe imperfect suppressio

onger mixing times. The first-order correction is given by

Figure 1 shows a comparison of an exact integration oolomon equations with a simulation using an average Lio

ian composed of zero- and first-order terms and a 33 3elaxation matrix derived from experimental data. Simulatorrespond to a single inversion of spin I2 at tm/2. The twopproaches agree well for short mixing times, but divergigher order corrections to the average Liouvillian bececessary. Relaxation during the inversion pulse waslected. It should be noted that in reality, for a nonideal pu

he midpoint of the mixing time becomes ill-defined asnversion is only really defined at the end of the pulse.

G ~1! 5 21

2tmFG91

tm

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tm

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tm

4 F 0 ~r1s12 2 r~2r1s12 1 r2s12 2 s13s23!

0 ~r3s23 2 r

FIG. 1. Comparison of exact calculations with simulations using anefined in Eqs. [1–6]. (a) Buildup of I2z without inversion (solid line) and reithout inversion of I .

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ituation is further complicated for pulses that exhibit comrajectories of the magnetization (15).

The pulse sequences used in Fig. 2 are closely relatedecent selective NOE experiment (11). Selectivity is achievesing two-way cross-polarization to shuttle the magnetiza

rom HN to 15N and back. This leads to a selective excitatio1z which may be considered to be essentially instantaneuch that no cross-relaxation can occur during excitationormal NOE measurements two hardp pulses, which do noffect the relaxation behavior, were inserted during the mi

ime attm/4 and 3tm/4 to diminish the recovery of longitudinomponents, notably of the water resonance. There is noor further water suppression techniques. To investigateiffusion a selectivep pulse is inserted attm/2 with the carrieositioned at the chemical shift of a chosen clandestine prhis inverts the sign of the NOE between the source anelected proton and therefore suppresses to zero ordewo-step transfer that involves this selected proton. Applicaf selective pulses in such experiments leads to an increa

he water resonance. Convolution of the time domain data16)as used to eliminate the water signal.

[6]2 1 s13s23! 0

~2r3s23 1 r2s23 2 s12s13!

3 1 s12s13! 0G .

rage Liouvillian composed of zero- and first-order terms for the three-sining I2z after its inversion (dashed and dotted lines). (b) Buildup of I3z with and

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332 COMMUNICATIONS

All experiments were performed on a Bruker DRX 300 Mpectrometer at 303 K with a 1.5 mM sample of15N-labeleduman ubiquitin (VLI Research) in H2O:D2O 5 9:1 buffered aH 5 4.5 with 20 mM perdeuterated acetic acid. The selec

nversion pulse used in these experiments was a 40-ms I-Bulse (17) with a bandwidth of 120 Hz calibrated (18) for aroper inversion on-resonance.Figure 2a shows a spectrum recorded for source proton

N with a mixing time of 400 ms without quenching of spiffusion. The spectrum shows the source proton and va

arget protons within its vicinity. Figure 2b displays the sprum recorded using a selective inversion of E64 Ha, resultingn almost complete suppression of its signal. One maybserve a substantial attenuation of F4 H« while the remainingOEs remain largely unaffected. This is in agreement wit

FIG. 2. (a) 1D NOE spectrum with a mixing time of 400 ms whereource proton is HN in glutamic acid E64 of human ubiquitin, showing NOo various target protons. (b) Spectrum recorded with an I-Burp2 inveulse applied to Ha of E64. The E64 Ha and F4 H« resonances disappear.pectrum recorded with a triply modulated pulse for simultaneous inverspins HN and Ha in E64, and H« in F4. The carrier frequency is positionedhe midpoint between resonances E64 HN and E64 Ha. The E64 Ha and F4 H«

esonances reappear. Overall the spectrum is attenuated with respect tob) due to the triple inversion. All spectra are plotted to the same scale.pectrum took approximately 1 h with 2 k scans. (d) Inversion profile of EN using a triply modulated I-Burp2 pulse.

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OE from E64 HN to F4 H« that is primarily mediated bywo-step transfer via E64 Ha. Relaxation during the applicatiof the selective pulse results in almost negligible attenuatio

he noninverted resonances. To verify the proposed spinusion pathway the experiment of Fig. 2c is carried out wiriply modulated pulse. Figure 2d shows the offset proecorded for E64 HN in ubiquitin, using two-way cross-polazation (18). Thus we isolate the three-spin system E64 HN, F4

«, and E64 Ha allowing spin diffusion within this subnetwohile suppressing to zero order the transfer to and fromnvironment. The spin diffusion pathway which was prusly suppressed is now reactivated, as evidenced beappearance of the signal due to F4 H«.

Figure 3 shows a detail taken from the X-ray structure19)f ubiquitin. Protons were added using the program SRohm and Haas Company). Displayed are the spin diffuathways alluded to in Fig. 2. One may observe that E6a

s located between E64 HN and F4 H« accounting for thbserved two-step transfer. Conversely a one-step traeems more likely in the case of S65 HN.Figure 4 shows buildup curves for the targets S65 HN and F4

«. The curves have been normalized with respect to the seak extrapolated back to zero mixing time. In the fitrocedure we first determine the 43 4 relaxation matrix from

he unquenched experimental data. One then calculatverage Liouvillian composed ofG(0) and G(1) to describe thase where E64 Ha is inverted. Relaxation during the selectulse has been neglected. The resulting curves are ingreement with signal amplitudes observed in the quenxperiments. S65 HN remains substantially unchanged sugg

ng that the NOE is not mediated by E64 Ha. Conversely thuildup for F4 H« shows a large attenuation when spin diion is suppressed. Although the curves give an imprvaluation of the cross-relaxation rates, caution shoul

aken as only selected diffusion pathways have been eated. There will in general be many pathways that mediatow of magnetization.

FIG. 3. Detail from the X-ray structure of ubiquitin in the vicinity of tource proton E64 HN. Highlighted are the transfer steps corresponding touildup curves of Fig. 4.

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333COMMUNICATIONS

The use of average Liouvillian theory has been showield a more physical interpretation of spin diffusion effectsarticular imperfect suppression is readily described by in

ng a first-order correction without need to resort to an eolution of the Solomon equations.

ACKNOWLEDGMENTS

This work was supported by the Fonds National de la Recherche Sque, by the Commission pour la Technologie et l’Innovation of Switzerlnd by the Centre National de la Recherche Scientifique of France.

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FIG. 4. Normalized buildup curves for target protons E64 Ha (■), S65 HN

F), and F4 H« (Œ). Filled symbols and solid lines correspond to normal Neasurements, as in Fig. 2a. A 43 4 matrix was fitted to the filled symbosing an initial matrix calculated from the X-ray distances assuming aolecule in isotropic motion. This matrix is then used to calculate an aviouvillian for the case where E64 Ha is inverted attm/2 as in Fig. 2b (opeymbols and dashed lines).

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ti-,

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