sensitivity improvement in multi-dimensional nmr spectroscopy

54 Bulletin of Magnetic Resonance

Sensitivity Improvement in Multi-DimensionalNMR Spectroscopy

Mark Ranee

Department of Molecular BiologyThe Scripps Research Institute

10666 North Torrey Pines RoadLa Jolla, California 92037 U.S.A.

Contents

I. Introduction

II. Theory

54

54

III. Applications 601. TOCSY Experiments 612. 3D TOCSY-HMQC Experiment 613. 3D NOESY-HMQC Experiment 614. Heteronuclear Relaxation Experiments . . . . . . 625. Additional Applications 64

IV. Conclusion

V. Acknowledgments

VI. References

65

66

66

I. Introduction

A critical concern in many applications of nu-clear magnetic resonance spectroscopy is the sensi-tivity of the measurements, as determined by theachievable signal-to-noise ratio for a given experi-ment duration. The sensitivity of a NMR measure-ment is affected by many factors (1-3), and numer-ous schemes have been described over the years forimproving the sensitivity. These schemes can gener-ally be categorized into one or more of three broadareas: (i) modification of experimental techniques(i.e. spin physics); (ii) advancements in spectrome-ter hardware; and (iii) utilization of new data pro-cessing procedures. The present paper describes anovel methodology, falling under category (i), forproviding a factor of up to y/2 improvement in sensi-tivity for a variety of multi-dimensional NMR exper-iments. The principle upon which this new method-

ology is based will be reviewed below, followed by abrief description of a few practical applications.

II. Theory

In order to explain the basis of the sensitivity im-provement scheme for multi-dimensional NMR spec-troscopy, it would perhaps be useful first to men-tion a somewhat analogous method which involvesa hardware modification rather than a direct ma-nipulation of the spin system, and is applicable inany NMR experiment. Some time ago Hoult and co-workers (4) pointed out that, at least in principle,a y/2 improvement in sensitivity can be achieved inNMR measurements by using two orthogonal de-tection coils rather than the single coil normallyemployed. If the two rf coils are orthogonally po-sitioned but otherwise identical, the NMR signals

Vol. 16, No. 1/2 55

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To explain the basic principle underlying the sen-sitivity enhancement scheme, the response of an iso-lated spin-1/2 nucleus to the pulse sequence shownin Figure 1 will be described; application of thispulse sequence to a coupled spin system producesa 2D TOCSY spectrum (6-9), but for present pur-poses it can be viewed as simply producing a 2Dchemical shift-resolved spectrum of the uncoupledspin-1/2 nuclei. All relaxation effects are ignored.Starting from the equilibrium magnetization of thespin-1/2, the first 90° pulse creates transverse mag-netization which then evolves under the influence ofthe chemical shift/resonance offset, O, to:

a{t\) = Ix sin — Iy (1)where for convenience the single spin angular mo-mentum operators are used to indicate the relevantstate of the spin system, and constants of propor-tionality have been omitted. The 90°̂ pulse at thebeginning of the mixing period produces the follow-ing:

Figure 1: Pulse sequence, a diagram of the coher-ence transfer pathway, and the relevant density op-erator terms for a sensitivity-enhanced 2D TOCSYexperiment (34). The pulse sequence itself is identi-cal to the z-filtered TOCSY experiment in commonuse (8,9); the sensitivity enhancement is achieved byseparating the conventional phase-cycling into twohalves and recording the data separately.

detected in each will be identical except for a rel-ative phase shift of 90°; thus, after correcting forthe relative phase shift, the two NMR signals canbe combined to double the size of the detected sig-nal. On the other hand, the thermal noise gener-ated in the two receiver circuits (probe coils pluspreamplifiers) will be statistically independent, andthus when combined will increase the rms noise volt-age by only a factor of \/2- The net result of thisscheme therefore is a \[2 improvement in the overallsensitivity of the NMR experiment. Unfortunately,this concept has been difficult to implement due topractical problems in designing an efficient, crossed-coil probe. The sensitivity improvement scheme de-scribed below is essentially an analogue of cross-coil detection for evolution periods (5) in multi-dimensional NMR experiments.

<7a(*i, Tm = 0) = Ix sin 9,ti + alz cos fiii (2)

where a = —1 for fa = +x and a = +1 for fa = ~x-Assuming for the moment that some arbitrary pulsesequence is applied during the mixing period rm, thestate of the spin system just prior to the last 90°pulse can be written in general terms as:

z(Tm)} cos nti(3)

where the functions //3(rm) and gp(rm) express thenet effect of the mixing sequence on the Ix and Izcomponents, respectively. The last 90° pulse gener-ates the following:

o-a{ti,Tm,t2 =0) = [Ixfx(Tm) - Iyfz(rm)]

(4)

where unobservable Iz terms have been dropped. Fi-nally, precession due to the chemical shift or reso-nance offset during the detection period will producethe following result:


Ix[(fx(Tm) cos Qt2 + fz(Tm) sin Qt2) sin Qti+a(gx(T~m) cos Qt2 + gz(Tm) sin Qt2) cos Qt+Iy[(fx(Tm) sinttt2 - fz(Tm) cosQt2) sin fl+a.(gx(Tm)s'mQt2 - gz(rm) cos9,t2) cosfii (5)

Inspection of eqn. 5 indicates that for some arbitrarymixing sequence, a 2D Fourier transformation of thetime-domain NMR signal will result in complicatedlineshapes in the 2D spectrum.

To proceed, assume that instead of some arbi-trary mixing sequence being applied, a so-called'isotropic' sequence is employed (6). One of theproperties of an isotropic mixing sequence is thatthe total spin angular momentum Ia ( a= x,y or z)is conserved (10). Thus, eqn. 5 simplifies to:

0a(*l>Tm,*2) =Ix[fx{Tm) sin fiii cos 9,t2 + agz(Tm) cos Qti sin Q,t2]+Iy[fx(Tm) sin Clti sin Q,t2 — agz(Tm) cos Vtt\ cos Ut2]

(6)

2D Fourier transformation of the NMR signal rep-resented by eqn. 6 will still produce spectral peakswith a highly undesirable phase-twist (11,12). Thisphase twist can be removed, however, if either an ad-ditive or subtractive combination is made of the twodata sets collected separately for <fi2 = +x (a = — 1)and <p2 = —x (a — +1) :

= 2/x[/x(rTO) sinttti cos Ut2]+2Iy[fx(Tm) s i n ^ i sinful (7a)

~ O"_i(i i , rm, t2)= 21 x[gz(rm) cos \

-2L, COS fiti COS

A complex Fourier transformation with respect tot2 and a cosine or sine transformation with re-spect to t\ of the signals represented by eqns. 7will produce spectra with the desired pure phaselineshapes, due to the fact that the signals areamplitude-modulated with respect to t\ instead ofphase-modulated (11,12). The additive combina-tion of the two data sets for <j)2 = +x and — x ef-fectively eliminates the pathway evolving from the

Iy term present at the end of the evolution period;likewise, the subtractive combination eliminates thepathway from the Ix term. This phase-cycling pro-cedure is an inherent part of the z-nltered TOCSYexperiment (8,9); usually, the subtractive combina-tion of eqn. 7b is chosen for practical reasons (8).A popular alternative to phase-cycling for generat-ing amplitude-modulated signals in TOCSY experi-ments is the use of 'trim' pulses and/or non-isotropicmixing sequences to eliminate one of the orthogonalmagnetization components present at the end of theevolution period (7). Discrimination of the sign ofthe resonance frequencies during the evolution pe-riod (13) can be achieved via phase selection pulsesand hypercomplex Fourier transformations (12-15)or by the time-proportional phase incrementationscheme (13,16-18).

The NMR signals represented by eqns. 7 can beexpressed in an equivalent fashion using complex no-tation as:

&+(ti,Tm,t2) = 2fx(rm) sinntiexp(ittt2) (8a)

v~(h,Tm,t2) = -2igz(Tm) cos £lhex.p(ittt2)(8b)

where the real and imaginary components corre-spond to the coefficients of Ix and Iy, respectively.Inspection of eqns. 7 or 8 indicates that the NMRsignals represented by a+ and <r~ have a relativephase shift of 90° in both time dimensions. A 2DHilbert transformation (19) of the signal a~ gener-ates the result:

<r~(ti, rm, t2) = — 2gz(rm) sinfiti exp(illt2) (9)

where the hat symbol is used to represent the 2DHilbert transformation. The combination of eqns.8a and 9 yields the following:

)] si

If the assumption is made that fx(Tm) = gz(Tm),then eqn. 11 indicates that the combination repre-sented by eqn. 10 leads to a NMR signal with twicethe intensity of the signal which would convention-ally be obtained, i.e. the signals represented by ei-ther eqn. 8a or 8b. It should be emphasized that ex-tending the above analysis to include the steps nec-essary for frequency discrimination in the indirectly

Vol. 16, No. 1/2 57

detected dimension does not affect the conclusionregarding signal intensity. To determine whetheror not a sensitivity improvement is realized by themodified experimental procedures it is necessary toconsider the behaviour of the spectral noise whenmaking the combination indicated by eqn. 10; itwill be shown below that the random noise in a+

is uncorrelated to that in CT~, and thus the combi-nation which doubles the NMR signal intensity onlyincreases the noise by a factor of \/2, resulting there-fore in a \/2 improvement in sensitivity.

As illustrated by the trivial example describedabove, the general procedure and requisite con-ditions for implementing the sensitivity enhancedscheme in a 2D NMR experiment can be stated asfollows. The pulse sequence must be designed toretain the signals originating from both of the or-thogonal magnetization components, or higher orderspin operator terms, generated during the evolutionperiod by the chemical shift interaction; in conven-tional experiments one of these two components iseliminated either as an inherent feature of the pulsesequence or by specific design to purge the 2D spec-trum of undesirable features (12,13). The sensitivityenhancement scheme is applicable only to experi-ments in which the mixing sequence causes the rele-vant, orthogonal spin operator terms generated dur-ing the evolution period to have sufficiently similartransfer functions to observable magnetization com-ponents during the detection period; in the exampleabove this would require that /x(rm) & gz(Tm) sothat the data in eqn. 11 would combine construc-tively to enhance the signal strength. Some exper-iments are easily adapted to incorporate the sen-sitivity improvement scheme, such as the z-filteredTOCSY sequence discussed above, while other ex-periments can be modified to fulfill the necessaryconditions. Some pulse techniques, however, havesegments which inherently require a unique coher-ence transfer pathway (20,21), such as 2D lab-frame (22) or rotating-frame (23) NOE experiments(NOESY or ROESY, respectively), and thus thesensitivity enhancement scheme is inapplicable forthe evolution periods preceding the 'bottleneck'.

Since the sensitivity enhancement scheme relieson the ability to retain and combine essentiallyequivalent information from two orthogonal, coher-ence transfer pathways in a suitable NMR exper-iment, it will for convenience be referred to below

as PEP (Preservation of Equivalent Pathways) tech-nology. Also for convenience much of the discussionwill refer to 2D experiments, but it should be re-alized that the PEP methodology is applicable inexperiments of higher dimensionality as well (videinfra).

To implement the sensitivity enhancementscheme for a suitable NMR experiment, it is firstnecessary to ensure that the propagator for the rel-evant portion of the pulse sequence, i.e. the portionbetween the relevant evolution period and the de-tection period, transforms the appropriate, orthog-onal spin operator terms present at the end of theevolution period to observable magnetization termswith approximately equal efficiency (but not nec-essarily along exactly equivalent coherence transferpathways). To accomplish this it may be necessaryto re-design part of the pulse sequence; in a 2D ex-periment this part consists of just the mixing period,while in experiments of higher dimensionality it isnecessary to consider all the intervening mixing andevolution periods. In addition, the PEP scheme re-quires the elimination of the phase-cycling normallyemployed to select one of the two relevant, orthogo-nal spin operator terms at the end of the appropri-ate evolution period; instead, two experiments arerun in which the appropriate selection pulse (e.g.the second 90° pulse in the example above) is in-verted in phase between the two experiments andthe data sets are accumulated separately. After theacquisition is completed, additive and subtractivecombinations of the two raw data sets are made togenerate the sine and cosine, amplitude-modulateddata sets, as in eqns. 8. These two new data setscan be treated in either of two ways. First, the twodata sets can be independently processed to produceseparate 2D (or higher dimensional) spectra; as in-dicated above, there will be a relative phase shiftof 90° in both frequency dimensions (detection di-mension and relevant, indirect dimension), and it istherefore necessary to correct for this relative phaseshift. The two spectra can then be added togetherto enhance the signal intensity. While this first pro-cedure for handling the data provides the ability forspectral editing in some heteronuclear experiments(vide infra), it is often more convenient to do all ofthe required data manipulation on the time domaindata. The 90° phase shift in the detection dimen-sion of either the additive or subtractive data set is


trivially accomplished by simply interchanging thereal and imaginary parts of the complex free induc-tion decays. If the data has been collected usingthe so-called 'hypercomplex' (12-15) method for signdiscrimination in the relevant, indirectly detectedfrequency dimension, then the necessary 90° phaseshift in this dimension is trivially accomplished byswapping the two free induction decays collected foreach time increment (i.e. t\ point in a 2D experi-ment) as part of the 'hypercomplex' procedure; thisswap is usually done on the same data set, eitheradditive or subtractive, as was subjected to the 90°phase shift in the detection dimension. The doublyphase-shifted time domain data set is then combinedwith the second, unshifted data set (whether addedto or subtracted from is best determined by trial anderror) to produce a single, signal enhanced data setwhich is then processed to a 2D spectrum as desired.As implied in the above discussion, performing thephase shifts in the time domain requires that the xand y components of the free induction decays bedigitized at simultaneous time points and that thehypercomplex method, not TPPI, be used for signdiscrimination in the relevant, indirect dimension.

To summarize in brief form, the PEP data han-dling procedure is as follows, assuming hypercom-plex data collection:

(la) Collect two separate data sets ux(ti,t2) andvx{ti, *2) which are identically recorded exceptfor an inversion of the relevant phase selectionpulse for the PEP scheme.

(lb) Collect a second pair of data sets uy(ti,t2) andvy(ti,t2) similarly to the first, as part of thehypercomplex procedure (12-15). (The acqui-sition of the four data sets ux, vx, uy and vy isnormally interleaved so that four FIDs are col-lected before the parameter t% is incremented).

(2) Make the combinations ax = ux + vx, sx =ux - vx, ay = uy + vy and sy = uy - vy.

(3) Effect a 90° phase shift in the detection di-mension to create a new data set sx, sy:real(sx)=imag(s:c), imag(sx)=real(sa;), andthe same for sy (sx and sy were arbitrarilychosen over ax and ay).

(4) Effect a 90° phase shift in the indirect dimen-sion to create a new data set sx, sy: sx=sy

and sy=-sx.

(5) Make the combinations cx = ax + sx andcy = ay + sy (subtractive combination maybe necessary instead, the uncertainty is dueto hardware and pulse sequence details).

(6) Process the data cx(ti,t2), cy(t\,t2) as appro-priate for a hypercomplex data set. If theTPPI procedure is used for uj\ sign discrim-ination or if certain spectral editing capabili-ties need to be retained, then it is necessary toprocess the two data sets a{ti,t2) and s(ti, £2)separately and combine them afterward if de-sired.

In order to determine the sensitivity enhance-ment achievable using PEP methodology, it is nec-essary to analyze the behaviour of the signal noise(24) in these experiments. A general analysis of thenoise behaviour can be performed by considering theconsequences of the PEP procedure in the frequencydomain. The additive and subtractive combinationsof the raw, time domain data sets are made as indi-cated in step (2) above; no assumption is necessaryregarding how the data is digitized or LO\ frequencydiscrimination is achieved. The resulting two datasets are then processed separately but identically toproduce two, 2D spectra, A{u>i,u>2) and S(OJI,OJ2)(assume that only the real data has been retainedand that A(UJI,OJ2) is phased as desired). Accordingto the PEP protocol it is necessary to perform a 90°phase shift in each of the two frequency dimensionsof one of the spectra before combining the spectra.As Ernst has pointed out (25,26), a 90° phase shiftis equivalent to performing a Hilbert transformationof the data, due to the causality principle. Thus, thecombined spectrum C{LUI,OJ2) can be written as:

C(wi,w2) = i4(a;i,a;2)+5(a;i,W2) (12)Eqn. 12 can be rewritten in expanded terms as:

C(u1,UJ2) = [U(iOi,0J2) +V(ujX,uJ2)}+ {U{cul,uj2)-V(io1,uJ2)} (13)

where U(u)\,LO2) and V{w\,oj2) are the 2D spectraproduced by identical processing of the original, rawdata sets u[t\, t2) and v{t\, t2). Rearranging eqn. 13gives

(14)

Vol. 16, No. 1/2 59

Assume that the raw data consists only of randomnoise. In order to determine the behaviour of thespectral noise when combined according to eqn. 14,it is sufficient to calculate the cross-correlation func-tion Ruty(ai,a2), where

(15)and £ represents the mean value of the function inbrackets, averaged over io\ and UJ2, and it is assumedthat the spectral noise is stationary. The 2D Hilberttransform of U(u>i,uj2) is given by (19):

oo oc_ l r da r

n2 J fa - a) JU(P,*)

fa -a) J fa - P)dj3 (16)

where for simplicity it is assumed that U(UJI,LJ2) is acontinuous function and that the integration limitscan be extended to infinity. Inserting eqn. 16 intoeqn. 15 gives:

Making the substitutions r\ = (3 —leads to

and 7 = a — OJ2

Assuming that the order of integrations can be in-terchanged, eqn. 18 can be expressed as:

oo oo1 f C?7 f^ J (a2-7)/

dr]

d7

- 7) - V)^dr,

(19)

Eqn. 19 indicates that the cross-correlation functionof U(uiiiU)2) and its 2D Hilbert transform U(UJI,U>2)

is equal to the Hilbert transform of the autocorrela-tion function of U(001,0)2); this relationship is wellknown for functions of one variable (27,28). It istrivial to prove that Ruu(^1,^2) is an odd functionin both <7i and a2, using the fact that RUU(<TI,&2)is an even function by definition. Thus, since

and

it must be true that

Ruu{0,0) = = 0 (20)

Eqn. 20 indicates that a function U(u>i,u>2) and its2D Hilbert transform are uncorrelated, as is wellknown for ID Hilbert transform pairs (27,29). Thus,in making the combination U + 0 in eqn. 17 therms noise level increases only by a factor of y/2,and the same of course is true for V — V. The netresult therefore is that the PEP procedure increasesthe spectral rms noise level by a factor of y/2 overthat for a conventional spectrum (corresponding toeither the U + V or U — V combinations in eqn. 13);if the NMR signal is doubled in a PEP-modifiedexperiment, then an improvement in sensitivity bya factor of y/2 will be realized.

Perhaps the earliest example of PEP method-ology was in the work of Bachmann et al. (12)on phase separation in two-dimensional spectros-copy. Two techniques were described for obtainingpure phase, 2D resolved spectra; the first techniqueachieved phase separation by reversed precession,while the second relied on the use of phase selectionpulses between the evolution and detection periods.The reversed precession technique is really a PEPscheme, and as mentioned by Bachmann et al., pro-vides a factor of y/2 sensitivity enhancement overthe phase selection method.

Before proceeding on to describe some recent ap-plications of PEP methodology, it would perhaps beuseful to point out the existence of somewhat re-lated experiments. The PEP scheme is based on de-signing a pulse sequence so that the two orthogonalmagnetization components present during the evolu-tion period follow more or less equivalent coherencetransfer pathways to the detection period and there-fore provide essentially identical information. Otherschemes have been proposed in the past which also


H

<!>•, x

H

x y

<t>2<|>3

= X , - X

= X, X, X, X / -X, -X, -X, -X (collect data separately)

= x, x, -x, -x

* ! = X , - X

<t>2 = X, X, -X, -X / -X, -X, X, X (collect data

% = y,y,-y,-yrec = x, -x, -x, x

separately)

Figure 2: Pulse sequence for recording 3Dsensitivity-enhanced TOCSY-HMQC spectra (38).The isotropic mixing is performed using the DIPSI-2 pulse sequence (35) or other, suitable sequences.The thin and thick vertical lines represent 90° and180° pulses, respectively, applied to the H (proton)or X (heteronucleus) spins. The delay r is set to1/(2JHX)- Decoupling of the X spins during acqui-sition is accomplished using GARP-1 (54) or otherappropriate composite pulse sequences. Quadra-ture detection in the OJ\ and cu2 dimensions can beachieved via either the TPPI (13,16-18) or hyper-complex (12-15) methods. After the data is col-lected with the basic four step phase cycle (plus anyadditional cycling desired), the phase fo is invertedand the resulting data set is stored separately fromthe first.

retain signals originating from the two orthogonalcomponents in the evolution period; the differencein these schemes is that the information providedby the two signals is not the same, and thus cannotbe combined to achieve a sensitivity enhancementas it is normally denned. However, when the tech-niques are applicable they can provide a substan-tial increase in the information recorded per unitmeasuring time. One example of such techniquesis the COSY-NOESY (30) or COCONOSY (31) ex-periment, in which a COSY data set is recordedduring the mixing time of a NOESY experiment.

Figure 3: Pulse sequence for recording 3Dsensitivity-enhanced NOESY-HMQC spectra (38).The thin and thick vertical lines represent 90° and180° pulses, respectively, applied to the H (proton)or X (heteronucleus) spins. The delay r is set to1/(2JHX), while rm is the NOE mixing period. De-coupling of the X spins during acquisition is ac-complished using GARP-1 (54) or other appropriatecomposite pulse sequences. Quadrature detection inthe toi and o>2 dimensions can be achieved via ei-ther the TPPI (13,16-18) or hypercomplex (12-15)methods. After the data is collected with the basicfour step phase cycle (plus any additional cyclingdesired), the phase <f>2 is inverted and the resultingdata set is stored separately from the first.

Another, closely related example is the combinedrelayed NOESY-TOCSY experiment (32).

III. Applications

PEP technology can be applied to a wide varietyof experiments (33). Brief descriptions will be givenin the following sections for some representative ex-amples of sensitivity-enhanced, solution-state NMRexperiments.

Vol. 16, No. 1/2 61

1. TOCSY Experiments

Aside from the trivial case of a 2D chemi-cal shift-resolved experiment, perhaps the simplestexample of the application of PEP technology isa sensitivity-enhanced, 2D homonuclear TOCSYexperiment (34). The pulse sequence for thesensitivity-enhanced TOCSY experiment is shownin Fig. 1; this sequence is just the z-filtered TOCSYexperiment proposed some time ago (8,9), but withmodified phase-cycling and data acquisition. In-stead of phase-cycling the second 90° pulse to selectfor the z magnetization during the isotropic mixingperiod, both the z and x magnetization componentsare retained by performing two experiments withthe phase-cycle of fa inverted between them and thedata collected separately. The two data sets are thenprocessed according to the PEP procedure, as de-scribed above. The key to achieving sensitivity en-hancement in the TOCSY experiment is to employ amixing sequence which promotes coherence transferwith equal efficiency for the z and x magnetizationcomponents present at the beginning of the mix-ing period. A so-called 'isotropic' mixing sequence,such as the DIPSI-2 sequence described by Shaka etal. (35), is ideal for use in the sensitivity-enhancedTOCSY experiment; the defining characteristic ofan isotropic mixing sequence is that it creates an ef-fective Hamiltonian consisting only of the isotropicscalar coupling terms. Under such a Hamiltonianeach of the orthogonal magnetization componentsis conserved (neglecting relaxation), since they com-mute with the effective Hamiltonian; thus, there isno mixing of the terms arising from the z and xmagnetization present at the beginning of the mix-ing period. As indicated schematically in Fig. 1,z magnetization starting on one spin can be trans-ferred to z magnetization of another spin belongingto the same coupling network, and likewise for xmagnetization. In a conventional TOCSY experi-ment (6-9), one of these two components is inten-tionally destroyed in order to purge the 2D spectraof undesirable phase characteristics. With the PEPprocedure, however, it has been demonstrated (34)that pure phase TOCSY spectra can be recordedwith an improvement in sensitivity by a factor of

2. 3D TOCSY-HMQC Experiment

The PEP sensitivity enhancement scheme can beapplied in principle to a NMR experiment of any di-mensionality. For example, by concatenating the 2Dsensitivity-enhanced TOCSY pulse sequence with aconventional heteronuclear HMQC sequence (36,37)it is possible to create a 3D, sensitivity-enhancedTOCSY-HMQC experiment (38); this pulse se-quence is shown in Fig. 2. An analysis of this rela-tively simple experiment shows that the two, orthog-onal magnetization components created by evolu-tion under the chemical shift interaction during thet\ period undergo essentially identical transforma-tions during the rest of the pulse sequence, and leadto observable signals containing equivalent informa-tion. According to the PEP prescription, two datasets are collected for each increment of t\, with fabeing inverted between the two experiments. Datareduction is most conveniently accomplished in thetime domain as the data is being accumulated.

3. 3D NOESY-HMQC Experiment

The 2D TOCSY experiment shown in Fig. 1and the 3D TOCSY-HMQC experiment presentedin Fig. 2 are examples of PEP applications in whichno change in the actual pulse sequences of the corre-sponding, conventional experiments are required; inthese cases the only changes necessary in the exper-imental protocol are to the phase-cycling and to thedata collection procedure. This simplicity is largelydue to the inherent characteristic of an isotropicmixing sequence to act on orthogonal magnetiza-tion components with equal efficiency and identicaleffect; in the TOCSY experiments the two equiv-alent coherence transfer pathways required for thePEP scheme come as a natural part of the conven-tional pulse sequence. However, most other multi-dimensional NMR experiments have one or moresegments which normally treat differently the or-thogonal components present at the end of a givenevolution period. For example, in a 2D NOESY ex-periment only one of the orthogonal magnetizationcomponents present at the end of the evolution pe-riod can be converted to the longitudinal magneti-zation required during the NOE mixing period; thesecond, transverse component must be eliminatedto remove coherence transfer artifacts. Thus, it isnot possible to apply the PEP scheme for any evolu-


tion period which precedes a NOESY mixing periodor, by analogy, a ROESY spin-lock period; however,it may be possible to apply the PEP technique tosubsequent evolution periods.

Fig. 3 shows a pulse sequence for a sensitivity-enhanced, 3D NOESY-HMQC experiment (38).Unlike the TOCSY experiments, it is necessaryin this case to modify the conventional sequencefor this popular experiment. A detailed analysis(39,40) of the conventional HMQC experiment in-dicates that the two relevant, orthogonal spin oper-ator terms present at the end of the evolution period(*2 period in Fig. 3) are not transformed equivalentlyfollowing the evolution period; one term is convertedto anti-phase proton coherence which evolves intoin-phase magnetization observable during the detec-tion period, while the second term is left as unob-servable multi-spin coherence and is therefore lost.However, by modifying the pulse sequence (39,40)(adding the pulses after the 90^2 pulse in Fig. 3), itis possible to have both of the relevant spin operatorterms from the evolution period transformed to ob-servable magnetization for IS spin systems. Whilethe resulting propagator does not cause the orthog-onal terms to follow exactly equivalent pathways,under suitable conditions a substantial sensitivityenhancement can be achieved (39); the degree ofnon-equivalence is dependent on various relaxationrates. A modification analogous to that shown inFig. 3 has also been described (39,40) for the HSQCexperiment (41).

The modifications to the HMQC and HSQC ex-periments only allow sensitivity enhancement forIS spin systems, i.e. heteronuclear spin systems inwhich only one proton is directly coupled to the het-eronucleus. In applications where both IS and InS(n>l) spin systems are present, it is sometimes use-ful to process separately the two data sets recordedas part of the PEP procedure; by doing so one ofthe two spectra will only contain resonances fromthe IS spin systems, while the other will contain allthe resonances, thus allowing easy distinction of ISfrom InS spin systems.

4. Heteronuclear Relaxation Experi-ments

Over the past several years there has beena resurgence of interest in measuring heteronu-clear relaxation rate constants and heteronuclear

NOEs for use in studying the internal dynamics ofbiomolecules (42). This renaissance is due partlyto the availability of methods for biosyntheticallyenriching biomolecules with 13C and/or 15N nu-clei and partly due to the development of meth-ods for indirectly measuring the heteronuclear relax-ation rate constants and {1H}-X NOEs with protonsignal detection. The general scheme of the pro-ton detection methods is to concatenate a conven-tional heteronuclear relaxation experiment with aHSQC experiment. For example, an experiment formeasuring heteronuclear spin-spin relaxation rateconstants (43,44) consists of a refocussed-INEPT(45,46) segment to enhance the sensitivity by trans-ferring the larger proton equilibrium magnetizationto the heteronuclei, a CPMG sequence (47,48) witha parametrically varied length T, and a HSQC type2D sequence (omitting the initial INEPT segmentsince the desired heteronuclear coherence has al-ready been created) to record the data. A seriesof 2D experiments are collected as T is varied, anda plot of the cross-peak intensities in the 2D spec-tra as a function of T can be analyzed as usual forCPMG experiments. If the improved resolution of a2D correlation spectrum is unnecessary, then a sim-ple reverse, refocussed-INEPT sequence can be usedin place of the HSQC segment.

Multi-dimensional, heteronuclear NMR experi-ments which contain a reverse polarization trans-fer step lend themselves well for application of thePEP scheme (39,40). An example of a sensitivity-enhanced pulse sequence for measuring heteronu-clear spin-spin relaxation rate constants is shownin Fig. 4. The section leading up to and includ-ing the t\ evolution period is a conventional se-quence, with the initial refocussed-INEPT segment,the CPMG sequence modified so that dipolar-CSAcross-correlation effects are eliminated (43,44), andthe t\ evolution period for frequency labelling theX nucleus coherences. In a conventional experimentthe evolution period would be followed by a reversepolarization transfer sequence such as refocussed-INEPT or DEPT (49); these sequences transfer onlyone of the two, orthogonal magnetization compo-nents present at the end of the evolution period toobservable proton signals. However, with relativelysimple modifications (39,50), these sequences canbe made to transfer both components with approxi-mately equal efficiency to observable proton magne-

Vol. 16, No. 1/2 63

)

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X

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)

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<t>3 = y, y, -y , - yrec = x, -x, -x, x A = 1/4J

T =4nx

Figure 4: Sensitivity-enhanced pulse sequence for measuring heteronuclear spin-spin relaxation time constantswith proton detection (50). The thin and thick bars represent 90° and 180° pulses, respectively. After the datais recorded using the basic four step phase cycle (plus any additional cycling desired), the phase (fi2 is invertedand a second data set is recorded separately from the first. The 180° pulses without phase designation areapplied along the y axis. The value of A is set to l/(4JHx)- A CPMG sequence is applied to the X nucleusspins during the parametrically varied period T; the periodic proton 180° pulses applied during the CPMGsequence eliminate effects from cross-correlation between CSA and dipolar relaxation mechanisms (43,44).For each value of T a 2D X-H correlation experiment is recorded.

tization, thus allowing the PEP scheme to be im-plemented; in the sequence of Fig. 4 a modified,refocussed-INEPT sequence is employed. The de-tails of these modifications have been described indetail elsewhere (39,50).

To demonstrate the use of the sensitivity-enhanced pulse sequence of Fig. 4, experimentaldata (Ranee, Chazin and Palmer, unpublished)which was recorded for a sample of 15% uniformly,fractionally 13C-enriched calbindin D9k dissolved inD2O is shown in Figs. 5 and 6. Calbindin D9k isa small (76 amino acids) calcium-binding protein.Presented in Fig. 5 are contour plots of the CQ-Haregion of heteronuclear correlation spectra recordedusing the pulse sequence of Fig. 4; the length of theCPMG cycle, T, was 4 ms. The data in Fig. 5ais the result of making the additive combination ofthe raw data recorded according to the PEP scheme,while the data in Fig. 5b results from the subtractivecombination; except for a relative, 90° phase shift in

both frequency dimensions, the processing and plot-ting parameters are identical for the two spectra.Inspection of the two contour plots shows that theyare essentially identical, and thus when they arecombined the sensitivity will be enhanced, since thespectral noise is uncorrelated (vide supra). In con-ventional experiments only one of these two spectrais obtained, whereas in the sensitivity-enhanced ex-periment both spectra are produced from the sameraw data set.

Presented in Fig. 6 are ID slices, along the protonchemical shift axis, taken from the 2D heteronuclearcorrelation spectra recorded with the sensitivity-enhanced pulse sequence of Fig. 4 and using aCPMG length of 108 ms. The top slice is takenfrom the data set representing the additive combi-nation of the raw data, the middle slice is from thesubtractive data set, and the bottom slice is the re-sult of co-adding the two slices above. The spectraare plotted such that the rms noise level is the same


4.8 4.01H (ppm)

3.2 4.8 4.01H (ppm)

3.2

Figure 5: Contour plots of the Ca-Ha region of 13C-1H 2D correlation spectra for a sample of 15% fractionally13C-enriched calbindin Dgk, recorded using the sensitivity-enhanced pulse sequence of Figure 4 for measuring13C spin-spin relaxation time constants. The two sets of data recorded during the experiment were addedtogether to produce plot (a) and subtracted to produce plot (b); all processing and plotting parameters wereidentical for the two plots except for a 90° relative phase shift in both frequency dimensions (i.e. the zerothorder phase corrections necessary for spectrum (b) were shifted by 90° from the parameters used for spectrum(a)). The length of the CPMG cycle employed in this experiment was 4 ms. All data processing was doneusing the FTNMR software from Hare Research.

for all slices, which required that the combined databe reduced in size by a factor of v 2 before plottingwith the same scaling factors as the additive andsubtractive data. The sensitivity enhancement ex-pected for the PEP scheme is clearly demonstratedby the data in Fig. 6.

5. Additional Applications

The PEP scheme is a general concept, not a spe-cific design. In addition to the examples describedabove and presented in detail elsewhere (33,34,38-40), many other applications are possible. Kay andcoworkers (51) have recently reported the use ofPEP technology in pulsed field gradient versionsof the HSQC experiment. Their new method al-lows pure absorption heteronuclear correlation spec-

tra to be recorded with the use of pulsed field gra-dients for eliminating undesired coherence trans-fer pathways. PEP technology is employed in thegradient-enhanced experiment to extract separatesignals which are cosine- and sine-modulated as afunction of the evolution time t\\ this data can thenbe processed with a hypercomplex Fourier transfor-mation to yield a pure absorption spectrum withu>i frequency discrimination. Madsen and S0rensen(52) have recently described very useful modifica-tions to a variety of constant-time experiments forachieving optimal spectral resolution; PEP technol-ogy was incorporated into these experiments to en-hance the sensitivity. Similarly, Madsen et al. (53)have employed the PEP scheme in designing newpulse sequences for measuring coupling constants in13C,15N-labelled proteins.

Vol. 16, No. 1/2 65

add

sub

com

ppm

Figure 6: One-dimensional slices taken parallel to the w2 frequency axis (proton chemical shift) from 13C-XH 2D correlation spectra for the 15% fractionally 13C-enriched calbindin D9k; the 2D spectra were recordedusing the sensitivity-enhanced pulse sequence of Figure 4 for measuring heteronuclear spin-spin relaxationtime constants. The length of the CPMG cycle employed in this experiment was 108 ms. The two data setsrecorded during the experiment were added together to produce the 2D spectrum from which slice (a) wastaken; slice (b) is from the 2D spectrum resulting from the subtractive combination; and slice (c) is the resultof co-adding slices (a) and (b). The data are plotted such that the rms noise level appears the same for allslices; this required slice (c) to be reduced in absolute terms by a factor of A/2- The slices intersect peaks forthe Ca-HQ correlations of Val 61 (5.10 ppm), Thr 45 (4.43 ppm), Tyr 13 (4.00 ppm), and Lys 25 (3.46 ppm).

IV. Conclusion

The general scheme of the PEP methodol-ogy for obtaining sensitivity improvements in multi-dimensional NMR experiments is simple. However,its implementation in practice may or may not bestraightforward. The basic requirement which mustbe satisfied in order to exploit PEP technology isthat the relevant, orthogonal spin operator compo-nents generated by the chemical shift/resonance off-set precession during an evolution period be trans-formed to observable NMR signals along suitablyequivalent coherence transfer pathways with ap-proximately equal efficiency. In some applicationsno change in the actual pulse sequence is necessaryin order to implement the PEP scheme, while otherapplications require some segments of the conven-

tional pulse sequence to be re-engineered to meetthe requisite conditions. It should be anticipatedthat PEP technology will be applicable in additionalclasses of experiments not specifically addressed inthis paper. The maximum achievable sensitivity en-hancement factor for PEP technology applied to oneevolution period of a multi-dimensional NMR ex-periment is V2) which of course translates to a re-duction by a factor of two in the measuring timerequired to record a data set with a given S/N ra-tio. Such improvement is extremely important inapplications where the sensitivity is limited by prac-tical factors such as low sample concentrations orinherent features such as the requirement for largenumbers of individual free induction decays in 3Dor 4D experiments or in relaxation rate measure-ments. Sensitivity improvements are also extremely


useful in experiments which require the data to becollected in a limited period of time.

V. Acknowledgments

I would like to acknowledge the fundamen-tal contributions of Dr. John Cavanagh and Prof.Arthur Palmer to the development of the sensitivity-enhanced NMR experiments and the collaborationwith Dr. R. Andrew Byrd on extending the origi-nal techniques to 3D applications. Helpful discus-sions during the course of the research with Dr.Malcolm Levitt, Prof. Geoffrey Bodenhausen andDr. Ole S0rensen are also gratefully acknowledged.This work was supported by the National Institutesof Health (RO1-GM40089).

VI. ReferencesXR.R. Ernst, Adv. Magn. Reson., vol. 2, Aca-

demic Press, New York, 1966, pp. 1-135.2W.P. Aue, P. Bachmann, A. Wokaun and R.R.

Ernst, J. Magn. Reson. 29, 523 (1978).3M.H. Levitt, G. Bodenhausen and R.R. Ernst,

J. Magn. Reson. 58, 462 (1984).4C.-N. Chen, D.I. Hoult and V.J. Sank, J. Magn.

Reson. 54, 324 (1983).5W.P. Aue, E. Bartholdi and R.R. Ernst, J.

Chem. Phys. 64, 2229 (1976).6L. Braunschweiler and R.R. Ernst, J. Magn.

Reson. 53, 521 (1983).7A. Bax and D.G. Davis, J. Magn. Reson. 65,

355 (1985).8M. Ranee, J. Magn. Reson. 74, 557 (1987).9R. Bazzo and I.D. Campbell, J. Magn. Reson.

76, 358 (1988).10M. Ranee, Chem. Phys. Lett. 154, 242 (1989).n G . Bodenhausen, R. Freeman, R. Niedermeyer

and D.L. Turner, J. Magn. Reson. 26, 133 (1977).12P. Bachmann, W.P. Aue, L. Miiller and R.R.

Ernst, J. Magn. Reson. 28, 29 (1977).13J. Keeler and D. Neuhaus, J. Magn. Reson.

63, 454 (1985).14L. Miiller and R.R. Ernst, Mol. Phys. 38, 963

(1979).15D.J. States, R.A. Haberkorn and D.J. Ruben,

J. Magn. Reson. 48, 286 (1982).

16G. Drobny, A. Pines, S. Sinton, D. Weitekampand D. Wemmer, Symp. Faraday Soc. 13, 49(1979).

17G. Bodenhausen, R.L. Void and R.R. Void, J.Magn. Reson. 37, 93 (1980).

18D. Marion and K. Wiithrich, Biochem. Bio-phys. Res. Commun. 113, 967 (1983).

19R.N. Bracewell, The Fourier Transform andIts Applications, 2nd Ed., McGraw-Hill, New York,1986.

20G. Bodenhausen, H. Kogler and R.R. Ernst, J.Magn. Reson. 58, 370 (1984).

21A.D. Bain, J. Magn. Reson. 56, 418 (1984).22J. Jeener, B.H. Meier, P. Bachmann and R.R.

Ernst, J. Chem. Phys. 71, 4546 (1979).23A.A. Bothner-By, R.L. Stephens, J. Lee, CD.

Warren and R.W. Jeanloz, J. Am. Chem. Soc. 106,811 (1984).

24R.R. Ernst, Rev. Sci. Instrum. 36, 1689(1965).

25R.R. Ernst, J. Magn. Reson. 1, 7 (1969).26E. Bartholdi and R.R. Ernst, J. Magn. Reson.

11, 9 (1973).27R. Deutsch, Nonlinear Transformations of

Random Processes, Prentice-Hall, Englewood Cliffs,New Jersey, 1962.

28J.S. Bendat and A.G. Piersol, Random Data,2nd Ed., John Wiley and Sons, New York, 1986.

29R.R. Ernst and H. Primas, Helv. Phys. Ada36, 583 (1963).

30A.Z. Gurevich, I.L. Barsukov, A.S. Arsenievand V.F. Bystrov, J. Magn. Reson. 56, 471 (1984).

31C.A.G. Haasnoot, F.J.M. van de Ven and C.W.Hilbers, J. Magn. Reson. 56, 343 (1984).

32J. Cavanagh and M. Ranee, J. Magn. Reson.87, 408 (1990).

33J. Cavanagh and M. Ranee, Ann. ReportsNMR Sped. 27, 1 (1993).

34J. Cavanagh and M. Ranee, J. Magn. Reson.88, 72 (1990).

35(a) A.J. Shaka, C.J. Lee and A. Pines, J. Magn.Reson. 77, 274 (1988); (b) S.P. Rucker and A.J.Shaka, Mol. Phys. 68, 509 (1989).

36M.R. Bendall, D.T. Pegg and D.M. Doddrell,J. Magn. Reson. 52, 81 (1983).

37A. Bax, R.H. Griffey and B.L. Hawkins, J.Magn. Reson. 55, 301 (1983).

38A.G. Palmer, III, J. Cavanagh, R.A. Byrd andM. Ranee, J. Magn. Reson. 96, 416 (1992).

Vol. 16, No. 1/2 67

39A.G. Palmer, III, J. Cavanagh, P.E. Wrightand M. Ranee, J. Magn. Reson. 93, 151 (1991).

40J. Cavanagh, A.G. Palmer, III, P.E. Wrightand M. Ranee, J. Magn. Reson. 91, 429 (1991).

41G. Bodenhausen and D. J. Ruben, Chem. Phys.Lett. 69, 185 (1980).

42A.G. Palmer, III, Current Opinion in Biotech-nology, 4, 385 (1993).

43A.G. Palmer, III, N.J. Skelton, W.J. Chazin,P.E. Wright and M. Ranee, Mol. Phys. 75, 699(1992).

44L.E. Kay, L.K. Nicholson, F. Delagio, A. Baxand D.A. Torchia, J. Magn. Reson. 97, 359 (1992).

45G.A. Morris and R. Freeman, J. Am. Chem.Soc. 101, 760 (1979).

46D.P. Burum and R.R. Ernst, J. Magn. Reson.39, 163 (1980).

47H.Y. Carr and E.M. Purcell, Phys. Rev. 94,630 (1954).

4 8S. Meiboom and D. Gill, Rev. Sci. Instrum.29, 688 (1958).

49D.M. Doddrell, D.T. Pegg and M.R. Bendall,J. Magn. Reson. 48, 323 (1982).

50N.J. Skelton, A.G. Palmer, III, M. Akke, J.Kordel, M. Ranee and W.J. Chazin, J. Magn. Re-son., Ser. B, 102, (in press, 1993).

51L.E. Kay, P. Keifer and T. Saarinen, J. Am.Chem. Soc. 114, 10663 (1992).

52J.C. Madsen and O.W. S0rensen, J. Magn. Re-son. 100, 431 (1992).

53J.C. Madsen, O.W. S0rensen, P. S0rensen andF.M. Poulsen, J. Biomol. NMR 3, 239 (1993).

54A.J. Shaka, P.B. Barker and R. Freeman, J.Magn. Reson. 64, 547 (1985).

sensitivity improvement in multi-dimensional nmr spectroscopy

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