NUCLEAR MA G NETIC RES O NA NCE F OURIER TRANSFOR M SPECTROSCOPY

Nobel Lect ure, Dece mber 9, 1992 b y

R IC H AR D R. E R N S T Laboratoriu m für Physikalische Che mie, Eidgenössische Technische Hoch- sch ule, E T H- Zentr u m 8092 Z urich, S witzerlan d

T he worl d of t he n uclear s pi ns is a tr ue para dise for t heoretical a n d e x p eri m e nt al p h ysi cists. It s u p pli es, f or e x a m pl e, m ost si m pl e test s yst e ms for de monstrating the basic concepts of quantu m mechanics and quantu m statistics, an d n u mero us textbook-like exa m ples have e merge d. On the ot her ha n d, t he ease of ha n dli n g n uclear s pi n s yste ms pre desti nates t he m for testi ng no vel ex peri me ntal co nce pts. I n dee d, t he u ni versal proce d ures of coherent spectroscopy have been developed predo minantly within nucle- ar magnetic resonance ( N M R) and have found widespread application in a v ari et y of ot h er fi el ds. Se veral key ex peri me nts of mag netic reso na nce ha ve alrea dy bee n ho n- ore d b y p h ysics No bel prizes, starti ng wit h t he fa mo us molec ular bea m experi ments by Isi dor I. Rabi (1-3) ackno wle dge d in 1944, follo we d by the classical N M R experi ments by E d war d M. Purcell (4) an d Felix Bloch (5,6), h o n or e d wit h t h e 1 9 5 2 pri z e, a n d t h e o pti c al d et e cti o n s c h e m es b y Alfr e d K astl er ( 7), l e a di n g t o a pri z e i n 1 9 6 6. S o m e f urt h er p h ysi cs N o b el pri z e wi n ners have bee n associate d i n vario us ways wit h mag netic reso na nce: Jo h n H. Va n Vleck develo pe d t he t heory of dia- a n d para mag netis m a n d i ntro- d uce d the mo ment metho d into N M R, Nicolaas Bloe mbergen ha d a major i mpact on early relaxation theory and measure ments; Karl Alex Müller has contrib ute d significantly to electron para magnetic resonance; Nor man F. R a m s e y is r e s p o n si bl e f or t h e b asi c t h e or y of c h e mi c al s hifts a n d J co u pli ngs; a n d Ha ns G. De h melt has develo pe d p ure n uclear q ua dr u pole reso na nce. B ut not o nly for p hysicists is n uclear mag netic reso na nce of great fasci na- tio n. More a n d more c he mists, biologists, a n d me dical doctors discover N M R, not so m uc h for its co nce pt ual bea uty b ut for its extraor di nary usef ul ness. I n t his co ntext, a great n u mber of ma g netic reso na nce tools h a v e b e e n i n v e nt e d t o e n h a n c e t h e p o w er of N M R i n vi e w of a v ari et y of a p plicatio ns (8-15). T his Nobel lect ure provi des a gli m pse be hi n d t he scene of an N M R tool maker’s workshop. N uclear s pi n syste ms possess u ni q ue pro perties t hat pre desti nate t he m for molec ular st u dies: Ric h ar d R. Er nst 1 3

(i) The n uclear sensors provi de d by nat ure are extre mely well localize d, with a dia meter of a fe w fe mto meters, an d can re port on local affairs i n t h eir i m m e di at e vi ci nit y. It is t h us p ossi bl e t o e x pl or e m ol e c ul es a n d matter i n great detail. (ii) T he i nteractio n e ner g y of t he se nsors wit h t he e n viro n me nt is ex- tr e m el y s m all, wit h l ess t h a n 0. 2 J / m ol, c orr es p o n di n g t o t h e t h er m al e nergy at 30 m K, a n d t he mo nitori ng of molec ular pro perties is virt ually pert urbatio n-free. Nevert heless, t he i nteractio n is hig hly se n- sitive to t he local e nviro n me nt. (iii) Geo metrical i nfor matio n ca n be obtai ne d fro m n uclear pair i nterac- tio ns. Mag netic di polar i nteractio ns provi de dista nce i nfor matio n, w hil e s c al ar J- c o u pli n g i nt er a cti o ns all o w o n e t o d et er mi n e di h e dr al b o n d a n gl es.

O n first si g ht, it m a y b e ast o nis hi n g t h at it is p ossi bl e t o a c c ur at el y d et er- mine intern uclear distances by ra dio freq uencies with wavelengths 1 m, t h at s e e mi n gl y vi ol at e t h e q u a nt u m m e c h a ni c al u n c ert ai nt y r el a- ti o n, wit h t h e li n e ar m o m e nt u m p = 2 π h / λ , as it a p pli es t o scattering ex peri ments or to a microsco pe. It is i m portant that in magnetic r es o n a n c e t h e g e o m etri c i nf or m ati o n is e n c o d e d i n t h e s pi n H a milt o ni a n, w h er e are t he n uclear coor di nates. A n acc urate geo metric measure ment, therefore, boils do wn to an accurate energy mea- s ure ment that can be ma de as precise as desire d, provi de d that the observa- ti o n ti m e t is e xt e n d e d a c c or di n g t o A n u p p er li mit of t is i n practice give n by t he fi nite lifeti me of t he e nergy eige nstates d ue to relax- ation processes. Thus, the accuracy of N M R measure ments is not restricte d by t he wavele ngt h b ut rat her by relaxatio n-li mite d lifeti mes. The infor mation content of a nuclear spin Ha miltonian an d the associat- e d relaxation s u pero perator of a large molec ule, e.g. a protein, is i m mense. It is p ossi ble t o deter mi ne t he c he mical s hift fre q ue ncies of h u n dre ds of s pins in a molec ule to an acc uracy of 16-18 bits. Intern uclear distances for thousan ds of proton pairs can be measure d to about 0.1 A. Several hun dre d dihe dral angles in a molec ule can be deter mine d with an uncertainty of less t h a n 1 0°. T he wea k ness of t he n uclear s pi n i nteractio ns, so far descri be d as a n a d va ntage, lea ds o n t he ot her ha n d to se vere detectio n proble ms. Large n u mbers of s pins are req uire d to discri minate the weak signals fro m noise. Un der o pti m u m con ditions with mo dern high fiel d N M R s pectro meters, 1 0 1 4 - 1 0 1 5 s pi ns of o n e ki n d ar e n e e d e d t o d et e ct a si g n al wit hi n a p erf or m- a n c e ti m e of o n e h o ur. T h e l o w si g n al-t o- n ois e r ati o is t h e m ost li miti n g ha n dica p of N M R. A ny i ncrease by tec h nical mea ns will sig nifica ntly exte n d t he possible ra nge of N M R a p plicatio ns. This clearly defines the t wo goals that ha d to be achieve d d uring the past t hree deca des to pro mote N M R as a practical tool for molec ular str uct ure deter mi natio n: (i) O pti mizatio n of t he sig nal-to- noise ratio. 1 4 Che mistry 1991

(ii) Develo p ment of proce d ures to co pe with the enor mo us a mo unt of i n here nt molec ular i nfor matio n.

O NE-DI ME NSIO NAL FOURIER TRA NSFOR M SPECTROSCOPY A major i m prove me nt i n t he sig nal-to- noise ratio of N M R has bee n achieve d in 1964 by the conception of Fourier transfor m spectroscopy. The b asi c pri n ci pl e, p ar all el d at a a c q uisiti o n, l e a di n g t o t h e m ulti pl e x a d v a n- ta ge, was a p plie d alrea d y b y Mic helso n i n 1891 for o ptical s pectrosco p y (16) a n d e x pli citl y f or m ul at e d b y F ell g ett i n 1 9 5 1 ( 1 7). H o w e v er, t h e a p pr o a c h use d in o ptics, s patial interfero metry, is uns uite d for N M R where an inter- f er o m et er wit h t h e n e c ess ar y r es ol uti o n w o ul d r e q uir e a p at h le n gt h of at l e ast 3 1 0 8 m. Weston A. Anderson at Varian Associates, Palo Alto, was experi menting i n t he earl y sixties wit h a mec ha nical m ulti ple fre q ue nc y ge nerator, t he “ w h e el of f ort u n e ” t h at w as c o n c ei v e d t o si m ult a n e o usl y e x cit e t h e s pi n syste m with N frequencies in order to shorten the perfor mance ti me of an experi ment by a factor N, recor ding the response of N spectral ele ments in parallel (18). It was soo n recog nize d t hat more elega nt sol utio ns were nee de d for a co m mercial s uccess. N u mero us possibilities are co ncei vable for t he ge neratio n of a broa d ban d freq uency so urce that allo ws the si m ultaneo us irra diation of an entire s p e ctr u m. W e m e nti o n f o ur s c h e m es: (i) R a di o fr e q u e n c y p uls e e x cit ati o n, (ii) stoc hastic ra n do m noise excitatio n, (iii) ra pi d sca n excitatio n, (i v) excita- tion by a co m p uter-synthesize d m ulti ple-freq uency wavefor m. For each sc he me, a differe nt ty pe of data processi ng is req uire d to derive t he desire d N M R spectru m. The a p plication of ra dio freq uency (rf) p ulse excitation was s uggeste d by Westo n A. A n derso n to t he a ut hor for a detaile d ex peri me ntal st u d y i n 1 9 6 4 ( 1 9- 2 1). T h e e x p eri m e nt is e x pl ai n e d i n Fi g. 1. T o t h e s a m pl e t h at is p ol ari z e d i n a st ati c m a g n eti c fi el d al o n g t h e z- a xis, a n rf p uls e is a p pli e d al o n g t he y-axis. It r otates t he ma g netizati o n vect ors M k of all s pi ns I k b y π/ 2 i nt o a n ori e nt ati o n p er p e n di c ul ar t o t h e st ati c fi el d:

usi n g a co n ve nie nt arro w notatio n (23) wit h t he acti n g o perator, here a rotation, on the to p of the arro w. The follo wing free in d uction decay ( FI D) co nsists of t he s u per positio n of all ei ge n mo des of t he s yste m. A n o bser va ble o perat or D is use d t o detect t he si g nal t hat is F o urier-tra ns- for me d for se parati n g t he differe nt s pectral co ntrib utio ns. Fi g ure 1 co n- tains an early exa mple of Fourier transfor m spectroscopy using the sa mple 7-et hoxy-4- met hyl-co u mari n of w hic h 500 FI D’s were co-a d de d a n d Fo ur- ier-transfor me d to pro d uce the Fo urier transfor m s pectr u m (F T) sho wn (22). A slo w passage continuous wave spectru m (c w), recorded in the sa me total ti me of 500 s, is sho wn also in Fig. 1 for co m parison of the signal-to- n ois e r ati os. Ric h ar d R. Er nst 1 5

F REE PRECESSI O N

Fig ure 1. Sc he matic re prese ntatio n of p ulse Fo urier tra nsfor m s pectrosco py by t he exa m ple of 60 M Hz proto n reso na nce of 7-et hoxy-4- met hyl-co u mari n (22). A i niti al rf p ulse, re pre- se nte d by t he rotatio n s u pero perator P, excites fro m t he e q uili bri u m state tra ns verse mag netizatio n Free precessio n of all co here nces i n parallel u n der t he evol utio n s u pero per- at or E(t) lea ds t o t he fi nal state Detectio n wit h t he detectio n o perator D pro d uces t he s ho w n FI D (s u m of 500 sca ns) w hic h, after Fo urier tra nsfor matio n, pro d uces t he s pectr u m F T. For co m pariso n, a co nti n uo us wave s pectr u m C W is s ho w n t hat has bee n recor de d i n t he sa me total ti me of 500 s u n der i de ntical co n ditio ns.

T o pl e as e t h e m or e m at h e m ati c all y i n cli n e d r e a d er, t h e e x p eri m e nt c a n als o be ex presse d b y t he e v ol uti o n of t he de nsit y o perat or σ(t) u n d er t h e pre paration s u pero perator = e x p -i a n d t he e vol utio n s u per- o perat or = e x p Γ t}. T he s u pero perator is d efi n e d b y

= [ F y , A] wit h where is a co m ponent ang ular mo ment u m o pe- r at or of s pi n k. the Ha miltonian co m mutator superoperator, [H ,A ], a n d is t he relaxatio n s u pero perator. T he ex pectatio n val ue < D > (t) of t he observable o perator D is t he n give n by

(t) = Tr [ 2] w h er e r e pr es e nts t h e t h er m al e q uili bri u m d e nsit y o p er at or of t h e s pi n syste m. The re d uction in perfor mance ti me is deter mine d by the n u mber of s p e ctr al el e m e nts N, i. e. t h e n u m b er of si g nifi c a nt p oi nts i n t h e s p e ctr u m, ro u g hl y gi ve n b y N = w h er e F is t h e t ot al s p e ctr al wi dt h a n d ∆ f a t y pi c al si g n al li n e wi dt h. A c orr es p o n di n g i n cr e as e i n t h e si g n al-t o- n ois e r ati o of per u nit ti me ca n be obtai ne d by co-a d di ng a n a p pro priate nu mber of FI D signals originating fro m a repetitive pulse experi ment. The signal-to-noise gain can be a p preciate d fro m Fig. 1. It has been kno wn since a long ti me that the freq uency res ponse f unction (s pectr u m) of a li near syste m is t he Fo urier tra nsfor m of t he i m p ulse 1 6 Che mistry 1991 res ponse (free in d uction decay). This was alrea dy i m plicitly evi dent in the wor k of Jea n Ba ptiste Jose p h Fo urier w ho i n vesti gate d i n 1822 t he heat con d uction in soli d bo dies (24). Lo we an d Norberg have prove d in 1957 this relatio n also to hol d for s pi n syste ms des pite t heir stro ngly no nli near res p o nse c haracteristics (25). Stoc hastic testi ng of u nk no w n syste ms by w hite ra n do m noise has bee n pr o p os e d i n t h e 1 9 4 0s b y N or b ert Wi e n er ( 2 6). S o t o s a y, t h e c ol or of t h e o ut p ut noise carries t he s pectral i nfor matio n o n t he i n vesti gate d s yste m. T he first a p plicatio ns of ra n do m noise excitatio n i n N M R ha ve bee n pro- pose d in depen dently by Russel H. Varian (27) an d by Hans Pri mas (28, 29), for broa dban d testing an d for broa dban d deco u pling, res pectively. The first s uccessf ul experi ments using ran do m noise irra diation le d to heteron uclear “ n ois e d e c o u pli n g ” ( 3 0, 3 1), a m et h o d t h at pr o v e d t o b e ess e nti al f or t h e practical s uccess of carbon-l 3 resonance in che mical a p plications. In 1971, Reinhold Raiser (32) and the author (33) independently de mon- strate d stochastic resonance as a means to i m prove the signal-to-noise ratio of N M R by broa dba n d irra diatio n. Here, t he co m p ute d cross-correlatio n f u nctio n

Fig ure 2. Sc he matic re prese ntatio n of stoc hastic reso na nce by t he exa m ple of 56.4 M Hz fl uori ne reso na nce of 2,4- difl uorotol ue ne (33). Excitatio n wit h a bi nary pse u do-ra n do m se q ue nce of le ngt h 1023 ge nerates t he res po nse n,(t). Cross-correlatio n of t he t wo sig nals pro d uces w hic h, after Fo urier tra nsfor matio n, delivers t he s ho w n s pectr u m. A n alter native procedure, t hat has act ually bee n use d i n t his case, co m p utes t he i n divi d ual Fo urier tra nsfor ms of n,(t) a n d n o (t) a n d m ulti plies t he co m plex co nj ugate wit h to o btai n t he sa me s pectr u m. Ric h ar d R. Er nst 1 7 ori ne reso na nce of 2,4- difl uorotol ue ne. A bi nary pse u do-ra n do m seq ue nce of l e n gt h 1 0 2 3 wit h a m a xi m al w hit e s p e ctr u m is us e d f or e x cit ati o n. Its a dva ntages are t he pre dictable s pectral pro perties a n d t he co nsta nt rf po wer. T he lo w pea k po wer p uts less stri n ge nt re q uire me nts o n t he elec- tronic equip ment. Disadvantages concern the si multaneous irradiation and detection that can lea d to line broa dening effects which are absent in p ulse Fourier transfor m spectroscopy where perturbation an d detection are sepa- rate d in ti me. A f urther disa dvantage, when using real ran do m noise, is the pro ba bilistic nat ure of t he res po nse t hat re q uires exte nsi ve a vera gi n g to obtain a stable mean val ue. Higher or der correlation f unctions, s uch as allo w also t he c haracterizatio n of no nli near tra nsfer pro perties of t he i nvestigate d syste m (26). T his has bee n ex ploite d exte nsively by Bl ü mic h a n d Ziesso w for N M R measure ments (34, 35). A t hir d a p pr o a c h, r a pi d s c a n s p e ctr os c o p y, i niti all y pr o p os e d b y D a d o k a n d S prec her (36), ac hie ves a virt uall y si m ulta ne o us excitati o n of all s pi ns b y a ra pi d freq ue ncy s wee p t hro ug h t he s pectr u m (37, 38). T he res ulti ng s pectr u m is strongly distorte d, b ut can be correcte d mathe matically beca use of the deter ministic nat ure of the distortions. Correction a mo unts to convo- l utio n wit h t he sig nal of a si ngle reso na nce meas ure d u n der i de ntical c o n diti o ns or si m ul at e d o n a c o m p ut er. A n e x a m pl e is gi v e n i n Fi g. 3. It is interesting to note the si milarity of a ra pi d scan s pectr u m with a FI D exce pt for t he s uccessively i ncreasi ng oscillatio n freq ue ncy. Fi n all y, b y c o m p ut er s y nt h esis, it is p ossi bl e t o c o m p ut e a n e x cit ati o n f u n cti o n wit h a virt u all y ar bitr ar y e x cit ati o n pr ofil e. T his h as ori gi n all y b e e n utilize d for deco u pling p ur poses by To mlinson an d Hill (39) b ut is also the

Fig ure 3. Sc he matic re prese ntatio n of ra pi d sca n s pectrosco py. T he stro ngly distorte d sa m ple s pectr u m o btai ne d by a ra pi d fre q ue ncy s wee p ca n be correcte d by co nvol utio n wit h t he e q ually s wee p- distorte d s pectr u m of a o ne-li ne test sa m ple. 1 8 Che mistry 1991 basis f or c o m p osite p ulse excitati o n sc he mes t hat ha ve pr o ve d t o be ver y po werf ul (40,41). A mong the broa dban d excitation techniques, pulse excitation is the only o ne t hat allo ws for a ri goro us a nal ytical treat me nt irres pecti ve of t he co m plexity of the s pin syste m. It does not lea d to any metho d-inflicte d line broa de ni ng as i n stoc hastic reso na nce nor to correctio n-resista nt sig nal distortio ns as i n ra pi d sca n s pectrosco py of co u ple d s pi n syste ms (38). P ulse Fo urier tra nsfor m s pectrosco py is co nce pt ually a n d ex peri me ntally si m ple a n d, last b ut not least, it ca n easily be ex pa n de d a n d a da pte d to virt ually all conceivable ex peri mental sit uations. Relaxation meas ure ments, for exa m- ple, req uire j ust a mo difie d relaxation-sensitive pre paration seq uence, s uch as a p uls e p air f or T 1 meas ure me nts (42) a n d a p ulse pair f or T 2 m e as ur e m e nts ( 4 3). Als o t h e e xt e nsi o n t o c h e mi c al e x c h a n g e st u di es usi ng t he sat uratio n tra nsfer ex peri me nt of Forsé n a n d Hoff ma n (44) is e asil y p ossi bl e. It should be mentioned at this point that pulsed N M R experi ments were s uggeste d alrea dy by Felix Bloch in his fa mo us 1946 pa per (6), an d the first ti me- do main magnetic resonance experi ments have been perfor me d 1949 b y H. C. T orr e y ( 4 5) a n d, i n p arti c ul ar, b y Er wi n L. H a h n ( 4 6- 4 8) w h o m a y be regar de d as the tr ue father of p ulse s pectrosco py. He invente d the s pin ec ho ex peri me nt (46) a n d devise d extre mely i m porta nt a n d co nce pt ually bea utif ul soli d state ex peri me nts (49, 50). P ulse Fo urier tra nsfor m s pectrosco py has not o nly re vol utio nize d hig h resolution liquid state N M R spectroscopy, but it has unified N M R method- ology across all fiel ds, fro m soli d state resonance, thro ugh relaxation mea- s ure me nts, to hig h resol utio n N M R, wit h n u mero us s pill-overs also i nto ot her fiel ds s uc h as io n c yclotro n reso na nce (51), micro wa ve s pectrosco p y (52), a n d electr o n para ma g netic res o na nce (53). I n t he prese nt c o ntext, it provi de d also the ger m for the develo p ment of m ulti di mensional N M R s pectrosco py.

T WO-DI ME NSIO NAL FOURIER TRA NSFOR M SPECTROSCOPY As lo ng as p urely s pectrosco pic meas ure me nts are ma de, deter mi ni ng t he eige nfreq ue ncies or nor mal mo des of a syste m, o ne- di me nsio nal s pectros- c o p y is f ull y a d e q u at e. I n N M R, t his a p pli es t o t h e m e as ur e m e nt of t h e c he mical s hifts t hat c haracterize t he local c he mical e n viro n me nt of t he diff er e nt n u cl ei. H o w e v er, n o i nf or m ati o n c a n b e o bt ai n e d i n t his m a n n er on the s patial an d to pological relations bet ween the observe d n uclei. T here are t wo i m porta nt pair i nteractio ns i n n uclear s pi n s yste ms, t he scalar thro ugh-bon d electron- me diate d s pin-s pin interaction, the so-calle d J co u pli ng, an d the thro ugh-s pace magnetic di polar interaction. They ar e ill ustr at e d i n Fi g. 4. T h e J c o u pli n g is r e pr es e nt e d b y t h e s c al ar t er m = I, i n t h e s pi n H a milt o ni a n. It is r es p o nsi bl e f or t h e m ulti pl et s plitti ngs i n hig h resol utio n liq ui d-state s pectra. U n der s uitable co n ditio ns, it can lea d to an oscillatory transfer of s pin or der bet ween the t wo s pins I k Ric h ar d R. Er nst 1 9

a n d I 1 . T he ma g netic di polar i nteractio n D m n , o n t h e ot h er h a n d, is r e pr e- se nte d by a traceless te nsor of seco n d ra nk. Its average i n isotro pic sol utio n is z er o a n d it c a n l e a d t o a li n e s plitti n g o nl y i n a nis otr o pi c m e di a. H o w e v er, its ti me mo d ulatio n ca uses also i n isotro pic sol utio n relaxatio n processes that are responsible for a multiexponential recovery to war ds ther mal equi- libri u m a mo n g s pi ns after a pert urbatio n. K no wle d ge of t hese i nteractio ns allo ws one to de d uce geo metric infor mation on molec ular str uct ure in sol ution (54, 55) an d ato mic arrange ments in soli ds. In the o pti m u m case, a co mplete S- di mensional structure of a molecule can be de duce d (56). Alt ho ug h t hese i nteractio ns affect 1 D s pectra, s pecial tec h niq ues are n e e d e d f or t h eir m e as ur e m e nt. I n t h e li n e ar r es p o ns e a p pr o xi m ati o n, it is, b y first pri n ci pl e, i m p ossi bl e t o disti n g uis h b et w e e n t w o i n d e p e n d e nt r es- o na nces a n d a do ublet ca use d b y a s pi n-s pi n i nteractio n. Ex peri me nts to ex plore t he no nli near res po nse pro perties of n uclear s pi n syste ms have bee n k no w n si nce t he fifties. Sat uratio n st u dies usi ng stro ng rf fiel ds yiel d m ulti ple q uant u m transitions that contain connectivity infor mation thro ugh the si multaneous excitation of several spins belonging to the sa me couple d s pi n syste m (57). Partic ularly fr uitf ul were do uble a n d tri ple reso na nce ex peri ments where t wo or three rf fiel ds are a p plie d si m ultaneo usly, res ult- i n g i n d e c o u pli n g a n d s pi n ti c kli n g eff e cts ( 5 8- 6 0). 2 0 Che mistry 1991

T he early m ulti ple reso na nce ex peri me nts have i n t he mea nti me bee n re place d by m ulti- di me nsio nal ex peri me nts. Pair interactio ns a mo ng s pi ns are most co n ve nie ntly re prese nte d i n ter ms of a correlatio n diagra m as s h o w n i n Fi g. 5. T his s u g g ests t h e r e c or di n g of a “t w o- di m e nsi o n al s p e c- tr u m” that establishes s uch a correlation ma p of the corres pon ding s pectral features. The most straight for ward approach may be a syste matic double- reso na nce ex peri me nt w hose res ult ca n be re prese nte d as a n a m plit u de depen ding on the freq uencies a n d of t w o a p pli e d rf fi el ds ( 8, 5 8). A ne w a p proach to meas ure t wo- di mensional (2 D) s pectra has been pro pose d by Jea n Jee ner at a n A m pere S u m mer Sc hool i n Basko Polje, Y ugoslavia, 1971 (61). He s uggeste d a 2 D Fo urier tra nsfor m ex peri me nt c o nsisti n g of t w o π/ 2 p uls es wit h a v ari a bl e ti m e t 1 bet wee n t he p ulses a n d t h e ti m e v ari a bl e t 2 m e as uri n g t h e ti m e el a ps e d aft er t h e s e c o n d p uls e as s ho w n i n Fig. 6 t hat ex pa n ds t he pri nci ples of Fig. 1. Meas uri ng t he res po nse s(t 1 , t 2 ) of the t wo-pulse sequence an d Fourier-transfor mation with respect to both ti me variables produces a t wo-di mensional spectru m of t he desire d for m (62, 63). T his t w o- p uls e e x p eri m e nt b y J e a n J e e n er is t h e f or ef at h er of a w h ol e class of 2 D ex peri me nts (8,63) t hat ca n als o easil y be ex pa n de d t o m ulti- di mensional spectroscopy. Each 2 D experi ment, as sho wn in Figs. 6 and 7, starts wit h a pre paratio n p ulse se q ue nce p w hic h excites co here nces, i.e. co here nt s u per positio ns re prese nte d by t he de nsity o perator σ ( O), t h at ar e allo we d to precess for an evol ution ti me t 1 u n der t he evol utio n s u pero per- at or D uri ng t his perio d, t he co here nces are so-to-say freq ue ncy- l a b ell e d. A f oll o wi n g mi xi n g s e q u e n c e perf or ms a c o ntr olle d tra nsfer of coherence to different n uclear s pin transitions that evolve then d uring t h e detectio n perio d as a f u nctio n of t 2 u n der t he e vol utio n s u pero perator Ê(t 2 ). Ric har d R. Er n st 2 1

Fi g ure 6 . Sc he matic re prese ntatio n of a 2 D ex peri me nt, here wit h a si m ple t wo- p ulse se q ue nce.

T he first p ulse excites co here nces t hat precess d uri ng t 1 a n d are tra nsfere d by t he seco n d p ulse to differe nt tra nsitio ns w here t he co here nces co nti n ue to precess wit h a ne w fre q ue ncy. T he 2 D s pectr u m o btai ne d by a 2 D Fo urier tra nsfor matio n of < D > (t 1 , t2 ) provi des a vis ual re prese nta- ti o n of t he tra nsfer matrix R.

D et e cti o n is p erf or m e d wit h t h e d et e cti o n o p er at or D i n a n al o g y t o Fi g. 1, lea ding to the ex pression

A mo n g t he n u mero us tra nsfer processes t hat ca n be re prese nte d i n t his manner, the most i m portant ones are (8) (i) t h e s c al ar J c o u pli n g, l e a di n g t o “2 D correlatio n s pectrosco py”, ab- breviated C OS Y, (ii) intern uclear cross relaxation, lea ding to “2 D n uclear Overha user effect s pectrosco py”, abbreviate d N O ES Y, a n d (iii) che mical exchange, leading to “2 D exchange spectroscopy”, abbrevi- ate d E XS Y. 2 2 Che mistry 1991

Fig ure 7. Ge neral 2 D ex peri me nt co nsisti ng of a pre paratio n, a n evol utio n, a mixi ng, a n d a detectio n perio d. T he d uratio n t, of t he evol utio n perio d is varie d syste matically fro m ex peri- me nt to ex peri me nt. T he res ulti ng sig nal < D is Fo urier-tra nsfor me d i n t wo di me nsio ns to pro d uce t he 2 D s pectr u m

T he C OS Y tra nsfer (i), w hic h procee ds t hro ug h J co u pli ng, is tr uly a q ua nt u m mec ha nical effect t hat does not fi n d a satisfactory classical ex pla- n ati o n. B y m e a ns of a si n gl e rf mi xi n g p uls e, as i n Fi g. 6, it is p ossi bl e to tra nsfer co here nce of s pi n k, a nti- p hase wit h res pect to s pi n 1 a n d re presente d in the density o perator by the o perator ter m i nto co her- e nce of s pi n 1, a nti- p hase wit h res pect to s pi n k, re prese nte d by

whereby each factor of the above pro duct spin operator can be consi dere d t o b e r ot at e d b y π/ 2 a b o ut t h e x a xis. A nti- p hase co here nce of t he t y pe

l z is o nl y f or m e d d uri n g t h e e v ol uti o n p eri o d w h e n t h er e is a dir e ct s pin-s pin co u pling bet ween the s pins I k a n d I I: Ric h ar d R. Er nst 2 3

This i m plies that in a t wo- di mensional correlation s pectr u m there are cross p e a ks o nl y b et w e e n dir e ctl y c o u pl e d s pi ns ( as l o n g as t h e w e a k c o u pli n g a p pr o xi m ati o n h ol ds). It is als o o b vi o us fr o m E q.[ 7] t h at t h er e is n o n et c o here nce tra nsfer, e. g. a n d t he cross- peak i ntegral m ust disa p- pear, in other wor ds, there is an eq ual n u mber of cross- peak m ulti plet lines wit h positi ve a n d ne gati ve i nte nsit y. A C OS Y s pectr u m, s uc h as t he o ne s ho w n i n Fi g. 8 for t he c yclic deca pe pti de anta mani de (I)

can be use d to fin d pairs of s pins belonging to the sa me co u pling net work of a n a mi n o a ci d r esi d u e i n t h e m ol e c ul e. All str o n g cr oss p e a ks aris e fr o m t wo-bon d an d three-bon d co u plings that allo w, first of all, the assign ment of t h e p airs of N H a n d backbone protons, as in dicate d by C in Fig. 9 for t h e si x a mi n o a ci d r esi d u es wit h N H pr ot o ns. I n a d diti o n, it is als o p ossi bl e to assig n t he si de-c hai n proto ns. T he tra nsfers (ii) a n d (iii) of N O ES Y a n d E XS Y ex peri me nts i nvolve incoherent, dissi pative processes that drive the syste m back to eq uilibri u m after an initial pert urbation in an ex ponential or m ultiex ponential manner. They require an extended mixing ti me during which the rando m processes are gi ve n a c ha nce t o occ ur. B ot h pr ocesses ca n be i n vesti gate d wit h t he s a m e t hr e e- p uls e s c h e m e s h o w n i n Fi g. 1 0 b ( 8, 6 4- 6 7). T h e mi xi n g p eri o d is brac kete d b y t w o π /2 p ulses t hat tra nsf or m c o here nce i nt o static s pi n or der a n d bac k i nto co here nce. T he exc ha n ge processes tra nsfer t he s pi n or der bet wee n differe nt s pi ns or bet wee n differe nt c he mical s pecies, re- s pectively. T his ty pe of tra nsfer ca n be u n derstoo d base d o n classical ki netic m o d els. T h e r es ulti n g 2 D s p e ctr u m r e pr es e nts a ki n eti c m atri x wit h cr oss- peak intensities pro portional to the exchange-rate constants of pse u do first or der reacti o ns 2 4 Che mistry 1991

for m sol utio n (at 250 K) i n a co nto ur-li ne re prese ntatio n. Positi ve a n d negati ve co nto urs are not disting uishe d. The s pectr u m has been recor de d by Dr. Martin Blackle dge.

F o r t h e N O E S Y t r a n s f e r , t h e e x c h a n g e - r a t e c o n s t a n t s a r e g i v e n b y t h e cross-relaxatio n rate co nsta nts, t hat are d ue to mag netic di polar i nterac-

ti o n, a n d are pr o p orti o nal t o f or n ucle ar p airs I k a n d I 1 i n a d d i t i o n t o a d e p e n d e n c e o n t h e c o r r e l a t i o n t i m e o f t h e m o l e c u l a r t u m b l i n g i n s ol uti o n. T he dista nce de pe n de nce ca n be use d t o meas ure relati ve or, if is k no w n, absol ute dista nces i n molec ules. I n t he co urse of t he assi g n me nt process, t he N O ES Y cross pea ks allo w a n i de ntificatio n of s patiall y nei g h- b ori n g pr ot o ns i n a m olec ule, i m p orta nt f or pr ot o ns t hat bel o n g t o a djace nt a mino aci d resi d ues in pe pti des. A N O ES Y s pectr u m of anta mani de is given i n Fig. 11. T he cross peaks bet wee n seq ue ntial backbo ne proto ns of a dja- ce nt a mi n o aci d resi d ues, c o ntai ne d i n Fi g. 11, are mar ke d i n Fi g. 9 b y N. It is see n t hat, toget her wit h t he J-cross peaks fro m t he C OS Y s pectr u m of Fig. 8, t wo u nbroke n c hai ns of co n necti vities are fo u n d t hat ca n be use d for t he i de ntificatio n of t he bac kbo ne proto ns. T he t wo c hai ns are disjoi nt d ue to t h e a b s e n c e o f N H p r o t o n s i n t h e f o u r p r o l i n e r e s i d u e s . T h e g e n e r a l a s s i g n m e n t p r o c e d u r e o f p r o t o n r e s o n a n c e f r e q u e n c i e s b a s e d o n C O S Y Ric h ar d R. Er nst 2 5

Fig ure 9. Assig n me nt of bac k bo ne proto ns i n anta manide by the co mbination of C OS Y ( C) and N O E S Y ( N) cross pea ks. T he missi ng N H proto ns i n t he fo ur proli ne resi d ues brea k t he c hai n of se q ue ntial C, N co n nectivities. a n d N O ES Y s pectra has bee n establis he d by W üt hric h a n d his researc h gr o u p ( 5 6). Base d o n a c o m plete or partial set of assi g ne d res o na nces, it is t he n possible to de d uce molec ular str uct ural i nfor matio n. Eac h N O ES Y cross- pea k i nte nsit y deli vers a n i nter n uclear dista nce t hat ca n be use d i n a ma n ual or co mputerize d process to construct a molecular mo del that is co mpatible wit h t h e e x p eri m e nt al d at a. I n t his pr o c ess it is als o p ossi bl e t o e m pl o y scalar co u pli ng co nsta nts extracte d fro m C OS Y-ty pe s pectra ( most co nve- nie ntly fro m E. C OS Y s pectra, as me ntio ne d later). Accor di ng to t he Kar- pl us-r el ati o ns ( 5 4), t h er e is a n a c c ur at e r el ati o n b et w e e n vi ci n al c o u pli n g co nsta nts a n d di he dral a ngles. I nge nio us co m p uter proce d ures to deter- mine molec ular str uct ures base d on N M R data have, for the first ti me, been 2 6 Che mistry 1991

Fi g ure 1 0 . So me of t he most usef ul ho mo n uclear 2 D ex peri me nts: (a) C O S Y, ( b) N O E S Y or E X S Y, (c) relaye d C O S Y, ( d) T O C S Y or R O E S Y i n t he rotati ng coor di nate syste m, (e) m ulti ple quantu m spectroscopy. d e v el o p e d b y K urt W üt hri c h a n d his r es e ar c h te a m a n d test e d o n a l ar g e n u mber of s mall to me di u m-size protei ns (56, 68-71). At prese nt, mai nl y t wo co m p uter algorit h ms for t he str uct ure deter mi natio n are i n use, t he dista nce ge o metr y al g orit h m (72, 73) a n d m o dificati o ns of it a n d t he re- strai ne d molec ular dy na mics algorit h m (74, 75), agai n wit h ma ny variatio ns. The str uct ural proble m in anta mani de will be disc usse d later, as it involves intra molec ular dyna mic processes that co mplicate the sit uation. Cross peaks in a N OES Y-type exchange spectru m can also originate fro m process (iii), i.e. fro m c he mical exc ha nge, a n d t he t hree- p ulse ex peri me nt of Fi g. 1 0 b is i n d e e d v er y s uit e d t o i n v esti g at e c h e mi c al e x c h a n g e n et w or ks (64, 65, 76). A disti ncti o n of t he t w o t y pes of pea ks is n ot p ossi ble b y inspection of a single 2 D spectru m. Ho wever, variable te mperature studies are ofte n co ncl usi ve. At s ufficie ntly lo w te m perat ure w here c he mical ex- change beco mes slo w, only N O ES Y cross peaks sho ul d re main. Another way of disti nctio n are rotati ng fra me ex peri me nts as me ntio ne d i n t he next s e cti o n. 2 7

4

5

6

7

8

7 6 5 4 3 2

Figure 11. 400 M Hz proton resonance N OES Y spectru m of anta manide in chlorofor m (at 25 O K) i n a co nto ur-li ne re prese ntatio n. T he s pectr u m has bee n recor de d by Dr. Marti n Blac kle dge.

A t y pi c al 1 3 C che mical exchange spectru m of a mixture of cis- decalin an d trans- decalin is given in Fig. 12. The s pectr u m de monstrates the well kno wn confor mational stability of trans- decalin whereas fo ur pairs of carbon s pins of cis- decali n are i nvolve d i n a co nfor matio nal exc ha nge process, givi ng rise to t wo pairs of cross peaks (76).

M O DIFIE D T W O- DI ME NSI O N AL F O URIER EXPERI ME NTS Starting fro m the t wo prototy pe 2 D Fo urier ex peri ments, an enor mo us n u mber of mo difie d, ex pa n de d, a n d i m prove d ex peri me nts has bee n s ug- geste d. Many of the m have foun d a place in the routine arsenal of the N M R s pectrosco pist. A first class of ex peri me nts, as vis ualize d i n Fig. 13, ca uses exte n de d correlatio n t hro u g h t wo or more tra nsfer ste ps: Rela ye d correla- tio n ex peri me nts i n vol ve t wo-ste p correlatio n a n d total correlatio n s pec- troscopy ( T O CS Y) achieves m ultiple step correlation. The latter experi ment lea ds to the i m portant class of rotating fra me ex peri ments, incl u ding rotat- i ng fra me Over ha user effect s pectrosco py ( R O ES Y) a n alter native to 2 8 Che mistry 1991

N O ES Y. Fi nally, also m ulti ple q ua nt u m s pectrosco py allo ws o ne to i nvesti- gate co n necti vity i n s pi n syste ms. A seco n d class of ex peri me nts atte m pts t h e s i m p l i f i c a t i o n o f s p e c t r a b y e x c l u s i v e c o r r e l a t i o n ( E . C O S Y ) , m u l t i p l e q ua nt u m filteri ng, a n d s pi n-to pology filtratio n.

Relayed Correlatio n I n a s t a n d a r d C O S Y e x p e r i m e n t , c o h e r e n c e i s t r a n s f e r e d e x c l u s i v e l y b e - t wee n t wo directl y co u ple d s pi ns b y mea ns of a si n gle mixi n g p ulse. B y a

Fi g ure 1 2. 2 D 1 3 C c he mical exc ha n ge s pectr u m ( E XS Y) of a mixt ure of cis- a n d tra ns- decali n recorded at 22.5 M Hz and 241 K (76). A stacked plot and a contour representation are given wit h t he assi g n me nt of t he pea ks. Ric h ar d R. Er nst 2 9 s e q u e n c e of t w o π/ 2 p ulses, as i n Fi g. 10c, it is p ossi ble t o effect a tra nsfer

across t wo seq uential co u plings fro m s pin I k t o s pi n I 1 thro ugh the relay s pin

I r ( 7 7, 7 8)

= During the extended mixing period (assu mingJ kr t1 = =

it is t h us necessar y to refoc us t he a nti- p hase c haracter of t he I r s pi n

co here nces wit h res pect to s pi n I k a n d create a nti- p hase c haracter wit h

res pect t o s pi n I 1 to allo w for a secon d transfer by the secon d mixing p ulse.

R el a y e d c orr el ati o n is us ef ul w h e n e v er t h e r es o n a n c e of t h e r el a y s pi n I r c a n n ot u n a m bi g u o usl y b e i d e ntifi e d. Wit h a r el a y e x p eri m e nt it is t h e n

n e v ert h el ess p ossi bl e t o assi g n s pi ns I k a n d I l t o t h e s a m e c o u pli n g n et w or k (e.g. belo ngi ng to t he sa me a mi no aci d resi d ue i n a poly pe pti de c hai n). It is

Fi g ure 13. Exte nsio ns of t he sta n dar d C O S Y ex peri me nt. Relaye d correlatio n, total correlatio n spectroscopy ( T O CS Y), and multiple quantu m spectroscopy ( M QS) increase the infor mation co nte nt, w hile excl usive correlatio n ( E. C O S Y), m ulti ple q ua nt u m filteri ng ( M QF), a n d s pi n to pology filtratio n re d uce t he co m plexity. Bot h ave n ues ca n lea d to t hree- di me nsio nal s pectros- c o p y. 3 0 Che mistry 1991

us ually of a dvantage to refoc us the effects of the che mical shift precession d uri ng t he mixi ng perio d by i ncor porati ng a ce ntral π p uls e as i n Fi g. Relaye d co here nce tra nsfer is de mo nstrate d by 300 M Hz proto n reso- na nce s pectra of t he li near no na pe pti de b userili n, pyro- Gl u- His- Tr p-Ser-

Tyr- D-Ser-Leu- Arg-Pro- N H C H 2 C H 3 . Figure 14a sho ws a (double-quantu m filtere d) C OS Y s pectr u m an d Fig. 14b the corres pon ding relaye d C OS Y s pectr u m (79). In both s pectra, the resonance connectivities for the resi d ue l e u ci n e ar e m ar k e d. It is e vi d e nt t h at i n t h e C O S Y s p e ctr u m o nl y n e ar est nei g h bor proto ns are co n necte d b y cross pea ks: a n d On the other hand in the relayed C OS Y s pectr u m, also t he next nearest neig hbors a n d are connecte d. The thir d pair of relaye d cross peaks is w e a k d u e t o t h e hi g h m ulti pli cit y of t h e r es o n a n c e a n d n ot visi bl e i n t h e co nto ur re prese ntatio n of Fig. 14b. Si milar relaye d cross peaks ca n be fo un d for the other a mino aci d resi d ues.

Rotating Fra me Experi ments By means of an exten de d mixing pulse sequence, transfer of coherence over a n arbitrary n u mber of ste ps is i n pri nci ple possible. I n partic ular, co nti n u- o us wave irra diation lea ds to the mixing of all eigen mo des of a s pin syste m an d corres pon dingly to transfers of coherence bet ween all of the m. This is ex ploite d i n total correlatio n s pectrosco py ( T O CS Y) wit h t he se q ue nce of Fig. 10 d. All s pins belonging to the sa me J-co u pling net work can be i denti- fie d with T O CS Y (80,81). The accurate matching of the precession frequen- cies of t he vario us s pi ns i n t he prese nce of a ra dio freq ue ncy fiel d is cr ucial to e nable a n efficie nt tra nsfer of co here nce. Eit her very stro ng ra dio freq uency fiel ds or specially designe d p ulse seq uences are nee de d for this p ur pose (81). Co here nce tra nsfer is possible w he n t he effecti ve a verage ma g netic fiel d stre n gt hs B i n t h e r ot ati n g fr a m e ar e e q u al wit hi n a co u pli ng co nsta nt, corres po n di n g to a stro n g co u pli ng case i n t he rotati ng fra me. T h e T O C S Y e x p eri m e nt is of i nt er est f or assi g ni n g pr ot o n r es o n a n c es t o i n di vi d u al a mi n o a ci d r esi d u es i n a pr ot ei n. Of p arti c ul ar v al u e is t h at its tr a nsf er r at e is e n h a n c e d b y a f a ct or 2 i n c o m p aris o n t o C O S Y or r el a y e d transfer ex peri ments in the laboratory fra me (80). Another pro perty is that, d ue to the presence of a ra dio-freq uency fiel d, in- phase coherence transfer of t he t y pe Ric h ar d R. Er nst

Fig ure 14. 300 M Hz correlatio n s pectra of t he no na pe pti de b userili n dissolve d i n di met hyl s ulfoxi de. P hase-se nsitive plots wit h e q ual re prese ntatio n of positive a n d negative co nto urs are s ho w n. T he reso na nce co n nectivities are i n dicate d for le uci ne (79). (a) Do u ble q ua nt u m-filtere d C O S Y s pectr u m usi ng t he se q ue nce of Fig. 18. ( b) Relaye d C O S Y s pectr u m usi ng t he se q ue nce of Fi g. 1 0 c wit h = 25 ms. (c) T O C S Y s pectr u m usi ng t he se q ue nce of Fig. 10 d wit h = 112 ms and an MLE V-17 pulse sequence applied during

T he eli mi nati o n of t he c he mical s hift precessi o n b y t he rf irra diati o n l e a ds, i n a d diti o n t o t h e c o h er e nt tr a nsf er t hr o u g h t h e J- c o u pli n g n et w or k, also to a n i nco here nt tra nsfer of s pi n or der t hro ug h tra nsverse cross relaxatio n. T he tra ns verse cross-relaxatio n ter ms are, i n pri nci ple, al wa ys prese nt. Ho wever, stro ng differe ntial c he mical s hift precessio n of s pi n pairs ca uses n or mall y a q ue nc hi n g of t he tra nsfer i n t he se nse of first or der p ert ur b ati o n t h e or y. I n t h e pr es e n c e of a str o n g rf fi el d, t his q u e n c hi n g is no lo nger o perati ve a n d tra ns verse cross relaxatio n occ urs. T his is t he tra nsfer mec ha nis m of t he rotati ng fra me Over ha user effect s pectrosco py ( R O ES Y) ex peri ment (82). R O ES Y has si milar pro perties as N O ES Y b ut differs i n t he de pe n de nce of t he cr oss-relaxati o n rate c o nsta nt o n t h e c orr el ati o n ti m e of t h e m ol e c ul ar r ot ati o n al m oti o n t h at m o d ul at es t h e i nt er n u cl e ar di p ol ar i nt er- a cti o n, r es p o nsi bl e f or cr oss r el a x ati o n: 3 2 Che mistry 1991

Fig ure 14 b

[ 1 1] wit h t he s pectral de nsit y Ric h ar d R. Er nst

T h e diff er e nt s e nsiti vit y of N O E a n d R O E o n all o ws o n e, i n a d diti o n, to deduce infor mation on intra molecular mobility by co mparison of the t wo meas ure ments (83). An a dvantage of R O ES Y in co m parison to N O ES Y is the negative cross- peak a m plit u de for R O ES Y while the si m ultaneo usly occ urring che mical exchange cross peaks are positive an d allo w for an easy disti nctio n u nless t hey o verla p. It s ho ul d be recog nize d t hat i n t he rotati ng fra me co here nce tra nsfer thro ugh J co u plings an d cross relaxation occ ur si m ultaneo usly, T O CS Y cross peaks being positive while R OES Y cross peaks appear with negative a m plit u de. This co m plicates the 2 D s pectra an d calls for se paration proce- d ures. T he s u p pressio n of t he co here nt tra nsfer t hro ug h J co u pli ngs ( T O C S Y) is e as y as it is j ust n e c ess ar y t o mis m at c h t h e c o n diti o n or exa m ple by a slight freq uency offset in the presence of not too stro ng rf fiel ds. T he cross-relaxatio n rates are m uc h less se nsitive to such a mis match such that a clean R OES Y spectru m results. To obtain a clean T O CS Y s pectr u m is more de man ding as relaxation ca n not easily be ma ni p ulate d. A “clea n T O CS Y” tec h niq ue has bee n pro- pose d by C. Griesi nger (84). It relies o n a co mbi natio n of Eqs. [10] a n d [I I] to ca use a vanishing average cross-relaxation rate constant: 3 4 Che mistry 1991

[ 1 3]

A s uita ble wei g ht p ca n be fo u n d w he ne ver i. e. f or s uffi ci e ntl y large molec ules wit h T his req uires t he mag netizatio n to move on a trajectory that s pen ds a fractional ti me p along the z axis an d a fr a cti o n ( 1 - p) i n t h e tr a ns v ers e pl a n e. F or C C , o n e fi n ds p = 2 / 3 f or = 0. A s uitable p ulse se q ue nce, mo difyi ng a n M L E V-17 s pi n locki ng seq uence, has been pro pose d in Ref. 84. Another o pti mize d seq uence, c all e d ‘cl e a n CI T Y’, h as b e e n d e v el o p e d b y J. Bri a n d ( 8 5). A cl e a n T O C S Y s p e ctr u m of b asi c p a n cr e ati c tr y psi n i n hi bit or ( B P TI) usi n g t h e cl e a n CI T Y s e q u e n c e is c o m p ar e d i n Fi g. 1 5 wit h a c o n v e nti o n al T O C S Y s p e ctr u m t o de monstrate the efficient s uppression of the (negative) R O ES Y peaks.

Multiple Quantu m Spectroscopy I n s pectr osc o p y, i n ge neral, o nl y t h ose tra nsiti o ns are directl y o bser va ble for which the observable operator has matrix ele ments different fro m zero, l e a di n g t o t h e s o- c all e d all o w e d tr a nsiti o ns. I n hi g h fi el d m a g n eti c r es o- nance with weak continuous wave perturbation or observing the free in duc- tio n deca y i n t he a bse nce of rf, t he tra ns verse ma g netizatio n o bser va ble o perat or = has matrix ele me nts o nl y bet wee n ei ge nstates of t he Ha milto nia n differi ng i n t he mag netic q ua nt u m n u mber M by ± 1. T h us, si n gl e q u a nt u m tr a nsiti o ns ar e t h e all o w e d tr a nsiti o ns, m ulti pl e q u a nt u m tr a nsiti o ns wit h > 1 b ei n g f or bi d d e n. M ulti pl e q u a nt u m tr a nsiti o ns c a n h o w e v er b e i n d u c e d b y str o n g c o nti n u o us w a v e rf fi el ds t h at c a us e a mixi ng of states (8, 57) or by a se q ue nce of at least t wo rf p ulses (8, 63, 86, 87). Obser vatio n is possible agai n i n t he prese nce of a stro ng rf fiel d (8, 57) or aft er a f urt h er d et e cti o n p uls e ( 8, 6 3, 8 6, 8 7). For s pin I = 1 /2 syste ms, m ulti ple q uant u m transitions invariably involve several s pi ns, a n d m ulti ple q ua nt u m s pectra co ntai n i nfor matio n o n t he co n necti vit y of s pi ns wit hi n t he J-co u pli n g net wor k i n a nalo g y to 2 D correla- tio n s pectra. I n partic ular, t he hig hest or der tra nsitio n allo ws o ne to deter- mi ne t he n u mber of co u ple d s pi ns. Relaxatio n rate co nsta nts of m ulti ple q uant u m coherences are de pen dent on the correlation of the ran do m perturbations affecting the involve d spins an d deliver infor mation on mo- tio nal processes (88). A si mple instructive exa mple of a 2 D double quantu m spectru m is given i n Fi g. 1 6 t o d e m o nstr at e t h e us e of m ulti pl e q u a nt u m tr a nsiti o ns f or t h e assi g n m e nt of r es o n a n c es ( 8 9). Al o n g d o u bl e q u a nt u m tr a nsiti o ns a n d al o n g single q uant u m transitions are dis playe d for the six-s pin syste m of

3-a minopropanol-d 3 (DOC H 2 C H 2 C H 2 N D 2 ). I n g e n er al, t h er e ar e t hr e e different categories of do uble q uant u m transitions: (I) Do uble q ua nt u m tra nsitio ns i nvolvi ng t wo directly co u ple d s pi ns. T h e y l e a d t o p airs of cr oss p e a ks dis pl a c e d s y m m etri c all y fr o m t h e double quantu m diagonal = wit h coor di nates corres po n d- i n g t o t h e L ar m or fr e q u e n ci es of t h e t w o s pi ns ( e. g. = + Ric h ar d R. Er nst

Fi g ure 15. P hase-se nsitive 300 M Hz 1 H T O C S Y s pectra of 15 m M bovi ne pa ncreatic try psi n i n hi bit or i n D 2 O recor de d wit h a 69 ms mixi ng ti me (85). (a) Mixi ng process wit h M L E V-17 p ulse se q ue nce. Negative pea ks are s ho w n by co nto urs fille d i n blac k. ( b) Mixi ng process wit h clea n CI T Y p ulse se q ue nce. (c) Cross sectio ns alo ng t hr o u g h t he T yr 2 3 dia g o nal pea k at 6.33 p p m i n t he t w o s pectra (a) a n d ( b) (see br o ke n li nes). (II) Do uble q uant u m transition involving t wo magnetically eq uivalent s pi ns. T h e y le a d t o o n e or m or e cr oss p e a ks at a n fr e q u e n c y t h at i ntersects t he do uble q ua nt u m diago nal at t he fre q ue ncy corre- sponding to the co m mon Lar mor frequency of the t wo spins (e.g. = 2 2 2 alt ho ug h t he s pi ns are o nly wit hi n ex peri me ntal acc uracy magnetically eq uivalent). 3 6 Che mistry 1991

( 1 1 1) D o u bl e q u a nt u m tr a nsiti o ns i n v ol vi n g t w o r e m ot el y c o u pl e d s pi ns. T hey lea d to si ngle cross peaks at a n fre q ue nc y t hat i ntersects t he double quantu m diagonal at equal to the mean of the t wo Lar mor fr e q u e n ci es ( e. g. = + T hese cross pea ks carr y i nfor matio n i de ntical to t hat i n relaye d correlatio n s pectra.

For t he practical a p plicatio n it is esse ntial t hat a m ulti ple q ua nt u m s pectr u m never contains a strong diagonal peak array. It sho ul d be mentione d that a

Fig ure 16. 90 M Hz 2 D correlatio n s pectr u m of 3-a mi no- pro pa nol- d 3 wit h do u ble q ua nt u m tra nsitio ns alo ng a n d si ngle q ua nt u m tra nsitio ns alo ng T he t hree cate g ories I, II, a n d III of do u ble q ua nt u m tra nsitio ns me ntio ne d i n t he text are i n dicate d. Blo w- u ps of all cross pea ks are s ho w n o n t he left. T he s pectr u m is s ho w n i n a n a bsol ute val ue re prese ntatio n (fro m Ref.89). Ric h ar d R. Er nst 3 7 b e a utif ul a n d us ef ul f or m of a d o u bl e q u a nt u m e x p eri m e nt is 2 D I N A D- E Q U A T E s pectrosco py pro pose d by Bax, Free man an d Ke m psell (90,91). There, only ty pe I peaks can occ ur. T he met ho ds me ntio ne d so far pro d uce a d ditio nal cross pea ks t hat pro- vi de i nfor matio n not accessible wit h t he sta n dar d C OS Y a n d N O ES Y ex- peri me nts. I n t he follo wi ng, tec h niq ues are disc usse d t hat lea d to si m plifie d s pectra w hic h may facilitate t heir i nter pretatio n.

M ultiple Q ua nt u m Filteri ng A selective filteri ng effect ca n be ac hieve d by exciti ng i nter me diately m ulti- ple q ua nt u m co here nce, selecti ng a partic ular q ua nt u m or der, a n d reco n- verting the selecte d or der into observable magnetization. De pen ding on the s el e ct e d or d er, t his l e a ds t o m ulti pl e- q u a nt u m filt eri n g of v ari o us or d ers. T he s pi n-s yste m-selecti ve effect relies o n c o here nce tra nsfer selecti o n r ules t hat li mit t he allo we d tra nsfers for weakly co u ple d s pi ns (8,92):

(i) It is i m p ossi bl e t o e x cit e p- q u a nt u m c o h er e n c e i n s pi n s yst e ms wit h less t ha n p co u ple d s pi ns I = 1 /2.

(ii) F or t he a p peara nce of a dia g o nal pea k of s pi n I k in a p-quantu m

filtere d C OS Y s pectr u m, t he s pi n I k m ust be directl y c o u ple d t o at l e ast p- 1 f urt h er s pi ns. 3 8 Che mistry 1991

(iii) F or t h e a p p e ar a n c e of t h e cr oss p e a ks b et w e e n s pi ns I k a n d I, i n a p- quantu m filtered C OS Y spectru m, both spins must si multaneously be co u ple d to at least p-2 f urt her s pi ns.

Violatio ns of t hese co here nce tra nsfer selectio n r ules occ ur for stro ng co u pli ng a n d for certai n s pecial relaxatio n sit uatio ns (93). In Fig. 17, the effect of 4-q uant u m filtering on vario us fo ur-s pin syste ms is de mo nstrate d. T he sa m ple co nsists of t he fi ve molec ules tra ns- p he nyl- cyclo pro panecarboxylic aci d ( K 4 ), D L-is o citri c a ci d-l a ct o n e ( P 3, 1 ), 1, 1- di c h- loroet ha ne (S 4 ), 2- c hl or o pr o pi o ni c a ci d ( C 4 ), a n d D-sacc haric aci d-l, 4-lac- to ne ( L 4 ) with the co upling topologies sho wn on the previo us page (94).

Fig ure 17a gives a co nve ntio nal ( do uble-q ua nt u m-filtere d) C OS Y s pec- tru m of the mixture while in Fig. 17b the correspon ding 4-quantu m filtere d s pectr u m is re pro d uce d. The filtering effect can easily be un derstoo d base d on the given r ules an d the sho wn co u pling to pologies. The inter pretation is l eft t o t h e r e a d er. O nl y cr oss p e a ks of t h e m ol e c ul e wit h K 4 topology and dia g o nal pea ks of m olec ules wit h P 3, 1 , S 4 , a n d K 4 t o p ol o g y r e m ai n. Technically, m ulti ple q uant u m filtering ex ploits the characteristic de pen- de nce of a m ulti ple q ua nt u m co here nce tra nsfer o n t he rf p hase of t he acti n g p ulse se q ue nce (8,92,95,96). Let us ass u me a tra nsfer of c o here nce by a u nitary tra nsfor matio n U( O), re prese nti ng a partic ular p ulse h se q ue nce, to co here nce c p 2 (t), w er e p 1 a n d p 2 are t he or ders of c o here nce,

All rf p uls es i n t h e s e q u e n c e s h all n o w b e p h as e-s hift e d b y le a di n g t o T he n it ca n be s ho w n t hat t he res ulti n g co here nce is p h as e- s hift e d b y

N - l [ 1 6]

T he req uire d n u mber of i ncre me nts N of t he p hase de pe n ds o n t he n u mber of A p val ues that have to be discri minate d (96). It is obvio us that u nl ess t h e i niti al or d er of c o h er e n c e is k n o w n, n o partic ular or der of co here nce p 2 ca n be filtere d o ut i n t his ma n ner. Most co n ve nie ntl y t he i niti al st at e is s el e ct e d t o b e i n t h er m al e q uili bri u m wit h p 1 = 0. T h e n, t h e e ntire p ulse seq ue nce prece di ng t he poi nt at w hic h a co here nce or der Ric h ar d R. Er nst 3 9

Figure 17. Multiple quantu m-filtered and spin-topology-filtered 300 M Hz C OS Y spectra of a mixt ure of t he fo ur-s pi n syste ms tra ns- p he nyl cyclo pro pa nccar boxylir aci d ( K 4 ), D L.-is ocitric aci d-lacto ne ( P 3, 1 ), 1,1- dic hloroet ha ne ( S 4 ), 2-c hloro- pro pio nic aci d ( C 4 ), a n d D-sacc haric aci d-

1,4-lacto ne ( L 4 ). (a) Do u ble- q ua nt u m-filtere d s pectr u m usi ng t he p ulse se q ue nce of Fig. 18. ( b)

4- q ua nt u m-filtere d s pectr u m usi ng t he p ulse se q ue nce of Fig. 18. (c) C 4 s pi n-to pology-filtere d s pectr u m usi ng t he p ulse se q ue nce of Fig. 19 (fro m Ref. 94). 4 0 Che mistry 1991

s ho ul d be selecte d m ust be p hase-cycle d. For m ulti ple-q ua nt u m filtere d C OS Y, this lea ds to the p ulse seq uence sho wn in Fig. 18. Obvio usly, m ulti ple q uant u m filtering an d phase-cycling req uire N-ti mes m or e e x p eri m e nts t o b e p erf or m e d. H o w e v er, n o i nf or m ati o n is l ost as i n e a c h t er m of E q. [ 1 6] j ust t h e p h as e f a ct or is c o m p e ns at e d a n d i d e nti c al si g nals are co-a d de d for t he rele va nt pat h wa ys. T h us t he lo n ger perfor m- a nce ti me is ref u n de d i n ter ms of a n i ncrease d sig nal-to- noise ratio.

Spi n Topology Filtratio n It m a y b e d esir a bl e t o e n h a n c e t h e filt eri n g eff e ct d e m o nstr at e d i n Fi g. 1 7 a n d t o s el e ct i n di vi d u al s pi n c o u pli n g t o p ol o gi es. I n d e e d it is p ossi bl e t o desig n exte n de d p ulse seq ue nces, i n co mbi natio n wit h m ulti ple q ua nt u m filtratio n, t hat are tailor- ma de for s pecific s pi n co u pli ng to pologies (94, 97, - 9 8). A p uls e s e q u e n c e, b uilt i nt o a 2 D C O S Y e x p eri m e nt, t h at is s el e cti v e f or c y cli c C 4 s pi n c o u pli n g t o p ol o gi es is s h o w n i n Fi g. 1 9. A p pli e d t o t h e pre vio us mixt ure of fo ur-s pi n syste ms, t he 2 D s pectr u m of Fig. 17c is obtai ne d. It s ho ws efficie nt s u p pressio n of all ot her s pi n syste ms. It s ho ul d ho wever be note d t hat t he sit uatio n is here rat her i deal. Ofte n, t hese filters do not perfor m as well beca use t heir desig n relies o n t he eq uality of all no n- z er o s pi n c o u pli n gs. I n r e alit y, t h er e ar e w e a k a n d str o n g c o u pli n gs t h at cannot be characterize d by to pological consi derations alone. Often also the signals decay during the exten de d pulse sequences due to relaxation. This li mits t he practical usef ul ness of t hese desig ns.

Excl usive Correlatio n Spectroscopy M ulti ple q uant u m filtering s u p presses not only diagonal an d cross peaks in 2 D s pectra b ut als o c ha n ges t he si g n patter n i n t he cr oss- pea k m ulti plet Ric h ar d R. Er nst 4 1

str uct ure. By a p pro priate co mbination of differently m ulti ple-q uant u m filtere d 2 D s pectra, it is p ossi ble t o si m plif y t he m ulti plet str uct ure b y re d ucing the n u mber of m ulti plet co m ponents. The reci pe of excl usive correlation s pectrosco py ( E. C OS Y), pro pose d by O. W. S ∅ r e ns e n, eli mi- nates all m ulti plet co m po ne nts fro m a C OS Y s pectr u m exce pt for t hose belonging to pairs of transitions with an energy level in co m mon (99-l01). I n pr a cti c e, it is n ot n e c ess ar y t o lit er all y c o m bi n e m ulti pl e- q u a nt u m-fil- t er e d s p e ctr a b ut it is p ossi bl e t o dir e ctl y c o- a d d t h e e x p eri m e nt al r es ults fro m a phase cycle with the a p pro priate weight factors. Fi g ur e 2 0 s h o ws s c h e m ati c all y t h e c o m bi n ati o n of cr oss- p e a k m ulti pl ets

co n necti ng s pi ns I 1 a n d I 2 i n a t hree-s pi n syste m after 2- a n d 3-q ua nt u m filteri n g. T he re mai ni n g patter n co nsists of t wo basic s q uares wit h si de

l e n gt hs e q u al t o t h e a cti v e c o u pli n g c o nst a nt J 1 2 r es p o nsi bl e f or t h e c o h er- ence transfer. The displace ment vector bet ween the t wo sq uares is given by

t h e t w o p assi v e c o u pli n gs J 1 3 a n d J 2 3 to t he t hir d ( passive) s pi n. It s ho ul d be me ntio ne d t hat t his m ulti plet str uct ure is i de ntical to t he o ne obtai ne d by a C O S Y e x p eri m e nt wit h a n e xtr e m el y s m all fli p a n gl e of t h e mi xi n g p uls e ( 1 0 2). E. C OS Y is of practical use w he ne ver t he cross- pea k m ulti plet str uct ure has to be analyze d in or der to deter mine J-co u pling constants. This can be do ne co nve nie ntly by ha n d by meas uri ng t he dis place me nt of peri p heral m ulti plet co m ponents (101) or by an a uto matic rec ursive contraction proce- d ure (103).

Fig ure 18. P ulse se q ue nce for m ulti ple- q ua nt u m-filtere d C O S Y wit h t he co here nce tra nsfer diagra m for do u ble- q ua nt u m filteri ng. T he p hase is i ncre me nte d s yste maticall y i n a set of N ex peri me nts a n d t he res ulti ng ex peri me ntal res ults co m bi ne d accor di ng to E q. [16]. 4 2 Che mistry 1991

Fig ure 19. P ulse se q ue nce for C 4 s pi n to pology filtratio n co nsisti ng of π/ 2 a n d π p ulses. T he dela ys are a dj uste d t o = a n d ∆ = h is t he u nifor m J-co u pli ng co nsta nt. i s p hase-cycle d for fo ur- q ua nt u m selectio n a n d f or t he s u p pressi o n of axial pea ks (94).

Heteronuclear 2 D Experi ments In a d dition to the ho mon uclear 2 D ex peri ments disc usse d so far, at least an eq ual n u mber of hetero n uclear ex peri me nts has bee n pro pose d a n d i ntro- d uce d i n t he r o uti ne s pectr osc o p y la b orat or y. Of greatest practical i m p or- tance are heteron uclear shift correlation s pectra that correlate the che mical s hifts of dir e ctl y b o n d e d or r e m ot el y c o n n e ct e d h et er o n u cl ei ( 1 0 4, 1 0 5). I n t his co ntext, so-calle d i n verse detectio n ex peri me nts w here proto n I-s pi n c o h er e n c e is o bs er v e d i n t 2 w hile lo w-ab u n da nce, lo w se nsitivity S-s pi n are of partic ular i nterest (104). T he most c o h er e n c e is e v ol vi n g i n t 1 , efficient sche mes create heteron uclear t wo-s pin coherence that evolves in t 1 an d that acq uires the freq uency infor mation of the S-s pin resonance (106). Also i n t he hetero n uclear e n viro n me nt, relaye d co here nce tra nsfer is of i m p ort a n c e ( 7 8) as w ell as e x p eri m e nts i n t h e r ot ati n g fr a m e ( 1 0 7). S pi n filt eri n g is us e d i n t h e f or m of m ulti pli cit y s el e cti vit y, disti n g uis hi n g S s pi ns co u ple d to o ne, t wo, or t hree I s pi ns (1 OS), a n d i n t he for m of J filteri ng for t he disti nctio n of o ne-bo n d a n d m ulti ple-bo n d co u pli ngs (109). T his e n u- meration of heteronuclear experi ments is by no means exhaustive.

T HREE- DI ME NSI O N AL F O URIER SPECTR OSC OPY N o n e w pri n ci pl es ar e r e q uir e d t o d e v el o p 3 D s p e ctr os c o p y t h at is j ust a lo gical exte nsio n of 2 D s pectrosco p y. I nstea d of a si n gle mixi n g process w hic h relates t wo freq ue ncy variables, t wo seq ue ntial mixi ng processes relate t hree fre q ue ncies: t he ori gi n fre q ue nc y ω 1 t he rela y fre q ue nc y ω 2 , a n d t he detectio n freq ue ncy ω 3 , as s h o w n i n Fi g. 2 1. I n t his s e ns e, a 3 D e x p eri m e nt c a n b e c o nsi d er e d as t h e c o m bi n ati o n of t w o 2 D e x p eri m e nts. Ob vio usly, a very large n u mber of possible 3 D ex peri me nts ca n be co n- ceived. Ho wever, only fe w of the m have so far proved to be indispensible (110-118). T w o a p pli c ati o ns of t h e 3 D s p e ctr os c o p y c o n c e pt h a v e e m er g e d: (i) 3 D correlatio n a n d (ii) 3 D dis persio n (see also Fig.13). T hree- di me nsio nal correlatio n is of i m porta nce i n ho mo n uclear ex peri me nts. It has bee n mentione d that the assign ment proce d ure in bio molec ules req uires a C OS Y-type and a N OES Y-type 2 D spectru m. The t wo 2 D experi ments co ul d be contracte d into one 3 D ex peri ment, co mbining a J-co u pling- me diate d an d a cross-relaxation transfer. A 3 D C OS Y- N O ES Y s pectr u m p ossesses t he a d va nta ge t hat t he e ntire assi g n me nt pr ocess ca n be carrie d Ric h ar d R. Er nst 4 3

Fig ure 20. E. C O S Y ex peri me nt to si m plify t he m ulti plet str uct ure of cross pea ks. T he do u ble- quantu m- and the triple-quantu m-filtered cross peak bet ween spins I 1 a n d I 2 of a t hree-s pi n syste m are co mbined to produce an E. C OS Y pattern. Positive and negative multiplet co mpo- ne nts are disti ng uis he d by e m pty a n d fille d circles. o ut wit h a si n gle ho mo ge neo us data set (115, 116). It i ncor porates also re d u n da ncies t hat allo w cross c hecks of t he assig n me nts. For obtai ni ng q ua ntitati ve i nf or mati o n, h o we ver, 3 D s pectra are less s uite d as all pea k i nte nsities are pro d ucts of t wo tra nsfer coefficie nts t hat are so me ti mes diffic ult t o se parate.

A 3 D R O ES Y- T O CS Y spectru m of the linear nonapepti de buserilin is s h o w n i n Fi g. 2 2 ( 1 1 6). A R O E S Y i nst e a d of a N O E S Y st e p is r e q uir e d f or b userilin, being a molec ule of inter me diate size where the N O E intensities ar e s m all. T h e T O C S Y st e p h as t h e a d v a nt a g e t h at c h ai ns of m ulti pl e-st e p cr oss p e a ks e xt e n di n g i nt o t h e si d e c h ai ns ar e o bt ai n e d t h at f a cilit at e t h e i de ntificatio n of t he a mi no aci d resi d ues. It s ho ul d be recog nize d t hat recor di ng a 3 D s pectr u m is co nsi derably more ti me-consu ming than t wo 2 D spectra as t wo ti me para meters t 1 a n d t 2 ha ve to be i ncre me nte d i n de pe n de ntl y, lea di n g to a 2 D arra y of ex peri- ments. Here the q uestion arises; when is it worth the effort to recor d a 3 D s pectr u m? T his q uesti o n has bee n disc usse d bef ore (116, 119, 120). L et us c o nsi d er a p arti c ul ar cr oss p e a k i n a 3 D s p e ctr u m t h at c orr el at es t he c o here nces {t u} i n ω 1 , {rs} i n ω 2 , a n d { p q} i n ω 3 di me nsi o ns. Its intensity is deter mine d by the follo wing pro d uct of matrix ele ments (in the eige nbasis of t he u n pert urbe d Ha milto nia n ( 1 1 6):

A no n-va nis hi ng i nte nsity establis hes a t wo-ste p correlatio n {t u}-{rs}- { p q}. 4 4 Che mistry 1991

Fig ure 21. Sc he matic re prese ntatio n of a 3 D ex peri me nt, exte n di n g Fi gs. 1 a n d 6. T hree

evol utio n perio ds wit h t he ti me varia bles t 1 t 2 , a n d t 3 are se parate d by t wo tra nsfer or mixi ng processes. A 3 D ex peri me nt ca n be co nceive d as t he co ntractio n of t wo 2 D ex peri me nts.

W he n i n t he 2 D s pectra t he t wo releva nt peaks wit h i nte nsities a n d can be i dentifie d, possibly in cro w de d regions, the t wo-ste p correla- tion, represente d by a 3 D peak, co ul d also be establishe d base d on the t wo 2 D s p e ct r a {t u}-{ r s} a n d { r s}-{ p q}. P r o vi d e d t h at 0, t h e i nt e nsiti es a n d Z are different fro m zero when in a d dition 0 a n d 0. T his i m pli es t h at t h e “r el a y-tr a nsiti o n ” {rs} m ust b e e x cit e d i n t h e pr e p ar ati o n st at e P ( 2) an d must be detectable by the observ- a bl e D ( 1) . For “allo we d” o ne-s pi n si ngle-q ua nt u m co here nces, t his co n di- tio n is f ulfille d for si ngle p ulse excitatio n a n d direct detectio n. O n t he ot her han d, “forbi d den” m ulti ple-s pin single-q uant u m coherences (co mbination lines) an d multiple-quantu m coherences can neither be excite d by a single no n-selecti ve p ulse nor directl y detecte d. S uc h co here nces re g ularl y occ ur i n t h e of a 3 D s pectr u m. The excitation an d in direct detection of t hese co here nces i n 2 D ex peri me nts req uires s pecial excitatio n a n d detectio n p ulse seq uences. I n co ncl usio n, t he t wo co nstit ue nt 2 D ex peri me nts deliver t he sa me i nf or m ati o n o n t h e s pi n s yst e m as t h e 3 D s p e ctr u m, pr o vi d e d t h at (i) t h e

rele va nt freq ue ncies i n t he ω 2 -di mension of the 3 D spectru m can be excite d an d detecte d in the 2 D ex peri ments, an d (ii) the cross- peaks are not hi d den b y s pectral o verla p a n d ca n be i de ntifie d i n t he 2 D s pectra. T he first con dition is nor mally not severe as the 2 D experi ments can be mo difie d for excitatio n a n d detectio n of forbi d de n tra nsitio ns w he never req uire d. O n t he ot her ha n d, t he li mite d resol vi ng po wer of 2 D s pectra is t he most i m porta nt moti vatio n for j ustifyi ng 3 D (a n d possibly hig her di me nsio nal) s pectrosco py. Beca use t he gai n i n resol utio n j ustifies 3 D s pectrosco py, it may be wort h- w hile to i ntro d uce a t hir d fre q ue nc y axis j ust for resol utio n p ur poses, rather than co mbining t wo processes relevant for the assign ment requiring hi g h r es ol uti o n i n all t hr e e di m e nsi o ns. It is t h e n p ossi bl e t o ar bitr aril y choose the extent of 3 D resol ution an d to opti mize the perfor mance ti me of t h e 3 D e x p eri m e nt. F or t h e 3 D s pr e a di n g of a 2 D s p e ctr u m, h o m o n u cl e ar or hetero n uclear tra nsfers ca n be use d. Hetero n uclear o ne-bo n d tra nsfers Ric h ar d R. Er nst

Fig ure 22. 3 D vie w of a 300 M Hz 3 D ho monuclear R OES Y- T O CS Y spectru m of buserilin in

D MS O-d 6 p hotogra p he d fro m a pict ure syste m (116). are ho we ver far more efficie nt beca use t he stro ng hetero n uclear o ne-bo n d co u pli ngs preve nt leakage to f urt her s pi ns. T his allo ws a n efficie nt tra nsfer, virt u all y wit h o ut l oss of m a g n eti z ati o n. I n a d diti o n, n u cl ei li k e 1 3 C a n d 1 5 N exhibit large che mical shift ranges with high resolving po wer. The princi ple of s prea di n g is i n di c at e d i n Fi g. 2 3. A 3 D 1 5 N-s prea de d T O CS Y s pectr u m of ribon uclease A is sho wn in Fi g. 2 4. T h e us e of h et er o n u cl e ar s pr e a di n g r e q uir es us u all y is ot o pi c la b el- ling of the molec ule. In this case, ribon uclease A has been gro wn in a 1 5 N- labelle d nutrients-containing E. Coli me diu m (courtesy of Prof. Steven Ben- ner). T he s pectr u m has bee n o btai ne d wit h t he p ulse se q ue nce of Fi g.25. 1 5 I nitially, proto n co here nce is excite d a n d precesses d uri ng t 1 u n d er N r ef o c usi n g b y t h e a p pli e d π p uls e. D uri n g t h e mi xi n g ti m e co here nce tra nsfer fr o m ot her pr ot o ns t o t he N H pr ot o ns is effecte d i n t he r otati n g fra me by t he a p plicatio n of a T O CS Y m ulti ple- p ulse seq ue nce. T he N H co here nce is t he n co n verte d i nto 1 5 N H heteronuclear multiple-quantu m 1 5 coherence ( H M Q C) which precesses d uring t 2 a n d ac q uires N reso na nce i nfor matio n ( u n der proto n refoc usi ng). After reco nversio n into N H proto n 1 5 co here nce, detectio n follo ws d uri ng t 3 u n d er N deco u pli n g. For a co m- plete assig n me nt of t he proto n reso na nces, i n a d diti o n a 1 5 N-s prea de d N OES Y spectru m is required. T he ste p to 4 D s pectrosco p y (121) is a s mall a n d lo gical o ne: i n 2 D ex peri me nts, s pi ns are pair wise correlate d, e.g. N H a n d proto ns. 1 5 1 3 T hree- di me nsio nal dis persio n uses eit her N or C α , r es o n a n c e f or s pr e a d- 4 6 Che mistry 1991

i n g t h e r es o n a n c es of N H or r es p e cti v el y. I n a 4 D e x p eri m e nt, b ot h s prea ding processes are a p plie d si m ultaneo usly:

T he or der of t he freq ue ncies i n t he act ual ex peri me nt is a matter of

co nve nie nce. Nor mally, t he detectio n freq ue ncy ω 4 refers t o pr ot o n s pi ns for se nsiti vit y reaso ns. I n most cases, t he t wo s prea di n g coor di nates are rat her coarsely digitize d to li mit t he perfor ma nce ti me, j ust e no ug h to achieve separation of peaks overlapping in the 2 D spectru m. Often 8 to 32 poi nts i n eac h of t he t wo di me nsio ns are s ufficie nt.

M OLEC UL AR DY N A MICS I NVESTI G ATE D BY N MR The molec ular str uct ures, deter mine d by N M R in sol ution, by X-ray diffrac- tio n i n si n gle cr ystals, or b y ot her mea ns, are i n varia bl y motio nall y a vera ge d str uct ures, w hereby t he averagi ng process is stro ngly de pe n de nt o n t he meas ure ment techniq ue. To interpret experi mental “str uct ures”, so me kno wle dge of the motional pro perties of the molec ule is in fact in dis pensi- ble. Molec ular dyna mics is also relevant for its o wn sake, in partic ular for u n dersta n di ng reactivity a n d i nteractio n wit h ot her molec ules. I n ma ny cases, acti ve sites i n a m olec ular p oc ket are o nl y accessi ble d ue t o t he fl e xi bilit y of t h e m ol e c ul e its elf. The characterization of the motional pro perties of a molec ule is by or ders of magnitu de more difficult than the description of an average d molecular str u ct ur e. W hil e 3 N- 6 c o or di n at es ar e s uffi ci e nt t o fi x a str u ct ur e c o nt ai n- i ng N ato ms, t he c haracterizatio n of molec ular dy na mics req uires 3 N-6 variances of the intra molec ular coor dinates, (3 N-6)(3 N-5) /2 covar- ia nces, a n d t he sa me n u mber of a uto- a n d cross-correlatio n f u nctio ns, r es p e cti v el y. I n a d diti o n, als o hi g h er or d er c orr el ati o n f u n cti o ns ar e n e e d- e d f or a m ore refi ne d descri pti o n of d y na mics. I n practice, a s ufficie nt n u mber of observables is never available for a f ull descri ption of dyna mics. In this sense, the study of dyna mics is an open-ended proble m. Nu merous techniques are available to obtain data on dyna mics: Debye- Waller factors in X-ray diffraction give hints on the variances of the n uclear coor dinates, h o w e v er wit h o ut a m e as ur e f or t h e ti m e s c al e. I n el asti c a n d q u asi- el asti c ne utron scattering deliver correlation f unctions, b ut witho ut a reference to t he str uct ure. Fl uoresce nce de polarizatio n allo ws o ne to deter mi ne t he m oti o n al c orr el ati o n f u n cti o n of fl u or es c e nt gr o u ps, s u c h as t yr osi n e r esi- d ues in proteins. Ultrasonic absor ption gives an in dication of the do minant motional mo de freq uencies, again witho ut a str uct ural reference. Ric h ar d R. Er nst 4 7

Fig ure 23. 3 D resol utio n of a 2 D proto n-reso na nce s pectr u m by 1 5 N reso na nce s prea di ng. T he cross pea ks are dis place d i n a t hir d di me nsio n by t he corres po n di ng 1 5 N c he mical s hifts.

N M R is more universally applicable to motional st u dies than most of the ot h er t e c h ni q u es. T h e r a n g e of c orr el ati o n ti m es that can be covere d by various N M R methods is enor mous, fro m picoseconds to seconds and m or e:

narro wing

Exce pt for slo w motio ns o n a milliseco n d or slo wer ti me scale w here lineshape, saturation transfer, an d 2 D exchange stu dies can be perfor me d, many dyna mics st u dies by N M R rely on relaxation meas ure ments. The v ari o us r el a x ati o n p ar a m et ers, s u c h as t h e l o n git u di n al r el a x ati o n ti m e T 1 , t he tra ns verse relaxatio n ti me T 2 , t h e r ot ati n g fr a m e r el a x ati o n ti m e T 1 p, a n d cr oss-relaxati o n rate c o nsta nts de pen d on the correlation ti me of the underlying rando m process. The disc ussion shall be restricte d to a recent st u dy of the intra molec ular dy na mics i n a nta ma ni de (I) (83, 122, 123) (see Figs. 8, 9, 11). A nta ma ni de is a n a nti dote for toxic co m po ne nts of t he m us hroo m A ma nita p halloi des. 4 8 Che mistry 1991

Fi g ur e 2 4. 3 D 1 5 N-spreaded 600 M Hz proton resonance T O CS Y spectru m of 1 5 N-la belle d

1 5 ri bo n uclease A i n H 2 O sol utio n. T he 3 D s pectr u m s ho ws t he N reso na nces alo ng t he ω 22 a xi s. T he s pectr u m has bee n recor de d by C. Griesi nger, usi ng t he p ulse se q ue nce of Fig. 25, a n d processe d by S. Boe ntges. T he sa m ple was provi de d by Prof. S. Be n ner of E T H Z üric h. Ric h ar d R. Er nst 4 9

Astonishingly, the antidote occurs as a co mponent of the sa me mushroo m. I n dicatio ns ha ve bee n fo u n d i n early ultraso nic absor ptio n st u dies (124) that the peptide ring see ms to undergo a confor mational exchange process with a freq uency of abo ut 1 M Hz. In the co urse of extensive investigations of anta mani de by the research gro u p of Professor Horst Kessler (125), it has also bee n notice d t hat t he dista nce co nstrai nts obtai ne d fro m N M R mea- sure ments coul d not be fitte d by a single confor mation. Martin Blackle dge has perfor me d i n o ur laboratory rotati ng fra me relaxatio n meas ure me nts and localized a hydrogen-bond exchange process with an activation energy of 25 kJ / mol a n d a lifeti me of 25 µs at roo m te m perat ure ( u n p ublis he d res ults, see also Ref. 126). Wit h a ne w dy na mic str uct ure deter mi natio n procedure, called ME D US A (123), the confor mational space of anta manide has bee n i n vesti gate d more s yste maticall y t ha n e ver before. 1176 feasi ble lo w-energy structures have been found. They have been co mbined in dyna- mi c all y i nt er c h a n gi n g p airs i n a n att e m pt t o f ulfill all e x p eri m e nt al c o n- strai nts t hat co nsist of N O E dista nce co nstrai nts, J-co u pli n g a n g ular co n- straints an d s pecific infor mation on hy drogen bon d dyna mics. A large set of feasible str uct ural pairs has been constr ucte d. Many pairs are within ex peri- mental acc uracy co m patible with the ex peri mental data. For a more restric- tive description of the dyna mic syste m of anta manide, additional and more a c c ur at e e x p eri m e nt al d at a ar e r e q uir e d. Fi g ur e 2 6 s h o ws, as a n e x a m pl e, t h e d y n a mi c p air of str u ct ur es t h at s o f ar fits t h e e x p eri m e nt al d at a b est. T he t wo i nterco n verti n g str uct ures differ pri maril y i n t he h y dro ge n bo n ds V a l 1 N H-Phe 9 O a n d P he 6 N H- Ala 4 O, t h at e xist o nl y i n o n e of t h e t w o c o nf or m ati o ns, a n d i n t h e t orsi o n al a n gl es a n d A secon d stu dy concentrate d on the ring puckering dyna mics of the four proli ne resi d ues i n a nta ma ni de (122). T he co nfor matio n of t he fi ve-ri ng syste ms can be deter mined fro m the dihedral bond angles a n d t h at in turn can be de duce d fro m the vicinal proton-proton J-coupling constants usi n g t h e K ar pl us r el ati o ns ( 5 4). T h e r el e v a nt c o u pli n g c o nst a nts ( 2 1 p er resi d ue) have been deter mine d fro m E. C OS Y spectra. Base d on these measure ments, a mo del was constructe d for each of the proline resi dues by l e ast s q u ar es fitti n g. It w as f o u n d t h at f or Pr o 3 a n d Pro 8 a g o o d fit c a n b e obtai ne d wit h a si ngle rigi d co nfor matio n, w hile for Pro 2 a n d Pro 7 t w o rapi dly exchanging confor mations were require d to re duce the fitting error i nt o a n a c c e pt a bl e r a n g e. At t h e s a m e ti m e, 1 3 C relaxatio n-ti me meas ure- me nts co nfir me d t hat Pro 3 a n d Pr o 8 a p p e ar t o b e ri gi d w hil e Pr o 2 a n d Pr o 7 s h o w d y n a mi cs wit h c orr el ati o n ti m es b et w e e n 3 0 a n d 4 0 ps. T his i m pli es t hat t he pe pti de ri ng dy na mics a n d t he proli ne ri ng dy na mics are not correlate d an d procee d on entirely different ti me scales. The t wo exchang- i n g co nfor matio ns t hat ha ve bee n fo u n d for Pro 2 ar e s h o w n i n Fi g. 2 7. It is s e e n t h at t h e m oti o n i n v ol v es a n e n v el o p e-t y p e pr o c ess w h er e t h e ‘fl a p of t h e e n v el o p e’ ( C y) is m o vi n g u p a n d d o w n. 5 0 Che mistry 1991

M AG NETIC RES O N A NCE F O URIER I M AGI NG Magnetic resonance i maging ( M RI) has had an enor mous i mpact on medical diagnosis an d beca me rapi dly a po werful routine tool. The basic proce dure for recording a 2 D or 3 D N M R i mage of an object is due to Paul Lauterbur (127). A magnetic fiel d gra die nt, a p plie d alo ng different directio ns in s pace i n a seq ue nce of ex peri me nts, pro d uces projectio ns of t he n uclear s pi n de nsity of t he object o nto t he directio n of t he gra die nt. Fro m a s ufficie ntly l ar g e s et of s u c h pr oj e cti o ns it is p ossi bl e t o r e c o nstr u ct a n i m a g e of t h e o bj e ct, f or e x a m pl e b y filt er e d b a c k pr oj e cti o n i n a n al o g y t o X-r a y t o m o- gra p hy. A diff er e nt a p pr o a c h is dir e ctl y r el at e d t o 2 D a n d 3 D F o uri er tr a nsf or m s pectrosco py. Freq ue ncy e nco di ng of t he t hree s patial di me nsio ns is ac hie ve d by a li near mag netic fiel d gra die nt a p plie d s uccessi vely alo ng t hree ort h o g o n al dir e cti o ns f or t h e d ur ati o ns t 1 , t 2 , a n d t 3 , r es p e cti v el y, i n a p uls e Fo urier tra nsfor m ex peri me nt (128). I n f ull a nalogy to 3 D s pectrosco py, t he ti me para meters t 1 a n d t 2 are i ncre me nte d i n reg ular i ntervals fro m ex peri me nt to ex peri me nt. T he recor de d sig nal s(t 1 ,t 2 ,t 3 ) is F o urier-tra ns- for me d i n t hree di me nsio ns to pro d uce a f u nctio n t h at is e q ui v al e nt t o a 3 D s p ati al i m a g e w h e n t h e s p ati al i nf or m ati o n is d e c o d e d usi n g t h e r el ati o ns x = y = a n d z = wit h t h e t hr e e fi el d gra die nts g x , g y , a n d g z . T he pr oce d ure is ill ustrate d i n Fi g. 28 f or t w o di mensions. I n a f urt her refi ne me nt, pro pose d b y E delstei n et al. (129), t he ti me v ari a bl es t 1 a n d t 2 are re place d by variable fiel d gra dient strengths g x a n d g y a p pli e d d uri n g a c o nst a nt e v ol uti o n ti m e. Wit h r e g ar d t o t h e a c c u m ul at e d p h a s e,

In me dical i maging, 3 D ex peri ments have a nat ural j ustification, altho ugh it is so meti mes si m pler to a p ply selective excitatio n tec h niq ues to select a 2 D slice t hro ug h t he object to be i mage d (130). E ve n exte nsio ns to hig her di mensions are q uite realistic. In a fo urth di mension, for exa m ple, che mical shift infor mation can be acco m mo date d (131). Also 2 D spectroscopic infor- m ati o n c o ul d b e c o m bi n e d wit h t hr e e s p ati al di m e nsi o ns, le a di n g t o a 5 D experi ment. No li mitations see m to exist for the hu man i magination. Ho w- ever, the practical li mits will soon be reache d when the req uire d perfor m- a nce ti mes is also take n i nto co nsi deratio n.

CO NCLUSIO N I a m not a ware of any other fiel d of science o utsi de of magnetic resonance that offers so m uch free do m an d o p port unities for a creative min d to invent a n d e x pl or e n e w e x p eri m e nt al s c h e m es t h at c a n b e fr uitf ull y a p pli e d i n a Ric h ar d R. Er nst

I I

Fig ure 26 . Co nfor matio nal pair of a nta ma ni de t hat f ulfills t he ex peri me ntal co nstrai nts. T he t wo pairs are s ho w n i n stereogra p hic as well as i n a bstract for m. I n t he for mer, hy droge n bo n ds are i n dicate d by bro ke n li nes, i n t he latter by arro ws poi nti ng to war ds t he hy droge n- bo n de d oxyge n (fr o m Ref. 123). 5 2 Che mistry 1991

Fi g ur e 2 7. The t wo experi mentally deter mined confor mations of probe-2 in anta manide (see R ef. 1 2 2). variety of disci pli nes. N M R is i ntellect ually attractive beca use t he observe d p he no me na ca n be u n derstoo d base d o n a so u n d t heory, a n d al most all co nceits ca n also be teste d b y eas y ex peri me nts. At t he sa me ti me, t he practical i m porta nce of N M R is e nor mo us a n d ca n j ustify ma ny of t he playf ul acti vities of a n a d dicte d s pectrosco pist.

ACKNO WLEDG MENTS M ost of t h e cr e dit f or t h e i ns pir ati o n a n d e x e c uti o n of t h e w or k d es cri b e d sho ul d go to my teachers Hans Pri mas an d Hans H. G ünthar d, to my s u pervisor Weston A. An derson, to the ins pirator Jean Jeener, to my co workers (in more or less chronological order): Tho mas Bau mann, Enrico Bart hol di, Robert Morga n, Stefa n Sc hä ubli n, A nil K u mar, Dieter Welti, L ucia no M üller, Alexa n der Woka u n, Walter P. A ue, Jiri Kar ha n, Peter Bach mann, Geoffrey Bo denhausen, Peter Brunner, Alfre d Höhener, An- dre w A. Mau dsley, Kuniaki Nagaya ma, Max Lin der, Michael Reinhol d, Ronal d Haberkorn, Thierry Schaffha user, Do uglas B ur u m, Fe derico Graf, Yongren H uang, Slobo dan Mac ura, Beat H. Meier, Dieter S uter, Pablo Caravatti, Ole W. Sørensen, Lukas Braunsch weiler, Malcol m H. Levitt, Rolf Meyer, Mark Ra nce, Art h ur Sc h weiger, Mic hael H. Frey, Beat U. Meier, Marcel M üri, C hristo p her Co u ncell, Herbert Kogler, Rola n d Kreis, Nor- bert M üller, A n nalisa Pastore, C hristia n Sc hö ne nberger, Walter St u der, Christian Ra dloff, Albert Tho mas, Rafael Brusch weiler, Her man Cho, Cla u di us Ge m perle, C hristia n Griesi n ger, Z olt a n L. M á di, P et er M ei er, Serge Boentges, Marc Mc Coy, Ar min Stöckli, Gabriele Aebli, Martin Black- le d ge, Jac q ues Bria n d, Matt hias Er nst, Tilo Le va nte, Pierre Rob yr, T ho mas Sch ulte- Herbr üggen, J ürgen Sch mi dt an d Scott S mith; to my technical st aff, H a nsr u e di H a g er, Al e x a n dr a Fr ei, J a n os A. D eli, Je a n- Pi err e Mi c h ot, Robert Ritz, Tho mas Schneider, Markus Hinter mann, Gerhard Gucher, Josef Eise negger, Walter Lä m mler, a n d Marti n Ne uko m m; to my secretary Irene M üller; an d to several research gro ups with which I ha d the pleas ure t o c olla b orate, first of all t he researc h gr o u p of K urt W üt hric h, a n d t he Ric h ar d R. Er nst 5 3

I

Figure 28. Sche matic representation of Fourier N M R i maging, here sho wn in t wo di mensions.

T wo ort hogo nal gra die nts are a p plie d d uri ng t he t 1 a n d t Z perio ds of a 2 D ex peri me nt. A 2 D

Fo urier tra nsfor matio n of t he data set s(t lr t 2 ) pro d uces a 2 D i mage of t he i nvestigate d s u bject ( R. R. E.). gro up of Horst Kessler. I also o we m uch gratit u de for s upport in the early days to Varia n Associates a n d more rece ntly to t he S wiss Fe deral I nstit ute of Tec h nology, t he S wiss Natio nal Scie nce Fo u n datio n, t he Ko m missio n z ur För der u ng der Wisse nsc haftlic he n Forsc h u ng, a n d last b ut not least to Spectrospin A G. 5 4 Che mistry 1991

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