Lecture 12
Transcription
Lecture 12
NMR Course. Lecture 12 May 10,1999 Maltseva T. V. Lecture Practical multinuclear, 12 introduction to theory and multidimensional nuclear implementation of magnetic resonance experiment. 1""""- Book: II Protein NMR speectroscopy" by Cavanagh, J., Fairbrother, W. J., Palmer III, A. G., Skelton, N. J. Academic Press. Inc., San Diego, N.Y., Boston, London, Sydney, Tokyo, Toronto, f" ..; 1996 The main reyiews from the books: * 'Method in Enzymology.V.239, Nuclear Magnetic Resonanc,Part C' by Thomas L.james and Norman j. Oppenheimer. p.3- 79 Good reyiews: * Kessler,H.,Gehrke,M.,Griesinger,C.'Two-dimensional NMR spectrosopy:background and oyerview of the experiments' Angew. Chem. Int. Ed.Engl. (1988) pp.490-536 * Sorensen,O.W., Eich,G.W., Leyitt. M.H., Bodenhausen,G., Ernst,R.R.'Product operator formalism for the description of NMR pulse experiments' Progress in NMR spectroscopy, (1983) Y. 16,pp.163-192 I'""' This book is quite difficult : * 'Principle of Nuclear Magnetic Resonancein One and T wo Dimensions' by Emst,R Bodenhausen,G., Wokaun,A. pp 1-69 and pp.3-79 ry 1 Practical introduction multidimensional to theory and implementation nuclear magnetic resonance (I) Pulse Sequences. of multinuclear experiment. , The easiest way to understand complex NMR experiments is to be able to identify the small number of building blocks from which all experiment are constructed. Once the input and output characteristics of the building blocks are known, a coherence flow network can be constructed to illustrate graphically the flow of coherence through an experiment. For this purposes we will introduce a small number of product operator rules. Although many of these experiments correlate tour or more different spins, the majority of interactions can be understood in terms of pairwise, ~ sl2ininteraction. We will focus on the NMR experiments for through bond, sequential assignments. Part ,,-. (I): Product Operators In the context of an 2-spin systern, we distinguish one-spin and two-spin operators. One-spin operators are associated with a rnagnetisation. We willIabeIled t wo spins by I and S. A subscript to I and S refers to the rotating frame axis along which the rnagnetisation is oriented. Thus Ix, refer to the rnagnetisation of the I spin oriented along the x axis. r-- For the two-s12ininteraction there are 15 combination of the magnetization: Iz, Sz (longitudinal) Ix, Sx, ly, Sy (transverse) 21zSz (J -ordered spin state ) ""'"" I'""""' ,.". 21xSz , 21ySz , 2Sxlz ,2Sylz (antiphase) 21xSx , 21xSy , 21ySx ,2lySy (multiple quantum) (The coefficient of 2 arises as a normallsation factor) When only a single spin is involved , they call the inphasemagnetisation. x -and y- magnetisation are narned as transverse z -aligned along the magnetic field, is called longitudinal . Only three operators are neededto describemost NMR experiments: 1) radio frequency (rf) pulse 2) chemical shift 3) coupling Both the rf pulse and chemical shift operators describe simple rotations in the three- dimensional space. The notation of product operatorsis: a operator b where the operator transforrns a into b. In our case a and b are 15 combinations presented above the operator we will discuss below. You should know that "hats" indicate an operator. 2 The directionof rotationfrom rf pulsesor chemicalshift betterdeterminethrough" right-handrule" RULE: The thumb of the right hand points along the positive axis, the direction of the rotation is the direction the fingers will close to make a fist. (I) Radio frequency pulse lz x (\ y z Ix " ~ If3-~If3COS(l/J) + Irsin(l/J) a,~, y are x,y ,z axis; <I>is the pulse flip angle A A 4>1x 4>1y Iz ~Izcos(4» -Iysin(4» Iz lz ~Ix 180° Ix Iz ~lx Ix 90° ix Iz ~-Iz ~-Iy 180° ix 1800Iy ~-lz + Ixsin(4» 9001 y 90°j y t/>lx Ix ~Izcos(4» Ix Ix ~-Ix (II) Chemical ~Ix shift The chemical shift has the effect of an "rf' pulse along the z axis. r' r Ix QI tiz -~IxCOS(QIt) ly A !2Itlz -~ lyCOS(!2It)-Ixsin(QIt) + Iysin(QIt) !2 is the chemical Except of strongly coopled state (where JIS>~cr) shifts act on combination of I and S as if the other Example: 2IzSx~2(lzCOS(l/» polses and chemical spins were absent. -lysin(l/»)Sx = 2IzSxcos(l/» -2IySxsin(l/» .Q.Itiz -~2(IxCOS(.Q.It)+Iysin(.Q.It)Sz= 2Ix SzCOS(.Q.I t) + 2IySzsin(.Q.I t) Conclusion Chemical shift and rf polses are operations dimensional rotation. Theyare not able to starting on spin I to spin S . 2IxSz 3 interpreted transfer as magnetisation three- (II) Conpling The coupling operator is the essentia!feature of multidimensiona! experiments that provide correlation through coherent transfer of magnetisation from spin I to spin S. la ~ (a,f3 7rJ1St2izsz --~ . laCOS(1rJlst) + 2IpSzsm(1rJlst) = x,y) I""""' Ix 1rJ1St2iz§z . --~ Ixcos(1T:Jlst) + 2IySzsm(1T:Jlst) 2IySz Example: {"l 1IJJst2iz§z --~2Iy Sz 1IJJst2iz§z z 2IySz .--~-Ix Conpling operator can antiphase r . -Ixsm(1T:Jlst) if =} COS(1T:J1St) = O,=} 1T:J1St = !E.then =} t = ~ 2 2J1S Ix RULE: 1rJlst2iz§zz --~2IySzCOS(1T:Jlst) conrse inphase coherence to go to antiphase, or coherence to go inphase. Part (2): Building Blocks and Coherence Flow Networks. There are surprisingly few ways to transfer magnetisation ( coherence)from one spin to another ( for t wo spin system). All of the method can be placed into two broad categories: I) Coherent ( All multinuclear, multidimensional experimentsrely on one or more coherenttransfer stepsmediated by scalar coupling) 2) Incoherent transfer ( including the dipolar interactions going rise to NOEs and ROEs as weIl as chemically exchanging nuclei) For the former one, the main (coherent) building blocks are: a) HMQC ( heteronuclearmultiple-quantum correlation spectroscopy) b) INEPT (Intensive nucleus enhancementby polarisation transfer) c) TOCSY (Total correlated spectroscopy) d) COSY (Correlated spectroscopy) We discuss how these building blocks work by using the product operator rules given above. 4 . An important component of many of the "building blocks" are variations of the "spin-echo experiment, tt so we will describe these first. (I) "Spin-echo"The spin echo is simply a clelay followecl by 180° pulse followecl by a seconcl clelay.We will consiclerin present only the casewith two equal clelays.In part "a" we have Ix (At this step it is not important how we get this magnetisation ). (A),(B): Dec SE 180x Ix I 't -'t a I b (C): JIS SE I t c d 180 D , -.: b c 1- r'- s L---O---, a (D): d Dec CS I 't s 0 180 't 1a I b c d Variation of the spin-echo building block. (A) and (B) Building block DEC SE which refocuses I chemical shift and decouples S. (C) Building block JIS SE which refocuses I chemical shift hut ~ J allows coupling to occur with S. (D) Building block Dec CS allows chemical on I to occur while decoupling S. 5 (A) In first case we assume no scalar a r" b c conpling the spin I spin S. d The following steps show the product operator transfornlations (Let us go together through all step): A QI 'l"lz . a-+b: Ix -~lxCOS(QI'l")+lysm(QI'l") from points "a" to "d": b ~ c: Sin(.aI C~ d: ~ IxCOS(.aI nI 'l'lz ~[ IxcoS(nI 'f) + [Iycos(1800) 'l') + lysin(nI + Lsin(1800)] 'l') ]cos(nI = Ix[ cos2(nI 'l') + sin2(nI 'l') ] + ly[ cos(nI 'l')sin(nI 'l') -[ lycos(nI 'l') -cos(nI "a"."b" 'l')] ~ 'I"",, y Sin(.aI 'f) 'l') = Ix z "c"."d" -- Iysin(c!I) 'f) -I 'l') ]sin(nI z "b"-"c" -- xY-'- 'l') -Ixsin(nI 'l')sin(nI If to repeat the same, but using the vector representation: z z 'f) =:} IxCOS(.aI -- -Iysin(~) y ar y ~ Ix x ~ 180 o . The net result: WE END UP WITH WHAT WE START WITH!!! RULE: Whenever a 180° pulse is placed syrnmetrically between t wo time intervals, no chemical shift takes place. (ECHO) (B) In next case, consider the same spin -echo experiment in the presence of scalar coupling between I and S spin: (We neglect the chemical shift) The following steps show the product operator transformations from points "a" to "d": " a~ b : Ix 7r.l1s't2iz§z b ~ c: ~ r-- c ~ d: . ~IxCOS(7r.l1S't)+2IySzsm(7r.l1s't) Ixcos(7r.l1s't) + Sz[Iycos(180O) + Izsin(180O) ] x sin(7r.l1S't)=> Ixcos(7r.l1s't) -2IySzsin(1rJ1s't) 1r.Ils'Z"2i.s. ~[ Ix cos( 1r.I1S'Z") + 2Iy S. sin( 1r.I1S'Z") ] COS(1r.I1S'Z") -[ 2Iy S. COS(1r.I1S'Z") -Ix sin( 1r.I1S'Z") ] sin( 1r.I1S'Z") ~ => Ix[ cos2(QI 'Z")+ sin2(QI 'Z")] + [ 2Iy S. -2IyS.]sin(1r.I1S'Z")COS(1r.I1S'Z") => Ix The Det from S This Ix resDit: In addition is a decoupled Dec SE to refocusing chernical shift, spin-echo: ~ Ix a b in teml of a CFN Diagram : 6 this simple experiment decouples spin I ( C) Let us consider two additional related experiments. First, we include a 180° pulse on S spin simultaneous to the 180° pulse on I spin (C):JISSE ~O IzSz I 't IZ~ '-- 0180 x IySz ly s zQy 1- I a b c IX~ IX~ d ( presenceof scalar conpling betweenI andS spin) Note: That since Ix and Sx do not interfere with unlike spins( Sy~Sy) a 180° S and I pulses can be applied together or in tandem, in either order. " Once again, we start with Ix magnetisation and neglect chemical shift which is refocnsed by a 180°1 pulse. n a ~ b ~ b : 1r:.lls'r2IzSz Ix c: 180° 180° c ~ d: ix -I. ~ Ixcos(/IJls'r) ~ Ix cos( 1r:.llS'r) + Sz [ Iycos(180° A Sx ~ Ixcos(7rJ1s'r) 7rJls't'2jz§z =} Ixcos(7rJls2't') The )and 2sin( S. cos(180° + 2IySzsin(7rJ1S't') (7rJ1S't') ] + +2IySz[ ( 'P ) = cos(2'P ) + Iz sin(180° -2Iysin(7rJ1S'r)[ ~[IxCOS(7rJls't') =} Ix [ COS2(7rJ1S't') -sin2 Iicos2 ( 'P) -sin2 + 2IySzsm(1r:.llS'r) ) -sysin(180° ) ]=> Ixcos(7rJ1s'r) + Sin(7rJ1S't')COS(7rJ1S't') Det Jr JrJls2't"= -=> 2 resDit: In ternl ] = The result of this building block is 't"= the same as the single on both S and I in spin echo + 2IySzsin(1CJIs2T) 1 Then Ix 1tllSr2iz§z ~2IySz {=> Ix JlsSE ~2IySz 4JIs 1rJJs'r2iz§z 2IySz ~ + 2IySzsin(7rJ1S2't') IxCOS(1CJIs2T) or ]Sin(7rJ1S't') 'P) = sin(2'P)11 operation, 7r.lIs(2r)2Iz §z Unlike the previous example, simultaneous by a 180° pulses experiment leave the t wo spin coDpled. Tum back to the final resu1t: r- Sz sin( 1r:.llS'r) + 2IyS.sin(7rJ1S't") ]COS(7rJ1S't') + +[ 2IySz COS(7rJ1S't') -Ixsin(7rJ1S't') Sin(7rJ1S't')COS(7rJ1S't') 'P)cos( ) ] x sin( 1r:.llS'r) => Ix cos( 1r:.llS'r) -2Iy -Ix ~ JIsSE ~ 2IySz ~ -Ix of a CFN . I a d CFN s represents changes in state both from in-phase '7 to antiphase and antiphase to in-phase. ~ (D) Finally, consider the experiment shown in Fig. (D): Deccs I 0 't 180 s 't 1- I a b C d As ahove, we start the analysis with chemical a-tb: Ix Ix magnetization at point "a", hut this time we cannot neglect shift! ! ! QI 't"lz . IxCOS(QI 't") + IySm(QI 't") -~ 7rJls't"2Iz§z ~[IxCOS(QI 't") + Iysin(QI 't")] cos(7rJlS't") + [2IySzCOS(QI't") -2IxSzsin(QI 't")] sin( 7rJ1S't") ~ b ~ C:~[ [ S.cos(180° r C~ - IxCOS(.0.1 'r) + Iysin(.0.1 ) -Sysin(180° A A 1I:JIs'r2I.S. d: )J ~ 'r) JCOS(1I:JIS'r) + [ 2IyCOS(.0.1 'r) -2lxsin(.0.1 [ IxCOS(.0.1 'r) + Iysin(.0.1 'r) JCOS(1I:JIS'r) -[ 21yS. COS(.0.1 'r) -2IxS.sin(.0.1 ~[ Ix COS(.0.1 'r) + ly sin(.0.1 'r) J cos2 ( 1I:JIS'r) + [ 21y S. COS(.0.1 'r) -21x {[ 21yS. COS(.0.1'r) -21~ 'r) ]sin(1I:JIs'r) S. sin( .0.1'r) ]sin( 'r) ]sin(1I:JIs'r) 1I:JIS'r) cos( 1I:JIS'r) - S. sin(.0.1 'r) ] sin( 1I:JIS'r)COS(1I:JIS'r) -- = -[ Ix COS(.0.1'r) + ly sm(.0.1 'r) Jsin2 ( 1I:JIS'r) -[ Ix COS(.0.1'r) + ly sin(.0.1 'r) J[ cos2( 1I:JIS'r) + sin2 ( 1I:JIS'r)] = ~ IxCOS(QI 'f) + Iysin(QI 'f) A ~ Ixcos2(.QI'f) + IyCOS(.QI 'f) sin (.QI 'f) + IyCOS(.QI 'f)sin(.QI 'f)-Iysin2(.QI'f) =.J => Ix [ cos2(.QI'f) -sin2 (.QI'f) ] + 21y[sin(.QI'f) COS(.QI 'f) ] = => Ix COS(.QI 2 'f) + lysin(.QI2 'f) The Det result: The experiment decouples I from S while letting I evolve under chemical shift for the period 2't. This experiments are referred as a decoupled chemical shift (DecCS) and can be represented as: Ix DecCS ~ Ix COS(.Q.I 2 -r) + ly sin(.Q.I 2 -r) ~ In term of a CFN l'"' evvvvvvvvvvvvvve a d RULES l. Only products having a single transverse component give rise to detected NMR signal (e.g., Ix, Sy, 2IxSz, and 2IzSy). 2. Products having more than one transversecomponent correspond to multiple quantum coherence,and are not detected (e.g., 2IxSx, 2IySx, or for a three-spin system, .4IxSxXx, 4IxSzXx). 3. Products having one transverse term and one or several z terms represent antiphase signal. In other words, the I doublet appears in the spectrum with one line up and the other line down, having an overall integral of zero. 8