Advanced Multidimensional NMR-I

Advanced Multidimensional NMR-I K.V.R. Chary chary@tifr.res.in Workshop on NMR and it s applications in Biological Systems TIFR November 24, 2009 1

RECAP 2

[I 1x, I 1y ] = ii 1z [I 1y, I 1z ] = ii 1x [I 1z, I 1x ] = ii 1y [I 2x, I 2y ] = ii 2z [I 2y, I 2z ] = ii 2x [I 2z, I 2x ] = ii 2y 3

Evolution of spin operator under a pulse (π/2 X Pulse: X 1 Η I z -I y I y -I z 4

Evolution of spin operator under a pulse (π/2 Y Pulse: Y 1 Η I z I x -I x -I z 5

Evolution of spin operator under a pulse β y I z I z cos(β I x sin(β β x I z I z cos(β I y sin(β 6

Evolution under Chemical Shift (H δ = Ω Η I z Y M x Cos (Ωt M y Sin (Ωt Ωt Y X X M x 7

Evolution under Chemical Shift (H δ = Ω Η I z Rotation about the z-axis I1x I 1x cos(ωt I 1y sin(ωt I1y I 1y cos(ωt I 1x sin(ωt I1z I 1z 8

Evolution under Chemical Shift (H δ = Ω Ι I z X/Y Magnetization : y 1 Η H δ = Ω Ι I z I x I y Angle = Ω Ι t -I y -I x 9

Evolution under Couplings (H J = 2πJ 12 I 1z I 2z I 1x I 1x cos(πj 12 t 2I 1y I 2z sin(πj 12 t I 1y I 1y cos(πj 12 t 2I 1x I 2z sin(πj 12 t 2I 1x I 2z 2I 1x I 2z cos(πj 12 t I 1y sin(πj 12 t 2I 1y I 2z 2I 1y I 2z cos(πj 12 t I 1x sin(πj 12 t 10

Evolution under Couplings (H J = 2πJ 12 I 1z I 2z X Magnetization : y 1 Η H J =2πJ 12 I 1z I 2z I 1x 2I 1y I 2z Angle =2πJ 12 t -2I 1y I 2z -I 1x 11

Evolution under Couplings (H J = 2πJ 12 I 1z I 2z Y Magnetization : x 1 Η H J =2πJ 12 I 1z I 2z I 1y 2I 1x I 2z Angle =2πJ 12 t -2I 1x I 2z -I 1y 12

Evolution under Couplings (H J = 2πJ 12 I 1z I 2z I 1x I 1x cos(πj 12 t 2I 1y I 2z sin(πj 12 t I 1y I 1y cos(πj 12 t 2I 1x I 2z sin(πj 12 t 2I 1x I 2z 2I 1x I 2z cos(πj 12 t I 1y sin(πj 12 t 2I 1y I 2z 2I 1y I 2z cos(πj 12 t I 1x sin(πj 12 t 13

Vector repre tion of in-phase and antiphase magnetization Z Z I 1X Y I 1Y Y Z X X 2I 1x I 2z Y X 14

Vector repre tion of in-phase and antiphase magnetization Z Z I 1X Y 2I 1Y I 2Z Y X Z Z -X -2I 1Y I 2Z Y -I 1X Y X 15

In-phase/anti-phase magnetization α l β l α k β k α l β l α k β k I kx I lx I ky I ly Ω k Ω l Ω k Ω l α l β l α k β k α l β l α k β k 2I kx I lz 2I kz I lx 2I ky I lz 2I kz I ly Ω k Ω l Ω k Ω l 16

2D Homonuclear NMR 17

General 2D Experiment PREPA- RATION PERIOD EVOLU- TION PERIOD MIXING PERIOD DETECTION PERIOD H (1 H (2 t 2 18

Preparation Evolution Mixing Detection Period Period ( Period Period (t 2 1 2 3 (n-1 P E M D ν Α Cross peak Diagonal peak ν Β ν Β ν Α 19

Jeener s Idea (2D NMR (π/2 y 2I x S z -2I z S x I & S spins are through-bond (J coupled Jean Jeener A single non-selective 90 0 r.f. pulse transfers the magnetisation of spin I to S 20

R.R.Ernst s Experimentation COSY (J Φ 21

Threonine 1 H N 1 H α O N OH C α C C β 1 H β C γ Η γ 3 22

Threonine (π/2 x,y Transmitter Receiver t Fourier Transformation H H α O H γ 3 H N C C OH H β H α H β C OH CH γ 3 Threonine 4.0 3.5 3.0 2.5 2.0 1.5 1.0 ppm 23

Threonine (Thr; T COSY THR 1 H α Η γ 3 1 H β 24

2D COSY φ φ 1 2 3 4 φ = φ = x σ 1 = I kz σ 2 = -I ky σ 3 = -I ky cos(ω k I kx sin(ω k σ 3 = [-I ky cos(πj kl 2I kx I lz sin(πj kl ]cos(ω k [I kx cos(πj kl 2I ky I lz sin(πj kl ]sin(ω k σ 4 = [-I kz cos(πj kl -2I kx I ly sin(πj kl ]cos(ω k [I kx cos(πj kl -2I kz I ly sin(πj kl ]sin(ω k 25

2D COSY φ φ 1 2 3 4 σ 3 = [-I ky cos(πj kl -2I kx I lz sin(πj kl ]cos(ω k [I kx cos(πj kl 2I ky I lz sin(πj kl ]sin(ω k (π/2 X σ 4 = [-I kz cos(πj kl -2I kx I ly sin(πj kl ]cos(ω k [I kx cos(πj kl -2I kz I ly sin(πj kl ]sin(ω k 26

2D COSY φ φ 1 2 3 4 σ 4 = [-I kz cos(πj kl -2I kx I ly sin(πj kl ]cos(ω k NO superposition of ZQ and 2Q coherences [I kx cos(πj kl -2I kz I ly sin(πj kl ]sin(ω k in-phase anti-phase SQC SQC 27

2D COSY φ φ 1 2 3 4 σ 4 = [I kx cos(πj kl -2I kz I ly sin(πj kl ]sin(ω k in-phase anti-phase SQC SQC x-magnetization y-magnetization of spin k of spin l Diagonal peak Cross peak 28

COSY diagonal peak φ φ 1 2 3 4 DP = I kx cos(πj kl sin(ω k I kx corresponds to an in-phase k spin doublet centered at F 2 = ω k. Its amplitude depends on ω k. The modulation Coefficient cos(πj kl sin(ω k can be expanded as ½ [sin(ω k πj kl sin(ω k -πj kl ] 29

In-phase/anti-phase magnetization α l β l α k β k α l β l α k β k I kx I lx I ky I ly Ω k Ω l Ω k Ω l α l β l α k β k α l β l α k β k 2I kx I lz 2I kz I lx 2I ky I lz 2I kz I ly Ω k Ω l Ω k Ω l 30

Fine structure of diagonal-peaks COSY Two-spin ( k & l system 31

COSY diagonal peak 32

COSY cross peak φ φ 1 2 3 4 CP = -2I kz I ly sin(πj kl sin(ω k -2I kz I ly corresponds to an anti-phase l spin doublet centered at F 2 = ω l. Its amplitude depends on ω k. The modulation Coefficient sin(πj kl sin(ω k can be expanded as ½ [-cos(ω k πj kl cos(ω k -πj kl ] 33

In-phase/anti-phase magnetization α l β l α k β k α l β l α k β k I kx I lx I ky I ly Ω k Ω l Ω k Ω l α l β l α k β k α l β l α k β k 2I kx I lz 2I kz I lx 2I ky I lz 2I kz I ly Ω k Ω l Ω k Ω l 34

Fine structure of cross-peaks COSY Two-spin ( k & l system 35

COSY cross peak 36

Fine structure of cross-peaks COSY Two-spin ( k & l system 37

A Ω Α - - Cross peak Diagonal peak Ω 1 Ω X - - B Ω X Ω 2 Ω Α Ω 1 Ω 2 38

COSY 2D-COSY of HSPI (94 amino acid residues long protein 39

2D Relayed COSY A J AM M J MX X A M X Prep Evol Mix Det J AM & J MX = 0 40

2D Relayed COSY A J AM M J MX X A M X Prep Evol Mix Det τ M t 2 J AM & J MX = 0 41

2D Relayed COSY X M M A M X A M X Relay Peak 42

2D Relayed COSY H α i H α j H β i / Hβ j H γ j H γ i H α H δ H β2 Hβ3 H γ2hγ3 C D Relay Peak 43

2D Relayed COSY 1 2 3 4 5 τ M t 2 J kl & J lm = 0 Requires three spin sytem k, l & m spins (AMX Spin system (π/2 X, H δ, H J(kl, H J(lm σ 1 σ 5 44

2D Relayed COSY 1 2 3 4 5 τ M t 2 σ 4 = [-I kz cos(πj kl -2I kx I ly sin(πj kl ]cos(ω k [I kx cos(πj kl -2I kz I ly sin(πj kl ]sin(ω k σ 4 = -2I kz I ly sin(πj kl sin(ω k H J(kl, H J(lm -2I kz I ly cos(πj kl τsin(πj kl sin(ω k [I lx cos(πj lm τ 2I ly I mz sin (πj lm τ] sin(πj kl τsin(πj kl sin(ω k 45

2D Relayed COSY 1 2 3 4 5 τ M t 2-2I kz I ly cos(πj kl τsin(πj kl sin(ω k [I lx cos(πj lm τ 2I ly I mz sin (πj lm τ] sin(πj kl τsin(πj kl sin(ω k (π/2 X 2I ky I lz cos(πj kl τsin(πj kl sin(ω k [I lx cos(πj lm τ- 2I lz I my sin (πj lm τ] sin(πj kl τsin(πj kl sin(ω k 46

2D Relayed COSY 1 2 3 4 5 τ M t 2 2I ky I lz cos(πj kl τsin(πj kl sin(ω k [I lx cos(πj lm τ- 2I lz I my sin (πj lm τ]sin(πj kl τsin(πj kl sin(ω k -2I lz I my sin(πj lm τsin(πj kl τsin(πj kl sin(ω k I mx sin(πj lm t 2 sin(πj lm τsin(πj kl τsin(πj kl sin(ω k 47

2D Relayed COSY 1 2 3 4 5 τ M t 2 I mx sin(πj lm t 2 sin(πj lm τsin(πj kl τsin(πj kl sin(ω k Thus, the transfer function is sin(πj lm τsin(πj kl τ 48

Threonine (Thr; T COSY THR 1 H α Η γ 3 1 H β 49

Threonine (Thr; T Relayed COSY THR 1 H α Η γ 3 1 H β Relayed peaks 50

2QF-COSY σ resultant = -[2I kx I ly 2I ky I lx ] sin(πj kl cos(ω k (π/2 X σ detected = [2I kx I lz 2I kz I lx ] sin(πj t cos(ω t kl 1 k 1 DP CP 51

2QF-COSY σ detected = [2I kx I lz 2I kz I lx ] sin(πj t cos(ω t kl 1 k 1 DP CP Both of them are anti-phase coherences. Both have same modulation coefficient. 2I kx I lz corresponds to an anti-phase k spin doublet centered at F 2 = ω k. 2I kz I lx corresponds to an anti-phase l spin doublet centered at F 2 = ω l. 52

2QF-COSY σ detected = [2I kx I lz 2I kz I lx ] sin(πj t cos(ω t kl 1 k 1 DP CP The modulation Coefficient sin(πj kl cos(ω k can be expanded as ½ [sin(ω k πj kl - sin(ω k -πj kl ] 53

Fine structure of cross-peaks 2QF COSY Two-spin ( k & l system Anti-symmetric w.r.t chemical shift axis. 54

Fine Structures of cross-peaks Fine structures Fine Structures of cross-peaks of cross-peaks 2QF COSY k and l active spins in the presence of one passive spin Characteristic of even quantum filtered COSY 55

Fine structure of cross-peaks 2QF COSY Two-spin ( k & l system Anti-symmetric w.r.t chemical shift axis. 56

Fine Structures of cross-peaks Fine structures Fine Structures of cross-peaks of cross-peaks 2QF COSY k and l active spins in the presence of one passive spin Characteristic of even quantum filtered COSY 57

A Ω Α - - Cross peak Diagonal peak Ω 1 Ω X - - B Ω X Ω 2 Ω Α Ω 1 Ω 2 58

COSY 2D-COSY of HSPI (94 amino acid residues long protein 59

Advanced Multidimensional NMR-I K.V.R. Chary chary@tifr.res.in Workshop on NMR and it s applications in Biological Systems TIFR November 24, 2009 60

Multiple Quantum Filtering 61

Multiple Quantum Filtering Multiple Quantum Filtered COSY: Singlets are suppressed Purely absorptive peaks Diagonal peaks are anti-phase Multiplets structures and symmetry properties of cross-peaks can give new information With p-quantum filter, it is possible to suppress resonances of spin systems with less than p-coupled spins ; particularly those stemming from solvents 2QF COSY : singlets 3QF COSY : singlets, AB & AX Sensitivity goes down rapidly as higher orders are selected. 62

Multiple Quantum Filtering The effects of MQ Filtering on COSY spectra have been ratinalised by the following cohenrence transfer rules: A DP in pqf-cosy spectrum can only appear when the active spin has resolved couplings to at least p-1 further spins. A pqf-cosy cross-peak between two resonances can only appear when the two active spins have (p-2 additional common coupling partners with resolved couplings. These rules hold for weakly coupled systems δ >> J 63

What is I kx I ly? <α k β l I kx I ly α k β l > = <α k I kx α k > <α l I ly α l > = <α k β k > <α l β l > = 0 64

2I kx I ly = 2 0 1/2 1/2 0 0 -i/2 -i/2 0 = 2 0 1/2 0 -i/2 i/2 0 0 -i/2 i/2 0 1/2 0 0 -i/2 i/2 0 0 -i/2 i/2 0 = 0 0 0 -i/2 0 0 i/2 0 0 -i/2 0 0 i/2 0 0 0 65

2I kx I ly Similarly, 2I ky I lx = = 0 0 0 -i/2 0 0 i/2 0 0 -i/2 0 0 i/2 0 0 0 0 0 0 -i/2 0 0 -i/2 0 0 i/2 0 0 i/2 0 0 0 66

2I kx I ly 2I ky I lx Pure 2QF Similarly, 2I ky I lx -2I ky I lx Pure ZQF = = 0 0 0 -i/2 0 0 0 0 0 0 0 0 i/2 0 0 0 0 0 0 0 0 0 -i/2 0 0 i/2 0 0 0 0 0 0 67

2QF COSY 68

2QF COSY φ φ β 1 2 3 5 φ = φ = x 4 σ 1 = I kz σ 2 = -I ky σ 3 = -I ky cos(ω k I kx sin(ω k σ 3 = [-I ky cos(πj kl -2I kx I lz sin(πj kl ]cos(ω k [I kx cos(πj kl 2I ky I lz sin(πj kl ]sin(ω k σ 4 = [-I kz cos(πj kl -2I kx I ly sin(πj kl ]cos(ω k [I kx cos(πj kl -2I kz I ly sin(πj kl ]sin(ω k 69

2QF-COSY φ = φ = x σ 4 = [-I kz cos(πj kl -2I kx I ly sin(πj kl ]cos(ω k [I kx cos(πj kl -2I kz I ly sin(πj kl ]sin(ω k We use this term, which we have ignored so far. It represents superposition of ZQ and 2Q coherences 70

2QF-COSY ================================ φ φ Receiver =============================== x x y y - -x -x -y -y - =============================== 71

2QF-COSY φ = φ = x σ 4 = [-I kz cos(πj kl -2I kx I ly sin(πj kl ]cos(ω k [I kx cos(πj kl -2I kz I ly sin(πj kl ]sin(ω k φ = φ = x σ 4 = [-I kz cos(πj kl -2I kx I ly sin(πj kl ]cos(ω k [-I kx cos(πj kl 2I kz I ly sin(πj kl ]sin(ω k φ = φ = y σ 4 = [-I kz cos(πj kl -2I ky I lx sin(πj kl ]cos(ω k [I ky cos(πj kl -2I kz I lx sin(πj kl ]sin(ω k φ = φ = y σ 4 = [-I kz cos(πj kl -2I ky I lx sin(πj kl ]cos(ω k [-I ky cos(πj kl 2I kz I lx sin(πj kl ]sin(ω k 72

2QF-COSY φ = φ = x σ 4 = [-I kz cos(πj kl -2I kx I ly sin(πj kl ]cos(ω k [I kx cos(πj X kl -2I kz I ly sin(πj X kl ]sin(ω k φ = φ = x σ 4 = [-I kz cos(πj kl -2I kx I ly sin(πj kl ]cos(ω k X X [-I kx cos(πj kl 2I kz I ly sin(πj kl ]sin(ω k ============================= σ 4 = 2[-I kz cos(πj kl -2I kx I ly sin(πj kl ]cos(ω k ============================= 73

2QF-COSY φ = φ = y σ 4 = [-I kz cos(πj kl -2I ky I lx sin(πj kl ]cos(ω k [I ky cos(πj kl -2I kz I lx sin(πj kl ]sin(ω k X X φ = φ = y σ 4 = [-I kz cos(πj kl -2I ky I lx sin(πj kl ]cos(ω k X X [-I ky cos(πj kl 2I kz I lx sin(πj kl ]sin(ω k ============================= σ 4 = 2[-I kz cos(πj kl -2I ky I lx sin(πj kl ]cos(ω k ============================= 74

2QF-COSY X σ 4 = 2[-I kz cos(πj kl -2I kx I ly sin(πj kl ]cos(ω k X σ 4 = 2[-I kz cos(πj kl -2I ky I lx sin(πj kl ]cos(ω k ============================= σ 4 = -[2I kx I ly 2I ky I lx ] sin(πj kl cos(ω k ============================= 75

2QF-COSY ============================================= σ resultant = -[2I kx I ly 2I ky I lx ] sin(πj kl cos(ω k ============================================= 76

3QF COSY 77

3QF COSY φ φ β 1 2 3 5 4 Requires three spin sytem k, l & m spins (AMX Spin system l o k o J kl = J km = 0 m o (π/2 X, H δ, H J(kl, H J(km σ 1 σ 3 78

3QF COSY φ φ β 1 2 3 5 σ 1 σ 3 4 (π/2 X, H δ, H J(kl, H J(km σ 3 σ 3 = [-I ky cos(πj kl 2I kx I lz sin(πj kl ]cos(ω k [I kx cos(πj kl 2I ky I lz sin(πj kl ]sin(ω k 79

3QF COSY φ φ β 1 2 3 5 σ 1 σ 3 4 (π/2 X, H δ, H J(kl, H J(km σ 3 σ 3 = 2I ky I lz sin(πj kl ]sin(ω k σ 3 = 2I ky I lz cos(πj km sin(πj kl sin(ω k -4I kx I lz I mz sin(πj km sin(πj kl sin(ω k 80

3QF COSY φ φ β 1 2 3 5 (π/2 X σ 3 σ 4 σ 3 = 2I ky I lz cos(πj km sin(πj kl sin(ω k -4I kx I lz I mz sin(πj km sin(πj kl sin(ω k transforms into σ 4 = -2I kz I ly cos(πj km sin(πj kl sin(ω k 4-4I kx I ly I my sin(πj km sin(πj kl sin(ω k 81

3QF COSY φ φ β 1 2 3 5 (π/2 X σ 3 σ 4 σ 4 = -4I kx I ly I my sin(πj km sin(πj kl sin(ω k can be expanded as σ 4 = ¼[4I kx I ly I my 4I ky I lx I my 4I ky I ly I mx - 4I kx I lx I mx ] sin(πj km sin(πj kl sin(ω k 4 82

3QF COSY φ φ β 1 2 3 5 (π/2 X σ 4 σ 5 σ 4 = ¼[4I kx I ly I my 4I ky I lx I my 4I ky I ly I mx - 4I kx I lx I mx ] sin(πj km sin(πj kl sin(ω k 4 transforms into σ 5 = ¼[4I kx I lz I mz 4I kz I lx I mz 4I kz I lz I mx - 4I kx I lx I mx ] sin(πj km sin(πj kl sin(ω k 83

3QF COSY φ φ β 1 2 3 5 σ detectable = ¼[4I kx I lz I mz 4I kz I lx I mz 4I kz I lz I mx - 4I kx I lx I mx ] sin(πj km sin(πj kl sin(ω k DP CP1 CP2 Non-observable 4 superposition of 3QC 3 spin SQC 84

3QF COSY φ φ β 1 2 3 5 CP1 = 4I kz I lx I mz sin(πj km sin(πj kl sin(ω k & CP2 = 4I kz I lz I mx sin(πj km sin(πj kl sin(ω k 4 85

3QF COSY φ φ β 1 2 3 5 CP1 = 4I kz I lx I mz sin(πj km sin(πj kl sin(ω k The modulation Coefficient sin(πj km sin(πj kl sin(ω k can be expanded as sin(ω k πj km /2πJ kl /2 -sin(ω k πj km /2-πJ kl /2 4 -sin(ω k -πj km /2πJ kl /2 sin(ω k -πj km /2-πJ kl /2 86

Fine Structures of cross-peaks Fine structures Fine Structures of cross-peaks of cross-peaks 3QF COSY K, l and m are active spins Characteristic of three quantum filtered COSY 87

3QF COSY φ φ β 1 2 3 5 In an AMX spin system, 4 Geminal cross-peak has ve center as both the Couplings with the third spin are vicinal and have the same sign. While, the vicinal cross-peaks have ve center as the couplings with the third spin have different sign. Hence, the distinction beween vicinal and geminal cross peaks. 88

Exclusive COSY 89

Fine Structures of cross-peaks Fine structures Fine Structures of cross-peaks of cross-peaks 2QF COSY k and l active spins in the presence of one passive spin Characteristic of even quantum filtered COSY 90

Fine Structures of cross-peaks Fine structures Fine Structures of cross-peaks of cross-peaks 3QF COSY K, l and m are active spins Characteristic of three quantum filtered COSY 91

Fine Structures of cross-peaks 2QF Fine COSY/-3QF Structures of COSY cross-peaks = E.COSY K, l and m are active spins = - = 92