Heteronuclear Decoupling and Recoupling

Transcription

1 Heteronuclear Decoupling and Recoupling Christopher Jaroniec, Ohio State University 1. Brief review of nuclear spin interactions, MAS, etc. 2. Heteronuclear decoupling (average Hamiltonian analysis of CW decoupling, intro to improved decoupling schemes) 3. Heteronuclear recoupling (R 3, REDOR) 4. AHT analysis of finite pulse REDOR C- 15 N distance measurements in multispin systems (frequency selective REDOR, 3D TEDOR methods) 6. Intro to dipole tensor correlation experiments for measuring torsion angles

2 Isolated Spin-1/2 (I-S) System = CS + CS + J + D int I S IS IS H H H H H H H H CS I D IS J IS = γ I = I D S IS = 2 I J S π I σ B IS Relevant interactions expressed in general as coupling of two vectors by a 2 nd rank Cartesian tensor (3 x 3 matrix)

3 Rotate Tensors: PAS Lab 1 {,, } σ = R( Ω) σ R( Ω) ; Ω= α βγ LAB PAS SSNMR spectra determined by interactions in lab frame Rotate tensors from their principal axis systems (matrices diagonal) into lab frame (B 0 z-axis) In general, a rotation is accomplished using a set of 3 Euler angles {α,β,γ}

4 Multiple Interactions In case of multiple interactions first transform all tensors into common frame (molecular- or crystallitefixed frame) Powder samples: rotate each crystallite into lab frame

5 High Field Truncation: H CS ( sin 2 cos 2 sin 2 sin 2 cos 2 ) H = γ Bσ I = γ B σ θ φ+ σ θ φ+ σ θ I CS LAB I I 0 zz z I 0 xx yy zz z IB0 iso IB 0 3cos 1 sin cos(2 ) Iz = γ σ + γ δ θ η θ φ 2 1 σ = σ + σ + σ 3 δ = σ σ ( ) iso xx yy zz σ η = zz yy σ δ iso xx Retain only parts of H CS that commute with I z

6 High Field Truncation: H J and H D J HIS = π JIS 2IzSz D 1 ( 3cos 2 H = b θ 1 ) 2 I S 2 µ γ γ 0 bis = 4π r IS IS z z I S 3 IS J-anisotropy negligible in most cases b IS in rad/s; directly related to I-S distance

7 Dipolar Couplings in Proteins Spin 1 Spin 2 r 12 (Å) b 12 /2π (Hz) 1 H 13 C 1.12 ~21,500 1 H 15 N 1.04 ~10, C 13 C 1.5 ~2, C 15 N 1.5 ~ C 15 N 2.5 ~ C 15 N 4.0 ~50

8 Static Powder Spectra: H CS & H D { ( ) ( )} CS x CS I + () t dφ dθsinθ Tr I + exp ih t I exp ih t σ yy σzz θ σ xx σ xx φ σ yy B 0 θ σ zz

9 NMR of Rotating Samples H = ω () t I CS I I z D H = ω ()2 t I S IS IS z z J H = π J 2I S IS IS z z 2 ( m) λ() = λ exp m= 2 ω t ω imω t { } r

10 H D for Rotation at Magic Angle (θ m = o ) H im t I S 2 D ( m) exp( ) IS = ωis ωr 2 z z m= 2 ( 2 ) ( 2 3cos β 1 3cos 1) PR θm (0) ωis = bis = 2 2 ( ± 1) bis ω sin ( 2 ) exp{ } IS = βpr ± iγpr 2 2 ( ± 2) bis 2 ω sin exp{ 2 } IS = βpr ± i γpr 4 For spinning at the magic angle the time-independent dipolar (and CSA) components vanish; terms modulated at ω r and 2ω r vanish when averaged over the rotor cycle 0

11 13 C- 1 H Dipolar Spectra under MAS Static ν r = 2 khz Increasing Resolution ν r = 20 khz Frequency (Hz)

12 13 C SSNMR Spectra at High MAS Rates 13 C- 1 H 13 C- 1 H 2 a f ( ν r ) = + b ν r 13 C Frequency Presence of many strong 1 H- 1 H couplings leads to an incomplete averaging of 13 C- 1 H dipolar coupling by MAS M. Ernst, JMR 2003

13 High-Power CW Decoupling 13 C-VF, 28 khz MAS CW off 150 khz Average 13 C- 1 H couplings by simultaneously using MAS and high-power 1 H RF irradiation Traditionally for efficient decoupling 1 H RF fields of ~ khz were used (i.e., ω 1H >> b HH, b HX )

14 CW Decoupling: AHT Analysis (I) (S) iso iso H = ω S + ω () t S + ω I + ω () t I + πj 2 IS + ω ( t)2is + ω I tot S z S z I z I z IS z z IS z z 1 x Average Hamiltonian analysis: RF and MAS modulations must be synchronized to obtain cyclic propagator

15 ρ AHT: Summary { t } { t } { } { t } = = + 1 () t Utot () t ρ(0) Utot () t ; Utot () t Texp i dt ( H H ) 0 RF U () t = U () t U() t = U () t Texp i dt H ; H = U HU 1 tot RF RF 0 RF RF c U ( t ) = U( t ) = Texp i dt H = exp iht (for U ( t ) = 1) tot c c 0 c RF c (0) (1) (2) = H H H H t (0) c t (1) c t = = t c itc H 1 1 dt H ; H dt dt H ( t ), H ( t ) ; Haeberlen & Waugh, Phys. Rev. 1968

16 Interaction Frame Hamiltonian H = U HU = exp iωti Hexp iωti { } { } 1 RF RF 1 x 1 x J H = H + H + H + H iso H = ω S + ω () t S D S I IS IS S S z S z H = πj 2S I cos( ωt) + I sin( ωt) { } J IS IS z z 1 y 1 { ( inω ) ( )} rt inωrt inωrt inωrt = π J S I e + e ii e e IS z z y H = ω ()2 t S I cos( ωt) + I sin( ωt) { } D IS IS z z 1 y 1 = ω in IS () ts{ z I( ω z e ) ( )} rt in ω rt in ω rt e ii in ω + rt y e e

17 Interaction Frame Cont. H = ω ( t)2s I cos( ωt) + I sin( ωt) { } D IS IS z z 1 y 1 2 m= 2 { ( inω ) ( )} rt inωrt inωrt inωrt = ω () ts I e + e ii e e IS z z y = { ω e + e I S ( m) i( m+ n) ωrt i( m n) ωrt IS z z iω e e I S ( m) i( m+ n) ωrt i( m n) ωrt IS y z }

18 Lowest-Order Average Hamiltonian H = H + H + H (0) (0) (0) (0) S J, IS D, IS H ω S dt S dt e S iso τ 2 (0) r τr S z z ( m) imωr t iso S = + ω 0 0 S = ωs z τr m= 2 τr J S H π = dt I e + e ii e e = { ( inω ) ( )} rt inωrt inωrt inωrt τ (0) r IS z JIS, 0 z y τ r 0 S-spin CSA refocused by MAS, I-S J-coupling eliminated by I-spin decoupling RF field

19 Lowest-Order Average H D 1 H dt e e I S τ 2 (0) r ( m) i( m+ n) ωrt i( m n) ωrt S = { ω 0 IS z z τ + r m= 2 iω e e I S ( m) i( m+ n) ωrt i( m n) ωrt IS y z } 1 τ r τ 0 r dtω ( m) IS e i( m± n) ω t r 0 if m± n 0 = ( n) ωis if m± n= 0

20 H (0) DIS, Lowest-Order Average H D n π 1,2 ô I-S Decoupling = 0 n =1,2 ô I-S Dipolar Recoupling! H = + I S i I S ( n n ) ( n n ω ω ω ω ) (0) ( ) ( ) ( ) ( ) DIS, IS IS z z IS IS y z Rotary resonance recoupling (R 3 ) arises from the interference of MAS and I-spin RF (when ω 1 = ω r or 2ω r ) Additional (much-weaker) resonances (n = 3,4, ) are also possible due to higher order average Hamiltonian terms involving the I-spin CSA

21 Improved heteronuclear decoupling: Two pulse phase modulation (TPPM) The first truly effective pulse scheme (and still one of the best) for achieving efficient heteronuclear decoupling in samples under MAS TPPM reduces magnitude of cross-term between 1 H CSA and 1 H-X dipolar coupling which dominates the residual linewidth Bennett, Rienstra, Auger & Griffin, JCP 1995

22 Optimization of TPPM Decoupling φ β = ω τ π p 1, H p Parameters optimized empirically Under moderate MAS rates (~10-25 khz) and 1 H RF fields (~ khz) best results usually obtained for φ and β in ranges given above

23 Other Useful Decoupling Schemes TPPM-related schemes (similar to TPPM for most rigid solids): FMPM (Gan & Ernst, SSNMR 1997) frequency and phase modulated decoupling SPINAL (Fung et al., JMR 2000) TPPM combined with supercycles XiX(Detken et al., Chem. Phys. Lett. 2002) offers improvements over TPPM at high MAS rates (>20 khz) and high 1 H RF (>100 khz) Low-power CW decoupling (~10 khz) at very high MAS rates, khz (Ernst, Samoson & Meier, Chem. Phys. Lett. 2001)

24 X inverse-x (XiX) Decoupling t p = 3.1 µs φ = 27 o t p = 94.9 µs 2-13 C alanine ν r = 30 khz ν 1 = 150 khz Detken et al., Chem. Phys. Lett Technically XiX is equivalent to TPPM with φ = 180 o but pulse width considerations are very different

25 XiX Decoupling ν r = 30 khz ν 1 = 150 khz Performance determined mainly by t p in units of τ r simulation Best when t p > τ r (e.g., optimize around 2.85τ r ) and when strong resonances at t p = nτ r /4 avoided

26 XiX Decoupling 13 C- 1 H 13 C- 1 H 13 C- 1 H 2 13 C- 1 H 2

27 Rotary Resonance Recoupling H = + C N i C N ( ω ω ) ( ω ω ) (0) ( 1) (1) ( 1) (1) DCN, IS IS z z IS IS z y = exp iγ N ω2c N exp iγ N ω = { }( ) { } b PR x z z PR x IS sin(2 β ) PR Oas, Levitt & Griffin, JCP 1988

28 Rotary Resonance Recoupling ρ( t) = exp{ ih t} C exp{ ih t} (0) (0) DCN, x DCN, = C cos( ωt) + 2C N sin( ωt) x N = N cosγ N γ y sin γ z PR y PR γ <C <Sx> x > (t) D CN = 900 Hz ω r = 25 khz Intensity (a.u.) D CN / Time (ms) Frequency (Hz)

29 R 3 in Real Systems: Effect of CSA of Irradiated Spin 1.0 <Sx> <C x > (t) no CSA typical 15 N CSA Intensity (a.u.) Time (ms) Frequency (Hz) R 3 also recouples 15 N CSA, which doesn t commute with dipolar term Dipolar dephasing depends on CSA magnitude and orientation: problem for quantitative distance measurements In experiments also have to consider effects of RF inhomogeneity

30 Rotational Echo Double Resonance (REDOR) Apply a series of rotor-synchronized π pulses (2 per τ r ) to 15 N spins (this is usually called a dephasing or S experiment) Typically a reference (or S 0 ) experiment with pulses turned off is also, acquired normally report S/S 0 ratio (or S/S 0 = 1-S/S 0 ) Gullion & Schaefer, JMR 1989

31 REDOR: AHT Summary H t t I S b t t I S 1 2 IS() = ωis()2 z z = 2 IS{sin ( β)cos[2( γ + ωr )] 2sin(2 β)cos( γ + ωr )}2 z z S S z 0 < t τ S z = S z τ < t τ +τ r /2 S z τ + τ r /2< t τ r H b sin(2 β)sin( γ ψ) 2 I S ; ψ ωτ (sequence phase) π (0) 2 IS = IS + z z = r H (0) IS 2 bis sin(2 β )sin( γ) 2 IzSz for τ = τr /2 π = 2 bis sin(2 β)sin( γ) 2 IzSz for τ = 0 π Effective Hamiltonian changes sign as a function of position of pulses within the rotor cycle (must be careful about this in some implementations of REDOR)

32 REDOR: Typical Implementation Rotor synchronized spin-echo on 13 C channel refocuses 13 C isotropic chemical shift and CSA evolution 2 nd group of pulses moved by -τ r /2 relative to 1 st group to change sign of H D and avoid refocusing the 13 C- 15 N dipolar coupling xy-type phase cycling of 15 N pulses is critical (Gullion, JMR 1990)

33 REDOR Dipolar Evolution ρ( t) = exp{ i ω2 C N t} C exp{ i ω2 C N t} z z x z z = C cos( ωt) + 2C N sin( ωt) x y z 2 ω = bis sin(2 β)sin( γ) π

34 REDOR: Example [2-13 C, 15 N]Glycine 1.51 ± 0.01 Å Experiment highly robust toward 15 N CSA, experimental imperfections, resonance offset and finite pulse effects (xy-4/xy-8 phase cycling is critical for this) REDOR is used routinely to measure distances up to ~5-6 Å (D ~ 25 Hz) in isolated 13 C- 15 N spin pairs

35 REDOR: More Challenging Case S112( 13 C )-Y114( 15 N) Distance Measurement in TTR( ) Amyloid Fibrils 4.06 ± 0.06 Å

36 REDOR: 15 N CSA Effects xy xy xy 4: 8: 16 : xyxy Gullion, Baker & Conradi, JMR 1990 xyxy yxyx xyxy yxyx xyxy yxyx Simpler schemes (xy-4, xy-8) seem to perform better with respect to 15 N CSA compensation than the longer xy-16 Since [H D (0),H CSA (0) ] = 0 the behavior is likely due to finite pulses and higher order terms in the average Hamiltonian expansion

37 REDOR at High MAS Rates ϕ = 2τ p τ r τ p (µs) ν r (khz) ϕ

38 REDOR (xy-4) at High MAS: AHT H () t = ω () t f()2 t I S + g()2 t I S + h()2 t I S { } IS IS z z z x z y (0) 1 H { ( ac + bc ) dt 2 I S τ IS z z r t 1 + ( ac + bc )cos[ θ( t)] dt 2 I S + ( ac + bc )sin[ θ( t)] dt 2I S t 2 2 ( ac + bc ) dt 2I S t 3 ( ac + bc )cos[ θ ( t)] dt 2 I S ( ac + bc )sin[ θ ( t)] dt 2I S t 4 + ( ac + bc ) dt 2I S t z z z z z y t z z + ( ac + bc )cos[ θ( t)] dt 2 I S ( ac + bc )sin[ θ( t)] dt 2I S t ( ac + bc ) dt 2I S t t z z z z t ( ac + bc )cos[ θ( t)] dt 2 I S + ( ac + bc )sin[ θ( t)] dt 2 I S } z z z y t z z z x t z x Jaroniec et al, JMR 2000

39 REDOR (xy-4) at High MAS: AHT H (0) IS = 2 b π 2 b π cos ( π ϕ ) sin(2 β)sin( γ)2 I S 2 IS 2 z z 1 ϕ sin(2 β)sin( γ)2 I S IS z z ; finite pulses ; ideal pulses ( π ϕ ) b cos = ; / 4 1 eff IS 2 κ π κ 2 bis 1 ϕ For xy-4 phase cycling, finite π pulses result only in a simple scaling of the dipolar coupling constant by an additional factor, κ, between π/4 and 1 For xx-4 spin dynamics are more complicated and converge to R 3 dynamics in the limit of ϕ = 1

40 REDOR (xy-4) at High MAS: AHT vs. Numerical Simulations 10 µs 15 N pulses no 15 N CSA

41 REDOR (xy-4) Experiments

42 REDOR in Multispin Systems H = ω 2I S + ω 2I S IS 1 z 1z 2 z 2z I () t = cos ωt cos ω t x ( ) ( ) Hz I (2.5 Å) 50 Hz 45 o (4 Å) S S Strong 13 C- 15 N couplings dominate REDOR dipolar dephasing; weak couplings become effectively invisible

43 Frequency Selective REDOR H = FS-REDOR i, j ω ij 2I iz S jz + πj ij 2I iz I jz i< j Jaroniec et al, JACS 1999, 2001 H = ω kl 2I kz S lz Use a pair of weak frequency-selective pulses to isolate the 13 C- 15 N dipolar coupling of interest; all other couplings refocused This trick is possible because all relevant interactions commute

44 FS-REDOR Evolution Ut e e e e e e e e ih (/2) t iπikx iπslx ih (/2) t iπslx iπikx iπikx iπslx () = = = ih (/2) t 0 (/2) ih2(/2) t ih1(/2) t π kx e e e e e e ih t i I iπs 0 ih2t π kx e e e e ih t i I iπs lx [ ] [ ] [ ] [ ] [ ] H = H + H + H ; H, H = H, H = H, H = H = ω 2I S + πj 2 I I ; H, I = H, S = 0 0 ij iz jz ij iz jz 0 kx 0 lx i k j l i< j k H = ω 2I S + ω 2I S + πj 2 I I ; 1 H1 [ Ikx ] [ Slx ] ki kz iz il iz lz ki kz iz i l i k i k for each term in, 0 or, 0 [ ] [ ] H = ω 2 I S ; H, I 0 and H, S 0 2 kl kz lz 2 kx 2 lx ρ = kx ρ = ρ = ρ = iπslx iπikx ih0t (0) I ; (0), e (0), e (0), e 0 ρ = = ω + ω ih2t ih2t () t e I e I cos( t) 2I S sin( t) kx kx kl ky lz kl 1 lx Dipolar evolution under only b kl

45 13 C Selective Pulses: U- 13 C Thr

46 FS-REDOR: U- 13 C, 15 N Asn 1 ms 6 ms 2 ms 8 ms 4 ms 10 ms

47 FS-REDOR: U- 13 C, 15 N Asn

48 FS-REDOR: U- 13 C, 15 N-f-MLF

49 FS-REDOR: U- 13 C, 15 N-f-MLF Leu C β -Leu N Leu C β -Phe N Met C β -Phe N X-ray: 2.50 Å NMR: 2.46 ± 0.02 Å X-ray: 3.12 Å NMR: 3.24 ± 0.12 Å X-ray: 4.06 Å NMR: 4.12 ± 0.15 Å

50 FS-REDOR: U- 13 C, 15 N-f-MLF C- 15 N distances could be measured in MLF tripeptide Selectivity of 15 N pulse + need of prior knowledge of which distances to probe is a major limitation to U- 13 C, 15 N proteins

51 Simultaneous 13 C- 15 N Distance Measurements in U- 13 C, 15 N Molecules General Pseudo-3D HETCOR (Heteronuclear Correlation) Scheme I-S coherence transfer as function of t mix via D IS Identify coupled I and S spins by chemical shift labeling in t 1, t 2

52 Transferred Echo Double Resonance 3D TEDOR Pulse Sequence Hing, Vega & Schaefer, JMR 1992 REDOR S 2I S sin( ω t /2) x z y IS mix ( π/2) Ix+ ( π/2) Sx REDOR 2 2IS y z sin( ωistmix / 2) Ix sin ( ωistmix / 2) Similar idea to INEPT experiment in solution NMR Cross-peak intensities depend on all 13 C- 15 N dipolar couplings Experiment not directly applicable to U- 13 C-labeled samples

53 3D TEDOR: U- 13 C, 15 N Molecules Modified 3D TEDOR Pulse Sequence REDOR I 2I S sin( ω t /2) x y z IS mix 2IS sin( ω t /2) z y IS mix ( π/2) Sx+ ( π/2) Ix ( π/2) Sx ( π/2) Ix REDOR 2 2IS y z sin( ωistmix / 2) Ix sin ( ωistmix / 2) Michal & Jelinski, JACS 1997

54 3D TEDOR: U- 13 C, 15 N Molecules N-acetyl-Val-Leu Cross-peak intensities roughly proportional to 13 C- 15 N dipolar couplings

55 3D TEDOR: U- 13 C, 15 N N-ac-VL Spectral artifacts (spurious cross-peaks, phase twisted lineshapes) appear at longer mixing times as result of 13 C- 13 C J-evolution

56 Improved Scheme: 3D Z-Filtered TEDOR 3D ZF TEDOR Pulse Sequence Unwanted anti-phase and mulitple-quantum coherences responsible for artifacts eliminated using two z-filter periods Jaroniec, Filip & Griffin, JACS 2002

57 Results in N-ac-VL 3D TEDOR 3D ZF TEDOR 3D ZF TEDOR generates purely absorptive 2D spectra Cross-peak intensities give qualitative distance information

58 13 C- 13 C J-Evolution Effects: ZF-TEDOR Simulated 13 C Cross-Peak Buildup 4 Å C-N Distance (D CN = 50 Hz) N 50 Hz C J 1 J 2 C C 13 C- 15 N cross-peak intensities reduced 2- to 5-fold

59 13 C Band-Selective 3D TEDOR Scheme 13 C- 13 C J-couplings refocused using band-selective 13 C pulses (no z-filters required) Most useful for strongly J-coupled sites (e.g., C ) but requires resolution in 13 C dimension

60 ZF-TEDOR vs. BASE-TEDOR Gly 13 Cα- 15 N Gly 13 C - 15 N Thr 13 Cγ- 15 N

61 Cross-Peak Trajectories in TEDOR Expts. 3D ZF TEDOR 3D BASE TEDOR S j I i S j I i mi 2 ij i (0) cos il l i sin N 2 2 ( π τ ) V = V J i ( ωijτ) cos ( ωikτ) k j ( ) ( ) V = V(0) sin ω τ cos ω τ 2 2 ij i ij ik k j N i Intensities depend on all spin-spin couplings to particular 13 C Use approximate models based on Bessel expansions of REDOR signals to describe cross-peak trajectories (Mueller, JMR 1995)

62 3D ZF-TEDOR: N-ac-VL X-ray: 2.95 Å NMR: 3.1 Å X-ray: 4.69 Å NMR: 4.7 Å Val(N) Leu(N) X-ray: 3.81 Å NMR: 4.0 Å X-ray: 3.38 Å NMR: 3.5 Å Val(N) Leu(N)

63 3D BASE TEDOR: N-ac-VL X-ray: 2.39 Å NMR: 2.4 Å X-ray: 1.33 Å NMR: 1.3 Å Val(N) Leu(N) X-ray: 1.33 Å NMR: 1.4 Å X-ray: 4.28 Å NMR: 4.1 Å Val(N) Leu(N)

64 Summary of Distance Measurements in N-ac-VL

65 Application to TTR( ) Amyloid Fibrils Cross-Peak Trajectories (T106) Slice from 3D ZF TEDOR Expt. Y105 I107 T106 A108 Y105 I107 T106 A108 ~70 13 C- 15 N distances measured by 3D ZF TEDOR in several U- 13 C, 15 N labeled fibril samples (30+ between 3-6 Å)

66 REDOR in Multispin Systems H = ω 2I S + ω 2I S IS 1 z 1z 2 z 2z I () t = cos ωt cos ω t x ( ) ( ) Hz I (2.5 Å) 50 Hz 45 o (4 Å) S S Strong 13 C- 15 N couplings dominate REDOR dipolar dephasing; weak couplings become effectively invisible

67 Dipole Tensor Correlation Experiments: Torsion Angles 1. Torsion angle methods: Evolve a correlated spin state between two nuclei under their local dipolar fields Evolution highly sensitive to deviations from parallel arrangement of dipole vectors Observable signal () = cos( Φ ) cos( Φ ) S t f mix Φ Φ 1 2 ( D, Ω, t) λ λ λ λ 2. Typical experiments: 1 H- 15 N- 13 C α - 1 H φ 15 N- 13 C α - 13 C - 15 N ψ 1 H- 13 C- 13 C- 1 H χ

68 Measurement of ψ in Peptides DQ-NCCN Pulse Sequence 13 C- 13 C DQC generated using SPC-5 (Hohwy et al. JCP 1999) 13 C- 15 N dipolar interactions recoupled using REDOR Costa, Gross, Hong & Griffin, CPL 1997 Levitt et al., JACS 1997

69 Dephasing Trajectories vs. ψ Dephasing of 13 C- 13 C DQ coherence is very sensitive to the relative orientation of 13 C- 15 N dipolar tensors for ψ o

70 Application to TTR( ) Fibrils Reference DQ-SQ correlation spectrum for U- 13 C, 15 N YTIA labeled sample YTIAALLSPYS 13 C- 13 C DQ coherences evolve under the sum of CO and C α resonance offsets during t 1

71 TTR( ): Dephasing Trajectories