Heteronuclear Decoupling. Distance and Torsion Angle Restraints in

Transcription

1 Heteronuclear Decoupling and Recoupling: Measurements of Distance and Torsion Angle Restraints in Peptides and Proteins 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 U- 13 C, 15 N peptides & proteins (frequency selective REDOR, 3D TEDOR) 6. Intro to dipole tensor correlation methods for torsion angle measurements in peptides & proteins

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 σ B = I D S IS = 2π I J S IS NMR interactions are anisotropic: can be generally expressed 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 In general, a rotation is accomplished using a set of 3 Euler angles {α,β,γ}

4 Tensor Rotations: Euler Rotation ti Matrices σ = R ( Ω ) σ R ( Ω ) 1 LAB Ω= { αβγ,, } PAS σ PAS σ xx 0 0 = 0 σyy σ zz cos αcosβcos γ sin αsin γ sin αcosβcos γ+ cos αsin γ sin βcos γ R( ( Ω ) = cos cos sin sin cos sin cos sin cos cos sin sin α β γ α γ α β γ+ α γ β γ cos αsin β sin αsin β cosβ

5 Multiple Interactions In case of multiple interactions first transform all tensors into common frame (usually called molecular- or crystallitefixed frame) Powder samples: rotate each crystallite into lab frame (for numerical simulations of NMR spectra trick is to accurately describe an infinite ensemble of crystallites with min. # of angles)

6 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 cos 1 sin cos(2 ) IB 0 iso + I B I 0 z = γ σ + γ δ θ η θ φ 2 1 ( ) σ = σ + σ + σ 3 δ = σ σ η = iso xx yy zz = zz iso σ yy σ δ xx Retain only parts of H CS that commute with I z

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

8 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 ~10, C 13 C 1.5 ~2, C 15 N 1.5 ~ C 15 N 2.5 ~ C 15 N ~50

9 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 σxx σ yy φ σ zz B 0 θ

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

11 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 β ) PR θm 3cos 1 3cos 1 (0) ωis = bis = ( ± 1) bis ω sin ( 2 ) exp{ } IS = βpr ± iγpr 2 2 ( ± 2) bis 2 ω sin exp{ 2 = ± i } IS βpr γ PR 4 For spinning at the magic angle the time-independent dipolar (and CSA) components vanish; terms modulated d at ω r and 2ω r vanish when averaged over the rotor cycle

12 13 C- 1 H Dipolar Spectra under MAS Static ν r =2kHz Increasin ng Resolutio on ν r =20kHz Frequency (Hz)

13 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

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

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

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

17 Interaction Frame Hamiltonian 1 = = exp{ ω } exp{ ω } H U HU i ti H i ti RF RF 1 x 1 x H = H + H + H + H J D S I IS IS iso H = ω S + ω () t S S S z S z J H = π J 2 S I cos( ωt ) + I sin( ωt ) { } 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 { } inω = ω IS () tsz I( z e ) ( ) r t in ωr t in ωr t in ωr + e ii t y e e

18 Interaction Frame Cont. { } D H = ω ()2 t S I cos( ωt ) + I sin( ωt) IS IS z z 1 y 1 { ( inω t inω t ) ( inω t inω t ) } = ω + r r r r () ts I e e ii e e IS z z y 2 ( m ) i ( m+ n ) ω rt i ( m n ) ω rt { ω + IS e e Iz Sz m= 2 = + ω ( m ) i ( m+ n ) ω rt i ( m n ) ω rt iωis e e Iy Sz }

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

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

21 (0) H DIS, = 0 Lowest-Order Average H D n π 1,2 ô I-S Decoupling n = 12 1,2 ô I-S SDipolar Recoupling! ( n n n n ω ω ) ( ω ω ) (0) ( ) ( ) ( ) ( ) HDIS, = IS + IS Iz Sz i IS IS Iy Sz 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

22 Improved heteronuclear decoupling: Two pulse phase modulation (TPPM) -φ +φ -φ +φ 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

23 Optimization of TPPM Decoupling φ 5 25 β p 1, H p β = ω τ π Optimal parameters generally obtained 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

24 Other Useful Decoupling Schemes TPPM-related schemes (similar or somewhat improved performance for rigid solids): SPINAL-64 (Fung et al., JMR 2000) CM (De Paepe & Emsley, JCP 2004) SW f -TPPM (Madhu, Vega et al., JCP 2007) XiX(Detken & Meier, CPL 2002) can offer significant improvements over TPPM, especially at high MAS rates (>20 khz) and high 1 H RF fields (>100 khz)

25 X inverse-x (XiX) Decoupling t p = 3.1 μs φ = 13.5 o t p = μss 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 = 90 o but pulse width considerations are very different

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

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

28 Low Power Decoupling at High MAS Rates Low-power decoupling (CW, TPPM, ~5-15 khz) at high MAS rates, ~40+ khz (Ernst & Meier, Ishii et al., Tekely & Bodenhausen) has been shown to be similar (and in many cases superior) to high power decoupling Some additional advantages: - avoid heating/destruction of biological i l samples - amenable to sensitivity enhancement schemes based on rapid recycling (Ishii et al., Emsley, Bertini & Pintacuda) - less sample required due to smaller rotors, improved probe performance, etc.

29 Rotary Resonance Recoupling H = ω + ω C N i ω ω C N ( ) ( ) (0) ( 1) (1) ( 1) (1) D, CN IS IS z z IS IS z y = exp iγ N ω2c N exp iγ N { }( ) { } PR x z z PR x b b ω β ω β γ IS ( ± 1) IS = sin(2 PR ); IS = sin 2 PR exp ±ii PR ( ) { } Oas, Levitt & Griffin, JCP 1988

30 Rotary Resonance Recoupling ρ( t) = exp{ ih t} C exp{ ih t} (0) (0) DCN, x DCN, = C cos( ω t ) + 2 C N sin( ω t ) 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 r ) Inte ensity (a.u. D CN / Time (ms) Frequency (Hz)

31 R 3 in Real Spin Systems: Effect of CSA of Irradiated Spin 1.0 <Sx <C x> x (t) no CSA typical 15 N CSA ity (a.u.) Intens 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

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

33 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 )] 2 sin(2 β )cos( γ + ωr )}2 z z S S z 0 < t τ S S z = SS 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 Eff ti H ilt i h i f ti f iti f 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)

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

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

36 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 y y 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

37 REDOR: More Challenging Case S112( 13 C )-Y114( 15 N) Distance Measurement in TTR( ) 115) Amyloid Fibrils 4.06 ± 0.06 Å

38 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, these effects are likely due to finite pulses and higher order terms in the average Hamiltonian expansion

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

40 REDOR (xy-4) at High MAS: AHT { } H () t = ω () t f ()2 t IS + gt ()2 IS + ht ()2 IS IS IS z z z x z y Jaroniec et al, JMR 2000

41 REDOR (xy-4) at High MAS: AHT { } H () t = ω () t f ()2 t IS + gt ()2 IS + ht ()2 IS 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 z z z z z y t ( ac + bc )cos[ θ ( t)] dt 2 I zsz ( ac + bc )sin[ θ ( t)] dt 2I z S x t4 t4 + ( ac + bc ) dt 2I S t 5 z z + ( ac + bc )cos[ θ( t)] dt 2 I S ( ac + bc )sin[ θ( t)] dt 2I S t 6 6 ( ac + bc ) dt 2I S t 7 t z z z z z y t ( ac + bc )cos[ θ ()] t dt 2 I S + ( ac + bc )sin[ θ ()] t dt 2 I S } 8 8 z z z x t Jaroniec et al, JMR 2000

42 REDOR (xy-4) at High MAS: AHT 2 b cos ( π ϕ ) sin(2 β)sin( γ)2 I S 2 IS 2 z z 1 (0) π ϕ IS H = 2 b π sin(2 β)sin( γ)2 I S IS z z ( π ϕ ) ; finite pulses ; ideal pulses cos = ; /4 1 2 eff b IS 2 κ π κ b IS 1 ϕ For xy-4 phase cycling, finite it 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

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

44 REDOR (xy-4) Experiments

45 REDOR in Multispin Systems H = ω 2I S + ω 2I S IS 1 z 1z 2 z 2z I () x t cos 1t cos 2t = ( ω ) ( ω ) 200 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

46 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

47 FS-REDOR Evolution [ ] [ ] [ ] [ ] [ ] 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 I S 1 [ kx ] [ lx ] H = ω 2I S + ω 2I S + πj 2 I I ; 1 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 Ut e e e e e e e e ih (/2) t iπikx iπslx ih (/2) t iπslx iπikx iπikx iπslx () = = = ih t ih (/2) t ih ( t /2) ih ( t /2) i π I i π S e e e e e e (/2) kx lx 0 ih2t π kx e e e e ih t i I iπs ρ = kx ρ = ρ = ρ = lx iπslx iπikx ih0t (0) I ; (0), e (0), e (0), e 0 ρ ω ω ih 2 t ih 2 t () t = e I e = I cos( t ) + 2 I S sin( t ) kx kx kl ky lz kl 1 Dipolar evolution under only b kl

48 13 C Selective Pulses: U- 13 C Thr

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

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

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

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

53 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 X-ray: 3.12 Å X-ray: 4.06 Å NMR: 2.46 ± 0.02 Å NMR: 3.24 ± 0.12 Å NMR: 4.12 ± 0.15 Å

54 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 for U- 13 C, 15 N proteins

55 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

56 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 2 IS y z sin( ω IS tmix / 2) Ix sin ( ω IS tmix / 2) Similar idea to INEPT experiment in solution NMR Cross-peak intensities formally depend on all 13 C- 15 N couplings Experiment not directly applicable to U- 13 C-labeled samples

57 3D TEDOR: U- 13 C, 15 N Molecules Out-and-back 3D TEDOR Pulse Sequence I I S t REDOR ( π/2) Sx+ ( π/2) Ix x 2 y zsin( ω IS mix /2) 2IS sin( ω t /2) z y IS mix ( π/2) Sx ( π/2) Ix REDOR 2 2 IS y z sin( ωis tmix / 2) Ix sin ( ωis tmix / 2) Michal & Jelinski, JACS 1997

58 3D TEDOR: U- 13 C, 15 N Molecules N-acetyl-Val-Leu Cross-peak intensities roughly proportional to 13 C- 15 N dipolar couplings

59 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

60 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

61 Results in N-ac-VL 3D TEDOR 3D ZF TEDOR

62 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

63 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 J C 1 J 2 C C 13 C- 15 N cross-peak intensities iti reduced d 2- to 5-fold Effective dipolar evolution times limited to ~10-14 ms

64 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

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

66 Cross-Peak Trajectories in TEDOR Expts. 3D ZF TEDOR 3D BASE TEDOR S j I i S j I i m i ( π τ ) 2 Vij Vi (0) cos Jil l i = sin N 2 2 i ( ω ijτ ) cos ( ω ikτ ) 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)

67 3D ZF-TEDOR: N-ac-VL X-ray: 2.95 Å NMR: 3.1 Å X-ray: 4.69 Å NMR: 47Å 4.7 Val(N) Leu(N) X-ray: 3.81 Å NMR: 4.0 Å Val(N) X-ray: 3.38 Å NMR: 3.5 Å Leu(N)

68 3D BASE TEDOR: N-ac-VL X-ray: 2.39 Å NMR: 2.4 Å X-ray: 1.33 Å NMR: 13Å 1.3 Val(N) Leu(N) X-ray: 1.33 Å NMR: 1.4 Å Val(N) X-ray: 4.28 Å NMR: 4.1 Å Leu(N)

69 Summary of Distance Measurements in N-ac-VL

70 Application to TTR( ) Amyloid Fibrils Slice from 3D ZF TEDOR Expt. Cross-Peak Trajectories (T106) Y105 I107 T106 A108 Ensemble of 20 NMR Structures Y105 I107 Y105 T106 A108 S115 ~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) Jaroniec et al, PNAS 2004

71 3D SCT-TEDOR Pulse Scheme Dipolar 13 C- 15 N SSNMR version of HMQC Constant time spin-echo (2T+ 4δ = ~1/J CC ) used to refocus 13 C- 13 C J-coupling, with encoding of 15 Nshift(t 13 C ) and N DD coupling (τ CN ) Experiment can offer improved resolution and sensitivity Need isolated 13 C- 13 C pairs (C -Cα, C C methyl -C aliphatic ) Helmus et al, JCP 2008

72 Methyl Groups in Proteins Highly sensitive probes of protein structure, dynamics and interactions in solution (Kay) and solids (Zilm, McDermott) Over-represented in proteins: ~37% of residues overall (GB1, ~45%) ~50-60% in membrane proteins

73 3D SCT-TEDOR: Methyl 13 C in GB1 500 MHz, ~2.7 h ~3 Å ~4 Å Effects of 13 C- 13 C J-couplings and relaxation removed from trajectories t longer dipolar evolution times accessible

74 Sensitivity of ZF vs. CT-TEDOR ~2-3 fold gains in sensitivity predicted for CT-TEDOR for ~4-5 Å 13 C- 15 N distances at typical 13 C methyl R 2 rates

75 3D SCT-TEDOR: GB1

76 3D SCT-TEDOR: GB1 Most NMR distances are within ~10% of X-ray structure Useful information about protein side-chain rotamers

77 T11 Side-Chain Conformation 3.77 Å Rotamer χ1 ( o ) N-Cγ distance (Å) % occurrence X-ray NMR S 2 RMS Barchi et al. Protein Sci. (1994)

78 4D SCT-TEDOR Pulse Scheme Additional relaxation-free CT 13 C methyl chemical shift labeling period easily implemented for improved resolution

79 4D SCT-TEDOR: N-Acetyl-Valine N-Cγ distances detected via both N-Cγγ and N-Cββ correlations Distances within ~0.1 Å of NAV X-ray structure 4D recorded in ~37 h

80 4D SCT-TEDOR: GB1

81 4D SCT-TEDOR: GB1

82 J-Decoupling by 13 C Spin Dilution GB1 spectra from Rienstra group, UIUC

83 ZF-TEDOR: 1,3-13 C, 15 N GB1 Nieuwkoop et al, JCP 2009

84 ZF-TEDOR: 1,3-13 C, 15 N GB1 ~ C- 15 N distances + dihedral restraints (TALOS) Nieuwkoop et al, JCP 2009

85 ZF-TEDOR: 1,3-13 C, 15 N PrP amyloid fibrils

86 Chemical Shifts and Secondary Structure Characteristic deviations from random coil shifts for α-helix and β- β sheet secondary structures form the basis for TALOS and other CS-based structure prediction programs Spera & Bax, JACS 113 (1991) 5491

87 TALOS CS-Based Torsion Angle Prediction: TTR( ) Amyloid Fibrils Cornilescu, Delaglion & Bax JBNMR 1999

88 Dipolar Evolution in Multispin Systems H = ω 2I S + ω 2 I S ; I () t = cos ωt cos ω t S S ( ) ( ) IS 1 z 1z 2 z 2z x Hz I (2.5 Å) 50 Hz 45 o (4 Å) S S Evolution under several orientation-dependent DD couplings is detrimental to schemes where main goal is to determine weak DD couplings (e.g., REDOR) Put this to good use for determining projection angles between DD tensors Put this to good use for determining projection angles between DD tensors by matching dipolar phases (i.e., make ω 1 t ~ ω 2 t above) such expts. yield dihedral restraints that can be combined with CS-based data

89 T-MREV NH Recoupling with HH Decoupling bnh Nx( t1) cos ( ωt1) ; ω = κ sin(2 βpr) e 2 2 iγ PR Hohwy et al. JACS 2000

90 T-MREV Recoupling in NH and NH 2 Groups FT of dipolar dephasing trajectory in time domain Dipolar trajectories & spectra depend on the relative orientation of NH dipolar tensors report on the H-N-H bond angle Hohwy et al. JACS 2000

91 HC-CH Experiment (Levitt et al, CPL 1996) Θ = projection angle

92 HC-CH Experiment (Levitt et al, CPL 1996) Θ = projection angle CC CC + + ρ ρ C1 + C2 Double-quantum coherence (correlated C 1 -C 2 spin state)

93 HC-CH Experiment (Levitt et al, CPL 1996) Θ = projection angle CC CC + + ρ ρ C1 + C2 Double-quantum coherence (correlated C 1 -C 2 spin state) Dipolar phases depend on the relative orientations of the two dipolar coupling tensors (most pronounced changes in signal as function of projection angle for Θ = 0 or 180 o ±~30 o due to diff. term) S t Φ Φ 1 Φ Φ + Φ +Φ 2 H κω ( ( t )2 C H + ω( t )2 C H ) ( ) cos ( Φ ) cos ( Φ ) = cos ( Φ Φ ) + cos ( Φ +Φ ) MREV 1 1 1z 1z 2 1 2z 2z t 2 Φ 1 = = λ 0 λ λ λ m= 2 1 ( m) ( ) (); () exp { } t κ dtω t ω t ω imω t r

94 HC-CH Experiment (Levitt et al, CPL 1996) Θ = projection angle Θ 60 ο Θ 0 ο /180 ο Large differences in dipolar dephasing trajectories for cis and trans topologies (in both time and frequency domain) zero-frequency feature from cos(φ 1 -ΦΦ 2 )term Dipolar spectrum generated from time domain data for one τ r, by multiplying signal by exp(rt), repeating many times, applying an overall apodization function followed by FT Dipolar Coupling Dimension (khz)

95 Backbone & Side-chain Torsion Angle Measurements in Peptides and Proteins Observable bl signal () cos( Φ ) cos( Φ ) S t f mix Φ Φ 1 2 ( b, Ω, t) λ λ λ λ Create various correlated spin states involving two nuclei (e.g., CO i -Cα i, N i -Cα i, N i+1 -Cα i, N i -N i+1, etc.) and evolve for some period of time under selected dipolar couplings (e.g., N-Hα, N-CO, etc.) Evolution trajectories highly sensitive to relative tensor orientations j g y for projection angles around 0 o /180 o (more info: Hong & Wi, in NMR Spect. of Biol. Solids 2005; Ladizhansky, Encycl. NMR, 2009)

96 Measurement of φ in Peptides: HN-CH ρ CN y x Multiple-quantum coherence (correlated N-C spin state; combination of ZQC & DQC) ( ) ( ) ( ) S t1 cos ΦCH cos Φ t Φ 1 = λ 0 1 ( t ) κ dtω ( t) λ NH N-ac-Val Hong, Gross & Griffin, JPC B 1997 Hong et al. JMR 1997

97 Θ Measurement of φ in Peptides: HN-CH φ Θ = 90 ο Experiment most sensitive around φ = -120 o (Θ~165 o ); resolution of ca. ±10 o Useful structural restraints despite degeneracies (use proj. angles directly in structure refinement) Implementations using passive evolution under DD couplings limited to slow MAS rates (<5-6 khz) Φ CH ~ 2Φ NH (CH coupling dominates; interference less pronounced) Hong et al. JPC B 1997 Hong et al. JMR 1997

98 φ Torsion Angles: 3D HN-CH Hohwy et al. JACS 2000 Rienstra et al. JACS 2002 NH & CH recoupling using T-MREV r = 2 St ( ) cos( ω t )cos( rω t ) 2 CH 2 NH 2 Expts. that employ active recoupling sequences to reintroduce DD couplings are better suited for applications to high MAS rates & U- 13 C, 15 N samples, and typically offer higher angular resolution

99 3D HN-CH: PrP Amyloid Fibrils Record series of 2D N-Cα spectra Observe crosspeak volumes as function of t 2 (DD evolution time) t 2 = 0 (reference spectrum)

100 3D HN-CH: PrP Amyloid Fibrils

101 Measurement of ψ in Peptides: NC-CN ( ) ( ) ( ) S t cos Φ cos Φ ; Φ ( t ) = ω t 1 NCα NCO λ 1 λ 1 Costa et al., CPL 1997 Levitt et al., JACS 1997

102 Trajectories & Projection Angle 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

103 Trajectories & Dipolar Spectra vs. ψ zero-frequency feature from cos(φ 1 -ΦΦ 2 )t term

104 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

105 TTR( ): Dephasing Trajectories

106 Measurement of ψ in β-sheet peptides β-sheet protein backbone conformation (ψ ~ 120 o ) falls outside of the sensitive region of NCCN experiment correlate other set of couplings

107 Measurement of ψ in β-sheet peptides: 3D HN(CO)CH experiment Same idea as original 3D HNCH with exception that N and Cα belong to adjacent residues and magnetization transfer relayed via CO spin Jaroniec et al. PNAS 2004

108 TTR( ) Fibrils: 3D HN(CO)CH trajectories Complementary to NCCN data for same residues

109 Measurement of ψ in α-helical peptides: 3D HCCN experiment N-CO and Cα Hα tensors are nearly co-linear for ψ ~ -60 o Ladizhansky et al., JMR 2002

110 HN-NH Tensor Correlation: φ and ψ U- 15 N GB1 (Franks et al. JACS 2006) ( 1) cos( Φ ) NH cos( Φ ) NH S t 1 NH i NH i + 1 Reif et al., JMR 2000

111 HN-NH Tensor Correlation: GB1 Θ ~ 0.5 o Projection angle depends on intervening φ and ψ angles (see Reif et al. JMR 2000) Θ ~ 19 o Θ ~ 49 o Franks et al., JACS 2006

112 HN-NH Tensor Correlation: GB1 Franks et al., JACS 2006

113 Fold of GB1 Refined with Projection Angle Restraints H-H, C-C, N-N distances only + TALOS & ~110 angle restraints (HN- (~8 8,000 restraints!!!); RMSD bb ~ 1A HN, HN-HC HC, HA-HB); HB); RMSD bb ~ 03A 0.3 Franks et al., PNAS 2008