heteronuclear decoupling and recoupling: measurements...
TRANSCRIPT
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Heteronuclear Decouplingand Recoupling: Measurements ofand Recoupling: Measurements of
Distance and Torsion Angle Restraints in Peptides and ProteinsPeptides 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 improvedanalysis of CW decoupling, intro to improved decoupling schemes)
3. Heteronuclear recoupling (R3, REDOR)4 AHT analysis of finite pulse REDOR4. AHT analysis of finite pulse REDOR5. 13C-15N distance measurements in U-13C,15N peptides
& proteins (frequency selective REDOR, 3D TEDOR)6. Intro to dipole tensor correlation methods for torsion
angle measurements in peptides & proteins
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Isolated Spin-1/2 (I-S) SystemCS CS J D
int I S IS ISH H H H H= + + +
CSI IH γ= ⋅ ⋅I σ BI IDIS IS
H
H
γ
= ⋅ ⋅
I σ B
I D S
2IS ISJIS ISH π= ⋅ ⋅
S
I J SIS IS
• NMR interactions are anisotropic: can be generally expressed ascoupling of two vectors by a 2nd rank Cartesian tensor (3 x 3 matrix)
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Rotate Tensors: PAS Lab
{ }1( ) ( ) ; , ,LAB PAS α β γ−= Ω ⋅ ⋅ Ω Ω =σ R σ R
• SSNMR spectra determined by interactions in lab frame
• Rotate tensors from their principal axis systems( t i di l) i t l b(matrices diagonal) into lab frame (B0 || z-axis)
In general a rotation is• In general, a rotation is accomplished using a setof 3 Euler angles {α,β,γ}
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Tensor Rotations:E l R t ti M t iEuler Rotation Matrices
1( ) ( )−= Ω Ωσ R σ R
{ }( ) ( )
, ,LAB PAS= Ω ⋅ ⋅ Ω
Ω =
σ R σ Rα β γ{ }, ,β γ
0 0xxσ⎡ ⎤⎢ ⎥0 0
0 0PAS yy
zz
⎢ ⎥= σ⎢ ⎥⎢ ⎥σ⎣ ⎦
σ
cos cos cos sin sin sin cos cos cos sin sin cos( ) cos cos sin sin cos sin cos sin cos cos sin sin
α β γ − α γ α β γ + α γ − β γ⎡ ⎤⎢ ⎥Ω = − α β γ − α γ − α β γ + α γ β γ⎢ ⎥R( ) cos cos sin sin cos sin cos sin cos cos sin sin
cos sin sin sin cosΩ = − α β γ − α γ − α β γ + α γ β γ⎢ ⎥
⎢ ⎥α β α β β⎣ ⎦
R
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Multiple Interactions
• In case of multiple interactions first transform all tensors into common frame (usually called molecular- or crystallite-fixed 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)
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High Field Truncation: HCS
( )( )2 2 2 2 20 0
2 20 0
sin cos sin sin cos
1 3cos 1 sin cos(2 )
CS LABI I zz z I xx yy zz z
I i I
H B I B I
B B I
γ σ γ σ θ φ σ θ φ σ θ
γ σ γ δ θ η θ φ
= = + +
⎧ ⎫⎡ ⎤= + − −⎨ ⎬⎣ ⎦0 0 3cos 1 sin cos(2 )2I iso I zB B Iγ σ γ δ θ η θ φ⎡ ⎤+⎨ ⎬⎣ ⎦⎩ ⎭
( )1 ( )13iso xx yy zzσ σ σ σ
δ σ σ
= + +
= zz iso
yy xx
δ σ σσ σ
η
= −−
=ηδ
• Retain only parts of HCS that commute with Iz
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High Field Truncation: HJ and HD
21
JIS IS z zH J I Sπ=
( )21 3cos 1 22
DIS IS z zH b I Sθ= −
034
I SIS
IS
br
μ γ γπ
= −IS
• J-anisotropy negligiblein most cases
• bIS in rad/s; directly IS ; yrelated to I-S distance
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Dipolar Couplings in Proteins
Spin 1 Spin 2 r12 (Å) b12/2π (Hz)
1H 13C 1.12 ~21,500
1H 15N 1 04 ~10 8001H 15N 1.04 ~10,800
13C 13C 1.5 ~2,200
13C 15N 1.5 ~900
13C 15N 2.5 ~200
13C 15N 4 0 ~5013C 15N 4.0 ~50
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Static Powder Spectra: HCS & HD
( ) ( ){ }( ) sin Tr exp expCS x CSI t d d I iH t I iH t+ +∝ ⋅ −∫ ∫φ θ θ
σyy σzzθ
B0
σxx σxx
σyy
φ
θB0
σzz
φ
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NMR of Rotating Samples
( )CSI I zD
H t Iω=
( )2
2
DIS IS z z
JIS IS
H t I S
H J I S
ω
π
=
=
{ }2
( )
2
( ) exp
IS IS z z
m
H J I S
t im tλ λ
π
ω ω ω= ∑ { }2
( ) exp rm
t im tλ λω ω ω=−∑
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HD for Rotation at Magic Angle (θm = 54.74o)
( )2
( )
2exp 2D m
IS IS r z zm
H im t I Sω ω=−
⎧ ⎫= ⎨ ⎬
⎩ ⎭∑
( ) ( )2 2(0)
3cos 1 3cos 10
2 2PR m
IS ISbβ θ
ω− −
= =
( ) { }( 1)
2 2
sin 2 exp2 2
ISIS PR PR
b iω β γ± = − ±( ) { }
{ }( 2) 2
2 2
sin exp 2ISIS PR PR
b iω β γ± = ±{ }p4IS PR PRβ γ
• For spinning at the magic angle the time-independent di l ( d CSA) t i h t d l t ddipolar (and CSA) components vanish; terms modulated at ωr and 2ωr vanish when averaged over the rotor cycle
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13C-1H DipolarSpectra under
Static
Spectra underMAS
ν = 2 kHzνr = 2 kHz
ng on
ν = 20 kHzIncr
easi
nR
esol
utio
Frequency (Hz)-30000 -20000 -10000 0 10000 20000 30000
νr = 20 kHz
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13C SSNMR Spectra atHi h MAS R tHigh MAS Rates
13C-1H 13C-1H22
( )rr
af bνν
= +
13C Frequency
• Presence of many strong 1H-1H couplings leads to anincomplete averaging of 13C-1H dipolar coupling by MAS
M. Ernst, JMR 2003
incomplete averaging of C H dipolar coupling by MAS
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CW Decoupling
CW off13C-VF, 28 kHz MAS
150 kHz
• Average 13C-1H couplings by simultaneouslyAverage C H couplings by simultaneously applying MAS and 1H RF irradiation
• Traditionally for efficient decoupling, 1H RF fieldsy p g,of ~50-200 kHz were used (i.e., ω1H >> bHH, bHX)
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CW Decoupling: AHT Analysis
(I)
(S)
( ) ( )2 ( )2
iso isotot S z S z I z I zH S t S I t I
J I S t I S Iω ω ω ω= + + +
+ + + 12 ( )2IS z z IS z z xJ I S t I S Iπ ω ω+ + +
• Average Hamiltonian analysis: RF and MAS modulations• Average Hamiltonian analysis: RF and MAS modulations must be synchronized to obtain cyclic propagator
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AHT: Summary{ }1
0( ) ( ) (0) ( ) ; ( ) exp ( )
t
tot tot tot RFt U t U t U t T i dt H Hρ ρ − ′= = − +∫
{ } 1
0( ) ( ) ( ) ( ) exp ;
t
tot RF RF RF RFU t U t U t U t T i dt H H U HU−′= = ⋅ − =∫
{ } { }( ) ( ) exp exp (for ( ) 1)ct
t t RFU t U t T i dt H iHt U t′= = − = − =∫{ } { }0
(0) (1) (2)
( ) ( ) exp exp (for ( ) 1)tot c c c RF cU t U t T i dt H iHt U t∫
(0) (1) (2)
(0)
H H H H
H
= + + +…
(1)
0 0 0
1 1; ( ), ( ) ; 2
c ct t tdt H H dt dt H t H t
t it′′
⎡ ⎤′ ′′ ′ ′′ ′= = ⎣ ⎦∫ ∫ ∫ …0 0 02c ct it ⎣ ⎦∫ ∫ ∫
Haeberlen & Waugh, Phys. Rev. 1968
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Interaction Frame Hamiltonian{ } { }1
1 1exp expRF RF x xH U HU i tI H i tI−= = −ω ω
J DS I IS ISH H H H H= + + +
{ }( )
2 ( ) i ( )
isoS S z S z
J
H S t S
H J S I I
= +ω ω
{ }( ) ( ){ }
1 12 cos( ) sin( )
r r r r
JIS IS z z y
in t in t in t in tIS z z y
H J S I t I t
J S I e e iI e e− −
= +
= + − −ω ω ω ω
π ω ω
π ( ) ( ){ }{ }1 1( )2 cos( ) sin( )
IS z z y
DIS IS z z yH t S I t I t= +ω ω ω
( ) inIS z zt S I e= ωω ( ) ( ){ }r r r rt in t in t in t
ye iI e e− −+ − −ω ω ω
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Interaction Frame Cont.
{ }( )2 ( ) i ( )DH S I I{ }( ) ( ){ }
1 1( )2 cos( ) sin( )
( ) r r r r
DIS IS z z y
in t in t in t in t
H t S I t I t
t S I e e iI e eω ω ω ω
ω ω ω
ω − −
= +
= +( ) ( ){ }2
( ) ( )( )
( )
{ r r
IS z z y
i m n t i m n tm
t S I e e iI e e
e e I Sω ω
ω
ω + −
= + − −
⎡ ⎤+⎣ ⎦∑ ( ) ( )( )
2
( ) ( )( )
{
}
r r
r r
IS z zm
i m n t i m n tm
e e I S
i e e I Sω ω
ω
ω=−
+ −
⎡ ⎤= +⎣ ⎦
⎡ ⎤⎣ ⎦
∑( ) ( )( ) }r r
IS y zi e e I Sω ⎡ ⎤− −⎣ ⎦
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Lowest-Order Average Hamiltonian
(0) (0) (0) (0), ,S J IS D ISH H H H= + +
2(0) ( )r r
isoim tm isoS z zS SH dt dt S
τ τ ωω ⎧ ⎫⎨ ⎬∑∫ ∫(0) ( )
0 02
rim tm isoS z zS S S z
mr r
H dt dt e Sωω ωτ τ=−
= + =⎨ ⎬⎩ ⎭
∑∫ ∫
( ) ( ){ }(0), 0
0rr r r rin t in t in t in tIS z
J IS z yJ SH dt I e e iI e e
τ ω ω ω ωπτ
− −= + − − =∫ { }0rτ
• S spin CSA refocused by MAS I S J coupling eliminated• S-spin CSA refocused by MAS, I-S J-coupling eliminatedby I-spin decoupling RF field
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Lowest-Order Average HD
2( ) ( )(0) ( )1 {r i m n t i m n tmH d I S+ −⎡ ⎤∑∫
τ ω ω( ) ( )(0) ( ), 0
2
( ) ( )( )
{ r ri m n t i m n tmD IS IS z z
mr
i t i t
H dt e e I S+
=−
+
⎡ ⎤= +⎣ ⎦
⎡ ⎤
∑∫ ω ωωτ
( ) ( )( ) }r ri m n t i m n tmIS y zi e e I S+ −⎡ ⎤− −⎣ ⎦
ω ωω
( )( )( )
0 if 01 rri m n tm
IS
m ndt e ± ± ≠⎧
= ⎨∫τ ωω ( )0 if 0IS n
ISr
dt em n⎨ ± =⎩
∫ ∓ωωτ
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Lowest-Order Average HD
(0) 0H =
n π 1,2 ô I-S Decoupling
, 0 D ISH =
1 2 I S Di l R li !
( ) ( )(0) ( ) ( ) ( ) ( )n n n nH I S i I Sω ω ω ω− −= + − −
n = 1,2 ô I-S Dipolar Recoupling!
( ) ( ),D IS IS IS z z IS IS y zH I S i I Sω ω ω ω= +
• Rotary resonance recoupling (R3) arises from the interference of MAS and I-spin RF (when ω1 = ωr or 2ωr)
• Additional (much weaker) resonances (n = 3,4,…) are also possible due to higher order average Hamiltonian terms involving the I-spin CSA
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Improved heteronuclear decoupling:Two pulse phase modulation (TPPM)p p ( )
-φ +φ -φ +φ
Th fi t t l ff ti l h ( d till f th b t) f• 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 1H CSA and 1H-X
Bennett, Rienstra, Auger & Griffin, JCP 1995
dipolar coupling which dominates the residual linewidth …
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Optimization of TPPM Decoupling
5 25≈ −φβ 1,p H p= ≈β ω τ π
O ti l t ll bt i d i i ll• Optimal parameters generally obtained empirically
• Under moderate MAS rates (~10-25 kHz) and 1H RF fields (~70 100 kHz) best results usually obtainedfields (~70-100 kHz) best results usually obtainedfor φ and β in ranges given above
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Other Useful Decoupling Schemes
• TPPM-related schemes (similar or somewhat improved performancesomewhat improved performance for rigid solids):
• SPINAL-64 (Fung et al., JMR 2000)CM (De Paepe & Emsley JCP• CM (De Paepe & Emsley, JCP
2004) • SWf-TPPM (Madhu, Vega et al., JCP 2007)JCP 2007)
• XiX (Detken & Meier, CPL 2002) –can offer significant improvements g pover TPPM, especially at high MAS rates (>20 kHz) and high 1H RF fields (>100 kHz)fields (>100 kHz)
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X inverse-X (XiX) Decoupling
tp = 3.1 μst 94 9 sφ = 13.5o tp = 94.9 μs
2-13C alanineνr = 30 kHzν1 = 150 kHz
Detken et al., Chem. Phys. Lett. 2002
• Technically XiX is equivalent to TPPM with φ = 90o
but pulse width considerations are very different
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XiX Decoupling
νr = 30 kHzν1 = 150 kHz
• Performance determinedmainly by t in units ofmainly by tp in units of τr
• Best when tp > τr (e.g., optimize around 2.85τr) and when strong
simulation
r) gresonances at tp = nτr/4 avoided
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XiX Decoupling
13C 1H 13C 1H13C-1H 13C-1H
13C-1H213C-1H2
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Low Power Decoupling at High MAS Rates• Low-power decoupling (CW• Low-power decoupling (CW, TPPM, XiX @ ~5-15 kHz) at high MAS rates, ~40+ kHz (Ernst & Meier, Ishii et al., Tekely & , , y &Bodenhausen) has been shown to be similar (and in many cases superior) to high power decoupling
• Some additional advantages:- avoid heating/destruction of bi l i l lbiological samples- amenable to sensitivity enhancement schemes based on rapid recycling (Ishii et alon rapid recycling (Ishii et al., Emsley, Bertini & Pintacuda)- less sample required due to smaller rotors improved probesmaller rotors, improved probe performance, etc.
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Rotary Resonance Recoupling
( ) ( ){ }( ) { }
(0) ( 1) (1) ( 1) (1),D CN IS IS z z IS IS z yH C N i C N− −= + − −ω ω ω ω
{ }( ) { }
( ) { }( 1)
exp 2 exp
sin(2 ); sin 2 exp
PR x z z PR x
IS ISPR IS PR PR
i N C N i Nb b i±
= −
= − = − ±
γ ω γ
ω β ω β γ
Oas, Levitt & Griffin, JCP 1988
( ) { }sin(2 ); sin 2 exp2 2 2 2PR IS PR PRi±ω β ω β γ
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Rotary Resonance Recoupling(0) (0)
, ,( ) exp{ } exp{ }cos( ) 2 sin( )
D CN x D CNt iH t C iH tC t C N t
ρ
ω ω
= −
= +cos( ) 2 sin( )
cos sinx y
z PR y PR
C t C N t
N N Nγ
γ
ω ω
γ γ
+
= −
0 6
0.8
1.0DCN = 900 Hzωr = 25 kHz )
/ 2CND
<Sx>
(t)
0 0
0.2
0.4
0.6 r
ensi
ty (a
.u.
<Cx>
(t)
<
-0.6
-0.4
-0.2
0.0In
te<
Time (ms)0 5 10 15 20
Frequency (Hz)-1000 -800 -600 -400 -200 0 200 400 600 800 1000
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R3 in Real Spin Systems:Effect of CSA of Irradiated Spin
0 8
1.0
no CSA
Effect of CSA of Irradiated Spinx>
(t)
0.2
0.4
0.6
0.8 no CSAtypical 15N CSA
ity (a
.u.)
x> (t
)<S
x
-0.4
-0.2
0.0
0.2
Inte
ns<Cx
Time (ms)0 5 10 15 20
-0.6
Frequency (Hz)-1000 -800 -600 -400 -200 0 200 400 600 800 1000
• R3 also recouples 15N CSA, which doesn’t commute with dipolar term
• Dipolar dephasing depends on CSA magnitude and orientation: problem for q antitati e distance meas rementsproblem for quantitative distance measurements
• In experiments also have to consider effects of RF inhomogeneity
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Rotational Echo DoubleResonance (REDOR)Resonance (REDOR)
Apply a series of rotor synchronized pulses (2 per ) to 15N spins• Apply a series of rotor-synchronized π pulses (2 per τr) to 15N spins(this is usually called a dephasing or S experiment)
• Typically a reference (or S0) experiment with pulses turned off is alsoyp y ( 0) p pacquired to account for R2 – report S/S0 ratio (or ΔS/S0 = 1-S/S0)
Gullion & Schaefer, JMR 1989
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REDOR: AHT Summary21
2( ) ( )2 {sin ( )cos[2( )] 2 sin(2 )cos( )}2IS IS ISH t t I S b t t I Sω β γ ω β γ ω= = − + − +
S̃Sz 0 < t ≤ τ
S ≤ / 2⎧
⎨ ⎪
2( ) ( )2 {sin ( )cos[2( )] 2 sin(2 )cos( )}2IS IS z z IS r r z zH t t I S b t t I Sω β γ ω β γ ω+ +
S z = −Sz τ < t ≤τ +τ r / 2Sz τ + τr / 2 < t ≤ τr
⎨
⎩ ⎪ S
(0) 2 sin(2 )sin( ) 2 ; (sequence phase)IS IS z z rH b I Sβ γ ψ ψ ω τπ
= + ⋅ =
(0)
2 sin(2 )sin( ) 2 for /2IS z z r
IS
b I SH
β γ τ τπ
⎧− ⋅ =⎪⎪= ⎨
2 sin(2 )sin( ) 2 for 0IS
IS z zb I Sβ γ τπ
⎨⎪ ⋅ =⎪⎩
Eff ti H ilt i h i f ti f iti f• Effective Hamiltonian changes sign as a function of position ofpulses within the rotor cycle (must be careful about this in some implementations of REDOR)
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REDOR: Typical Implementation
• Rotor synchronized spin-echo on 13C channel refocuses 13C isotropic chemical shift and CSA evolution
• Recoupled 15N CSA commutes with 13C-15N DD coupling!
• 2nd group of pulses shifted by -τr/2 relative to 1st group to change sign of H and avoid refocusing the 13C-15N dipolar couplingchange sign of HD and avoid refocusing the C- N dipolar coupling
• xy-type phase cycling of 15N pulses is critical (Gullion, JMR 1990)
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REDOR Dipolar Evolution
( ) exp{ 2 } exp{ 2 }t i C N t C i C N tρ ω ω= −( ) exp{ 2 } exp{ 2 }cos( ) 2 sin( )
2
z z x z z
x y z
t i C N t C i C N tC t C N t
ρ ω ωω ω
=
= +
2 sin(2 )sin( )ISbω β γπ
= −
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REDOR: Example
13 15
1.51 ± 0.01 Å
[2-13C,15N]Glycine
• Experiment highly robust toward 15N CSA, experimental imperfections, resonance offset and finite pulse effects(xy-4/xy-8 phase cycling is critical for this)( y y p y g )
• REDOR is used routinely to measure distances up to ~5-6 Å (D ~ 25 Hz) in isolated 13C-15N spin pairs
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REDOR: More Challenging Case
S112(13C′)-Y114(15N) Distance Measurement inTTR(105-115) Amyloid FibrilsTTR(105 115) Amyloid Fibrils
4.06 ± 0.06 Å
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REDOR: 15N CSA Effects4 : 8 :
xy xyxyxy xyxy yxyx
−−
Gullion, Baker & Conradi, JMR 1990
16 : xy xyxy yxyx xyxy yxyx−
• Simpler schemes (xy-4, xy-8) seem to perform better with respect to 15N CSA compensation than the longer xy-16
• Since [HD(0),HCSA
(0)] = 0, these effects are likely due to finite pulses and higher order terms in the average Hamiltonian expansion
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REDOR at High MAS Rates
2 pτϕ =
r
ϕτ
τp (μs) νr (kHz) ϕ
10 5 0.1
10 10 0 210 10 0.2
10 20 0.4
20 20 0.8
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REDOR (xy-4) at High MAS: AHT{ }( ) ( ) ( )2 ( )2 ( )2H f I S I S h I S{ }( ) ( ) ( )2 ( )2 ( )2IS IS z z z x z yH t t f t I S g t I S h t I Sω= + +
Jaroniec et al, JMR 2000
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REDOR (xy-4) at High MAS: AHT{ }( ) ( ) ( )2 ( )2 ( )2H f I S I S h I S{ }( ) ( ) ( )2 ( )2 ( )2IS IS z z z x z yH t t f t I S g t I S h t I Sω= + +
1
1
2 2
(0) 1 { ( ) 2
( ) cos[ ( )] 2 ( )sin[ ( )] 2
IS z zr t
z z z yt t
H ac bc dt I S
ac bc t dt I S ac bc t dt I S
τ
θ θ
′′ ′∝ + ⋅
′′ ′ ′′ ′+ + ⋅ + + ⋅
∫
∫ ∫2 2
3
( ) 2
( ) cos[ ( )] 2 (
z zt
z z
ac bc dt I S
ac bc t dt I S aθ
′′ ′− + ⋅
′′ ′ ′− + ⋅ −
∫
∫ )sin[ ( )] 2 z xc bc t dt I Sθ′ ′+ ⋅∫4t 4
5
( ) 2
( ) cos[ ( )] 2 ( )sin[ ( )] 2
t
z zt
z z z y
ac bc dt I S
ac bc t dt I S ac bc t dt I Sθ θ
′′ ′+ + ⋅
′′ ′ ′′ ′+ + ⋅ − + ⋅
∫
∫ ∫6 6
7
( ) 2
(
t t
z zt
ac bc dt I S
a
′′ ′− + ⋅
−
∫ ∫
∫
)cos[ ( )] 2 ( )sin[ ( )] 2 }z z z xc bc t dt I S ac bc t dt I Sθ θ′′ ′ ′′ ′+ ⋅ + + ⋅∫ ∫(8 8
) [ ( )] ( ) [ ( )] }z z z xt t∫ ∫
Jaroniec et al, JMR 2000
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REDOR (xy-4) at High MAS: AHT
( )22
(0)
cos2 sin(2 )sin( )2 ; finite pulses1IS z zb I S
H
π ϕβ γ
π ϕ⎧
−⎪ −⎪⎨
(0) 1
2 sin(2 )sin( )2 ; ideal pulsesIS
IS z z
H
b I S
π ϕ
β γπ
⎪= ⎨⎪ −⎪⎩ π⎩
( )2cos; / 4 1
effISb π ϕ
κ π κ≡ ≤ ≤
F 4 h li fi it l lt l i
( )2 ; / 4 1
1IS
ISbκ π κ
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 R3 dynamics in the limit of ϕ = 1
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REDOR (xy-4) at High MAS:AHT vs Numerical SimulationsAHT vs. Numerical Simulations
10 μs 15N pulsesno 15N CSA
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REDOR (xy-4) Experiments( y ) p
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REDOR in Multispin Systems
( ) ( )1 1 2 2
1 2
2 2
( ) cos cosIS z z z z
x
H I S I S
I t t t
ω ω
ω ω
= +
= ( ) ( )1 2( )x
I200 Hz(2.5 Å) 50 Hz
(4 Å)45o
S
S
(4 Å)45
• Strong 13C-15N couplings dominate REDOR dipolar dephasing;weak couplings become effectively ‘invisible’
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Frequency Selective REDOR
H = ω ij2Iiz S jzi, j∑
+ πJij2I izI jzi< j∑
FS-REDOR
Jaroniec et al, JACS 1999, 2001
H = ωkl2IkzSlz
• Use a pair of weak frequency-selective pulses to ‘isolate’ the 13C 15N dipolar coupling of interest; all other couplings refocused13C-15N dipolar coupling of interest; all other couplings refocused
• This trick is possible because all relevant interactions commute
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FS-REDOR Evolution[ ] [ ] [ ]0 1 2 0 1 0 2 1 2; , , , 0H H H H H H H H H H= + + = = =[ ] [ ] [ ][ ] [ ]
0 1 2 0 1 0 2 1 2
0 0 0
1
2 2 ; , , 0
2 2 2 ;
ij iz jz ij iz jz kx lxi k j l i j k
ki kz iz il iz lz ki kz iz
H I S J I I H I H S
H I S I S J I I
ω π
ω ω π≠ ≠ < ≠
= + = =
= + +
∑∑ ∑
∑ ∑ [ ] [ ]1 for each term in , 0 or , 0kx lxH I S≠ ≠∑1 ki kz iz il iz lz ki kz izi l i k i≠ ≠ ≠∑ ∑ [ ] [ ]
[ ] [ ]
1
2 2 22 ; , 0 and , 0
kx lxk
kl kz lz kx lxH I S H I H Sω= ≠ ≠
∑
1
0 2 1
( /2) ( /2)
( /2) ( /2) ( /2)( /2)
( ) kx lx lx kx kx lx
kx lx
i I i S i S i I i I i SiH t iH t
iH t i I i SiH t iH tiH t
U t e e e e e e e eπ π π π π π
π π
− − − −− −
− − −−−
=0 2 1
0 2
( /2) ( /2) ( /2)( /2) kx lx
kx lx
iH t i I i SiH t iH tiH t
iH t i I i SiH t
e e e e e ee e e e
π π
π π− − −−
=
=0
2 2
(0) ; (0), (0), (0), 0
( ) ( ) 2 i ( )
lx kxi S i I iH tkx
iH t iH t
I e e e
t I I t I S t
π πρ ρ ρ ρ− − −
−
⎡ ⎤ ⎡ ⎤ ⎡ ⎤= = = =⎣ ⎦ ⎣ ⎦ ⎣ ⎦+2 2( ) cos( ) 2 sin( )iH t iH t
kx kx kl ky lz klt e I e I t I S tρ ω ω= = +
Dipolar evolution under only bkl
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13C Selective Pulses: U-13C Thr
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FS-REDOR: U-13C,15N Asn
1 ms 6 ms
2 ms 8 ms
4 ms 10 ms
…
4 ms 10 ms
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FS-REDOR: U-13C,15N Asn
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FS-REDOR: U-13C,15N Asn
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FS-REDOR: U-13C,15N-f-MLF
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FS-REDOR: U-13C,15N-f-MLFMet Cβ-Phe NLeu Cβ-Phe NLeu Cβ-Leu N
X-ray: 2.50 ÅNMR 2 46 0 02 Å
X-ray: 3.12 ÅNMR 3 24 0 12 Å
X-ray: 4.06 ÅNMR 4 12 0 1 ÅNMR: 2.46 ± 0.02 Å NMR: 3.24 ± 0.12 Å NMR: 4.12 ± 0.15 Å
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FS-REDOR: U-13C,15N-f-MLF
• 16 13C-15N distances could be measured in MLF tripeptide
• Selectivity of 15N pulse + need of prior knowledge of which distances to probe is a major limitation for U-13C,15N proteins
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Simultaneous 13C-15N Distance Measurements in U-13C,15N MoleculesMeasurements in U C, N Molecules
General Pseudo-3D HETCOR(Heteronuclear Correlation) Scheme( )
• I-S coherence transfer as function of t i via DISI-S coherence transfer as function of tmix via DIS
• Identify coupled I and S spins by chemical shift labeling in t1, t2
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Transferred Echo Double Resonance3D TEDOR Pulse Sequence3D TEDOR Pulse Sequence
Hing, Vega & Schaefer, JMR 1992
( /2) ( /2)
2
2 sin( / 2)
2 sin( / 2) sin ( / 2)
x xI SREDORx z y IS mix
REDORIS i IS i
S I S t
I S t I t
π πω
ω ω
+⎯⎯⎯→ ⎯⎯⎯⎯⎯⎯→
− ⎯⎯⎯→
• Similar idea to INEPT experiment in solution NMR
C f 13C 15
2 sin( / 2) sin ( / 2)y z IS mix x IS mixI S t I tω ω→
• Cross-peak intensities formally depend on all 13C-15N couplings
• Experiment not directly applicable to U-13C-labeled samples
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3D TEDOR: U-13C,15N Molecules‘Out-and-back’ 3D TEDOR Pulse Sequence
( /2) ( /2)2 sin( / 2) x xS IREDORx y z IS mixI I S t π πω +⎯⎯⎯→ ⎯⎯⎯⎯⎯⎯→
( /2) ( /2)
2
( )
2 sin( / 2)
2 sin( / 2) sin ( / 2)
x x
x y z IS mix
S Iz y IS mix
REDOR
I S t
I S t I t
π πω
ω ω
−− ⎯⎯⎯⎯⎯⎯→
− ⎯⎯⎯→
Michal & Jelinski, JACS 1997
2 sin( / 2) sin ( / 2)y z IS mix x IS mixI S t I tω ω→
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3D TEDOR: U-13C,15N Molecules
N-acetyl-Val-Leu
• Cross-peak intensities roughly proportional to 13C-15N dipolar• Cross-peak intensities roughly proportional to C- N dipolar
couplings
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3D TEDOR: U-13C,15N N-ac-VL
• Spectral artifacts (spurious cross-peaks, phase twisted lineshapes) p ( p p p p )appear at longer mixing times as result of 13C-13C J-evolution
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Improved Scheme:3D Z-Filtered TEDOR3D Z Filtered TEDOR
3D ZF TEDOR Pulse Sequenceq
• Unwanted anti-phase and mulitple-quantum coherences
responsible for artifacts eliminated using two z-filter periodsg
Jaroniec, Filip & Griffin, JACS 2002
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Results in N-ac-VL3D ZF TEDOR3D TEDOR
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Results in N-ac-VL3D ZF TEDOR3D TEDOR
• 3D ZF TEDOR generates purely absorptive 2D spectra3D ZF TEDOR generates purely absorptive 2D spectra
• Cross-peak intensities give qualitative distance information
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13C-13C J-Evolution Effects: ZF-TEDOR Simulated 13C Cross-Peak Buildup
4 Å C-N Distance (DCN = 50 Hz)
N
50 Hz
J1 J2C
C
J1 J2
C
13C 15N k i t iti d d 2 t 5 f ld• 13C-15N cross-peak intensities reduced 2- to 5-fold
• Effective dipolar evolution times limited to ~10-14 ms
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13C Band-Selective 3D TEDOR Scheme
• 13C-13C J-couplings refocused using band-selective 13C pulses
(no z-filters required)
• Most useful for strongly J-coupled sites (e.g., C’) but requires
resolution in 13C dimension
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ZF-TEDOR vs. BASE-TEDORGly 13Cα-15N Gly 13C’-15NGly Cα- N Gly C - N
Thr 13Cγ-15NThr Cγ N
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Cross-Peak Trajectories in TEDOR Expts.3D ZF TEDOR 3D BASE TEDOR3D ZF TEDOR 3D BASE TEDOR
IiSj
( )2(0) cosim
V V Jπ τ= ×∏
IiSj
( )
( ) ( )2 2
(0) cos
sin cosi
ij i ill i
N
ij ik
V V Jπ τ
ω τ ω τ
≠
= ×∏
∏( ) ( )2 2(0) sin cos
iN
ij i ij ikk j
V V ω τ ω τ≠
= ∏
• Intensities depend on all spin-spin couplings to particular 13C
( ) ( )ij ikk j≠∏
• Use approximate models based on Bessel expansions of REDOR signals to describe cross-peak trajectories (Mueller, JMR 1995)
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3D ZF-TEDOR: N-ac-VL
X-ray: 2.95 ÅÅ Val(N)NMR: 3.1 Å
X-ray: 4.69 ÅNMR 4 7 Å
Val(N)
Leu(N)NMR: 4.7 Å ( )
X-ray: 3.81 ÅNMR: 4.0 Å Val(N)
X-ray: 3.38 ÅNMR: 3.5 Å Leu(N)
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3D BASE TEDOR: N-ac-VL
X-ray: 2.39 ÅÅ Val(N)NMR: 2.4 Å
X-ray: 1.33 ÅNMR: 1 3 Å
Val(N)
Leu(N)NMR: 1.3 Å ( )
X-ray: 1.33 ÅNMR: 1.4 Å Val(N)
X-ray: 4.28 ÅNMR: 4.1 Å Leu(N)
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Summary of DistanceMeasurements in N ac VLMeasurements in N-ac-VL
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Application to TTR(105-115)Amyloid Fibrilsy
Slice from 3D ZF TEDOR Expt.Cross-Peak Trajectories (T106)
Y105 I107
A108T106
Y105 I107Ensemble of 20 NMR Structures
T106A108
Ensemble of 20 NMR Structures
Y105
• ~70 13C-15N distances measured by 3D ZF TEDOR in several
S115
70 C- N distances measured by 3D ZF TEDOR in several U-13C,15N labeled fibril samples (30+ between 3-6 Å)
Jaroniec et al, PNAS 2004
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3D SCT-TEDOR Pulse Scheme
• Dipolar 13C 15N SSNMR version of HMQC• Dipolar 13C-15N SSNMR version of HMQC
• Constant time spin-echo (2T+ 4δ = ~1/JCC) used to refocus 13C-13CJ-coupling, with encoding of 15N shift (t1) and 13C-15N DD coupling (τCN)J coupling, with encoding of N shift (t1) and C N DD coupling (τCN)
• Experiment can offer improved resolution and sensitivity
N d i l t d 13C 13C i (C’ C Cmethyl Caliphatic)• Need isolated 13C-13C pairs (C’-Cα, Cmethyl-Caliphatic)
Helmus et al, JCP 2008
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Methyl Groups in Proteins
Hi hl iti b• Highly sensitive probesof protein structure,dynamics and interactionsin solution (Kay) andsolids (Zilm, McDermott)
• Over-represented inproteins:
• ~37% of residuesoverall (GB1, ~45%)
• ~50-60% in membraneproteinsp
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3D SCT-TEDOR: Methyl 13C in GB1500 MHz, ~2.7 h
~3 Å
4 Å~4 Å
• Effects of 13C-13C J-couplings and relaxation removed from t j t i l di l l ti ti ibltrajectories – longer dipolar evolution times accessible
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Sensitivity of ZF vs. CT-TEDOR
• ~2-3 fold gains in sensitivity predicted for CT-TEDOR for ~4-5 Å 13C-15N distances at typical 13Cmethyl R2 rates
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3D SCT-TEDOR: GB1
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3D SCT-TEDOR: GB1
• Most NMR distances are within ~10% of X-ray structure• Useful information about protein side-chain rotamers
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T11 Side-Chain Conformation
3.77 Å Rotamer χ1 (o) N-Cγdistance (Å)
% occurrence
1 +60 2.94 46
2 -60 3.81 45
3 180 2 94 93 180 2.94 9
X-ray -82 3.77 -
NMR - 3.1 -
S2S2
RMS
Barchi et al. Protein Sci. (1994)
RMS
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4D SCT-TEDOR Pulse Scheme
Addi i l “ l i f ” CT 13C th l h i l hif• Additional “relaxation-free” CT 13Cmethyl chemical shift labeling period easily implemented for improved resolution
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4D SCT-TEDOR: N-Acetyl-Valine
• N-Cγ distancesN-Cγ distancesdetected via bothN-Cγ and N-Cβγ βcorrelations
• Distances within• Distances within~0.1 Å of NAV X-ray structurey
• 4D recorded in ~37 h
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4D SCT-TEDOR: GB1
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4D SCT-TEDOR: GB1
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J-Decoupling by 13C ‘Spin Dilution’
GB1 spectra from Rienstra group, UIUC
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ZF-TEDOR: 1,3-13C,15N GB1
Nieuwkoop et al, JCP 2009
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ZF-TEDOR: 1,3-13C,15N GB1~750 13C-15N distances
+ dihedral restraints (TALOS)
Nieuwkoop et al, JCP 2009
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ZF-TEDOR:1,3-13C,15N PrP23-144 amyloid fibrilsy
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Chemical Shifts and Secondary StructureChemical Shifts and Secondary Structure
• Characteristic deviations from ‘random coil’ shifts for α-helix and β-βsheet secondary structures form the basis for TALOS and other CS-based structure prediction programs
Spera & Bax, JACS 113 (1991) 5491
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TALOS CS-Based Torsion Angle Prediction:TTR(105-115) Amyloid FibrilsTTR(105-115) Amyloid Fibrils
Cornilescu, Delaglion & Bax JBNMR 1999
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Dipolar Evolution in Multispin Systems( ) ( )2 2 ( )S S ( ) ( )1 1 2 2 1 22 2 ; ( ) cos cosIS z z z z xH I S I S I t t t= + =ω ω ω ω
I200 Hz(2.5 Å) 50 Hz
(4 Å)45o
S
S
(4 Å)45
• 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 ω1t ~ ω2t above) – such expts.yield dihedral restraints that can be combined with CS-based data
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T-MREV NH Recoupling with HH Decoupling
( )1 1( ) cos ; sin(2 )2 2
PRiNHx PR
bN t t e−≈ = γω ω κ β2 2
Hohwy et al. JACS 2000
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T-MREV Recoupling in NH and NH2 Groups
FT of dipolar dephasingtrajectory 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
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Θ = projection angle
HC-CH Experiment (Levitt et al, CPL 1996)Θ = projection angle
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Θ = projection angle
HC-CH Experiment (Levitt et al, CPL 1996)Θ = projection angle
1 2 1 2C C C C+ + − −+∼ρ 1 2C C+ ++∼ρ
Double-quantum coherence(correlated C1-C2 spin state)
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Θ = projection angle
HC-CH Experiment (Levitt et al, CPL 1996)Θ = projection angle
Dipolar phases depend on the relative orientations of the t o dipolar co pling
1 2 1 2C C C C+ + − −+∼ρ 1 2C C+ ++∼ρ
orientations of the two dipolar couplingtensors (most pronounced changes in signal as function of projection angle for Θ = 0 or 180o ± ~30o due to diff. term)
( ) ( ) ( ) ( ) ( )1S t Φ Φ Φ Φ + Φ + Φ
)Double-quantum coherence(correlated C1-C2 spin state)
( ) ( ) ( ) ( ) ( )1 1 2 1 2 1 2
1 1 1 1 2 1 2 2
cos cos cos cos2
( ( )2 ( )2 )MREV z z z z
S t
H t C H t C H
≈ Φ Φ = Φ − Φ + Φ + Φ
≈ +κ ω ω
{ }12
( )1 0
2
( ) ( ); ( ) expt m
rm
t dt t t im t=−
Φ = = ∑∫λ λ λ λκ ω ω ω ω
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Θ j ti l
HC-CH Experiment (Levitt et al, CPL 1996)Θ = projection angle
Θ ∼ 0ο/180οΘ ∼ 60ο
L diff i di l• Large differences in dipolardephasing trajectories for cisand trans topologies (in both time and frequency domain)q y )
• Dipolar spectrum generatedfrom time domain data forone by multiplying signal by
‘zero-frequency’ featurefrom cos(Φ1-Φ2) term one τr, by multiplying signal by
exp(Rt), repeating many times, applying an overall apodizationfunction followed by FT
from cos(Φ1 Φ2) term
y
Dipolar Coupling Dimension (kHz)
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Backbone & Side-chain Torsion AngleMeasurements in Peptides and ProteinsMeasurements in Peptides and Proteins
Ob bl i l
( ) ( ) ( )1 2cos cosmixS t f≈ Φ Φ
Observable signal
( ), ,b tΦ ≡ Φ Ωλ λ λ λ
• Create various correlated spin states involving two nuclei (e.g., CO Cα N Cα N Cα N N etc ) and evolve for some periodCOi-Cαi, Ni-Cαi, Ni+1-Cαi, Ni-Ni+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 yfor projection angles around 0o/180o (more info: Hong & Wi, in NMR Spect. of Biol. Solids 2005; Ladizhansky, Encycl. NMR, 2009)
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Measurement of φ in Peptides: HN-CH
C Ny xC N∼ρ
Multiple-quantum coherence(correlated N C spin state; combination(correlated N-C spin state; combination
of ZQC & DQC)
( ) ( ) ( )1 cos cosCH NHS t ≈ Φ Φ N-ac-Val
Hong, Gross & Griffin, JPC B 1997Hong et al. JMR 1997
1
1 0( ) ( )
tt dt tΦ = ∫λ λκ ω
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Measurement of φin Peptides: HN-CH
Θ
• Experiment most sensitived φ 120o (Θ 165o)
Θ = 90ο
φaround φ = -120o (Θ~165o);resolution of ca. ±10o
• Useful structural restraintsdespite degeneracies(use proj. angles directly in structure refinement)
• Implementations using ‘passive’ evolution under DD couplings limited to slow MAS rates (<5-6 kHz)
ΦCH ~ 2ΦNH (CH coupling dominates; interference l d)
Hong et al. JPC B 1997Hong et al. JMR 1997
less pronounced)
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φφ Torsion Angles: 3D HNTorsion Angles: 3D HN--CHCHNH & CH recoupling using T MREV
Hohwy et al. JACS 2000Rienstra et al. JACS 2002
NH & CH recoupling using T-MREV
( ) ( ) ( )S t t t
r = 2
2 2 2( ) cos( ) cos( )CH NHS t t r t≈ ω ω
• Expts. that employ active recoupling sequences to reintroduce DDcouplings are better suited for applications to high MAS rates & U-13C,15N samples, and typically offer higher angular resolution
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3D HN3D HN--CH: PrP23CH: PrP23--144 144 AmyloidAmyloid FibrilsFibrils
• Record series of 2D N-Cα spectra t2 = 0 (reference
spectrum)
• Observe cross-peak volumes as function of t2 (DD evolution time)evolution time)
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3D HN3D HN--CH: PrP23CH: PrP23--144 144 AmyloidAmyloid FibrilsFibrils
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Measurement of ψ in Peptides: NC-CN
( ) ( ) ( )1 1 1cos cos ; ( )NC NCOS t t t≈ Φ Φ Φ =α λ λω
Costa et al., CPL 1997Levitt et al., JACS 1997
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Trajectories & Projection Angle vs. ψ
• Dephasing of 13C 13C DQ coherence is very sensitive to the• Dephasing of 13C-13C DQ coherence is very sensitive to therelative orientation of 13C-15N dipolar tensors for |ψ| ≈ 150-180o
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Trajectories & Dipolar Spectra vs. ψ‘zero-frequency’ featuref (Φ Φ ) tfrom cos(Φ1-Φ2) term
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Application to TTR(105-115) FibrilsReference DQ SQ correlation spectrumReference DQ-SQ correlation spectrum
for U-13C,15N YTIA labeled sample
YTIAALLSPYSYTIAALLSPYS
• 13C-13C DQ coherences evolve under the sumof CO and Cα resonance offsets during t1
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TTR(105-115): Dephasing Trajectories
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Measurement of ψ in β-sheet peptides
• β-sheet protein backbone conformation (ψ ~ 120o) falls outside of the sensitive region of NCCN experiment – correlate other set of couplings
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Measurement of ψ in β-sheet peptides:3D HN(CO)CH experiment3D 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
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TTR(105-115) Fibrils: 3D HN(CO)CH trajectories
• Complementary to NCCN data for same residues
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Measurement of ψ in α-helical peptides:3D HCCN experiment
• N-CO and Cα−Hα tensors are nearly co-linear for ψ ~ -60o
Ladizhansky et al., JMR 2002
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HN-NH Tensor Correlation: φ and ψ
U-15N GB1 (Franks et al. JACS 2006)
( ) ( ) ( )11 cos cosi iNH NHS t
+≈ Φ Φ
Reif et al., JMR 2000
( ) ( ) ( )11 i iNH NH +
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HN-NH Tensor Correlation: GB1
Projection angle depends on intervening φΘ ~ 0.5o
and ψ angles (see Reif et al. JMR 2000)
Θ ~ 19o
Θ ~ 49o
Franks et al., JACS 2006
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HN-NH Tensor Correlation: GB1
Franks et al., JACS 2006
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Fold of GB1 Refined with ProjectionAngle RestraintsAngle Restraints
H-H, C-C, N-N distances only(~8 000 restraints!!!); RMSD bb ~ 1 A
+ TALOS & ~110 angle restraints (HN-HN HN-HC HA-HB); RMSD bb ~ 0 3 A
Franks et al., PNAS 2008
( 8,000 restraints!!!); RMSD bb 1 A HN, HN HC, HA HB); RMSD bb 0.3 A