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

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)

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}

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

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)

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

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

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

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

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=−∑

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

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

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

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)

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

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

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

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 ⎡ ⎤− −⎣ ⎦

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

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

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

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 …

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

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)

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

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

XiX Decoupling

13C 1H 13C 1H13C-1H 13C-1H

13C-1H213C-1H2

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.

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

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

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

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

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)

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)

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

= −

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

REDOR: More Challenging Case

S112(13C′)-Y114(15N) Distance Measurement inTTR(105-115) Amyloid FibrilsTTR(105 115) Amyloid Fibrils

4.06 ± 0.06 Å

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

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

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

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

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

REDOR (xy-4) at High MAS:AHT vs Numerical SimulationsAHT vs. Numerical Simulations

10 μs 15N pulsesno 15N CSA

REDOR (xy-4) Experiments( y ) p

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’

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

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

13C Selective Pulses: U-13C Thr

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

1 ms 6 ms

2 ms 8 ms

4 ms 10 ms

…

4 ms 10 ms

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

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

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

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

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

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

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

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→

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

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

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

Results in N-ac-VL3D ZF TEDOR3D TEDOR

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

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

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

ZF-TEDOR vs. BASE-TEDORGly 13Cα-15N Gly 13C’-15NGly Cα- N Gly C - N

Thr 13Cγ-15NThr Cγ N

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)

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)

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)

Summary of DistanceMeasurements in N ac VLMeasurements in N-ac-VL

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

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

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

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

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

3D SCT-TEDOR: GB1

3D SCT-TEDOR: GB1

• Most NMR distances are within ~10% of X-ray structure• Useful information about protein side-chain rotamers

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

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

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

4D SCT-TEDOR: GB1

4D SCT-TEDOR: GB1

J-Decoupling by 13C ‘Spin Dilution’

GB1 spectra from Rienstra group, UIUC

ZF-TEDOR: 1,3-13C,15N GB1

Nieuwkoop et al, JCP 2009

ZF-TEDOR: 1,3-13C,15N GB1~750 13C-15N distances

+ dihedral restraints (TALOS)

Nieuwkoop et al, JCP 2009

ZF-TEDOR:1,3-13C,15N PrP23-144 amyloid fibrilsy

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

TALOS CS-Based Torsion Angle Prediction:TTR(105-115) Amyloid FibrilsTTR(105-115) Amyloid Fibrils

Cornilescu, Delaglion & Bax JBNMR 1999

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

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

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

Θ = projection angle

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

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)

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

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)

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)

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

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)

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

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)

3D HN3D HN--CH: PrP23CH: PrP23--144 144 AmyloidAmyloid FibrilsFibrils

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

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

Trajectories & Dipolar Spectra vs. ψ‘zero-frequency’ featuref (Φ Φ ) tfrom cos(Φ1-Φ2) term

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

TTR(105-115): Dephasing Trajectories

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

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

TTR(105-115) Fibrils: 3D HN(CO)CH trajectories

• Complementary to NCCN data for same residues

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

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 +

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

HN-NH Tensor Correlation: GB1

Franks et al., JACS 2006

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