Heteronuclear Decouplingand Recoupling

Christopher Jaroniec, Ohio State University

1. Brief review of nuclear spin interactions, MAS, etc.2. Heteronuclear decoupling (average Hamiltonian

analysis of CW decoupling, intro to improved decoupling schemes)

3. Heteronuclear recoupling (R3, REDOR)4. AHT analysis of finite pulse REDOR5. 13C-15N distance measurements in multispin systems

(frequency selective REDOR, 3D TEDOR methods)6. Intro to dipole tensor correlation experiments for

measuring torsion angles

Isolated Spin-1/2 (I-S) SystemCS CS J D

int I S IS ISH H H H H= + + +

2

CSI IDIS ISJIS IS

H

H

H

γ

π

= ⋅ ⋅

= ⋅ ⋅

= ⋅ ⋅

I σ B

I D S

I J S

• Relevant interactions expressed in general as couplingof 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(matrices diagonal) into lab frame (B0 || z-axis)

• In general, a rotation is accomplished using a setof 3 Euler angles α,β,γ

Multiple Interactions

• In case of multiple interactions first transform all tensors into common frame (molecular- or crystallite-fixed frame)

• Powder samples: rotate each crystallite into lab frame

High Field Truncation: HCS( )2 2 2 2 2

0 0

2 20 0

sin cos sin sin cos

1 3cos 1 sin cos(2 )2

CS LABI I zz z I xx yy zz z

I iso I z

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

= = + +

⎧ ⎫⎡ ⎤= + − −⎨ ⎬⎣ ⎦⎩ ⎭

• Retain only parts of HCS that commute with Iz

( )13iso xx yy zz

zz iso

yy xx

σ σ σ σ

δ σ σσ σ

ηδ

= + +

= −−

=

High Field Truncation: HJ and HD

( )2

03

21 3cos 1 22

4

JIS IS z z

DIS IS z z

I SIS

IS

H J I S

H b I S

br

π

θ

µ γ γπ

=

= −

= −

• J-anisotropy negligiblein most cases

• bIS in rad/s; directly related to I-S distance

Dipolar Couplings in Proteins

~504.015N13C

~2002.515N13C

~9001.515N13C

~2,2001.513C13C

~10,8001.0415N1H

~21,5001.1213C1H

b12/2π (Hz)r12 (Å)Spin 2Spin 1

Static Powder Spectra: HCS & HD

( ) ( ) ( ) sin Tr exp expCS x CSI t d d I iH t I iH tφ θ θ+ +∝ ⋅ −∫ ∫

σzz

σxx

σyy σzz

σxx

σyy

φ

θ

θB0

NMR of Rotating Samples

2

( )

2

( )

( )2

2

( ) exp

CSI I zDIS IS z z

JIS IS z z

mr

m

H t I

H t I S

H J I S

t im tλ λ

ω

ω

π

ω ω ω=−

=

=

=

= ∑

HD for Rotation at Magic Angle (θm = 54.74o)

( )

( ) ( )

( )

2( )

2

2 2(0)

( 1)

( 2) 2

exp 2

3cos 1 3cos 10

2 2

sin 2 exp2 2

sin exp 24

D mIS IS r z z

m

PR mIS IS

ISIS PR PR

ISIS PR PR

H im t I S

b

b i

b i

ω ω

β θω

ω β γ

ω β γ

=−

±

±

⎧ ⎫= ⎨ ⎬

⎩ ⎭

− −= =

= − ±

= ±

∑

• For spinning at the magic angle the time-independent dipolar (and CSA) components vanish; terms modulated at ωr and 2ωr vanish when averaged over the rotor cycle

Frequency (Hz)-30000 -20000 -10000 0 10000 20000 30000

Static

νr = 2 kHz

νr = 20 kHz

13C-1H DipolarSpectra underMAS

Incr

easi

ngR

esol

utio

n

13C SSNMR Spectra atHigh MAS Rates

M. Ernst, JMR 2003

13C-1H 13C-1H2

• Presence of many strong 1H-1H couplings leads to anincomplete averaging of 13C-1H dipolar coupling by MAS

13C Frequency

( )rr

af bνν

= +

High-Power CW Decoupling

• Average 13C-1H couplings by simultaneously usingMAS and high-power 1H RF irradiation

• Traditionally for efficient decoupling 1H RF fieldsof ~50-200 kHz were used (i.e., ω1H >> bHH, bHX)

CW off

150 kHz

13C-VF, 28 kHz MAS

CW Decoupling: AHT Analysis

1

( ) ( )2 ( )2

iso isotot S z S z I z I z

IS z z IS z z x

H S t S I t IJ I S t I S I

ω ω ω ωπ ω ω

= + + ++ + +

(I)

(S)

• Average Hamiltonian analysis: RF and MAS modulations must be synchronized to obtain cyclic propagator

AHT: Summary

1

0

1

0

0

(0) (1) (2)

(0)

( ) ( ) (0) ( ) ; ( ) exp ( )

( ) ( ) ( ) ( ) exp ;

( ) ( ) exp exp (for ( ) 1)c

t

tot tot tot RF

t

tot RF RF RF RF

t

tot c c c RF c

t U t U t U t T i dt H H

U t U t U t U t T i dt H H U HU

U t U t T i dt H iHt U t

H H H H

H

ρ ρ −

−

′= = − +

′= = ⋅ − =

′= = − = − =

= + + +

∫

∫

∫

…

(1)

0 0 0

1 1; ( ), ( ) ; 2

c ct t t

c c

dt H H dt dt H t H tt it

′′⎡ ⎤′ ′′ ′ ′′ ′= = ⎣ ⎦∫ ∫ ∫ …

Haeberlen & Waugh, Phys. Rev. 1968

Interaction Frame Hamiltonian

( ) ( )

11 1

1 1

1 1

exp exp

( )

2 cos( ) sin( )

( )2 cos( ) sin( )

( )

r r r r

RF RF x x

J DS I IS IS

isoS S z S z

JIS IS z z y

in t in t in t in tIS z z y

DIS IS z z y

inIS z z

H U HU i tI H i tI

H H H H H

H S t S

H J S I t I t

J S I e e iI e e

H t S I t I t

t S I e

ω ω ω ω

ω

ω ω

ω ω

π ω ω

π

ω ω ω

ω

−

− −

= = −

= + + +

= +

= +

= + − −

= +

= ( ) ( ) r r r rt in t in t in tye iI e eω ω ω− −+ − −

Interaction Frame Cont.

( ) ( )

1 1

2( ) ( )( )

2

( ) ( )( )

( )2 cos( ) sin( )

( )

r r r r

r r

r r

DIS IS z z y

in t in t in t in tIS z z y

i m n t i m n tmIS z z

m

i m n t i m n tmIS y z

H t S I t I t

t S I e e iI e e

e e I S

i e e I S

ω ω ω ω

ω ω

ω ω

ω ω ω

ω

ω

ω

− −

+ −

=−

+ −

= +

= + − −

⎡ ⎤= +⎣ ⎦

⎡ ⎤− −⎣ ⎦

∑

Lowest-Order Average Hamiltonian

( ) ( )

(0) (0) (0) (0), ,

2(0) ( )

0 02

(0), 0

0

r rr

rr r r r

S J IS D IS

isoim tm isoS z z

S S S zmr r

in t in t in t in tIS zJ IS z y

r

H H H H

S SH dt dt e S

J SH dt I e e iI e e

τ τ ω

τ ω ω ω ω

ω ω ωτ τ

πτ

=−

− −

= + +

⎧ ⎫= + =⎨ ⎬

⎩ ⎭

= + − − =

∑∫ ∫

∫

• S-spin CSA refocused by MAS, I-S J-coupling eliminatedby I-spin decoupling RF field

Lowest-Order Average HD

2( ) ( )(0) ( )

02

( ) ( )( )

( )( )( )0

1

0 if 01 if 0

rr r

r r

rr

i m n t i m n tmS IS z z

mr

i m n t i m n tmIS y z

i m n tmIS n

ISr

H dt e e I S

i e e I S

m ndt e

m n

τ ω ω

ω ω

τ ω

ωτ

ω

ωωτ

+ −

=−

+ −

±

⎡ ⎤= +⎣ ⎦

⎡ ⎤− −⎣ ⎦

± ≠⎧= ⎨ ± =⎩

∑∫

∫ ∓

Lowest-Order Average HD

( ) ( )

(0),

(0) ( ) ( ) ( ) ( ),

0 D IS

n n n nD IS IS IS z z IS IS y z

H

H I S i I Sω ω ω ω− −

=

= + − −

n π 1,2 ô I-S Decoupling

n = 1,2 ô I-S Dipolar Recoupling!

• 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)

Bennett, Rienstra, Auger & Griffin, JCP 1995

• 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-Xdipolar coupling which dominates the residual linewidth …

Optimization of TPPM Decoupling

• Parameters optimized empirically

• Under moderate MAS rates (~10-25 kHz) and 1H RF fields (~70-100 kHz) best results usually obtainedfor φ and β in ranges given above

1,

10 50

p H p

φβ ω τ π

≈ −= ≈

Other Useful Decoupling Schemes

• TPPM-related schemes (similar to TPPM for most rigid solids):

• FMPM (Gan & Ernst, SSNMR 1997) – frequency and phase modulated decoupling

• SPINAL (Fung et al., JMR 2000) – TPPM combined with supercycles

• XiX (Detken et al., Chem. Phys. Lett. 2002) – offersimprovements over TPPM at high MAS rates (>20 kHz) and high 1H RF (>100 kHz)

• Low-power CW decoupling (~10 kHz) at very highMAS rates, 30-50+ kHz (Ernst, Samoson & Meier,Chem. Phys. Lett. 2001)

X inverse-X (XiX) Decoupling

• Technically XiX is equivalent to TPPM with ∆φ = 180o

but pulse width considerations are very different

2-13C alanineνr = 30 kHzν1 = 150 kHz

tp = 3.1 µsφ = 27o tp = 94.9 µs

Detken et al., Chem. Phys. Lett. 2002

XiX Decoupling

• Performance determinedmainly by tp in units of τr

• Best when tp > τr (e.g., optimize around 2.85τr) and when strong resonances at tp = nτr/4 avoided

simulation

νr = 30 kHzν1 = 150 kHz

XiX Decoupling

13C-1H

13C-1H2

13C-1H

13C-1H2

Rotary Resonance Recoupling

Oas, Levitt & Griffin, JCP 1988

( ) ( ) ( )

(0) ( 1) (1) ( 1) (1),

exp 2 exp1 sin(2 )

2 2

D CN IS IS z z IS IS z y

PR x z z PR x

IS PR

H C N i C N

i N C N i N

b

ω ω ω ω

γ ω γ

ω β

− −= + − −

= −

= −

Rotary Resonance Recoupling(0) (0)

, ,( ) exp exp cos( ) 2 sin( )

cos sin

D CN x D CN

x y

z PR y PR

t iH t C iH tC t C N t

N N Nγ

γ

ρ

ω ω

γ γ

= −

= +

= −

Time (ms)0 5 10 15 20

<Sx>

(t)

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0DCN = 900 Hzωr = 25 kHz

Frequency (Hz)-1000 -800 -600 -400 -200 0 200 400 600 800 1000

Inte

nsity

(a.u

.)

/ 2CND

<Cx>

(t)

Time (ms)0 5 10 15 20

<Sx>

(t)

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

no CSAtypical 15N CSA

R3 in Real Systems:Effect of CSA of Irradiated Spin

• R3 also recouples 15N 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

Frequency (Hz)-1000 -800 -600 -400 -200 0 200 400 600 800 1000

Inte

nsity

(a.u

.)

<Cx>

(t)

Rotational Echo DoubleResonance (REDOR)

• 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 also,acquired – normally report S/S0 ratio (or ∆S/S0 = 1-S/S0)

Gullion & Schaefer, JMR 1989

REDOR: AHT Summary

˜ S z =

Sz 0 < t ≤ τ−Sz τ < t ≤τ +τ r / 2Sz τ + τr / 2 < t ≤ τr

⎧

⎨ ⎪

⎩ ⎪ S

212( ) ( )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= = − + − +

(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 /2

2 sin(2 )sin( ) 2 for 0

IS z z r

IS

IS z z

b I SH

b I S

β γ τ τπ

β γ τπ

⎧− ⋅ =⎪⎪= ⎨

⎪ ⋅ =⎪⎩

• 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

• 2nd group of pulses moved by -τr/2 relative to 1st group to change sign of HD and avoid refocusing the 13C-15N dipolar coupling

• xy-type phase cycling of 15N pulses is critical (Gullion, JMR 1990)

REDOR Dipolar Evolution

( ) exp 2 exp 2 cos( ) 2 sin( )

2 sin(2 )sin( )

z z x z z

x y z

IS

t i C N t C i C N tC t C N t

b

ρ ω ωω ω

ω β γπ

= −

= +

= −

REDOR: Example

1.51 ± 0.01 Å

• Experiment highly robust toward 15N CSA, experimental imperfections, resonance offset and finite pulse effects(xy-4/xy-8 phase cycling is critical for this)

• REDOR is used routinely to measure distances up to ~5-6 Å(D ~ 25 Hz) in isolated 13C-15N spin pairs

[2-13C,15N]Glycine

REDOR: More Challenging Case

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

4.06 ± 0.06 Å

REDOR: 15N CSA Effects4 : 8 : 16 :

xy xyxyxy xyxy yxyxxy xyxy yxyx xyxy yxyx

−−−

Gullion, Baker & Conradi, JMR 1990

• 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 the behavior is likely due to finite pulses and higher order terms in the average Hamiltonian expansion

REDOR at High MAS Rates

2 p

r

τϕ

τ=

0.42010

0.82020

0.21010

0.1510

ϕνr (kHz)τp (µs)

REDOR (xy-4) at High MAS: AHT ( ) ( ) ( )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

2 2

3

4

(0) 1 ( ) 2

( ) cos[ ( )] 2 ( )sin[ ( )] 2

( ) 2

( ) cos[ ( )] 2 (

IS z zr t

z z z yt t

z zt

z zt

H ac bc dt I S

ac bc t dt I S ac bc t dt I S

ac bc dt I S

ac bc t dt I S a

τ

θ θ

θ

′′ ′∝ + ⋅

′′ ′ ′′ ′+ + ⋅ + + ⋅

′′ ′− + ⋅

′′ ′ ′− + ⋅ −

∫

∫ ∫

∫

∫4

5

6 6

7

) sin[ ( )] 2

( ) 2

( ) cos[ ( )] 2 ( )sin[ ( )] 2

( ) 2

(

z xt

z zt

z z z yt t

z zt

c bc t dt I S

ac bc dt I S

ac bc t dt I S ac bc t dt I S

ac bc dt I S

a

θ

θ θ

′ ′+ ⋅

′′ ′+ + ⋅

′′ ′ ′′ ′+ + ⋅ − + ⋅

′′ ′− + ⋅

−

∫

∫

∫ ∫

∫

8 8

) cos[ ( )] 2 ( )sin[ ( )] 2 z z z xt t

c bc t dt I S ac bc t dt I Sθ θ′′ ′ ′′ ′+ ⋅ + + ⋅∫ ∫

Jaroniec et al, JMR 2000

REDOR (xy-4) at High MAS: AHT

( )22

(0)

cos2 sin(2 )sin( )2 ; finite pulses1

2 sin(2 )sin( )2 ; ideal pulses

IS z z

IS

IS z z

b I SH

b I S

π ϕβ γ

π ϕ

β γπ

⎧−⎪ −⎪= ⎨

⎪ −⎪⎩

• 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

( )22

cos; / 4 1

1

effIS

IS

bb

π ϕκ π κ

ϕ≡ = ≤ ≤

−

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

10 µs 15N pulsesno 15N CSA

REDOR (xy-4) Experiments

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

= +

=

• Strong 13C-15N couplings dominate REDOR dipolar dephasing;weak couplings become effectively ‘invisible’

I

S

S

200 Hz(2.5 Å) 50 Hz

(4 Å)45o

Frequency Selective REDOR

Jaroniec et al, JACS 1999, 2001

• Use a pair of weak frequency-selective pulses to ‘isolate’ the 13C-15N dipolar coupling of interest; all other couplings refocused

• This trick is possible because all relevant interactions commute

FS-REDOR

H = ωkl2IkzSlz

H = ω ij2Iiz S jzi, j∑

+ πJij2I izI jzi< j∑

FS-REDOR Evolution

0 2 1

0 2

( /2) ( /2)

( /2) ( /2) ( /2)( /2)

( ) kx lx lx kx kx lx

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

iH t i I i SiH t

U t e e e e e e e ee e e e e ee e e e

π π π π π π

π π

π π

− − − −− −

− − −−−

− − −−

=

=

=

[ ] [ ] [ ][ ] [ ]

0 1 2 0 1 0 2 1 2

0 0 0

1

; , , , 0

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 izi l i k i

H H H H H H H H H H

H I S J I I H I H S

H I S I S J I I

ω π

ω ω π≠ ≠ < ≠

≠ ≠ ≠

= + + = = =

= + = =

= + +

∑∑ ∑

∑ ∑ [ ] [ ]

[ ] [ ]

1

2 2 2

for each term in , 0 or , 0

2 ; , 0 and , 0

kx lxk

kl kz lz kx lx

H I S

H I S H I H Sω

≠ ≠

= ≠ ≠

∑

0

2 2

(0) ; (0), (0), (0), 0

( ) cos( ) 2 sin( )

lx kxi S i I iH tkx

iH t iH tkx kx kl ky lz kl

I e e e

t e I e I t I S t

π πρ ρ ρ ρ

ρ ω ω

− − −

−

⎡ ⎤ ⎡ ⎤ ⎡ ⎤= = = =⎣ ⎦ ⎣ ⎦ ⎣ ⎦= = +

1

Dipolar evolution under only bkl

13C Selective Pulses: U-13C Thr

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

1 ms

2 ms

4 ms

6 ms

8 ms

10 ms

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 ± 0.15 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 to U-13C,15N proteins

Simultaneous 13C-15N Distance Measurements in U-13C,15N Molecules

General Pseudo-3D HETCOR(Heteronuclear Correlation) Scheme

• I-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 Resonance

Hing, Vega & Schaefer, JMR 1992

• Similar idea to INEPT experiment in solution NMR

• Cross-peak intensities depend on all 13C-15N dipolar couplings

• Experiment not directly applicable to U-13C-labeled samples

3D TEDOR Pulse Sequence

( /2) ( /2)

2

2 sin( / 2)

2 sin( / 2) sin ( / 2)

x xI SREDORx z y IS mix

REDORy z IS mix x IS mix

S I S t

I S t I t

π πω

ω ω

+⎯⎯⎯→ ⎯⎯⎯⎯⎯⎯→

− ⎯⎯⎯→

3D TEDOR: U-13C,15N Molecules

Michal & Jelinski, JACS 1997

Modified 3D TEDOR Pulse Sequence

( /2) ( /2)

( /2) ( /2)

2

2 sin( / 2)

2 sin( / 2)

2 sin( / 2) sin ( / 2)

x x

x x

S IREDORx y z IS mix

S Iz y IS mix

REDORy z IS mix x IS mix

I I S t

I S t

I S t I t

π π

π π

ω

ω

ω ω

+

−

⎯⎯⎯→ ⎯⎯⎯⎯⎯⎯→

− ⎯⎯⎯⎯⎯⎯→

− ⎯⎯⎯→

3D TEDOR: U-13C,15N Molecules

N-acetyl-Val-Leu

• Cross-peak intensities roughly proportional to 13C-15N dipolar

couplings

3D TEDOR: U-13C,15N N-ac-VL

• Spectral artifacts (spurious cross-peaks, phase twisted lineshapes) appear at longer mixing times as result of 13C-13C J-evolution

Improved Scheme:3D Z-Filtered TEDOR

• Unwanted anti-phase and mulitple-quantum coherences

responsible for artifacts eliminated using two z-filter periods

3D ZF TEDOR Pulse Sequence

Jaroniec, Filip & Griffin, JACS 2002

Results in N-ac-VL

• 3D ZF TEDOR generates purely absorptive 2D spectra

• Cross-peak intensities give qualitative distance information

3D ZF TEDOR3D TEDOR

13C-13C J-Evolution Effects: ZF-TEDOR Simulated 13C Cross-Peak Buildup

4 Å C-N Distance (DCN = 50 Hz)

• 13C-15N cross-peak intensities reduced 2- to 5-fold

C

N

50 Hz

J1 J2C

C

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

Thr 13Cγ-15N

Gly 13C’-15N

Cross-Peak Trajectories in TEDOR Expts.

• Intensities depend on all spin-spin couplings to particular 13C• Use approximate models based on Bessel expansions of REDOR signals to describe cross-peak trajectories (Mueller, JMR 1995)

3D ZF TEDOR

IiSj

( )

( ) ( )

2

2 2

(0) cos

sin cos

i

i

m

ij i ill i

N

ij ikk j

V V Jπ τ

ω τ ω τ

≠

≠

= ×∏

∏

3D BASE TEDOR

IiSj

( ) ( )2 2(0) sin cosiN

ij i ij ikk j

V V ω τ ω τ≠

= ∏

3D ZF-TEDOR: N-ac-VL

X-ray: 2.95 ÅNMR: 3.1 Å

X-ray: 4.69 ÅNMR: 4.7 Å

Val(N)

Leu(N)

X-ray: 3.81 ÅNMR: 4.0 Å

X-ray: 3.38 ÅNMR: 3.5 Å

Val(N)

Leu(N)

3D BASE TEDOR: N-ac-VL

X-ray: 2.39 ÅNMR: 2.4 Å

X-ray: 1.33 ÅNMR: 1.3 Å

Val(N)

Leu(N)

X-ray: 1.33 ÅNMR: 1.4 Å

X-ray: 4.28 ÅNMR: 4.1 Å

Val(N)

Leu(N)

Summary of DistanceMeasurements in N-ac-VL

Application to TTR(105-115)Amyloid Fibrils

• ~70 13C-15N distances measured by 3D ZF TEDOR in several U-13C,15N labeled fibril samples (30+ between 3-6 Å)

Slice from 3D ZF TEDOR Expt.

Cross-Peak Trajectories (T106)Y105

T106

I107

A108

Y105

T106

I107

A108

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

= +

=

• Strong 13C-15N couplings dominate REDOR dipolar dephasing;weak couplings become effectively ‘invisible’

I

S

S

200 Hz(2.5 Å) 50 Hz

(4 Å)45o

Dipole Tensor CorrelationExperiments: Torsion Angles

1. Torsion angle methods:• Evolve a correlated spin state

between two nuclei under their local dipolar fields

• Evolution highly sensitive to deviations from parallel arrangement of dipole vectors

2. Typical experiments:• 1H-15N-13Cα-1H ⇒ φ

• 15N-13Cα-13C’-15N ⇒ ψ

• 1H-13C-13C-1H ⇒ χ

( ) ( ) ( )( )

1 2cos cos

, ,

mixS t f

D tλ λ λ λ

= Φ Φ

Φ ≡ Φ Ω

Observable signal

Measurement of ψ in PeptidesDQ-NCCN Pulse Sequence

Costa, Gross, Hong & Griffin, CPL 1997Levitt et al., JACS 1997

• 13C-13C DQC generated using SPC-5 (Hohwy et al. JCP 1999)• 13C-15N dipolar interactions recoupled using REDOR

Dephasing Trajectories vs. ψ

• Dephasing of 13C-13C DQ coherence is very sensitive to therelative orientation of 13C-15N dipolar tensors for |ψ| ≈ 150-180o

Application to TTR(105-115) Fibrils

• 13C-13C DQ coherences evolve under the sumof CO and Cα resonance offsets during t1

Reference DQ-SQ correlation spectrumfor U-13C,15N YTIA labeled sample

YTIAALLSPYS

TTR(105-115): Dephasing Trajectories