Heteronuclear Dipolar Recoupling in Solid-State NMR

Christopher JaroniecThe Ohio State University

3rd Winter School on Biomolecular Solid-State NMR, Stowe, VT, January 6-11, 2013

Outline

1. Brief review of nuclear spin interactions, MAS, etc.2. Basics of heteronuclear recoupling (rotary resonance)3. REDOR & quantitative distance measurements in

isolated 13C-15N (and other low-) spin pairs4. Quantitative 13C-15N distance measurements in

U-13C,15N peptides and proteins using frequency selective REDOR & 3D TEDOR

5. Intro to dipole tensor correlation methods for torsion angle measurements in peptides & proteins(extra slides)

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

int I S IS ISH H H H H

2

CSI IDIS ISJIS IS

H

H

H

I σ B

I D S

I J S

• 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 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 {,,}

Tensor Rotations:Euler Rotation Matrices

1( ) ( ), ,

LAB PAS

σ R σ R

cos cos cos sin sin sin cos cos cos sin sin cos( ) cos cos sin sin cos sin cos sin cos cos sin sin

cos sin sin sin cos

R

0 00 00 0

xx

PAS yy

zz

σ

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 )2

CS LABI I zz z I xx yy zz z

I iso I z

H B I B I

B B I

• Retain only parts of HCS that commute with Iz

13iso xx yy zz

zz iso

yy xx

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

• J-anisotropy negligiblein most cases

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

Dipolar Couplings in Biomolecules

Spin 1 Spin 2 r12 (Å) b12/2 (Hz)

1H 13C 1.12 ~21,500

1H 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 ~50

Dipolar Couplings and Protein Structure

• Structural studies rely on DC-based distance restraints• Weakest couplings (~3+ Å distances) most useful

M.H. Levitt, “Spin Dynamics”

Spectra of Static Polycrystalline Samples ( ) sin Tr exp exp int x intI t d d I iH t I iH t

zz

xx

yy zz

xx

yy

B0

• Spectra determined by magnitudes and relative orientations of CS tensors and dipolar couplings for different sites (even with efficient 1H decoupling)

NMR of Rotating Samples

2

( )

2

( )

( )2

2

( ) exp

CSI I zDIS IS z zJIS IS z z

mr

m

H t I

H t I S

H J I S

t im t

HD for Rotation at Magic Angle (m = 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

• MAS: time-independent dipolar (and CSA) components are zero; terms modulated at r and 2r go to zero when averaged over the rotor cycle high-resolution spectrum

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

Static

r = 2 kHz

r = 20 kHz

Isolated 13C-1H Dipolar Coupling Under MAS(simulation of ideal case)

Incr

easi

ng R

esol

utio

n &

Sen

sitiv

ity

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

Static

r = 2 kHz

r = 20 kHz

Isolated 13C-1H Dipolar Coupling Under MAS(simulation of ideal case)

Incr

easi

ng R

esol

utio

n &

Sen

sitiv

ity

Interaction effectively “decoupled” by MAS:Good for resolutionBad for structural info

Dipolar Recoupling: Basic Concept

• MAS averages couplings to zero

• Multiple RF pulse sequences partially restore couplings

= /2

= 54.7o

= 0

H D Alm T

lm

MAS RF Pulses

Static

Recoupled

Let’s see how this works for simplecase of CW RF field on one of the spins

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

(I)

(S)

• For average Hamiltonian analysis: RF and MAS modulations must be synchronized (1 = nr) 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

(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

• Main idea: calculate effective spin Hamiltonian that does not contain RF term

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

r r r rt in t in t in tye iI e e

Interaction Frame Hamiltonian (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

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

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

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 tmD IS 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

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 S

n π 1,2 ô I-S Decoupling

n = 1,2 ô I-S Dipolar Recoupling

• This rotary resonance recoupling (R3) effect arises from interference of MAS and I-spin RF (when 1 = r or 2r)

• Additional (much weaker) resonances (for n = 3,4,…) are also possible due to higher order average Hamiltonian terms involving the I-spin CSA

Rotary Resonance Recoupling

Oas, Levitt & Griffin, JCP 1988

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

( 1)

exp 2 exp

sin(2 ); sin 2 exp2 2 2 2

D CN IS IS z z IS IS z y

PR x z z PR x

IS ISPR IS PR PR

H C N i C N

i N C N i Nb b i

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 N

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 Hzr = 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 Spin 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 Double Resonance (REDOR)

• Apply a series of rotor-synchronized pulses (2 per r) to 15N spins(this is usually called a dephasing or S experiment)

• Typically a reference (or S0) experiment with pulses turned off is alsoacquired to account for R2 – report S/S0 ratio (or S/S0 = 1-S/S0)

Gullion & Schaefer, JMR 1989

REDOR: Summary of AHT Analysis

˜ S z Sz 0 t Sz t r / 2Sz r / 2 t r

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 S

(0) 2 sin(2 )sin( ) 2 ; (sequence phase)IS IS z z rH b I S

(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

• Effective Hamiltonian changes sign as a function of position ofpulses within the rotor cycle (must pay attention to 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 -r/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

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

t/2 t/2

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

Jaroniec, Tounge, Herzfeld, Griffin JACS 2001

REDOR at High MAS Rates

2 p

r

p (s) r (kHz)

10 5 0.1

10 10 0.2

10 20 0.4

20 20 0.8

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 S

Jaroniec et al, JMR 2000

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 S

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

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

8 8

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

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

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

• For xy-4 phase cycling, finite pulses result only in a simple scaling of the dipolar coupling constant by an additional factor, , between /4 and 1

• For xx-4 spin dynamics are more complicated and converge to R3 dynamics in the limit of = 1

22

cos; / 4 1

1

effIS

IS

bb

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

10 s 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

• 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 kl2IkzSlz

H ij2Iiz S jzi, j

Jij2I 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

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

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 S

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

1

Dipolar evolution under only bkl

13C Selective Pulses: U-13C Thr

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

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

…

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 Asn

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

FS-REDOR: U-13C,15N-f-MLFMet C-Phe NLeu C-Phe NLeu C-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 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 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 (TEDOR)

Hing, Vega & Schaefer, JMR 1992

• Similar idea to INEPT experiment in solution NMR

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

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

on 13C channel recouples DCC and causes loss of magnetization)

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

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

Michal & Jelinski, JACS 1997

‘Out-and-back’ 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

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-Val-Leu

• 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-VL3D ZF TEDOR3D TEDOR

Results in N-ac-VL

• 3D ZF TEDOR generates purely absorptive 2D spectra

• Cross-peak intensities give qualitative distance information

3D ZF TEDOR3D TEDOR

ZF-TEDOR Cross-Peak Trajectories

• 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)

IiSj

2 2 2(0) cos sin cos

i im N

ij i il ij ikl i k j

V V J

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 ZF-TEDOR in Small Peptides: Summary

• Typical uncertainties in measured distances are ~ ±10% due to the use of approximate analytical simulation model

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

Jaroniec et al, PNAS 2004

Ensemble of 20 NMR Structures

Y105

S115

13C-13C J-Evolution Effects in ZF-TEDOR

Simulated 13C Cross-Peak Buildup4 Å C-N Distance (DCN = 50 Hz)

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

• Effective dipolar evolution times limited to ~10-14 ms

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 with unique chemical shifts

(e.g., 13CO) – less so for C/C and other aliphatic C’s due to

overlapping chemical shift ranges (e.g., C range is ~20-70 ppm)

ZF-TEDOR vs. BASE-TEDORGly 13C-15N

Thr 13C-15N

Gly 13C’-15N

Cross-Peak Trajectories in TEDOR Experiments

3D ZF TEDOR

IiSj

2

2 2

(0) cos

sin cos

i

i

m

ij i ill i

N

ij ikk j

V V J

3D BASE TEDOR

IiSj

2 2(0) sin cosiN

ij i ij ikk j

V V

3D BASE TEDOR Spectra: ac-VL & f-MLF

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)

3D SCT-TEDOR Pulse Scheme

• Dipolar 13C-15N SSNMR version of HMQC

• Constant time spin-echo (2T+ 4 = ~1/JCC) used to refocus 13C-13CJ-coupling, with encoding of 15N shift (t1) and 13C-15N DD coupling (CN)

• Experiment can offer improved resolution and sensitivity

• Need isolated 13C-13C pairs (C’-C, Cmethyl-Caliphatic)

Helmus et al, JCP 2008

3D SCT-TEDOR: Methyl 13C in GB1

~3 Å

~4 Å

500 MHz, ~2.7 h

• Effects of 13C-13C J-couplings and relaxation removed from trajectories – 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

Barchi et al. Protein Sci. (1994)

S2

RMS

3.77 Å Rotamer 1 (o) N-Cdistance (Å)

% occurrence

1 +60 2.94 46

2 -60 3.81 45

3 180 2.94 9

X-ray -82 3.77 -

NMR - 3.1 -

4D SCT-TEDOR Pulse Scheme

• Additional “relaxation-free” CT 13Cmethyl chemical shift labeling period easily implemented for improved resolution

4D SCT-TEDOR: N-Acetyl-Valine

• N-C distancesdetected via bothN-C and N-Ccorrelations

• Distances within~0.1 Å of NAV X-ray structure

• 4D recorded in ~37 h

4D SCT-TEDOR: GB1

4D SCT-TEDOR: GB1

GB1 spectra from Rienstra group, UIUC

J-Decoupling by 13C ‘Spin Dilution’

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

Nieuwkoop et al, JCP 2009

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

Nieuwkoop et al, JCP 2009

~750 13C-15N distances + dihedral restraints (TALOS)

Proton assisted heteronuclearrecoupling: PAIN-CP

Lewandowski, De Paepe and Griffin JACS 129, 728-29 (2007)De Paepe et al. JCP 134, 095101 (2011)

• Superficially similar to CP butRF fields satisfy different matching conditions

• Polarization transferred from15N to 13C via a 2nd ordermechanism using a cross terminvolving a 1H assisting spin(Heff ~ N+C-Hz)

• Works best at higher MAS rates (~20+ kHz)

PAIN-CP: f-MLF

De Paepe et al. JCP 134, 095101 (2011)

• Very flexible recoupling – by appropriately combining RF strength, offsetand mixing times broadband or selective recoupling can be achieved

Comparison of TEDOR and PAIN-CP transfer: 1,3-13C,15N GB1

PAIN-CP: Applications to Larger Proteins

De Paepe, Lewandowski, Bockmann, Griffin & co-workers

PAIN-CP: Applications to Larger Proteins

Bertini, Griffin & co-workers JACS 132, 1032 (2010)

Chemical Shifts and Secondary Structure

• Characteristic deviations from ‘random coil’ shifts for -helix and -sheet 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 Fibrils

Cornilescu, Delaglion & Bax JBNMR 1999

Dipolar Evolution in Multispin Systems 1 1 2 2 1 22 2 ; ( ) cos cosIS z z z z xH I S I S I t t t

• 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 by “matching” dipolar phases (i.e., make 1t ~ 2t above) – such expts.yield dihedral restraints that can be combined with CS-based data

I

S

S

200 Hz(2.5 Å) 50 Hz

(4 Å)45o

T-MREV NH Recoupling with HH Decoupling

1 1( ) cos ; sin(2 )2 2

PRiNHx PR

bN t t e

Hohwy et al. JACS 2000

• R-symmetry based sequences (Levitt) have been shown to be highly effectivefor N-H/C-H recoupling with H-H decoupling at high MAS rates (e.g., Polenova 2011)

• In highly deuterated proteins other (e.g., REDOR-type) sequences can also be used

T-MREV Recoupling in NH and NH2 Groups

Hohwy et al. JACS 2000

• Dipolar trajectories & spectra depend on the relative orientation of NH dipolar tensors –report on the H-N-H bond angle

FT of dipolar dephasing trajectory in time domain

projection angle

HC-CH Experiment (Levitt et al, CPL 1996)

1 2 1 2C C C C 1 2C C

projection angle

HC-CH Experiment (Levitt et al, CPL 1996)

Double-quantum coherence(correlated C1-C2 spin state)

1

1 1 2 1 2 1 2

1 1 1 1 2 1 2 2

2( )

1 02

1cos cos cos cos2

( ( )2 ( )2 )

( ) ( ); ( ) exp

MREV z z z z

t mr

m

S t

H t C H t C H

t dt t t im t

1 2 1 2C C C C 1 2C C

projection angle

Dipolar phases depend on the relative orientations of the two dipolar couplingtensors (most pronounced changes in signal as function of projection angle for = 0 or 180o ± ~30o due to diff. term)

HC-CH Experiment (Levitt et al, CPL 1996)

Double-quantum coherence(correlated C1-C2 spin state)

projection angle

HC-CH Experiment (Levitt et al, CPL 1996)

• Large differences in dipolardephasing trajectories for cisand trans topologies (in both time and frequency domain)

• Dipolar spectrum generatedfrom time domain data forone r, by multiplying signal byexp(Rt), repeating many times, applying an overall apodizationfunction followed by FT

‘zero-frequency’ featurefrom cos(1-2) term

Dipolar Coupling Dimension (kHz)

Backbone & Side-chain Torsion AngleMeasurements in Peptides and Proteins

1 2cos cos

, ,

mixS t f

b t

Observable signal

• Create various correlated spin states involving two nuclei (e.g., COi-Ci, Ni-Ci, Ni+1-Ci, Ni-Ni+1, etc.) and evolve for some period of time under selected dipolar couplings (e.g., N-H, N-CO, etc.)

• Evolution trajectories highly sensitive to relative tensor orientations for projection angles around 0o/180o (more info: Hong & Wi, in NMR Spect. of Biol. Solids 2005; Ladizhansky, Encycl. NMR, 2009)

Measurement of in Peptides: HN-CH

Hong, Gross & Griffin, JPC B 1997Hong et al. JMR 1997

y xC N

Multiple-quantum coherence(correlated N-C spin state; combination

of ZQC & DQC)

1

1

1 0

cos cos

( ) ( )

CH NH

t

S t

t dt t

N-ac-Val

Measurement of in Peptides: HN-CH

Hong et al. JPC B 1997Hong et al. JMR 1997

• Experiment most sensitivearound = -120o (~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)

CH ~ 2NH (CH coupling dominates; interference less pronounced)

Torsion Angles: 3D HN-CH

2 2 2( ) cos( )cos( )CH NHS t t r t

Hohwy et al. JACS 2000Rienstra et al. JACS 2002

• 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

r = 2

NH & CH recoupling using T-MREV

3D HN-CH: PrP23-144 Amyloid Fibrils

• Record series of 2D N-C spectra

• Observe cross-peak volumes as function of t2 (DD evolution time)

t2 = 0 (referencespectrum)

3D HN-CH: PrP23-144 Amyloid Fibrils

Measurement of in Peptides: NC-CN

Costa et al., CPL 1997Levitt et al., JACS 1997

1 1 1cos cos ; ( )NC NCOS t t t

Trajectories & Projection Angle vs.

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

Trajectories & Dipolar Spectra vs. ‘zero-frequency’ featurefrom cos(1-2) term

Application to TTR(105-115) Fibrils

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

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

YTIAALLSPYS

TTR(105-115): Dephasing Trajectories

Measurement of in -sheet peptides

• -sheet protein backbone conformation ( ~ 120o) falls outside of the sensitive region of NCCN experiment – correlate other set of couplings

Measurement of in -sheet peptides:3D HN(CO)CH experiment

• Same idea as original 3D HNCH with exception that N and C 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 in -helical peptides:3D HCCN experiment

• N-CO and CH tensors are nearly co-linear for ~ -60o

Ladizhansky et al., JMR 2002

HN-NH Tensor Correlation: and

Reif et al., JMR 2000

11 cos cosi iNH NHS t

U-15N GB1 (Franks et al. JACS 2006)

HN-NH Tensor Correlation: GB1

Franks et al., JACS 2006

Projection angle depends on intervening and angles (see Reif et al. JMR 2000)

~ 0.5o

~ 19o

~ 49o

HN-NH Tensor Correlation: GB1

Franks et al., JACS 2006

Fold of GB1 Refined with ProjectionAngle Restraints

Franks et al., PNAS 2008

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