heteronuclear dipolar recoupling in solid-state nmr dipolar recoupling in solid-state nmr...
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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