christopher jaroniec the ohio state university...basics of heteronuclear dipolar recoupling,...

Basics of Heteronuclear Dipolar Recoupling,

Polarization Transfer & Distance

Measurements in Proteins

Christopher Jaroniec

The Ohio State University

5th Winter School on Biomolecular Solid-State NMR, Stowe, VT, January 7-12, 2018

Outline

1. Brief review of nuclear spin interactions, MAS, etc.

2. Basics of heteronuclear recoupling (rotary resonance)

3. Basics of heteronuclear polarization transfer (INEPT,

CP, etc.)

4. REDOR & quantitative distance measurements in

isolated 13C-15N spin pairs

5. Quantitative 13C-15N distance measurements in

U-13C,15N peptides and proteins using frequency

selective REDOR & 3D TEDOR

6. Other 13C-15N distance measurement approaches

Isolated Two Spin-1/2 System (I-S)

CS CS J D

int I S IS ISH H H H H

2

CS

I I

D

IS IS

J

IS IS

H

H

H

I σ B

I D S

I J S

• NMR interactions are anisotropic: can be generally expressed as

coupling of two vectors by a 2nd rank Cartesian tensor (3 x 3 matrix)

Term Interaction Magnitude (Hz)

HCS CSA 103-105

HD Dipolar 101-105

HJ J-coupling 101-102

HRF Radiofrequency 103-105

𝐻𝐶𝑆~ 𝐻𝐷 ≫ 𝐻𝐽

Dipolar Couplings in Biomolecules

Spin 1 Spin 2 r12 (Å)b12/2 (Hz)

~ 12r12-3

1H 13C / 1H 1.12 / 1.78 ~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 5.0 ~25

1H 1H 10.0 ~125

• Structural studies of proteins by SSNMR extensively use dipolar couplings

for polarization transfer in 2D, 3D, … expts assignments & distance info

1-Pulse NMR Spectra of Static Polycrystalline Solids

( ) sin Tr exp exp int x intI t d d I iH t I iH t

szz

sxx

syy szz

sxx

syy

B0

• Spectra determined by magnitudes and relative orientations of CS tensors

and dipolar couplings for different sites (even with efficient 1H decoupling)

1H Decoupled 13C Spectra of Static

Polycrystalline Biomolecules

13C,15N-GB1 (56 aa)

NA-glycine

NMR of Rotating Samples

HI

CS = wI

iso +wI(t)é

ëùûI z

HIS

D =wIS

(t)2IzSz (heteronuclear)

HIS

J = p JIS

2IzSz

wl(t) = w

l

(m) exp imwrt{ }

m=-2

2

å

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 m

IS IS r z z

m

PR m

IS IS

ISIS PR PR

ISIS PR PR

H im t I S

b

bi

bi

• 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

nr = 2 kHz

nr = 20 kHz

Isolated 13C-1H Dipolar

Coupling Under MAS

(simulation of ideal case)

Incre

asin

g R

eso

lutio

n &

Se

nsitiv

ity

Interaction effectively

“decoupled” by MAS

MAS Solid-State NMR of Proteins

Singlemethyl 13C

aliphatic 13C

Static MAS (11 kHz)

GB1 (56 aa)

microcrystals

decoupling

Importance of Sample Preparation

• Highest quality SSNMR spectra are typically obtained for locally well-ordered

& hydrated samples at ambient temp. (minimizes inhomegenous broadening)

Inhomogeneous line

broadening due to

freezing out of multiple

similar conformers

(vs. hydrated sample where

shifts are averaged)

na-TTR105-115 Fibrils

Dipolar Recoupling: Basic Concept

• MAS averages

couplings to zero

• Multiple RF pulse

sequences partially

restore couplings

Q = /2

Q = 54.7o

Q = 0

H D Alm T

lm

MAS RF Pulses

Static

Recoupled

Let’s see how this works for simple

case of CW RF field on one of the spins

1

( ) ( )

2 ( )2

iso iso

tot S z S z I z I z

IS z z IS z z x

H S t S I t I

J I S t I S I

• For average Hamiltonian analysis: RF and MAS modulations

must be synchronized (1 = nr) to obtain cyclic propagator

S

I

Average Hamiltonian Theory: Summary

Haeberlen & Waugh, Phys. Rev. 1968

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

Interaction frame H

Effective Hamiltonian

Magnus expansionAHT analysis

requires cyclic RF

propagator

Dyson time-ordering operator

Zero-order term = “Average” Hamiltonian

Interaction Frame Hamiltonian

Similar term for HI

Interaction Frame Hamiltonian (Cont.)

Lowest-Order Average Hamiltonian

• S-spin CSA refocused by MAS, I-S J-coupling eliminated

by RF field on I-spin (decoupling)

Lowest-Order Average HD


n ≠ 1,2 I-S Decoupling

n = 1,2 I-S Dipolar Recoupling !!!

• The 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

13C

15N 1 = r


Time (ms)

0 5 10 15 20

<S

x>

(t)

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

DCN = 900 Hz

r = 25 kHz

Frequency (Hz)

-1000 -800 -600 -400 -200 0 200 400 600 800 1000

Inte

nsity (

a.u

.)

/ 2CND

<C

x>

(t)

Polarization Transfer in NMR

• Ability to transfer polarization between different

nuclear spins is one of the key concepts in NMR

• Polarization transfer is mediated via J and dipolar

couplings between the relevant spins

• Some important applications:o Spectral sensitivity enhancement achieved by transferring

spin polarization from high nuclei to low nuclei

(for ensemble of spin ½ nuclei: Meq ~ Na – N ~ 2B0T-1;

higher nuclei also tend to have shorter T1’s enabling more

scans to be recorded per unit time)

o Generate correlations in multidimensional NMR spectra

Heteronuclear Polarization

Transfer via One Bond J-Couplings

INEPT = Insensitive Nuclei Enhanced by Polarization Transfer

• Spin echoes on I and S refocus chemical shifts but not J-couplings

• I spin coherence evolution under J-coupling for time t generates

anti-phase coherence, which is transferred from spin I to S by pair

of /2 pulses

t (2J12)1

1

1

1

: 3.7 ms

: 5.4 ms

: 33 ms

CH

NH

NCO

J

J

J

t

t

t

INEPT pulse sequence

||


t (2J12)1

10 SIB B

(3 /2) ( )

( /2) ( /2)

ˆ ˆˆ ˆ

ˆ ˆ ˆ ˆˆ ˆ2 2

ˆ ˆˆ2

I Sx x IS

I Sy x

J

z z y z

x z z z z z

z y y

I S I S

I S S I S S

I S S

t

I S I S

I S I S

I S

B B B B

B B B B

B B

𝐁𝒊 =ℏ𝛾𝑖𝐵0𝑘𝐵𝑇

I = 1H; S = 15N


Transferred IS

magnetization

Non-transferred (steady-state or

Boltzmann) magnetization

t (2J12)1

10 SIB B

(3 /2) ( )

( /2) ( /2)

ˆ ˆˆ ˆ

ˆ ˆ ˆ ˆˆ ˆ2 2

ˆ ˆˆ2

I Sx x IS

I Sy x

J

z z y z

x z z z z z

z y y

I S I S

I S S I S S

I S S

t

I S I S

I S I S

I S

B B B B

B B B B

B B

𝐁𝒊 =ℏ𝛾𝑖𝐵0𝑘𝐵𝑇

I = 1H; S = 15N

INEPT NMR spectrum (single scan)

(anti-phase coherence ~ 2IzSy)

(in-phase coherence ~ Sy)

Transferred magnetization is

enhanced relative to Boltzmann: |BI| >> |BS|

Refocused INEPT

||

Refocused INEPT

( /2) ( /2)

( ) ( )

ˆ ˆ ˆ ˆˆ ˆ2 2

ˆ ˆˆ2

ˆ ˆˆ2

I Sy y

I Sx x

IS

x z z z x x

z x x

J

y z y

I S S I S S

I S S

S I S

t

I S I S

I S

I S

B B B B

B B

B B

3̂ 4̂

5̂

Transferred Non-transferred

Refocused INEPT spectrum

Is this useful in SSNMR?

• Generally not for 1H-X transfers

(t ~ 3-5 ms) in relatively rigid

domains of fully protonated

proteins -- due to short

effective 1H T2’s associated with

residual 1H-1H couplings that

are not fully averaged by MAS

• But … INEPT based methods

can be used for:

(i) polarization transfer at fast

MAS in highly deuterated

proteins, or

(ii) selective detection of highly

flexible domains in protonated

proteins

Is this useful in SSNMR?

• Generally not for 1H-X transfers

(t ~ 3-5 ms) in relatively rigid

domains of fully protonated

proteins -- due to short

effective 1H T2’s associated with

residual 1H-1H couplings that

are not fully averaged by MAS

• But … INEPT based methods

can be used for:

(i) polarization transfer at fast

MAS in highly deuterated

proteins, or

(ii) selective detection of highly

flexible domains in protonated

proteins

17-mer nucleosome array

Nucleosome: ~147 bp DNA + 2 x (H2A, H2B, H3, H4)

~ 4 MDa

2D Refocused INEPT / HSQC

1H

13C/15N

Compaction of 17-mer Nucleosome Arrays in MgCl2

Detection of Flexible H3 and H4 Tails in Arrays

Gao, Nadaud, Bernier, North, Hammel, Poirier & Jaroniec, JACS 2013, 135, 15278

Heteronuclear Polarization Transfer via

Dipolar Couplings: Cross Polarization

• Generally much shorter polarization transfer times

can be used relative to INEPT based experiments

since bIS/2 >> J

decouple

90y

x

x

CP-MAS Experiment: I-S spin pair

𝐻 = 𝜔𝐼𝑆 𝑡 2𝐼𝑧𝑆𝑧 + 𝜔1𝐼𝐼𝑥 + 𝜔1𝑆𝑆𝑥

𝐻𝑇 = 𝑈𝑇𝐻(𝑈𝑇)−1Transform to doubly tilted frame with z-axis along the spin lock field:

𝑈𝑇 = 𝑒−𝑖𝜋2𝐼𝑦𝑒−𝑖

𝜋2𝑆𝑦

𝐻𝑇 = 𝜔𝐼𝑆 𝑡 2𝐼𝑥𝑆𝑥 − 𝜔1𝐼𝐼𝑧 − 𝜔1𝑆𝑆𝑧 =𝜔𝐼𝑆 𝑡 (𝐼+𝑆− + 𝐼−𝑆+)/2 +

𝜔𝐼𝑆 𝑡 (𝐼+𝑆+ + 𝐼−𝑆−)/2 − 𝜔1𝐼𝐼𝑧 − 𝜔1𝑆𝑆𝑧

CP-MAS Experiment: I-S spin pairTransform HT into interaction frame to remove the effect of spin lock fields using:

𝑈 = 𝑒𝑖𝜔1𝐼𝑡𝐼𝑧𝑒𝑖𝜔1𝑆𝑡𝑆𝑧

𝐻𝐷,𝐼𝑆𝑇,(0)

= 𝑅𝑒 𝜔𝐼𝑆(𝑛)

(𝐼+𝑆− + 𝐼−𝑆+)/2 = 𝑅𝑒 𝜔𝐼𝑆(𝑛)

𝐼𝑥23

Taking average over the rotor cycle yields the following effective dipolar Hamiltonian:

for 𝜔1𝐼 −𝜔1𝑆 = 𝑛𝜔𝑟 𝑛 = ±1,±2 (ZQ match condition)

𝐻𝐷,𝐼𝑆𝑇,(0)

= 𝑅𝑒 𝜔𝐼𝑆(𝑛)

(𝐼+𝑆+ + 𝐼−𝑆−)/2 = 𝑅𝑒 𝜔𝐼𝑆(𝑛)

𝐼𝑥14

for 𝜔1𝐼 +𝜔1𝑆 = 𝑛𝜔𝑟 𝑛 = ±1,±2 (DQ match condition)

𝐼𝑥14 = (𝐼+𝑆+ + 𝐼−𝑆−)/2𝐼𝑥

23 = (𝐼+𝑆− + 𝐼−𝑆+)/2

CP-MAS Experiment: ZQ condition

decouple

90y

x

x

Initial I spin-locked magnetization

after 90o pulse in the tilted frame

𝐼𝑧23 𝜏𝐶𝑃 = 𝐼𝑧

23 cos 𝜔𝐼𝑆𝜏𝐶𝑃

𝜌𝑇 = 𝐼𝑧 = 𝐼𝑧14 + 𝐼𝑧

23

𝐼𝑧14 =

𝐼𝑧 + 𝑆𝑧2

𝐼𝑧23 =

𝐼𝑧 − 𝑆𝑧2

𝑆𝑧 𝜏𝐶𝑃 = 𝐼𝑧14 𝜏𝐶𝑃 − 𝐼𝑧

23 𝜏𝐶𝑃 =1

2𝐼𝑧 0 1 − cos 𝜔𝐼𝑆𝜏𝐶𝑃 = 𝐼𝑧 0 sin2(

𝜔𝐼𝑆𝜏𝐶𝑃

2)

• S-magnetization builds up along direction of spin lock field in rotating frame

CP Match Profile for Adamantane (5 kHz MAS)

-2

-1

+2

+1decouple

90y

x

x

decouple

90y

x

x

CP-MAS SummaryPines, Gibby & Waugh, JCP (1973)

Schaefer & Stejskal, JMR (1979)

w1I ±w1S = nwr, n = ±1,±2

HCP,ZQ µ (I+S- + I-S+) for w1I -w1S = nwr

HCP,DQ µ (I+S+ + I-S-) for w1I +w1S = nwr

Hartmann-Hahn CP Matching Conditions

• CP yields significant sensitivity enhancements for low- nuclei (13C, 15N, etc.) by:

(1) transferring the much larger 1H spin polarization

(2) enabling shorter recycle delays to be used (optimal is ~1.3 x 1H T1)

• ZQ CP is typical at moderate MAS rates (up to ~30 kHz); for fast fast MAS (40+ kHz)

DQ CP can be very useful (build up times ~0.1-1.5 ms for 1H-X, ~5-10 ms for 15N-13C)

• Linear or tangent ramp typically applied on one of the channels (reduce B1 inhom, …)

• To avoid accidental CSA and homonuclear recoupling avoid: w1I (S) = nwr, n = 12,1,2

𝐼𝑧90𝑜,𝐶𝑃

𝑆𝑥 = 𝐼𝑧 0 sin2( 𝜔𝐼𝑆𝜏𝐶𝑃2

)

2D 15N-13C Correlation Spectroscopy

Band-selective Double CP (DCP) Pulse Sequence

Schaefer et al., JMR 34 (1979) 443

Baldus et al., Mol. Phys. 95 (1998) 1197

ZQ CP Matching Condition

in Doubly Tilted Frame with Offsets

• Offset dependence of CP enables band-selective N-CO and N-Ca transfers

• Typical setup: carrier close to CO or Ca; N = 3.5r; C = 2.5r (or 2.5 & 1.5r)

β1 β2 β3

2D 15N-13C Correlation Spectra of huPrP23-144 Fibrils

• ~30-residue C-terminal residues form ordered parallel-in-register core;

~90 N-terminal residues dynamically disordered (not detectable in CP

based spectra but detectable in INEPT based spectra)

NCO NCA


Time (ms)

0 5 10 15 20

<S

x>

(t)

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

DCN = 900 Hz

r = 25 kHz

Frequency (Hz)

-1000 -800 -600 -400 -200 0 200 400 600 800 1000

Inte

nsity (

a.u

.)

/ 2CND

<C

x>

(t)

Time (ms)

0 5 10 15 20

<S

x>

(t)

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

no CSA

typical 15N CSA

R3 in Real Spin Systems:

Effect of CSA of Irradiated Spin

• R3 also recouples the CSA of irradiated spin (15N in our example),

which doesn’t commute with the dipolar term

• Dipolar dephasing depends strongly 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

.)

<C

x>

(t)

Rotational Echo Double Resonance

(REDOR)

• Apply a series of rotor-synchronized pulses (2 per tr) 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 to account for R2 – report S/S0 ratio (or DS/S0 = 1-S/S0)

Gullion & Schaefer, JMR 1989

REDOR: Summary of AHT Analysis

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

• Effective Hamiltonian changes sign as a function of position of

pulses 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 -tr/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

REDOR Dipolar Evolution

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 ~ 20 Hz) in isolated 13C-15N spin pairs

[2-13C,15N]Glycine

REDOR: More Challenging Case

S112(13C′)-Y114(15N) Distance Measurement in

TTR(105-115) Amyloid Fibrils

4.06 ± 0.06 Å

REDOR: 15N CSA Effects

4 :

8 :

16 :

xy xyxy

xy xyxy yxyx

xy 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

t

t

tp (s) nr (kHz)

10 5 0.1

10 10 0.2

10 20 0.4

20 20 0.8

REDOR (xy-4) at High MAS: AHT

Jaroniec et al, JMR 2000

REDOR (xy-4) at High MAS: AHT

• For xy-4 phase cycling, finite pulses result only in a

simple scaling of the dipolar coupling constant by an

additional factor, k, between /4 and 1

• For xx-4 spin dynamics are more complicated and

converge to R3 dynamics in the limit of = 1

2

2

cos; / 4 1

1

eff

IS

IS

b

b

k k

REDOR (xy-4) at High MAS:

AHT vs. Numerical Simulations

10 s 15N pulses

no 15N CSA

REDOR (xy-4) Experiments

REDOR in Multispin Systems

1 1 2 2

1 2

2 2

( ) cos cos

IS 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 kl2I kzSlz

H ij2IizS jzi, j

J ij2I 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 e

e e e e e e

e 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 lx

i k j l i j k

ki kz iz il iz lz ki kz iz

i 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 lx

k

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 t

kx

iH t iH t

kx 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


…


1 ms

2 ms

4 ms

6 ms

8 ms

10 ms

…

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


Met C-Phe NLeu C-Phe NLeu C-Leu N

X-ray: 2.50 Å

NMR: 2.46 ± 0.02 Å

X-ray: 3.12 Å

NMR: 3.24 ± 0.12 Å

X-ray: 4.06 Å

NMR: 4.12 ± 0.15 Å


• 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 the refocused INEPT experiment

• 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 SREDOR

x z y IS mix

REDOR

y 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 IREDOR

x y z IS mix

S I

z y IS mix

REDOR

y 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-VL

3D 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 t t t

i im N

ij i il ij ik

l i k j

V V J

3D ZF-TEDOR: N-ac-VL

X-ray: 2.95 Å

NMR: 3.1 Å

X-ray: 4.69 Å

NMR: 4.7 Å

Val(N)

Leu(N)

X-ray: 3.81 Å

NMR: 4.0 Å

X-ray: 3.38 Å

NMR: 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 Buildup

4 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 J2

C

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 Ca/C and other aliphatic C’s due to

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

ZF-TEDOR vs. BASE-TEDOR

Gly 13Ca-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 il

l i

N

ij ik

k j

V V J t

t t

3D BASE TEDOR

IiSj

2 2(0) sin cosiN

ij i ij ik

k j

V V t t

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

3D BASE TEDOR: N-ac-VL

X-ray: 2.39 Å

NMR: 2.4 Å

X-ray: 1.33 Å

NMR: 1.3 Å

Val(N)

Leu(N)

X-ray: 1.33 Å

NMR: 1.4 Å

X-ray: 4.28 Å

NMR: 4.1 Å

Val(N)

Leu(N)

3D SCT-TEDOR Pulse Scheme

• Dipolar 13C-15N SSNMR version of HMQC

• Constant time spin-echo (2T+ 4d = ~1/JCC) used to refocus 13C-13C

J-coupling, with encoding of 15N shift (t1) and 13C-15N DD coupling (tCN)

• Experiment can offer improved resolution and sensitivity

• Need isolated 13C-13C pairs (C’-Ca, 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 ÅRotamer c1 (o)

N-C

distance (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 distances

detected via both

N-C and N-C

correlations

• Distances within

~0.1 Å of NAV

X-ray structure

• 4D recorded in ~37 h

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)

[hu] [mo] [Sha]

[Sha138/139] [hu138] [hu138/139]

Jones & Surewicz, Cell 2005, 121, 63

Helmus et al. PNAS 2008, 105, 6284; Helmus et al. JACS 2010, 132, 2393

Helmus et al. JACS 2011, 133, 13934; Jones et al. J. Biol. Chem. 2011, 286, 42777

PrP23-144 Amyloid Fibrils

• Ordered ~30-residue C-terminal parallel-in-register amyloid β-core

human PrP23-144 Fibrils

ZF-TEDOR: huPrP23-144 Fibrils

3-13C-Pyruvate Labeling Specific Methyl 13C Labeling

Ala-, Val-2, Leu-d2, Ile-2

AVLI 13C methyl labeling: Kerfah, Boisbouvier et al. JBNMR 2015, 61, 73;

Curr. Opin. Struct. Biol. 2015, 32, 113; JBNMR 2015, 63, 389

Proton assisted heteronuclear

recoupling: PAIN-CP

Lewandowski, De Paepe and Griffin JACS 129, 728-29 (2007)

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

• Superficially similar to CP but

RF fields satisfy different

matching conditions

• Polarization transferred from

15N to 13C via a 2nd order

mechanism using a cross term

involving 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, offset

and mixing times broadband or selective recoupling can be achieved

Comparison of TEDOR and PAIN-CP

transfer: 1,3-13C,15N GB1

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

PAIN-CP: Applications to Larger Proteins

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 a-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

k

Hohwy et al. JACS 2000

• R-symmetry based sequences (Levitt, Encyclopedia NMR 2002) have been shown to

be highly effective for N-H/C-H recoupling with H-H decoupling at higher MAS rates

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

T-MREV Recoupling in NH and NH2 Groups


• 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

Qprojection angle

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

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

Qprojection angle


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( )

10

2

1cos cos cos cos

2

( ( )2 ( )2 )

( ) ( ); ( ) exp

MREV z z z z

tm

r

m

S t

H t C H t C H

t dt t t im t

k

k

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

Qprojection angle

Dipolar phases depend on the relative

orientations of the two dipolar coupling

tensors (most pronounced changes in

signal as function of projection angle for

Q = 0 or 180o ± ~30o due to diff. term)


Double-quantum coherence

(correlated C1-C2 spin state)

Qprojection angle


Q~0o/180oQ~60o

• Large differences in dipolar

dephasing trajectories for cis

and trans topologies (in both

time and frequency domain)

• Dipolar spectrum generated

from time domain data for

one tr, by multiplying signal by

exp(Rt), repeating many times,

applying an overall apodization

function followed by FT

‘zero-frequency’ feature

from cos(1-2) term

Dipolar Coupling Dimension (kHz)

Backbone & Side-chain Torsion Angle

Measurements 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-Cai, Ni-Cai, Ni+1-Cai, Ni-Ni+1, etc.) and evolve for some period

of time under selected dipolar couplings (e.g., N-Ha, 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 1997

Hong et al. JMR 1997

y xC N

Multiple-quantum coherence

(correlated N-C spin state; combination

of ZQC & DQC)

1

1

10

cos cos

( ) ( )

CH NH

t

S t

t dt t

k

N-ac-Val

Measurement of

in Peptides: HN-CH

Q

Hong et al. JPC B 1997

Hong et al. JMR 1997

• Experiment most sensitive

around = -120o (Q~165o);

resolution of ca. ±10o

• Useful structural restraints

despite degeneracies

(use proj. angles directly in

structure refinement)

• Implementations using

‘passive’ evolution under

DD couplings limited to

slow MAS rates (<5-6 kHz)

Q90o

CH ~ 2NH (CH coupling

dominates; interference

less pronounced)

Torsion Angles: 3D HN-CH

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


Rienstra et al. JACS 2002

• Expts. that employ active recoupling sequences to reintroduce DD

couplings 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-Ca spectra

• Observe cross-

peak volumes as

function of t2 (DD

evolution time)

t2 = 0 (reference

spectrum)

3D HN-CH: PrP23-144 Amyloid Fibrils

Measurement of y in Peptides: NC-CN

Costa et al., CPL 1997

Levitt et al., JACS 1997

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

Trajectories & Projection Angle vs. y

• Dephasing of 13C-13C DQ coherence is very sensitive to the

relative orientation of 13C-15N dipolar tensors for |y| ≈ 150-180o

Trajectories & Dipolar Spectra vs. y‘zero-frequency’ feature

from cos(1-2) term

Application to TTR(105-115) Fibrils

• 13C-13C DQ coherences evolve under the sum

of CO and Ca resonance offsets during t1

Reference DQ-SQ correlation spectrum

for U-13C,15N YTIA labeled sample

YTIAALLSPYS

TTR(105-115): Dephasing Trajectories

Measurement of y in -sheet peptides

• -sheet protein backbone conformation (y ~ 120o) falls outside of the

sensitive region of NCCN experiment – correlate other set of couplings

Measurement of y in -sheet peptides:

3D HN(CO)CH experiment

• Same idea as original 3D HNCH with exception that N and Ca 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 y in a-helical peptides:

3D HCCN experiment

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

Ladizhansky et al., JMR 2002

HN-NH Tensor Correlation: and y

Reif et al., JMR 2000

11 cos cos

i 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 y angles (see Reif et al. JMR 2000)

Q ~ 0.5o

Q ~ 19o

Q ~ 49o

HN-NH Tensor Correlation: GB1

Franks et al., JACS 2006

Fold of GB1 Refined with Projection

Angle 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

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

int I S IS ISH H H H H

2

CS

I I

D

IS IS

J

IS IS

H

H

H

I σ B

I D S

I J S

• NMR interactions are anisotropic: can be generally expressed as

coupling of two vectors by a 2nd rank Cartesian tensor (3 x 3 matrix)

Rotate Tensors: PAS Lab

1( ) ( ) ; , ,LAB PAS a 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 set

of 3 Euler angles {a,,}

Tensor Rotations:

Euler Rotation Matrices

1( ) ( )

, ,

LAB PAS

σ R σ R

a

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

a a a a

a a a a a a

R

0 0

0 0

0 0

xx

PAS yy

zz

s

s s

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 2

0 0

2 2

0 0

sin cos sin sin cos

13cos 1 sin cos(2 )

2

CS LAB

I I zz z I xx yy zz z

I iso I z

H B I B I

B B I

s s s s

s d

• Retain only parts of HCS that commute with Iz

1

3iso xx yy zz

zz iso

yy xx

s s s s

d s s

s s

d

High Field Truncation: HJ and HD

2

0

3

2

13cos 1 2

2

4

J

IS IS z z

D

IS IS z z

I SIS

IS

H J I S

H b I S

br

• J-anisotropy negligible

in 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

13C 15N 6.0 ~15

http://chemistry.osu.edu/~jaroniec/nmr/dipole.php

http://chemistry.osu.edu/~jaroniec/nmr/calcdist.php

http://chemistry.osu.edu/~jaroniec/nmr/dipole.php

http://chemistry.osu.edu/~jaroniec/nmr/calcdist.php

Dipolar Couplings and Protein Structure

• Structural studies rely on DC-based distance restraints

• Weakest couplings (~3-6 Å distances) are 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

szz

sxx

syy szz

sxx

syy

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

CS

I I z

D

IS IS z z

J

IS IS z z

m

r

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 m

IS IS r z z

m

PR m

IS IS

ISIS PR PR

ISIS PR PR

H im t I S

b

bi

bi

• 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

Dipolar Recoupling: Basic Concept

• MAS averages

couplings to zero

• Multiple RF pulse

sequences partially

restore couplings

Q = /2

Q = 54.7o

Q = 0

H D Alm T

lm

MAS RF Pulses

Static

Recoupled

Let’s see how this works for simple

case of CW RF field on one of the spins

1

( ) ( )

2 ( )2

iso iso

tot S z S z I z I z

IS z z IS z z x

H S t S I t I

J 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

Haeberlen & Waugh, Phys. Rev. 1968

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

Interaction Frame Hamiltonian

Interaction Frame Hamiltonian (Cont.)

Lowest-Order Average Hamiltonian

• S-spin CSA refocused by MAS, I-S J-coupling eliminated

by RF field on I-spin (decoupling)


n ≠ 1,2 I-S Decoupling

n = 1,2 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

christopher jaroniec the ohio state university...basics of heteronuclear dipolar recoupling,...

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