1. Single-Scan Multidimensional NMR Spectroscopy
7th CCPN Workshop, Ambleside, England, August 2, 2007
Single-Scan Multidimensional NMR Spectroscopy
Lucio Frydman
Department of Chemical Physics
Weizmann Institute - Israel zx
2D 1H-15N HMQC NMR spectrum of 2 mM 15N-enriched Ubiquitin in H2O
1H Shift [ppm] 9 8 7
129
108
115
122
15N Shift [ppm]
Total acquisition time: 85 ms

2. Eventually, we end up with too many peaks…
Why is it that Chemists “love” NMR?
Because what we get from its spectra is very simple: One Site - One Frequency - One Peak Two Sites - Two Frequencies - Two Peaks …
A direct atom-by-atom picture of a molecule, mapping chemical structure into sharp spectral peaks appearing at predictable frequency positions
Cholesterol
NMR Spectrum
Eventually, we end up with too many peaks…

3. And yet, where do we get these “two times” from?
The solution to this embarrassment of riches: 2D NMR
“2D time-domain experiments: A signal s(t1,t2) is measured as a function of two independent time variables defined by suitable segmentation of the time axes, and is converted by 2D Fourier transformation into a 2D frequency-domain spectrum S(1,2)”
Significant improvement in the resolution of the NMR spectra (2 dims vs. 1 dim)
New information about inter-nuclear correlations unavailable in the 1D
Paradigm for other branches of spectroscopy
2D 1H-1H TOCSY NMR - Antanamide
(Ernst, Noble Lecture, 1991)
And yet, where do we get these “two times” from?

4. The Jeener-Ernst canonical scheme of 2D NMR:
We get the two desired variables by giving them very different roles in the sampling of the time-domain: t2 is a physical time; t1 is monitored in a point-wise, scan-by-scan fashion
1D NMR: Single-scan (sub-second)
2D NMR: Series of 1D NMR acquisitions (minutes)
3D NMR: Series of 2D NMR acquisitions (hours) …

5. Nowadays not only Chemists & Biochemists love NMR…
Physicians do so too
Magnetic Resonance Imaging (MRI)
NMR Spectroscopy
w=gBo
Bo constant
Sample
(H2O)
NMR Imaging
B(z) = Bo + Gz
w = gBo + gG.z
Profile (z) z

6. The typical MRI exam is also carried out as a 2D/3D NMR Experiment
Y axis Y
X axis Z X

7. => S(kx,ky) = ∫∫r(x,y)exp[i(kxx+kyy)]dxdy
MRI practitioners have their own domain: k-Space
In MRI: Gradients help encode the “interactions” x, y
kx = Gxt1
ky = Gyt2
=>
=> S(kx,ky) = ∫∫r(x,y)exp[i(kxx+kyy)]dxdy
S(t1,t2) = ∫∫ r(x,y) exp[i(t1.Gxx+t2 .Gyy)] dxdy
Get the image by 2D FT vs kx,ky; wavenumbers in reciprocal space
Gx tx
Gy ty kx ky
FT imaging Gx Gy t kx ky
Back-Project Gx
Gy t ty kx ky
Spin-Warp

8. Gradients: Windings & Echoes Sxcos(gGtz)+Sysin(gGtz)
Due to their man-made nature, MRI interactions are 100% reversible. This gives an opportunity to “echo” their effects: t
G=∂B/∂z RF t
W(z) = gGz t
W(z) = -gGz
UNWINDINGGradient echo taking spins back to Sx
In the beginning: Sz M My
z,Mz Sx M My
z,Mz
Sxcos(gGtz)+Sysin(gGtz)
WINDING: no signal over the sample

9. Gradient echoes enable 2D MRI to be carried out in an “Ultrafast” mode (Mansfield, 1976; Nobel Prize in Medicine 2003) Gx Gy t
Echo Planar Imaging  Functional MRI kx ky

10. M+(z) ≈ exp[iCW1z]: NO OVERALL SIGNAL
2D NMR spectroscopy can also be carried out “Ultrafast”
Starting point: An alternative way to collect 1D NMR data based on encoding the MR interactions along a Spatial Domain
The Principle: Excite different z’s as a function of t
Excitation Offset /
Excitation Time
Sample Position (z) ∂O
Ge =
____ ∂z
Spins are excited and begin evolving under the action of an internal W1 z Mx My z Mx My z Mx My z Mx My z My z
Slope=C-1 D t 2D N 1
Start
This process creates a shift-driven winding of the x-y magnetization:
M+(z) ≈ exp[iCW1z]: NO OVERALL SIGNAL

11. Integrated Bloch equations in the presence of +Ga
An acquisition gradient can then unravel the W1 evolution frequencies - revealing them as echoes
Chemical shift #1 >>
Chemical shift #2
Integrated Bloch equations in the presence of +Ga
Behavior of 5 slices illustrated for simplicity.
Actual signals (bottom) calculated assuming a 17-slices excitation.
z Position
Overall
Signal
Acq. Time (a k, a n1)

12. Why bother with this strange approach to monitor NMR aided by a “spatial” domain?
Because the gradient-driven decoding process is 100% reversible, and hence it can be used to monitor an array of k/n1 spectra as a function of an acquisition time t2:
Physical dwell time
k/n1
(pre-mixing spectrum,
no FT required)
t2 (encodes post-mixing frequencies, needs FT)
Sampled points rf G O i N1
+Ge
Dt1
-Ge t2 …
Regular
Mixing
+Ga
-Ga Ta
FT of these data along t2 can therefore yield 2D NMR correlations within a single scan

13. A closer look at two ways of retrieving 2D NMR spectra:
In traditional time-encoded 2D NMR
We detect
and we get what we want by 2D FT
In spatially-encoded 2D NMR (where t1 = C.z)
We detect
and we get what we want by calling -k/C=n1, and doing a 1D FT

14. Ultrafast 2D NMR has been implemented on a number of platforms
Single-scan H,H-COSY on Ethanol Philips 3T/80 cm
(in collaboration with W. Köckenberger, Sir P. Mansfield MRC., Nottingham)
n1 (6 ppm)
n2 (6 ppm)
TOCSY Spectra on Mouse Brain: 300/89 Varian (w/OVS & Vapour water suppression)
256 (64 t1 points) scans
4 (ultrafast) scans

15. Some recent (800 MHz + cryoprobe) biomolecular examples
15N-1H 2D HMQC NMR spectrum; 2.3 mM 15N-Ubiquitin 85 ms acquisition time
1H shift [ppm]
15N shift [ppm]
1H shift [ppm]
13C shift [ppm]
13C-1H 2D HSQC NMR spectrum; 1.0 mM U(15N,13C)-protein A
60 ms acquisition time

16. Sensitivity-wise…
we should pay a price per scan due to the simultaneous sampling of two domains (larger bandwidth needed)
but we seem to be paying an additional sensitivity overhead
Grad H N
DEC
FID
1/2J 
/2 π
Time-domain signal (kpoints)
Signal amplitude (a.u.)
As-collected FID
Ubiquitin (280 K)
Time-domain signal (kpoints)
Signal amplitude (a.u.)
Identical conditions
No gradients or RF chirps

17. Ultrafast 2D Hyperpolarized NMR
(7T direct-excite NMR expts in collaboration with D. Blazina, OIMBL)
Single-Scan (0.15 sec) 2D HSQC NMR on a hyperpolarized pyridine solution in CD3OD
[pyridine] = 0.47 mM
Single-Scan 2D HSQC NMR (0.13 sec) on 15N-labeled hyperpolarized urea in CD3OD
[urea] = 200 nM
Natural abundance

18. 2 mM U-(15N,13C)-Leu-Ala-Phe
Ultrafast NMR and higher-dimensional acquisitions: Accelerated 3D HNCO on a fully-labeled tripeptide N 2
p p
p/2 D t 3 1H
15N
13CO
13C G D' F1
2 mM U-(15N,13C)-Leu-Ala-Phe
128 total scans
Amide region peaks
Acq time: 85 sec
F3 (NH proton)
F1 (NH nitrogens)
F2 (CO carbons)
14 ppm
1.7 ppm
16 ppm

19. 3D HNCO Acq time: 155 sec 2 mM U-(15N,13C)-Ubiquitin
6-10 ppm
2 mM U-(15N,13C)-Ubiquitin
@ 500 MHz (RT probe)
16 t2 increments; 256 total scans. Longitudinally-optimized HSQC-type sequence (BEST w/SLR pulses); amide region peaks
3D HNCO
Acq time: 155 sec
ppm
F1 (NH nitrogens)
ppm
F2 (CO carbons)
F3 (NH proton)

20. Yet another possibility: 3D NMR in a Single Scan
Spatial encoding of a 2D correlation
eiCzn1.z
eiCxn2.x
S(kx,kz,t3) ≈
eikzz.eikxx.ein3t3
Mixing #1
Mixing #2 D t 3 1 2 rf G z N x 4 T a

21. 3D HNCO UFNMR of U-15N/13C Leu-Ala-Phe2
p p
p/2 D t 3 1H
15N
13CO
13C Gz Gx D' F1 F2 1
F3 1H
F2 13C
F1 15N t3 kx kz
Interlaced FT: Integrated Processing of all Data
2 sec total acquisition time
2 mM in d6-DMSO; 2 phase-cycled 11.7 T

22. Then the spatial encoding… and a ki=∫Gi(t’)dt’ sampling…
In general…
Given a gradient set Gi = {∂Bo/∂Pi }i=1-n, based on Pi(r) geometries such that ∫Pi(r)Pj(r)d3r = dij (as in shimming coils)
Then the spatial encoding… rf G1 G2 Gn
eiC1n1P1.eiC2n2P2 … eiCnnnPn N 1 D t 2
Exc
Mix n
and a ki=∫Gi(t’)dt’ sampling…
k0 =∫P0dt=t ki kj
S(k)= eik0n0 . eik1P1.eik2P2 … eiknPn
…will furnish a signal from which an (n+1)D NMR spectrum could become available within a single scan

23. R. Battacharyyha (solids), S. Raz (high-res), F. Kramer (opt. control)
Acknowledgements
POSTDOCS:
R. Battacharyyha (solids), S. Raz (high-res), F. Kramer (opt. control)
GRADUATE STUDENTS:
B. Shapira (UF,high-res), Y. Shrot (UF, in vivo), M. Mishkovsky (UF), N. Ben-Eliezer (MRI), A. Tal (MRI), M. Gal (UF, dynamics), Z. Noy (CIDNP, DNP)
COLLABORATORS:
H. Degani, B. Brutscher, R. Esposito, R. Griffin, B. Blümich, W. Köckenberger, Bruker, Varian, OIMBL
Ilse Katz MR Center zx
Horowitz Foundation EC
Our sponsors:

24. Thank You