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

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…

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?

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) …

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

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

=> 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

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

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

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 spins @ 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

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)

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

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

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

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

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

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

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

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 170-180 ppm F1 (NH nitrogens) 110-130 ppm F2 (CO carbons) F3 (NH proton)

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

3D HNCO UFNMR of U-15N/13C Leu-Ala-Phe 2 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 scans @ 11.7 T

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

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:

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