# Nuclear Overhauser effect

(Redirected from Overhauser effect)

The nuclear Overhauser effect (NOE or nOe) is the transfer of nuclear spin polarization from one spin bath to another spin bath via cross-relaxation. When observed by nuclear magnetic resonance spectroscopy, the technique is used to elucidate the structures of organic compounds.

## NMR spectroscopy

The NOE is useful in NMR spectroscopy for assigning structures.[1] In this application, the NOE differs from the application of spin-spin coupling in that the NOE occurs through space, not through chemical bonds. Thus, atoms that are in close proximity to each other can give a NOE, whereas spin coupling is observed only when the atoms are connected by 2–3 chemical bonds. The inter-atomic distances derived from the observed NOE can often help to confirm the three-dimensional structure of a molecule. In 2002, Kurt Wüthrich was awarded the Nobel Prize in Chemistry for demonstrating that the NOE could be exploited using two-dimensional NMR spectroscopy to determine the three-dimensional structures of biological macromolecules in solution.[2]

Some examples of two-dimensional NMR experimental techniques exploiting the NOE include nuclear Overhauser effect spectroscopy (NOESY), heteronuclear Overhauser effect spectroscopy (HOESY), rotational frame nuclear Overhauser effect spectroscopy (ROESY), transferred nuclear Overhauser effect (TRNOE), and double pulsed field gradient spin echo NOE (DPFGSE-NOE). NOESY is the determination of the relative orientations of atoms in a molecule, producing a three-dimensional structure. HOESY is NOESY cross-correlation between atoms of different elements. ROESY involves spin-locking the magnetization to prevent it from going to zero, applied for molecules for which regular NOESY is not applicable. TRNOE measures the NOE between two different molecules interacting in the same solution, as in a ligand binding to a protein.[3] In a DPFGSE-NOE experiment, a transient experiment that allows for suppression of strong signals and thus detection of very small NOEs.

NOE volumes in NOESY experiments can be used to measure interatomic distances. The distance between two atoms ${\displaystyle i}$ and ${\displaystyle j}$ can be calculated based on measured NOE volumes ${\displaystyle V}$ and a scaling constant ${\displaystyle c}$

${\displaystyle r_{\text{NOE}}=\left({\frac {c}{V_{ij}}}\right)^{1/6}}$

where ${\displaystyle c}$ can be determined based on measurements of known fixed distances. The range of distances can be reported based on known distances and volumes in the spectrum, which gives a mean ${\displaystyle c}$ and a standard deviation ${\displaystyle c_{SD}}$, a measurement of 20 areas in the NOESY spectrum showing no peaks, i.e. noise ${\displaystyle V_{err}}$, and a measurement error ${\displaystyle m_{v}}$. The parameter ${\displaystyle x}$ is set so that all known distances are within the error bounds. This shows that the lower range of the NOESY volume can be shown

${\displaystyle r_{\text{NOE lower}}=\left({\frac {c-xc_{SD}}{{\frac {1}{m_{v}}}V_{ij}+V_{err}}}\right)^{1/6}}$

and that the upper bound is

${\displaystyle r_{\text{NOE higher}}=\left({\frac {c+xc_{SD}}{{\frac {1}{m_{v}}}V_{ij}-V_{err}}}\right)^{1/6}}$

Such "fixed distances" will depend on the system studied. For example, Locked Nucleic Acids have many atoms whose distance varies very little in the sugar, which allows estimation of the glycosidic torsion angles, which allowed NMR to benchmark LNA molecular dynamics predictions.[4] RNAs, however, have sugars that are much more conformationally flexible, and require wider estimations of low and high bounds.[5]

## History

The theoretical basis for the NOE was described and experimentally verified by Anderson and Freeman in 1962.[6] The NOE is an extension of the seminal work of American physicist Albert Overhauser who in 1953 proposed that nuclear spin polarization could be enhanced by the microwave irradiation of the conduction electrons in certain metals.[7] The general Overhauser effect was first demonstrated experimentally by T. R. Carver and C. P. Slichter, also in 1953.[8] Another early explanation and experimental observation of the NOE was by Kaiser in 1963 [9] in an NMR experiment where the spin polarization was transferred from one population of nuclear spins to another, rather than from electron spins to nuclear spins. However, the theoretical basis and the applicable Solomon equations[10] had already been published by Ionel Solomon in 1955.[11] Soon after its discovery, NOE was applied to the elucidation of structures of organic compounds.[12]

## References

1. ^ Horst Friebolin "Basic One- and Two-Dimensional NMR Spectroscopy", 5th Edition, 2010, Wiley-VCH, Weinhiem. ISBN 978-3-527-32782-9.
2. ^ "The Nobel Prize in Chemistry 2002". Nobelprize.org. Retrieved 2011-03-24.
3. ^ Ni, Feng; Scheraga, Harold A. (1994). "Use of the Transferred Nuclear Overhauser Effect To Determine the Conformations of Ligands Bound to Proteins". Accounts of Chemical Research. 27 (9): 257–264. ISSN 0001-4842. doi:10.1021/ar00045a001.
4. ^ David E. Condon; Ilyas Yildirim; Scott D. Kennedy; Brendan C. Mort; Ryszard Kierzek; Douglas H. Turner (December 2013). "Optimization of an AMBER Force Field for the Artificial Nucleic Acid, LNA, and Benchmarking with NMR of L(CAAU)". J. Phys. Chem. B. 118 (5): 1216–1228. doi:10.1021/jp408909t.
5. ^ Condon DE, Kennedy SD, Mort BC, Kierzek R, Yildirim I, Turner DH (June 2015). "Stacking in RNA: NMR of Four Tetramers Benchmark Molecular Dynamics". Journal of Chemical Theory and Computation. 11 (6): 2729–2742. PMC . PMID 26082675. doi:10.1021/ct501025q.
6. ^ Anderson, W. A.; Freeman, R. (1962). "Influence of a Second Radiofrequency Field on High-Resolution Nuclear Magnetic Resonance Spectra". The Journal of Chemical Physics. 37 (1): 411–5. Bibcode:1962JChPh..37...85A. doi:10.1063/1.1732980.
7. ^ Overhauser, Albert W. (1953). "Polarization of Nuclei in Metals". Physical Review. 92 (2): 411–5. Bibcode:1953PhRv...92..411O. doi:10.1103/PhysRev.92.411.
8. ^ Carver, T. R.; Slichter, C. P. (1953). "Polarization of Nuclear Spins in Metals". Physical Review. 92 (1): 212–213. Bibcode:1953PhRv...92..212C. doi:10.1103/PhysRev.92.212.2.
9. ^ Kaiser, R. (1962). "Use of the Nuclear Overhauser Effect in the Analysis of High‐Resolution Nuclear Magnetic Resonance Spectra". The Journal of Chemical Physics. 39 (1): 2435. Bibcode:1963JChPh..39.2435K. doi:10.1063/1.1734045.
10. ^ The Solomon Equations and NOE. chem.iitm.ac.in
11. ^ Solomon, I (1955). "Relaxation Processes in a System of Two Spins" (PDF). Phys. Rev. 99: 559. Bibcode:1955PhRv...99..559S. doi:10.1103/PhysRev.99.559.
12. ^ Anet, F. A. L.; Bourn, A. J. R (1965). "Nuclear Magnetic Resonance Spectral Assignments from Nuclear Overhauser Effects". Journal of the American Chemical Society. 87 (22): 5250–5251. doi:10.1021/ja00950a048.