Nuclear 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.
The NOE is useful in NMR spectroscopy for assigning structures. 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.
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. 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 and can be calculated based on measured NOE volumes and a scaling constant
where 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 and a standard deviation , a measurement of 20 areas in the NOESY spectrum showing no peaks, i.e. noise , and a measurement error . The parameter 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
and that the upper bound is
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. RNAs, however, have sugars that are much more conformationally flexible, and require wider estimations of low and high bounds.
The theoretical basis for the NOE was described and experimentally verified by Anderson and Freeman in 1962. 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. The general Overhauser effect was first demonstrated experimentally by T. R. Carver and C. P. Slichter, also in 1953. Another early explanation and experimental observation of the NOE was by Kaiser in 1963  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 had already been published by Ionel Solomon in 1955. Soon after its discovery, NOE was applied to the elucidation of structures of organic compounds.
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