The nuclear overhauser effect (or NOE) is a special case of nuclear relaxation in nuclear magnetic resonance (NMR) spectroscopy and magnetic resonance imaging (MRI). In a typical NMR or MRI experiment, a nucleus in a magnetic field absorbs photons of a frequency mostly determined by the elemental identity of the nucleus (e.g. hydrogen, carbon etc.) and the strength of the applied magnetic field (see Zeeman effect.) Nuclei so treated are said to be in an excited nuclear spin state, and they literally spin like a top in said magnetic field. They can be observed by the current their spinning generates in wire coils looped around the sample compartment, be it an NMR tube or the huge cavernous opening in an MRI device.

But they don't spin forever. One nucleus in an excited spin state can transfer its magnetization to another nucleus in a process called dipolar coupling. The rate at which this happens between a given pair of nuclei is inversely proportional to the cube of the distance between. It's also a complicated function of the angle between the line formed by the two atoms and the external magnetic field. Since most NMR experiments are performed in solution, and most MRI experiments involve observation of the protons on water molecules in a solution-like environment, this angle varies considerably during the time course of the experiment, as the molecules being observed are moving and spinning all over the place. This is called isotropic rotational averaging, and under these conditions the rate of magnetization transfer is independent of the angle between the magnetic field and the internuclear vector, but inversely proportional to the sixth power of the distance between them. Magnetization transfer by dipolar coupling under the conditions of isotropic rotational averaging is called the nuclear overhauser effect. This is the principal pathway by which any nucleus being observed in solution loses its magnetization, thus it is the main factor contributing to nuclear relaxation. Note that the magnitude of both the NOE and dipolar coupling are independent of the nature of the intervening medium, they are through-space interactions, as opposed to through-bond interactions like J-coupling.

This may seem pretty esoteric but in fact it forms the basis, along with J-coupling, for the determination of protein, DNA and RNA structures and their interactions with other molecules. One merely excites some particular nucleus, waits a period of time, and observes where the magnetization has been transferred. Because of the aforementioned distance dependence of the magnetization transfer, this allows the 3-dimensional mapping of the molecule when the experiment is repeated for a sufficient percentage of the nuclei in a molecule. The method of NMR has overtaken that of x-ray crystallography as the method of choice for rational drug design not because of its ability to determine structures, but because the nuclear overhauser effect allows one to quickly and easily observe the interaction of these biomolecules with small molecule drug candidates.

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