Nuclear Overhauser effect distance dependence

H is particularly important in NMR experiments because of its high sensitivity and natural abundance. For macromolecules, 1H NMR spectra can become quite complicated. Even a small protein has hundreds of 1H atoms, typically resulting in a one-dimensional NMR spectrum too complex for analysis. Structural analysis of proteins became possible with the advent of two-dimensional NMR techniques (Fig. 3). These methods allow measurement of distance-dependent coupling of nuclear spins in nearby atoms through space (the nuclear Overhauser effect (NOE), in a method dubbed NOESY) or the coupling of nuclear spins in atoms connected by covalent bonds (total correlation spectroscopy, or TOCSY). 

We have investigated peptides whose structures were known beforehand from NMR or x-ray spectroscopy and related these structures to 2D-IR spectroscopy. Ultimately, one would like to deduce the structure of an unknown sample from a 2D-IR spectrum. In the case of 2D NMR spectroscopy, two different phenomena are actually needed to determine peptide structures. Essentially, correlation spectroscopy (COSY) is utilized in a first step to assign protons that are adjacent in the chemical structure of the peptide so that J coupling gives rise to cross peaks in these 2D spectra. However, this through-bond effect cannot be directly related to the three-dimensional structure of the sample, since that would require quantum chemistry calculations, which presently cannot be performed with sufficient accuracy. The nuclear Overhauser effect (NOE), which is an incoherent population transfer process and has a simple distance dependence, is used as an additional piece of information in order to measure the distance in... 

Dipole-dipole relaxation occurs when two nuclei are located close together and are moving at an appropriate relative rate (Section 5-1). Irradiation of one of these nuclei with a Bi field alters the Boltzmann population distribution of the other nucleus and therefore perturbs the inten.sity of its resonance. No J coupling need be present between the nuclei. The original phenomenon was discovered by Overhauser, but between nuclei and unpaired electrons. The nuclear Overhauser effect (when both spins are of nuclei) was observed first by Anet and Bourn and is of more interest to the chemist. It has great structural utility, because the dipole-dipole mechanism for relaxation depends on the distance between the two spins. (See eq. 5-1.)... 

Most of protein structural information from NMR is obtained in the form of nuclear Overhauser effects or NOEs between pairs of protons that are less than 6 A apart through space. An NOE between a spin pair carries distance information, but only short distances are observed because NOEs have an inverse sixth power dependence on distance. However, the distance cannot be uniquely determined given a measured NOE intensity without making some assumption about the environment of the spin pair and the motion of the vector between them. The simplest model for obtaining a distance from cross peak intensities in a nuclear Overhauser effect spectrum (NOESY) is the isolated ri d spin pair (RRNN - rigid rotor nearest neither) approximation (Jardetzky and Roberts, 1981). In this approximation the observed cross peak intensity, which is proportional to the cross relaxation rate, is related to a sini e intemudear distance, r. 

Plainly, there will be no such effect unless relaxation pathways. It will be seen later on that such pathways are only present when there is dipolar relaxation between the two spins and that the resulting cross-relaxation rate constants have a strong dependence on the distance between the two spins. The observation of a nuclear Overhauser effect is therefore diagnostic of dipolar relaxation and hence the proximity of pairs of spins. The effect is of enormous value, therefore, in structure determination by NMR. 

The nuclear Overhauser effect (NOE), caused by dipole-dipole crossrelaxation, has great potential in the elucidation of the molecular structure and conformation (Noggle and Shirmer, 1971 Hall and Sanders, 1980). A homonuclear NOE can theoretically be as large as 50%, but is usually much smaller, and depends on the inverse sixth power of the distance between the nuclei, so that the relative magnitudes of enhancements reflect the spatial relationships of the atoms involved. 

NOE A valuable technique for determining the conformation of a molecule in solution is NOE (nuclear Overhauser effect). This is observed for any two nuclei in a molecule, say, Ha and Hb, that relax each other by the dipole-dipole mechanism. For this to be effective, the two nuclei need to be <2 A apart, again as a result of the r dependence shown in Eq. 10.10. Distance is the only criterion the two nuclei do not have to have a bond between them. 

In solution, the method of choice to study the three-dimensional structure of saccharides is NMR, through the parameters represented by chemical shifts, coupling constants, nuclear Overhauser effects (nOe), and also relaxation time measurements. Although the conformational dependence of the carbon chemical shifts is far from imderstood, coupling constants can be used to evaluate the magnitude of the torsion angles, and nOe measurements can provide estimations of distances between protons located in rather close proximity. In addition, relaxation time measurements give information on the mobility and the behavior of molecules in solution. 

A third type of information available from NMR comes from the nuclear Overhauser enhancement or NOE. This is a direct through-space interaction of two nuclei. Irradiation of one nucleus with a weak radio frequency signal at its resonant frequency will equalize the populations in its two energy levels. This perturbation of population levels disturbs the populations of nearby nuclei so as to enhance the intensity of absorbance at the resonant frequency of the nearby nuclei. This effect depends only on the distance between the two nuclei, even if they are far apart in the bonding network, and varies in intensity as the inverse sixth power of the distance. Generally the NOE can only be detected between protons (XH nuclei) that are separated by 5 A or less in distance. These measured distances are used to determine accurate three-dimensional structures of proteins and nucleic acids. 

NOESY (Nuclear Overhauser Enhancement Spectroscopy). This technique depends on the occurrence of dipolar cross-relaxation (Bodenhausen et al. 1984). This so-called nOe effect depends on the distance through space and is independent of direct bonding. In this way it is a powerful technique to establish the stereochemistry and conformation of molecules. In Fig. 6 the... 

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