Internuclear vector dipolar coupling

Dipolar couplings are very powerful restraints for structure determination of biomolecules and the determination of protein-protein or protein-ligand interactions [16]. They depend on the orientation of an internuclear vector, and its distance and the angular dependence is given by the following formula ... 

Fig. 4. For axially symmetric alignment, a single measured residual dipolar coupling is consistent with orientations of the corresponding internuclear vector, r, which deviate from the principal (z) axis of the order tensor by an angle , thus describing the surface of a cone, and its inverse. If alignment departs from axial symmetry, then the cone of permissible orientations will require further description in terms of an azimuth angle and exhibit some distortion along the x and directions.

RDC data can allow the five averages (i.e., the elements of r1- in Eq. (23)) describing each dipolar interaction tensor to be determined, and subsequently interpreted in terms of mean internuclear vector orientations and an associated description of dynamics. To date, there are a couple of different approaches which have been introduced for the analysis and interpretation of RDCs acquired in multiple alignment media. 

Figure 7.7 Fast but anisotropic segmental motion results in a solid-like contribution to the NMR signal. This contribution is expressed in terms of a fractional contribution q of the second moment M2 of the rigid lattice line of a single chain or residual dipolar interactions between protons. The line splitting caused by the dipole-dipole interaction depends on the orientation angle q of the internuclear vector of the coupling protons in the magnetic field B(). The distribution of orientation angles changes with the...

D is the dipolar coupling (cartesian) tensor, which although not necessarily diagonal in the axis system shown in figure 8.52, can be made so by choosing the z axis to lie along the internuclear vector R... 

The extent of this is dependent upon factors including the species involved and the internuclear distance between them. In a strong magnetic field, the dipolar coupling is dependent upon the orientation of the internuclear vector with the external magnetic field such that ... 

The anisotropic heteronuclear dipole-dipole interaction is a function of not only the distance between two nuclei but also the orientation of the internuclear vector with respect to Bq. Therefore, the dipolar coupling values directly provide geometrical parameters that can be translated into molecular conformations. For example, H- N, C- N, and H- C dipolar couplings are commonly used to determine the relative orientations of the chemical bonds, which are converted into the conformation and/or the topology of molecules using NMR methods.5 5" ... 

There are occasional cases in nature in which the internuclear vectors are already lined up. One example is oriented samples of fatty acids such as oleic acid. These molecules can be made into (oleic acidVDgO bilayers and oriented by glass plates. They are already rapidly tumbling about their axes and diffusing parallel to the surface of the plates. The rapid diffusion averages out intermolecular dipolar coupling... 

When the presence of both these interactions is taken into account, it is found that the appropriate truncated dipolar Hamiltonian must be expanded to include additional terms whose angular dependence corresponds to the C and D terms of the classical dipolar Hamiltonian (221. These terms contain the Euler angles a and pD which orient the internuclear vector in the coordinate system, which determines the dipolar coupling for the specific sites of interest. This is... 

The dependence of the dipolar couplings on the orientation of the internuclear vector in the principle axis system of the electric field gradient has Inherent information about the molecular geometry of the relevant and sites. For example, in a peptide bond, where two carbons are bound to the same nitrogen, the dipolar coupling of each depends on the orientation of its respective internuclear vector with respect to the common coordinate system of the nitrogen electric field gradient principle axis system. Thus, the NMR spectrum is analyzed in terms of the relative orientation of the internuclear vectors, In principle, this can lead to an independent determination of the conformation of the peptide bond. 

NMR residual dipolar couplings (RDCs), in the form of the projection angles between the respective internuclear bond vectors, have been used by Haliloglu et as structural restraints in the ab initio structure prediction of a test set of six proteins. The restraints have been applied using a recently developed SICHO (5/de CHain Only) lattice protein model that employs a replica exchange Monte Carlo algorithm to search conformational space. The proteins studied were ACP (77 residues), rubredoxin (53 residues), NSl, a 73 residue RNA binding/dimeriz-ation domain, Nodf (35 residues), Crd (137 residues) and Bret domain with 92 residues. 

The direct dipolar interaction, also known as direct dipole-dipole coupling, is a through-space interaction between the magnetic dipole moments of the two spins, I and S. Like the quadrupolar and the CS interaction, the dipolar interaction is anisotropic and depends on the orientation of the internuclear vector between two spins with respect to the direction of external magnetic field. The strength of the dipolar interaction increases... 

In the last decades a series of homonuclear and heteronuclear recoupling experiments have been developed that combine a 2D approach with fast MAS and dipolar multiple-quantum NMR spectroscopy. In this way, the chemical shift resolution of different chemical environments allows sites of interest to be distinguished and fully identified, and then it is possible to obtain structural information since dipole-dipole couplings are sensitive to the distances between the coupled nuclei as well as to the orientation of the internuclear vector. 

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