Orientation-dependent NMR

A common characteristic of the relevant spin interactions is that they are anisotropic and can be described by second-rank tensors. The resulting orientation-dependent NMR frequency is of the following form [1,9] ... 

To extract information on molecular orientation distribution from experimental data, the most widely known technique, the Legendre moment expansion approach can be taken. In this section, this approach will be discussed first, followed by methods to elucidate atomic resolution details of the structures of ordered polymers with orientation-dependent NMR interactions, such as those from chemical shielding, dipole-dipole and quadrupolar coupling. Then, solid-state NMR studies of the torsion angles of the peptide backbone of highly ordered silk fibroin fiber, a protein that has been studied extensively as a model for fibrous proteins, will be described. 

The determination of polymer structure at the atomic level is possible by analyzing orientation-dependent NMR interactions such as dipole-dipole, quadrupole and chemical shielding anisotropy as mentioned above. The outline of the atomic coordinate determination for oriented protein fibers used here is described more fully in Ref. [30]. The chemical shielding anisotropy (CSA) interaction for N nucleus in an amide (peptide) plane can be interpreted with the chemical shielding tensor transformation as shown in Fig. 8.3. [31, 32]. 

The solid-state NMR approach on the basis of orientation-dependent NMR interactions such as chemical shielding anisotropy, dipole-dipole and quadru-... 

Im and coworkers use orientation-dependent NMR observables (ssNMR CSA DC, solution RDC) to restrain MD simulations aimed at refining the structure of the Pfl Coat Protein in Explicit Membranes. The used approach gives access to information not obtainable with only NMR data, such as a detailed description of the interaction of the side chains with other side chains or with the lipids, and the depth of the protein insertion in the membrane. In order to avoid conflicting structural results and to reach a converged structure in the simulations, it is found that restraints measured in very different environment should be avoided, i.e. NMR data obtained in micelles were found not to be proper to restrain the simulation in bilayers. 

Altogether, all major peaks in the proton NMR spectrum of human skeletal muscle - except the water resonance and IMCL signals - are orientation-dependent, either resulting from susceptibility or from dipolar coupling... 

The isotropic chemical shift is the average value of the diagonal elements of the chemical shift tensor. Advances in solid state NMR spectroscopy allow one to determine the orientation dependence, or anisotropy, of the chemical shift interaction. It is now possible to determine the principal elements of a chemical shift powder pattern conveniently, and the orientation of the principal axes with more effort. Hence, instead of settling for just the average value of the chemical shift powder pattern, one can now aim for values of the three principal elements and the corresponding orientations in a molecular axis system. 

Let us suppose now that we have a solid with all molecules aligned with one another (Fig. 2.3) and that we perform the NMR experiment on a single crystal. If g of the S manifold equals ge, the contact shift contribution will be independent of the crystal orientation in the magnetic field. If, however, g has a different value in any k direction, then spin-orbit coupling is not negligible and the contact shift will be orientation dependent. Specific calculations are needed. If, however, we arbitrarily neglect the anisotropy of J/ Sz rlr), the following equation can be written... 

In elastomer samples with macroscopic segmental orientation, the residual dipolar couplings are oriented as well, so that also the transverse relaxation decay depends on orientation. Therefore, the relaxation rate 1/T2 of a strained rubber band exhibits an orientation dependence, which is characteristic of the orientational distribution function of the residual dipolar interactions in the network. For perfect order the orientation dependence is determined by the square of the second Legendre polynomial [14]. Nearly perfect molecular order has been observed in porcine tendon by the orientation dependence of 1/T2 [77]. It can be concluded, that the NMR-MOUSE appears suitable to discriminate effects of macroscopic molecular order from effects of temperature and cross-link density by the orientation dependence of T2. 

---