On the properties of residual dipolar coupling alignment tensors: Simulations illuminate how residual dipolar couplings depend on the relative orientations of the magnetic field, the director of the alignment phase and the bond vectors

The measurement of residual dipolar couplings (RDCs) exhibited by samples prepared in suitable alignment media can help in the elucidation of macromolecular structures. For any dipolar interactions that are not averaged to zero by molecular reorientations RDCs provide information about the possible orientations of the averaged interactions to the magnetic field. As such they contain information about the permitted relative positions of different motionally averaged bond vectors. This situation is often induced using nematic liquid crystalline phases with which the macromolecule under study interacts. While a single set of RDC measurements does not produce unique solutions for the orientation of each bond, multiple independent RDC datasets can be combined to restrict each bond to two diametrically opposed orientations. Attempts to obtain such datasets have primarily focused on performing experiments with multiple alignment media that interact with the macromolecule of interest in a different way. Other work has attempted to control the orientation of the media itself relative to that of the magnetic field. The latter has been explored using pre-formed gels and might also be potentially realized using the application of different external fields during signal acquisition. This article seeks to clarify which approaches might generate independent RDC datasets and their utility in further restricting possible bond orientations using pictorial representations of simulated data.