16-Fold Degeneracy of Peptide Plane Orientations from Residual Dipolar Couplings: Analytical Treatment and Implications for Protein Structure Determination

摘要

Residual dipolar couplings (RDCs) measured for internally rigid molecular fragments provide important information about the relative orientations of these fragments. Dependent on the symmetry of the alignment tensor and the symmetry of the molecular fragment, however, there generally exists more than one solution for the fragment orientation that is consistent with the measured RDCs. Analytical solutions are presented that describe the complete set of orientations of internally rigid fragments that are consistent with multiple dipolar couplings measured in a single alignment medium that is rhombic. For the first time, it is shown that for a planar fragment, such as the peptide plane, there generally exist 16 different solutions with their analytical expressions presented explicitly. The presence of these solutions is shown to be highly relevant for standard structure determination protocols using RDCs to refine molecular structures. In particular, when using standard protein structure refinement with RDCs that were measured in a single alignment medium as constraints, it is found that often more than one of the peptide plane solutions is physically viable, i.e. despite being consistent with measured RDCs, the local backbone structure can be incorrect. Based on experimental and simulated examples it is rationalized why protein and nucleic acid structures that are refined against RDCs measured in a single medium can have lower resolution (precision) than one would expect based on the experimental accuracy of the RDCs. Conditions are discussed under which the correct solution can be identified.