Protein structural analysis from solid-state NMR-derived orientational constraints.

High-resolution orientational constraints from solid-state NMR spectroscopy of uniformly aligned biological macromolecules provide a great structural analysis problem. Several approaches to this problem have been made in the past. Here a vector algebra method is developed that provides analytical solutions for the torsion angles and a concise and simple view of the structural possibilities. Numerical instabilities in this approach are easily predicted. Insight into how the structural ambiguities arise in the first place and how they can be reduced in number is demonstrated with this new approach.