Distributed torsion angle grid search in high dimensions: a systematic approach to NMR structure determination

Two complementary approaches for systematic search in torsion angle space are described for the generation of all conformations of polypeptides which satisfy experimental NMR restraints, hard-sphere van der Waals radii, and rigid covalent geometry. The first procedure is based on a recursive, tree search algorithm for the examination of linear chains of torsion angles, and uses a novel treatment to propagate the search results to neighboring regions so that the structural consequences of the restraints are fully realized. The second procedure is based on a binary combination of torsion vector spaces for connected submolecules, and produces intermediate results in Cartesian space for a more robust restraint analysis. Restraints for NMR applications include bounds on torsion angles and internuclear distances, including relational and degenerate restraints involving equivalent and nonstereoassigned protons. To illustrate these methods, conformation search results are given for the tetrapeptide APGA restrained to an idealized beta-turn conformation, an alanine octapeptide restrained to a right-handled helical conformation, and the structured region of the peptide SYPFDV.