Simultaneous determination of subunit and complex structures of symmetric homo-oligomers from ambiguous NMR data

Determining the structures of symmetric homo-oligomers provides critical insights into their roles in numerous vital cellular processes. Structure determination by nuclear magnetic resonance spectroscopy typically pieces together a structure based primarily on interatomic distance restraints, but for symmetric homo-oligomers each restraint may involve atoms in the same subunit or in different subunits, as the different homo-oligomeric "copies" of each atom are indistinguishable without special experimental approaches. This paper presents a novel method that simultaneously determines the structure of the individual subunits and their arrangement into a complex structure, so as to best satisfy the distance restraints under a consistent (but partial) disambiguation. Recognizing that there are likely to be multiple good solutions to this complex problem, our method provides a guarantee of completeness to within a user-specified resolution, generating representative backbone structures for the secondary structure elements, such that any structure that satisfies sufficiently many experimental restraints is sufficiently close to a representative. Our method employs a branch-and-bound algorithm to search a configuration space representation of the subunit and complex structure, identifying regions containing the structures that are most consistent with the data. We apply our method to three test cases with experimental data and demonstrate that it can handle the difficult configuration space search problem and substantial ambiguity, effectively pruning the configuration spaces and characterizing the actual diversity of structures supported by the data.