*Protein Science*, 2007, 16:69-81. [preprint] [paper]

Assignment of nuclear Overhauser effect (NOE) data is a key bottleneck in structure determination by nuclear magnetic resonance spectroscopy. NOE assignment resolves the ambiguity as to which pairs of protons generated the observed NOE peaks, and thus should be restrained in structure determination. In the case of inter-subunit NOEs in symmetric homo-oligomers, the ambiguity includes both the identities of the protons within a subunit, and the identities of the subunits to which they belong. This paper develops an algorithm to resolve ambiguity in inter-subunit NOE assignment and determine symmetric homo-oligomeric structures. Our algorithm is *complete*, in that it identifies structures representing, to within a user-defined similarity level, every structure consistent with the available data (ambiguous or not). However, while our approach is complete, it avoids explicit enumeration of the exponential number of combinations of possible assignments.

In order to be complete yet efficient, we employ a configuration space framework. This allows us to represent the set of all possible structures in terms of symmetry axis parameters and all possible assignments of the NOEs in terms of atom and subunit identities. Our algorithm considers NOEs sequentially, i.e., one after the other, pruning regions of the symmetry axis configuration space and assignments that are mutually inconsistent. Pruning occurs only due to provable inconsistency and thereby avoids the pitfall of local minima that could arise from best-first sampling-based approaches. Ultimately, we return a mutually-consistent set of conformations and NOE assignments. Our algorithm can draw two types of conclusions not possible under existing methods: (a) that different assignments for an NOE would lead to different structural classes, or (b) that it is not necessary to assign an NOE since the choice of assignment would have little impact on structural precision. We demonstrate the effectiveness of our algorithm on two test cases: the homo-dimeric topological specificity domain of *E. coli* MinE and the homo-trimeric coiled-coil domain of chicken cartilage matrix protein (CCMP). Our method reduces the average number of possible assignments per NOE by a factor of 2.6 for MinE and 4.2 for CCMP. It results in high structural precision, reducing the average variance in atomic positions by a factor of 1.5 for MinE and 3.6 for CCMP.