*Bioinformatics*, 2006, 22:172-80. [paper]

**Motivation:** Backbone resonance assignment is a critical bottleneck in studies of protein structure, dynamics, and interactions by nuclear magnetic resonance (NMR) spectroscopy. A minimalist approach to assignment, which we call "contact-based," seeks to dramatically reduce experimental time and expense by replacing the standard suite of through-bond experiments with the through-space (NOESY) experiment. In the contact-based approach, spectral data are represented in a graph with vertices for putative residues (of unknown relation to the primary sequence) and edges for hypothesized NOESY interactions, such that observed spectral peaks could be explained if the residues were "close enough." Due to experimental ambiguity, several incorrect edges can be hypothesized for each spectral peak. An assignment is derived by identifying consistent patterns of edges (e.g., for alpha-helices and beta-sheets) within a graph, and mapping the vertices to the primary sequence. The key algorithmic challenge is to be able to uncover these patterns even when they are obscured by significant noise.

**Results:** This paper develops, analyzes, and applies a novel algorithm for the identification of polytopes representing consistent patterns of edges in a corrupted NOESY graph. Our randomized algorithm aggregates simplices into polytopes and fixes inconsistencies with simple local modifications, called rotations, that maintain most of the structure already uncovered. In characterizing the effects of experimental noise, we employ an NMR-specific random graph model in proving that our algorithm gives optimal performance in expected polynomial time, even when the input graph is significantly corrupted. We confirm this analysis in simulation studies with graphs corrupted by up to 500 percent noise. Finally, we demonstrate the practical application of the algorithm on several experimental beta-sheet data sets. Our approach is able to eliminate a large majority of noise edges and uncover large consistent sets of interactions.