Nuclear magnetic resonance (NMR) spectroscopy allows scientists to study protein structure, dynamics and interactions in solution. A necessary first step for such applications is determining the resonance assignment, mapping spectral data to atoms and residues in the primary sequence. Automated resonance assignment algorithms rely on information regarding connectivity (e.g., through-bond atomic interactions) and amino acid type, typically using the former to determine strings of connected residues and the latter to map those strings to positions in the primary sequence. Significant ambiguity exists in both connectivity and amino acid type information. This paper focuses on the information content available in connectivity alone and develops a novel random-graph theoretic framework and algorithm for connectivity-driven NMR sequential assignment. Our random graph model captures the structure of chemical shift degeneracy, a key source of connectivity ambiguity. We then give a simple and natural randomized algorithm for finding optimal assignments as sets of connected fragments in NMR graphs. The algorithm naturally and efficiently reuses substrings while exploring connectivity choices; it overcomes local ambiguity by enforcing global consistency of all choices. By analyzing our algorithm under our random graph model, we show that it can provably tolerate relatively large ambiguity while still giving expected optimal performance in polynomial time. We present results from practical applications of the algorithm to experimental datasets from a variety of proteins and experimental set-ups. We demonstrate that our approach is able to overcome significant noise and local ambiguity in identifying significant fragments of sequential assignments. Key words: nuclear magnetic resonance (NMR) spectroscopy, automated sequential resonance assignment, random graph model, randomized algorithm, Hamiltonian path. 1.

Motivation: In the light of several ongoing structural genomics projects, faster and more reliable methods for structure calculation from NMR data are in great demand. The major bottleneck in the determination of solution NMR structures is the assignment of NOE peaks (nuclear Overhauser effect). Due to the high complexity of the assignment problem, most NOEs cannot be directly converted into unambiguous inter-proton distance restraints. Results: We present version 1.2 of our program ARIA (Ambiguous Restraints for Iterative Assignment) for automated assignment of NOE data and NMR structure calculation. We summarize recent progress in correcting for spin diffusion with a relaxation matrix approach, representing non-bonded interactions in the force field and refining final structures in explicit solvent. We also discuss book-keeping, data exchange with spectra assignment programs and deposition of the analysed experimental data to the databases. Availability: ARIA 1.2 is available from:

Motivation: Complementing its traditional role in structural studies of proteins, nuclear magnetic resonance (NMR) spectroscopy is playing an increasingly important role in functional studies. NMR dynamics experiments characterize motions involved in target recognition, ligand binding, etc., while NMR chemical shift perturbation experiments identify and localize protein-protein and protein-ligand interactions. The key bottleneck in these studies is to determine the backbone resonance assignment, which allows spectral peaks to be mapped to specific atoms. This paper develops a novel approach to address that bottleneck, exploiting an available x-ray structure or homology model to assign the entire backbone from a set of relatively fast and cheap NMR experiments. Results: We formulate contact replacement for resonance assignment as the problem of computing correspondences between a contact graph representing the structure and an NMR graph representing the data; the NMR graph is a significantly corrupted, ambiguous version of the contact graph. We first show that by combining connectivity and amino acid type information, and exploiting the random structure of the noise, one can provably determine unique correspondences in polynomial time with high probability, even in the presence of significant noise (a constant number of noisy edges per vertex). We then detail an efficient randomized algorithm and show that, over a variety of experimental and synthetic datasets, it is robust to typical levels of structural variation (1–2 ˚A), noise (250–600%) and missings (10–40%). Our algorithm achieves very good overall assignment accuracy, above 80 % in α-helices, 70 % in β-sheets, and 60% in loop regions. Availability: Our contact replacement algorithm is implemented in platform-independent Python code. The software can be freely obtained for academic use by request from the authors.

Summary: Modern structural genomics projects demand for integrated methods for the interpretation and storage of nuclear magnetic resonance (NMR) data. Here we present version 2.1 of our program ARIA (Ambiguous Restraints for Iterative Assignment) for automated assignment of nuclear Overhauser enhancement (NOE) data and NMR structure calculation. We report on recent developments, most notably a graphical user interface, and the incorporation of the object-oriented data model of the Collaborative Computing Project for NMR (CCPN). The CCPN data model defines a storage model for NMR data, which greatly facilitates the transfer of data between different NMR software packages. Availability: A distribution with the source code of ARIA 2.1 is freely available at

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We report a new residual dipolar couplings (RDCs) based NMR procedure for rapidly determining RNA tertiary structure demonstrated on a uniformly 15 N / 13 C-labeled 27 nt variant of the trans-activation response element (TAR) RNA from HIV-I. In this procedure, the time-consuming nuclear Overhauser enhancement (NOE)-based sequential assignment step is replaced by a fully automated RDC-based assignment strategy. This approach involves examination of all allowed sequence-specific resonance assignment permutations for best-fit agreement between measured RDCs and coordinates for sub-structures in a target RNA. Using idealized A-form geometries to model Watson–Crick helices and coordinates from a previous X-ray structure to model a hairpin loop in TAR, the best-fit RDC assignment solutions are determined very rapidly (,five minutes of computational time) and are in complete agreement with corresponding NOE-based assignments. Orientational constraints derived from RDCs are used simultaneously to assemble sub-structures into an RNA tertiary conformation. Through enhanced speeds of application and reduced reliance on chemical shift dispersion, this RDC-based approach lays the foundation for rapidly determining RNA conformations in a structural genomics context, and may increase the size limit of RNAs that can be examined by NMR.