, Volume 29, Issue 2, pp 111-138

An expectation/maximization nuclear vector replacement algorithm for automated NMR resonance assignments

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We report an automated procedure for high-throughput NMR resonance assignment for a protein of known structure, or of an homologous structure. Our algorithm performs Nuclear Vector Replacement (NVR) by Expectation/Maximization (EM) to compute assignments. NVR correlates experimentally-measured NH residual dipolar couplings (RDCs) and chemical shifts to a given a priori whole-protein 3D structural model. The algorithm requires only uniform 15N-labelling of the protein, and processes unassigned HN-15N HSQC spectra, HN-15N RDCs, and sparse HN-HN NOE's (d NNs). NVR runs in minutes and efficiently assigns the (HN,15N) backbone resonances as well as the sparse d NNs from the 3D 15N-NOESY spectrum, in O(n 3) time. The algorithm is demonstrated on NMR data from a 76-residue protein, human ubiquitin, matched to four structures, including one mutant (homolog), determined either by X-ray crystallography or by different NMR experiments (without RDCs). NVR achieves an average assignment accuracy of over 99%. We further demonstrate the feasibility of our algorithm for different and larger proteins, using different combinations of real and simulated NMR data for hen lysozyme (129 residues) and streptococcal protein G (56 residues), matched to a variety of 3D structural models. Abbreviations: NMR, nuclear magnetic resonance; NVR, nuclear vector replacement; RDC, residual dipolar coupling; 3D, three-dimensional; HSQC, heteronuclear single-quantum coherence; HN, amide proton; NOE, nuclear Overhauser effect; NOESY, nuclear Overhauser effect spectroscopy; d NN, nuclear Overhauser effect between two amide protons; MR, molecular replacement; SAR, structure activity relation; DOF, degrees of freedom; nt., nucleotides; SPG, Streptococcal protein G; SO(3), special orthogonal (rotation) group in 3D; EM, Expectation/Maximization; SVD, singular value decomposition.