Nuclear Overhauser effect (NOE) distance restraints are the main experimental data from protein nuclear magnetic resonance (NMR) spectroscopy for computing a complete three dimensional solution structure including sidechain conformations. In general, NOE restraints must be assigned before they can be used in a structure determination program. NOE assignment is very time-consuming to do manually, challenging to fully automate, and has become a key bottleneck for high-throughput NMR structure determination. The difficulty in automated NOE assignment is ambiguity: there can be tens of possible different assignments for an NOE peak based solely on its chemical shifts. Previous automated NOE assignment approaches rely on an ensemble of structures, computed from a subset of all the NOEs, to iteratively filter ambiguous assignments. These algorithms are heuristic in nature, provide no guarantees on solution quality or running time, and are slow in practice. In this paper we present an accurate, efficient NOE assignment algorithm. The algorithm first invokes the algorithm in [30, 29] to compute an accurate backbone structure using only two backbone residual dipolar couplings (RDCs) per residue. The algorithm then filters ambiguous NOE assignments by merging an ensemble of intra-residue vectors from a protein rotamer database, together with internuclear vectors from the computed backbone structure. The protein rotamer database was built from ultra-high resolution structures (<1.0 ˚A) in the Protein Data Bank (PDB). The algorithm has been successfully applied to assign more than 1,700 NOE distance restraints with better than 90% accuracy on the protein human ubiquitin using real experimentally-recorded NMR data. The algorithm as- signs these NOE restraints in less than one second on a single-processor workstation.

We develop an iterative relaxation algorithm, called RIBRA, for NMR protein backbone assignment. RIBRA applies nearest neighbor and weighted maximum independent set algorithms to solve the problem. To deal with noisy NMR spectral data, RIBRA is executed in an iterative fashion based on the quality of spectral peaks. We first produce spin system pairs using the spectral data without missing peaks, then the data group with one missing peak, and finally, the data group with two missing peaks. We test RIBRA on two real NMR datasets: hbSBD and hbLBD, and perfect BMRB data (with 902 proteins) and four synthetic BMRB data which simulate four kinds of errors. The accuracy of RIBRA on hbSBD and hbLBD are 91.4 % and 83.6%, respectively. The average accuracy of RIBRA on perfect BMRB datasets is 98.28%, and 98.28%, 95.61%, 98.16 % and 96.28 % on four kinds of synthetic datasets, respectively.

The constrained bipartite matching (CBM) problem is a variant of the classical bipartite matching problem that has been well studied in the Combinatorial Optimization community. The input to CBM is an edge-weighted complete bipartite graph in which there are a same number of vertices on both sides and vertices on one side are sequentially ordered while vertices on the other side are partitioned and connected into disjoint directed paths. In a feasible matching a path must be mapped to consecutive vertices on the other side. The optimization goal is to find a maximum or a minimum weight perfect matching. Such an optimization problem has its applications to scheduling and protein Nuclear Magnetic Resonance peak assignment. It has been shown to be NP-hard and MAX SNP-hard if the perfectness requirement is dropped. In this paper, more results on the inapproximability are presented and IDA*, a memory efficient variant of the well known A * search algorithm, is utilized to solve the problem. Accordingly, search heuristics and a set of heuristic evaluation functions are developed to assist the search, whose effectiveness is demonstrated by a simulation study using real protein NMR backbone resonance assignment instances.

Nuclear Overhauser effect (NOE) distance restraints are the main experimental data from protein nuclear magnetic resonance (NMR) spectroscopy for computing a complete three dimensional solution structure including sidechain conformations. In general, NOE restraints must be assigned before they can be used in a structure determination program. NOE assignment is very time-consuming to do manually, challenging to fully automate, and has become a key bottleneck for high-throughput NMR structure determination. The difficulty in automated NOE assignment is ambiguity: there can be tens of possible different assignments for an NOE peak based solely on its chemical shifts. Previous automated NOE assignment approaches rely on an ensemble of structures, computed from a subset of all the NOEs, to iteratively filter ambiguous assignments. These algorithms are heuristic in nature, provide no guarantees on solution quality or running time, and are slow in practice. In this paper we present an accurate, efficient NOE assignment algorithm. The algorithm first invokes the algorithm in [30, 29] to compute an accurate backbone structure using only two backbone residual dipolar couplings (RDCs) per residue. The algorithm then filters ambiguous NOE assignments by merging an ensemble of intra-residue vectors from a protein rotamer database, together with internuclear vectors from the computed backbone structure. The protein rotamer database was built from ultra-high resolution structures (&lt;1.0 ˚A) in the Protein Data Bank (PDB). The algorithm has been successfully applied to as-