Lincong Wang

A polynomial-time nuclear vector replacement algorithm for automated NMR resonance assignments.

High-throughput NMR structural biology can play an important role in structural genomics. We report an automated procedure for high-throughput NMR resonance assignment for a protein of known structure, or of a homologous structure. These assignments are a prerequisite for probing protein-protein interactions, protein-ligand binding, and dynamics by NMR. Assignments are also the starting point for structure determination and refinement. A new algorithm, called Nuclear Vector Replacement (NVR) is introduced to compute assignments that optimally correlate experimentally measured NH residual dipolar couplings (RDCs) to a given a priori whole-protein 3D structural model. The algorithm requires only uniform( 15)N-labeling of the protein and processes unassigned H(N)-(15)N HSQC spectra, H(N)-(15)N RDCs, and sparse H(N)-H(N) NOEs (d(NN)s), all of which can be acquired in a fraction of the time needed to record the traditional suite of experiments used to perform resonance assignments. NVR runs in minutes and efficiently assigns the (H(N),(15)N) backbone resonances as well as the d(NN)s of the 3D (15)N-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 assignment accuracy of 92-100%. We further demonstrate the feasibility of our algorithm for different and larger proteins, using NMR data for hen lysozyme (129 residues, 97-100% accuracy) and streptococcal protein G (56 residues, 100% accuracy), matched to a variety of 3D structural models. Finally, we extend NVR to a second application, 3D structural homology detection, and demonstrate that NVR is able to identify structural homologies between proteins with remote amino acid sequences using a database of structural models.

High-resolution protein structure determination starting with a global fold calculated from exact solutions to the RDC equations.

We present a novel structure determination approach that exploits the global orientational restraints from RDCs to resolve ambiguous NOE assignments. Unlike traditional approaches that bootstrap the initial fold from ambiguous NOE assignments, we start by using RDCs to compute accurate secondary structure element (SSE) backbones at the beginning of structure calculation. Our structure determination package, called rdc-Panda (RDC-based SSE PAcking with NOEs for Structure Determination and NOE Assignment), consists of three modules: (1) rdc-exact; (2) Packer; and (3) hana (HAusdorff-based NOE Assignment). rdc-exact computes the global optimal solution of backbone dihedral angles for each secondary structure element by exactly solving a system of quartic RDC equations derived by Wang and Donald (Proceedings of the IEEE computational systems bioinformatics conference (CSB), Stanford, CA, 2004a; J Biomol NMR 29(3):223–242, 2004b), and systematically searching over the roots, each of which is a backbone dihedral ϕ- or ψ-angle consistent with the RDC data. Using a small number of unambiguous inter-SSE NOEs extracted using only chemical shift information, Packer performs a systematic search for the core structure, including all SSE backbone conformations. hana uses a Hausdorff-based scoring function to measure the similarity between the experimental spectra and the back-computed NOE pattern for each side-chain from a statistically-diverse rotamer library, and drives the selection of optimal position-specific rotamers for filtering ambiguous NOE assignments. Finally, a local minimization approach is used to compute the loops and refine side-chain conformations by fixing the core structure as a rigid body while allowing movement of loops and side-chains. rdc-Panda was applied to NMR data for the FF Domain 2 of human transcription elongation factor CA150 (RNA polymerase II C-terminal domain interacting protein), human ubiquitin, the ubiquitin-binding zinc finger domain of the human Y-family DNA polymerase Eta (pol η UBZ), and the human Set2-Rpb1 interacting domain (hSRI). These results demonstrated the efficiency and accuracy of our algorithm, and show that rdc-Panda can be successfully applied for high-resolution protein structure determination using only a limited set of NMR data by first computing RDC-defined backbones.

A polynomial-time algorithm for de novo protein backbone structure determination from nuclear magnetic resonance data

We describe an efficient algorithm for protein backbone structure determination from solution Nuclear Magnetic Resonance (NMR) data. A key feature of our algorithm is that it finds the conformation and orientation of secondary structure elements as well as the global fold in polynomial time. This is the first polynomial-time algorithm for de novo high-resolution biomacromolecular structure determination using experimentally recorded data from either NMR spectroscopy or X-ray crystallography. Previous algorithmic formulations of this problem focused on using local distance restraints from NMR (e.g., nuclear Overhauser effect [NOE] restraints) to determine protein structure. This approach has been shown to be NP-hard, essentially due to the local nature of the constraints. In practice, approaches such as molecular dynamics and simulated annealing, which lack both combinatorial precision and guarantees on running time and solution quality, are used routinely for structure determination. We show that residual dipolar coupling (RDC) data, which gives global restraints on the orientation of internuclear bond vectors, can be used in conjunction with very sparse NOE data to obtain a polynomial-time algorithm for structure determination. Furthermore, an implementation of our algorithm has been applied to six different real biological NMR data sets recorded for three proteins. Our algorithm is combinatorially precise, polynomialtime, and uses much less NMR data to produce results that are as good or better than previous approaches in terms of accuracy of the computed structure as well as running time.

An efficient and accurate algorithm for assigning nuclear overhauser effect restraints using a rotamer library ensemble and residual dipolar couplings

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 (L. Wang, et. al., 2004) 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 /spl Aring/) 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 assigns these NOE restraints in less than one second on a single-processor workstation.

Analysis of a systematic search-based algorithm for determining protein backbone structure from a minimum number of residual dipolar couplings

We have developed an ab initio algorithm for determining a protein backbone structure using global orientational restraints on internuclear vectors derived from residual dipolar couplings (RDCs) measured in one or two different aligning media by solution nuclear magnetic resonance (NMR) spectroscopy. Specifically, the conformation and global orientations of individual secondary structure elements are computed, independently, by an exact solution, systematic search-based minimization algorithm using only 2 RDCs per residue. The systematic search is built upon a quartic equation for computing, exactly and in constant time, the directions of an internuclear vector from RDCs, and linear or quadratic equations for computing the sines and cosines of backbone dihedral (/spl phi/, /spl psi/) angles from two vectors in consecutive peptide planes. In contrast to heuristic search such as simulated annealing (SA) or Monte-Carlo (MC) used by other NMR structure determination algorithms, our minimization algorithm can be analyzed rigorously in terms of expected algorithmic complexity and the coordinate precision of the protein structure as a function of error in the input data. The algorithm has been successfully applied to compute the backbone structures of three proteins using real NMR data.

Large a polynomial-time nuclear vector replacement algorithm for automated NMR resonance assignments

High-throughput NMR structural biology can play an important role in structural genomics. We report an automated procedure for high-throughput NMR resonance assignment for a protein of known structure, or of an homologous structure. These assignments are a prerequisite for probing protein-protein interactions, protein-ligand binding, and dynamics by NMR. Assignments are also the starting point for structure determination and refinement. A new algorithm, called Nuclear Vector Replacement (NVR) is introduced to compute assignments that optimally correlate experimentally-measured NH residual dipolar couplings (RDCs) 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 NOEs dNNs), all of which can be acquired in a fraction of the time needed to record the traditional suite of experiments used to perform resonance assignments. NVR runs in minutes and efficiently assigns the (HN,15N) backbone resonances as well as the dNNs of the 3D \nfif-NOESY spectrum, in O(n3) 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 90%. We further demonstrate the feasibility of our algorithm for different and larger proteins, using NMR data for hen lysozyme (129 residues, 98% accuracy) and streptococcal protein G (56 residues, 95% accuracy), matched to a variety of 3D structural models. Finally, we extend NVR to a second application, 3D structural homology detection, and demonstrate that NVR is able to identify structural homologies between proteins with remote amino acid sequences using a database of structural models.

A data-driven, systematic search algorithm for structure determination of denatured or disordered proteins.

Traditional algorithms for the structure determination of native proteins by solution nuclear magnetic resonance (NMR) spectroscopy require a large number of experimental restraints. These algorithms formulate the structure determination problem as the computation of a structure or a set of similar structures that best fit the restraints. However, for both laboratory-denatured and natively-disordered proteins, the number of restraints measured by the current NMR techniques is well below that required by traditional algorithms. Furthermore, there presumably exists a heterogeneous set of structures in either the denatured or disordered state. We present a data-driven algorithm capable of computing a set of structures (ensemble) directly from sparse experimental restraints. For both denatured and disordered proteins, we formulate the structure determination problem as the computation of an ensemble of structures from the restraints. In this formulation, each experimental restraint is a distribution. Compared with previous algorithms, our algorithm can extract more structural information from the experimental data. In our algorithm, all the backbone conformations consistent with the data are computed by solving a series of low-degree monomials (yielding exact solutions in closed form) and systematic search with pruning. The algorithm has been successfully applied to determine the structural ensembles of two denatured proteins, acyl-coenzyme A binding protein (ACBP) and eglin C, using real experimental NMR data.

An exact algorithm for determining protein backbone structure from NH residual dipolar couplings

We have developed a novel algorithm for protein backbone structure determination using global orientational restraints on internuclear bond vectors derived from residual dipolar couplings (RDCs) measured in solution NMR. The algorithm is a depth-first search (DPS) strategy that is built upon two low-degree polynomial equations for computing the backbone (/spl phi/, /spl psi/) angles, exactly and in constant time, from two bond vectors in consecutive peptide planes.