Distance geometry and related methods for protein structure determination from NMR data

The method of choice to reveal the conformation of protein molecules in atomic detail has been X-ray single-crystal analysis. Since the first structural analysis of diffraction patterns, computer calculations have been an important tool in these studies (Blundell & Johnson, 1976). As is described by Sheldrick (1985), it has been taken for granted that a necessary first step in the determination of a protein structure would be writing computer programs to fit structure factors. In contrast the combined use of the structural analysis of NMR data and computer calculations has been quite limited. An early attempt of such structural calculations was the quantitative determination of mononucleotide conformations in solution using lanthanide ion shifts (Barry et al. 1971

Protein structure determination via an efficient geometric build-up algorithm

Abstract Background A protein structure can be determined by solving a so-called distance geometry problem whenever a set of inter-atomic distances is available and sufficient. However, the problem is intractable in general and has proved to be a NP hard problem. An updated geometric build-up algorithm (UGB) has been developed recently that controls numerical errors and is efficient in protein structure determination for cases where only sparse exact distance data is available. In this paper, the UGB method has been improved and revised with aims at solving distance geometry problems more efficiently and effectively. Methods An efficient algorithm (called the revised updated geometric build-up algorithm (RUGB)) to build up a protein structure from atomic distance data is presented and provides an effective way of determining a protein structure with sparse exact distance data. In the algorithm, the condition to determine an unpositioned atom iteratively is relaxed (when compared with the UGB algorithm) and data structure techniques are used to make the algorithm more efficient and effective. The algorithm is tested on a set of proteins selected randomly from the Protein Structure Database-PDB. Results We test a set of proteins selected randomly from the Protein Structure Database-PDB. We show that the numerical errors produced by the new RUGB algorithm are smaller when compared with the errors of the UGB algorithm and that the novel RUGB algorithm has a significantly smaller runtime than the UGB algorithm. Conclusions The RUGB algorithm relaxes the condition for updating and incorporates the data structure for accessing neighbours of an atom. The revisions result in an improvement over the UGB algorithm in two important areas: a reduction on the overall runtime and decrease of the numeric error.Peer Reviewe

New Approaches to Protein NMR Automation

The three-dimensional structure of a protein molecule is the key to understanding its biological and physiological properties. A major problem in bioinformatics is to efficiently determine the three-dimensional structures of query proteins. Protein NMR structure de- termination is one of the main experimental methods and is comprised of: (i) protein sample production and isotope labelling, (ii) collecting NMR spectra, and (iii) analysis of the spectra to produce the protein structure. In protein NMR, the three-dimensional struc- ture is determined by exploiting a set of distance restraints between spatially proximate atoms. Currently, no practical automated protein NMR method exists that is without human intervention. We first propose a complete automated protein NMR pipeline, which can efficiently be used to determine the structures of moderate sized proteins. Second, we propose a novel and efficient semidefinite programming-based (SDP) protein structure determination method. The proposed automated protein NMR pipeline consists of three modules: (i) an automated peak picking method, called PICKY, (ii) a backbone chemical shift assign- ment method, called IPASS, and (iii) a protein structure determination method, called FALCON-NMR. When tested on four real protein data sets, this pipeline can produce structures with reasonable accuracies, starting from NMR spectra. This general method can be applied to other macromolecule structure determination methods. For example, a promising application is RNA NMR-assisted secondary structure determination. In the second part of this thesis, due to the shortcomings of FALCON-NMR, we propose a novel SDP-based protein structure determination method from NMR data, called SPROS. Most of the existing prominent protein NMR structure determination methods are based on molecular dynamics coupled with a simulated annealing schedule. In these methods, an objective function representing the error between observed and given distance restraints is minimized; these objective functions are highly non-convex and difficult to optimize. Euclidean distance geometry methods based on SDP provide a natural formulation for realizing a three-dimensional structure from a set of given distance constraints. However, the complexity of the SDP solvers increases cubically with the input matrix size, i.e., the number of atoms in the protein, and the number of constraints. In fact, the complexity of SDP solvers is a major obstacle in their applicability to the protein NMR problem. To overcome these limitations, the SPROS method models the protein molecule as a set of intersecting two- and three-dimensional cliques. We adapt and extend a technique called semidefinite facial reduction for the SDP matrix size reduction, which makes the SDP problem size approximately one quarter of the original problem. The reduced problem is solved nearly one hundred times faster and is more robust against numerical problems. Reasonably accurate results were obtained when SPROS was applied to a set of 20 real protein data sets

PSAIA – Protein Structure and Interaction Analyzer

<p>Abstract</p> <p>Background</p> <p>PSAIA (Protein Structure and Interaction Analyzer) was developed to compute geometric parameters for large sets of protein structures in order to predict and investigate protein-protein interaction sites.</p> <p>Results</p> <p>In addition to most relevant established algorithms, PSAIA offers a new method PIADA (Protein Interaction Atom Distance Algorithm) for the determination of residue interaction pairs. We found that PIADA produced more satisfactory results than comparable algorithms implemented in PSAIA.</p> <p>Particular advantages of PSAIA include its capacity to combine different methods to detect the locations and types of interactions between residues and its ability, without any further automation steps, to handle large numbers of protein structures and complexes. Generally, the integration of a variety of methods enables PSAIA to offer easier automation of analysis and greater reliability of results.</p> <p>PSAIA can be used either via a graphical user interface or from the command-line. Results are generated in either tabular or XML format.</p> <p>Conclusion</p> <p>In a straightforward fashion and for large sets of protein structures, PSAIA enables the calculation of protein geometric parameters and the determination of location and type for protein-protein interaction sites. XML formatted output enables easy conversion of results to various formats suitable for statistic analysis.</p> <p>Results from smaller data sets demonstrated the influence of geometry on protein interaction sites. Comprehensive analysis of properties of large data sets lead to new information useful in the prediction of protein-protein interaction sites.</p

Euclidean distance geometry and applications

Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in Euclidean space that realizes the given distances. We survey some of the theory of Euclidean distance geometry and some of the most important applications: molecular conformation, localization of sensor networks and statics.Comment: 64 pages, 21 figure

Geometrical and probabilistic methods for determining association models and structures of protein complexes

Protein complexes play vital roles in cellular processes within living organisms. They are formed by interactions between either different proteins (hetero-oligomers) or identical proteins (homo-oligomers). In order to understand the functions of the complexes, it is important to know the manner in which they are assembled from the component subunits and their three dimensional structure. This thesis addresses both of these questions by developing geometrical and probabilistic methods for analyzing data from two complementary experiment types: Small Angle Scattering (SAS) and Nuclear Magnetic Resonance (NMR) spectroscopy. Data from an SAS experiment is a set of scattering intensities that can give the interatomic probability distributions. NMR experimental data used in this thesis is set of atom pairs and the maximum distance between them. From SAS data, this thesis determines the association model of the complex and intensities through an approach that is robust to noise and contaminants in solution. Using NMR data, this thesis computes the complex structure by using probabilistic inference and geometry of convex shapes. The structure determination methods are complete, that is they identify all consistent conformations and are data driven wherein the structures are evaluated separately for consistency to data and biophysical energy

GreMuTRRR: A Novel Genetic Algorithm to Solve Distance Geometry Problem for Protein Structures

Nuclear Magnetic Resonance (NMR) Spectroscopy is a widely used technique to predict the native structure of proteins. However, NMR machines are only able to report approximate and partial distances between pair of atoms. To build the protein structure one has to solve the Euclidean distance geometry problem given the incomplete interval distance data produced by NMR machines. In this paper, we propose a new genetic algorithm for solving the Euclidean distance geometry problem for protein structure prediction given sparse NMR data. Our genetic algorithm uses a greedy mutation operator to intensify the search, a twin removal technique for diversification in the population and a random restart method to recover stagnation. On a standard set of benchmark dataset, our algorithm significantly outperforms standard genetic algorithms.Comment: Accepted for publication in the 8th International Conference on Electrical and Computer Engineering (ICECE 2014

Protein structure validation and refinement using amide proton chemical shifts derived from quantum mechanics

We present the ProCS method for the rapid and accurate prediction of protein backbone amide proton chemical shifts - sensitive probes of the geometry of key hydrogen bonds that determine protein structure. ProCS is parameterized against quantum mechanical (QM) calculations and reproduces high level QM results obtained for a small protein with an RMSD of 0.25 ppm (r = 0.94). ProCS is interfaced with the PHAISTOS protein simulation program and is used to infer statistical protein ensembles that reflect experimentally measured amide proton chemical shift values. Such chemical shift-based structural refinements, starting from high-resolution X-ray structures of Protein G, ubiquitin, and SMN Tudor Domain, result in average chemical shifts, hydrogen bond geometries, and trans-hydrogen bond (h3JNC') spin-spin coupling constants that are in excellent agreement with experiment. We show that the structural sensitivity of the QM-based amide proton chemical shift predictions is needed to refine protein structures to this agreement. The ProCS method thus offers a powerful new tool for refining the structures of hydrogen bonding networks to high accuracy with many potential applications such as protein flexibility in ligand binding.Comment: PLOS ONE accepted, Nov 201

Heuristic Refinement Method for the Derivation of Protein Solution Structures: Validation on Cytochrome B562

A method is described for determining the family of protein structures compatible with solution data obtained primarily from nuclear magnetic resonance (NMR) spectroscopy. Starting with all possible conformations, the method systematically excludes conformations until the remaining structures are only those compatible with the data. The apparent computational intractability of this approach is reduced by assembling the protein in pieces, by considering the protein at several levels of abstraction, by utilizing constraint satisfaction methods to consider only a few atoms at a time, and by utilizing artificial intelligence methods of heuristic control to decide which actions will exclude the most conformations. Example results are presented for simulated NMR data from the known crystal structure of cytochrome b562 (103 residues). For 10 sample backbones an average root-mean-square deviation from the crystal of 4.1 A was found for all alpha-carbon atoms and 2.8 A for helix alpha-carbons alone. The 10 backbones define the family of all structures compatible with the data and provide nearly correct starting structures for adjustment by any of the current structure determination methods