6,561 research outputs found

    Graph algorithms for NMR resonance assignment and cross-link experiment planning

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    The study of three-dimensional protein structures produces insights into protein function at the molecular level. Graphs provide a natural representation of protein structures and associated experimental data, and enable the development of graph algorithms to analyze the structures and data. This thesis develops such graph representations and algorithms for two novel applications: structure-based NMR resonance assignment and disulfide cross-link experiment planning for protein fold determination. The first application seeks to identify correspondences between spectral peaks in NMR data and backbone atoms in a structure (from x-ray crystallography or homology modeling), by computing correspondences between a contact graph representing the structure and an analogous but very noisy and ambiguous graph representing the data. The assignment then supports further NMR studies of protein dynamics and protein-ligand interactions. A hierarchical grow-and-match algorithm was developed for smaller assignment problems, ensuring completeness of assignment, while a random graph approach was developed for larger problems, provably determining unique matches in polynomial time with high probability. Test results show that our algorithms are robust to typical levels of structural variation, noise, and missings, and achieve very good overall assignment accuracy. The second application aims to rapidly determine the overall organization of secondary structure elements of a target protein by probing it with a set of planned disulfide cross-links. A set of informative pairs of secondary structure elements is selected from graphs representing topologies of predicted structure models. For each pair in this ``fingerprint\u27\u27, a set of informative disulfide probes is selected from graphs representing residue proximity in the models. Information-theoretic planning algorithms were developed to maximize information gain while minimizing experimental complexity, and Bayes error plan assessment frameworks were developed to characterize the probability of making correct decisions given experimental data. Evaluation of the approach on a number of structure prediction case studies shows that the optimized plans have low risk of error while testing only a very small portion of the quadratic number of possible cross-link candidates

    Contact replacement for NMR resonance assignment

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    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 article 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

    Automated sequence-specific protein NMR assignment using the memetic algorithm MATCH

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    MATCH (Memetic Algorithm and Combinatorial Optimization Heuristics) is a new memetic algorithm for automated sequence-specific polypeptide backbone NMR assignment of proteins. MATCH employs local optimization for tracing partial sequence-specific assignments within a global, population-based search environment, where the simultaneous application of local and global optimization heuristics guarantees high efficiency and robustness. MATCH thus makes combined use of the two predominant concepts in use for automated NMR assignment of proteins. Dynamic transition and inherent mutation are new techniques that enable automatic adaptation to variable quality of the experimental input data. The concept of dynamic transition is incorporated in all major building blocks of the algorithm, where it enables switching between local and global optimization heuristics at any time during the assignment process. Inherent mutation restricts the intrinsically required randomness of the evolutionary algorithm to those regions of the conformation space that are compatible with the experimental input data. Using intact and artificially deteriorated APSY-NMR input data of proteins, MATCH performed sequence-specific resonance assignment with high efficiency and robustnes

    Semidefinite Programming Approach for the Quadratic Assignment Problem with a Sparse Graph

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    The matching problem between two adjacency matrices can be formulated as the NP-hard quadratic assignment problem (QAP). Previous work on semidefinite programming (SDP) relaxations to the QAP have produced solutions that are often tight in practice, but such SDPs typically scale badly, involving matrix variables of dimension n2n^2 where n is the number of nodes. To achieve a speed up, we propose a further relaxation of the SDP involving a number of positive semidefinite matrices of dimension O(n)\mathcal{O}(n) no greater than the number of edges in one of the graphs. The relaxation can be further strengthened by considering cliques in the graph, instead of edges. The dual problem of this novel relaxation has a natural three-block structure that can be solved via a convergent Augmented Direction Method of Multipliers (ADMM) in a distributed manner, where the most expensive step per iteration is computing the eigendecomposition of matrices of dimension O(n)\mathcal{O}(n). The new SDP relaxation produces strong bounds on quadratic assignment problems where one of the graphs is sparse with reduced computational complexity and running times, and can be used in the context of nuclear magnetic resonance spectroscopy (NMR) to tackle the assignment problem.Comment: 31 page

    Atomic-level structure characterization of an ultrafast folding mini-protein denatured state

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    Atomic-level analyses of non-native protein ensembles constitute an important aspect of protein folding studies to reach a more complete understanding of how proteins attain their native form exhibiting biological activity. Previously, formation of hydrophobic clusters in the 6 M urea-denatured state of an ultrafast folding mini-protein known as TC5b from both photo-CIDNP NOE transfer studies and FCS measurements was observed. Here, we elucidate the structural properties of this mini-protein denatured in 6 M urea performing 15N NMR relaxation studies together with a thorough NOE analysis. Even though our results demonstrate that no elements of secondary structure persist in the denatured state, the heterogeneous distribution of R2 rate constants together with observing pronounced heteronuclear NOEs along the peptide backbone reveals specific regions of urea-denatured TC5b exhibiting a high degree of structural rigidity more frequently observed for native proteins. The data are complemented with studies on two TC5b point mutants to verify the importance of hydrophobic interactions for fast folding. Our results corroborate earlier findings of a hydrophobic cluster present in urea-denatured TC5b comprising both native and non-native contacts underscoring their importance for ultra rapid folding. The data assist in finding ways of interpreting the effects of pre-existing native and/or non-native interactions on the ultrafast folding of proteins; a fact, which might have to be considered when defining the starting conditions for molecular dynamics simulation studies of protein folding

    Probabilistic Interaction Network of Evidence Algorithm and its Application to Complete Labeling of Peak Lists from Protein NMR Spectroscopy

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    The process of assigning a finite set of tags or labels to a collection of observations, subject to side conditions, is notable for its computational complexity. This labeling paradigm is of theoretical and practical relevance to a wide range of biological applications, including the analysis of data from DNA microarrays, metabolomics experiments, and biomolecular nuclear magnetic resonance (NMR) spectroscopy. We present a novel algorithm, called Probabilistic Interaction Network of Evidence (PINE), that achieves robust, unsupervised probabilistic labeling of data. The computational core of PINE uses estimates of evidence derived from empirical distributions of previously observed data, along with consistency measures, to drive a fictitious system M with Hamiltonian H to a quasi-stationary state that produces probabilistic label assignments for relevant subsets of the data. We demonstrate the successful application of PINE to a key task in protein NMR spectroscopy: that of converting peak lists extracted from various NMR experiments into assignments associated with probabilities for their correctness. This application, called PINE-NMR, is available from a freely accessible computer server (http://pine.nmrfam.wisc.edu). The PINE-NMR server accepts as input the sequence of the protein plus user-specified combinations of data corresponding to an extensive list of NMR experiments; it provides as output a probabilistic assignment of NMR signals (chemical shifts) to sequence-specific backbone and aliphatic side chain atoms plus a probabilistic determination of the protein secondary structure. PINE-NMR can accommodate prior information about assignments or stable isotope labeling schemes. As part of the analysis, PINE-NMR identifies, verifies, and rectifies problems related to chemical shift referencing or erroneous input data. PINE-NMR achieves robust and consistent results that have been shown to be effective in subsequent steps of NMR structure determination

    Robust structure-based resonance assignment for functional protein studies by NMR

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    High-throughput functional protein NMR studies, like protein interactions or dynamics, require an automated approach for the assignment of the protein backbone. With the availability of a growing number of protein 3D structures, a new class of automated approaches, called structure-based assignment, has been developed quite recently. Structure-based approaches use primarily NMR input data that are not based on J-coupling and for which connections between residues are not limited by through bonds magnetization transfer efficiency. We present here a robust structure-based assignment approach using mainly HN–HN NOEs networks, as well as 1H–15N residual dipolar couplings and chemical shifts. The NOEnet complete search algorithm is robust against assignment errors, even for sparse input data. Instead of a unique and partly erroneous assignment solution, an optimal assignment ensemble with an accuracy equal or near to 100% is given by NOEnet. We show that even low precision assignment ensembles give enough information for functional studies, like modeling of protein-complexes. Finally, the combination of NOEnet with a low number of ambiguous J-coupling sequential connectivities yields a high precision assignment ensemble. NOEnet will be available under: http://www.icsn.cnrs-gif.fr/download/nmr
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