THESEUS: maximum likelihood superpositioning and analysis of macromolecular structures

Theobald, Douglas L.; Wuttke, Deborah S.

doi:10.1093/bioinformatics/btl332

Cited by 194 publications

(224 citation statements)

References 7 publications

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“…5, Bst, Eco) that fit scattering data better than the initial manual models shown in Figure 3. Maximum-likelihood superposition (Theobald and Wuttke 2006) shows that conformations selected in the case of Bst RNA differ primarily by the relative orientations of the S-and C-domains (Fig. 5).…”

Section: Generation Of All-atom Rna Modelsmentioning

confidence: 99%

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Solution structure of RNase P RNA

Kazantsev¹,

Rambo²,

Karimpour³

et al. 2011

RNA

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The ribonucleoprotein enzyme ribonuclease P (RNase P) processes tRNAs by cleavage of precursor-tRNAs. RNase P is a ribozyme: The RNA component catalyzes tRNA maturation in vitro without proteins. Remarkable features of RNase P include multiple turnovers in vivo and ability to process diverse substrates. Structures of the bacterial RNase P, including full-length RNAs and a ternary complex with substrate, have been determined by X-ray crystallography. However, crystal structures of free RNA are significantly different from the ternary complex, and the solution structure of the RNA is unknown. Here, we report solution structures of three phylogenetically distinct bacterial RNase P RNAs from Escherichia coli, Agrobacterium tumefaciens, and Bacillus stearothermophilus, determined using small angle X-ray scattering (SAXS) and selective 29-hydroxyl acylation analyzed by primer extension (SHAPE) analysis. A combination of homology modeling, normal mode analysis, and molecular dynamics was used to refine the structural models against the empirical data of these RNAs in solution under the high ionic strength required for catalytic activity.

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Section: Generation Of All-atom Rna Modelsmentioning

confidence: 99%

“…Selected conformations were analyzed by maximum-likelihood superimposition with THESEUS (Theobald and Wuttke 2006).…”

Section: Saxs Data Collection and Processingmentioning

confidence: 99%

Solution structure of RNase P RNA

Kazantsev¹,

Rambo²,

Karimpour³

et al. 2011

RNA

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“…We have implemented this algorithm in THESEUS, a UNIX C program intended for likelihood analysis of biological macromolecules (25). Because of the complexity of the problem, the efficiency of the algorithm is difficult to determine generally.…”

Section: Estimate the Mean Find The New Average M According Tomentioning

confidence: 99%

Empirical Bayes hierarchical models for regularizing maximum likelihood estimation in the matrix Gaussian Procrustes problem

Theobald

Wuttke²

2006

Proc. Natl. Acad. Sci. U.S.A.

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104

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Procrustes analysis involves finding the optimal superposition of two or more ''forms'' via rotations, translations, and scalings. Procrustes problems arise in a wide range of scientific disciplines, especially when the geometrical shapes of objects are compared, contrasted, and analyzed. Classically, the optimal transformations are found by minimizing the sum of the squared distances between corresponding points in the forms. Despite its widespread use, the ordinary unweighted least-squares (LS) criterion can give erroneous solutions when the errors have heterogeneous variances (heteroscedasticity) or the errors are correlated, both common occurrences with real data. In contrast, maximum likelihood (ML) estimation can provide accurate and consistent statistical estimates in the presence of both heteroscedasticity and correlation. Here we provide a complete solution to the nonisotropic ML Procrustes problem assuming a matrix Gaussian distribution with factored covariances. Our analysis generalizes, simplifies, and extends results from previous discussions of the ML Procrustes problem. An iterative algorithm is presented for the simultaneous, numerical determination of the ML solutions.heteroscedasticity ͉ morphometrics ͉ Procrustes analysis ͉ superpositions ͉ least-squares T he goal of Procrustes analysis is to superpose non-identical shapes in an optimal manner via scalings, translations, and rotations (1-3). Classical Procrustes analysis uses the unweighted least-squares (LS) criterion for finding the optimal transformations. LS implicitly assumes that the landmarks describing the forms' shapes are uncorrelated and that they have identical variances (i.e., that they are homoscedastic). However, in many practical applications these assumptions are known to be violated. For instance, when superpositioning macromolecular proteins, individual atoms (the landmarks) are connected via covalent chemical bonds, and thus the variance of a given atom can be correlated with the variance of atoms to which it is connected. Furthermore, certain atoms may have larger mobilities than others, or they may have spatial positions with relatively greater uncertainty due to experimental error. Similarly, when comparing the skulls from different members of a species, some homologous features may be highly variable relative to others. Hence, different landmarks can have widely different variances. Under these conditions, ordinary LS can give misleading results, even with large samples of data (4).The method of maximum likelihood (ML) is a common alternative to LS and is widely considered to be fundamental for statistical modeling and parameter estimation (5). Given the proper model, ML can provide accurate and robust estimates of parameters in the presence of both heteroscedasticity and correlation. Incorporating heterogeneous variances and non-zero correlations into the ML Procrustes problem involves weighting by two covariance matrices (a landmark and a dimensional covariance matrix). However, estimation of these covariance matrices...

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“…We focus on observations for chromosome 1, but have observed similar trends for other chromosomes. For each filtering, the embeddings are aligned to each other using a maximum likelihood superpositioning technique [15].…”

Section: Metric Filtering Produces Low-variance More Biologically Plmentioning

confidence: 99%

Resolving Spatial Inconsistencies in Chromosome Conformation Data

Duggal

Patro

Sefer

et al. 2012

Lecture Notes in Computer Science

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Abstract. We introduce a new method for filtering noisy 3C interactions that selects subsets of interactions that obey metric constraints of various strictness. We demonstrate that, although the problem is computationally hard, near-optimal results are often attainable in practice using well-designed heuristics and approximation algorithms. Further, we show that, compared with a standard technique, this metric filtering approach leads to (a) subgraphs with higher total statistical significance, (b) lower embedding error, (c) lower sensitivity to initial conditions of the embedding algorithm, and (d) structures with better agreement with light microscopy measurements.

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THESEUS: maximum likelihood superpositioning and analysis of macromolecular structures

Abstract: ANSI C source code and selected binaries for various computing platforms are available under the GNU open source license from http://monkshood.colorado.edu/theseus/ or http://www.theseus3d.org.

Cited by 194 publications

References 7 publications

Solution structure of RNase P RNA

Solution structure of RNase P RNA

Empirical Bayes hierarchical models for regularizing maximum likelihood estimation in the matrix Gaussian Procrustes problem

Resolving Spatial Inconsistencies in Chromosome Conformation Data

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