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Deblurring algorithms accounting for the finite detector size in photoacoustic tomography.

Most reconstruction algorithms for photoacoustic tomography, like back projection or time reversal, work ideally for point-like detectors. For real detectors, which integrate the pressure over their finite size, images reconstructed by these algorithms show some blurring. Iterative reconstruction algorithms using an imaging matrix can take the finite size of real detectors directly into account, but the numerical effort is significantly higher compared to the use of direct algorithms. For spherical or cylindrical detection surfaces, the blurring caused by a finite detector size is proportional to the distance from the rotation center (spin blur) and is equal to the detector size at the detection surface. In this work, we apply deconvolution algorithms to reduce this type of blurring on simulated and on experimental data. Two particular deconvolution methods are compared, which both utilize the fact that a representation of the blurred image in polar coordinates decouples pixels at different radii from the rotation center. Experimental data have been obtained with a flat, rectangular piezoelectric detector measuring signals around a plastisol cylinder containing various small photoacoustic sources with variable distance from the center. Both simulated and experimental results demonstrate a nearly complete elimination of spin blur.

Beyond captions: linking figures with abstract sentences in biomedical articles.

Although figures in scientific articles have high information content and concisely communicate many key research findings, they are currently under utilized by literature search and retrieval systems. Many systems ignore figures, and those that do not typically only consider caption text. This study describes and evaluates a fully automated approach for associating figures in the body of a biomedical article with sentences in its abstract. We use supervised methods to learn probabilistic language models, hidden Markov models, and conditional random fields for predicting associations between abstract sentences and figures. Three kinds of evidence are used: text in abstract sentences and figures, relative positions of sentences and figures, and the patterns of sentence/figure associations across an article. Each information source is shown to have predictive value, and models that use all kinds of evidence are more accurate than models that do not. Our most accurate method has an F1-score of 69% on a cross-validation experiment, is competitive with the accuracy of human experts, has significantly better predictive accuracy than state-of-the-art methods and enables users to access figures associated with an abstract sentence with an average of 1.82 fewer mouse clicks. A user evaluation shows that human users find our system beneficial. The system is available at http://FigureItOut.askHERMES.org.

Fast approximations of the rotational diffusion tensor and their application to structural assembly of molecular complexes.

We present and evaluate a rigid-body, deterministic, molecular docking method, called ELMDOCK, that relies solely on the three-dimensional structure of the individual components and the overall rotational diffusion tensor of the complex, obtained from nuclear spin-relaxation measurements. We also introduce a docking method, called ELMPATIDOCK, derived from ELMDOCK and based on the new concept of combining the shape-related restraints from rotational diffusion with those from residual dipolar couplings, along with ambiguous contact/interface-related restraints obtained from chemical shift perturbations. ELMDOCK and ELMPATIDOCK use two novel approximations of the molecular rotational diffusion tensor that allow computationally efficient docking. We show that these approximations are accurate enough to properly dock the two components of a complex without the need to recompute the diffusion tensor at each iteration step. We analyze the accuracy, robustness, and efficiency of these methods using synthetic relaxation data for a large variety of protein-protein complexes. We also test our method on three protein systems for which the structure of the complex and experimental relaxation data are available, and analyze the effect of flexible unstructured tails on the outcome of docking. Additionally, we describe a method for integrating the new approximation methods into the existing docking approaches that use the rotational diffusion tensor as a restraint. The results show that the proposed docking method is robust against experimental errors in the relaxation data or structural rearrangements upon complex formation and is computationally more efficient than current methods. The developed approximations are accurate enough to be used in structure refinement protocols.

Structural assembly of molecular complexes based on residual dipolar couplings.

We present and evaluate a rigid-body molecular docking method, called PATIDOCK, that relies solely on the three-dimensional structure of the individual components and the experimentally derived residual dipolar couplings (RDCs) for the complex. We show that, given an accurate ab initio predictor of the alignment tensor from a protein structure, it is possible to accurately assemble a protein-protein complex by utilizing the RDCs' sensitivity to molecular shape to guide the docking. The proposed docking method is robust against experimental errors in the RDCs and computationally efficient. We analyze the accuracy and efficiency of this method using experimental or synthetic RDC data for several proteins, as well as synthetic data for a large variety of protein-protein complexes. We also test our method on two protein systems for which the structure of the complex and steric-alignment data are available (Lys48-linked diubiquitin and a complex of ubiquitin and a ubiquitin-associated domain) and analyze the effect of flexible unstructured tails on the outcome of docking. The results demonstrate that it is fundamentally possible to assemble a protein-protein complex solely on the basis of experimental RDC data and the prediction of the alignment tensor from 3D structures. Thus, despite the purely angular nature of RDCs, they can be converted into intermolecular distance/translational constraints. Additionally, we show a method for combining RDCs with other experimental data, such as ambiguous constraints from interface mapping, to further improve structure characterization of protein complexes.

Improvement and analysis of computational methods for prediction of residual dipolar couplings.

We describe a new, computationally efficient method for computing the molecular alignment tensor based on the molecular shape. The increase in speed is achieved by re-expressing the problem as one of numerical integration, rather than a simple uniform sampling (as in the PALES method), and by using a convex hull rather than a detailed representation of the surface of a molecule. This method is applicable to bicelles, PEG/hexanol, and other alignment media that can be modeled by steric restrictions introduced by a planar barrier. This method is used to further explore and compare various representations of protein shape by an equivalent ellipsoid. We also examine the accuracy of the alignment tensor and residual dipolar couplings (RDC) prediction using various ab initio methods. We separately quantify the inaccuracy in RDC prediction caused by the inaccuracy in the orientation and in the magnitude of the alignment tensor, concluding that orientation accuracy is much more important in accurate prediction of RDCs.

Why do hubs in the yeast protein interaction network tend to be essential: reexamining the connection between the network topology and essentiality.

The centrality-lethality rule, which notes that high-degree nodes in a protein interaction network tend to correspond to proteins that are essential, suggests that the topological prominence of a protein in a protein interaction network may be a good predictor of its biological importance. Even though the correlation between degree and essentiality was confirmed by many independent studies, the reason for this correlation remains illusive. Several hypotheses about putative connections between essentiality of hubs and the topology of protein-protein interaction networks have been proposed, but as we demonstrate, these explanations are not supported by the properties of protein interaction networks. To identify the main topological determinant of essentiality and to provide a biological explanation for the connection between the network topology and essentiality, we performed a rigorous analysis of six variants of the genomewide protein interaction network for Saccharomyces cerevisiae obtained using different techniques. We demonstrated that the majority of hubs are essential due to their involvement in Essential Complex Biological Modules, a group of densely connected proteins with shared biological function that are enriched in essential proteins. Moreover, we rejected two previously proposed explanations for the centrality-lethality rule, one relating the essentiality of hubs to their role in the overall network connectivity and another relying on the recently published essential protein interactions model.

Structural footprinting in protein structure comparison: the impact of structural fragments.

BACKGROUND: One approach for speeding-up protein structure comparison is the projection approach, where a protein structure is mapped to a high-dimensional vector and structural similarity is approximated by distance between the corresponding vectors. Structural footprinting methods are projection methods that employ the same general technique to produce the mapping: first select a representative set of structural fragments as models and then map a protein structure to a vector in which each dimension corresponds to a particular model and "counts" the number of times the model appears in the structure. The main difference between any two structural footprinting methods is in the set of models they use; in fact a large number of methods can be generated by varying the type of structural fragments used and the amount of detail in their representation. How do these choices affect the ability of the method to detect various types of structural similarity? RESULTS: To answer this question we benchmarked three structural footprinting methods that vary significantly in their selection of models against the CATH database. In the first set of experiments we compared the methods' ability to detect structural similarity characteristic of evolutionarily related structures, i.e., structures within the same CATH superfamily. In the second set of experiments we tested the methods' agreement with the boundaries imposed by classification groups at the Class, Architecture, and Fold levels of the CATH hierarchy. CONCLUSION: In both experiments we found that the method which uses secondary structure information has the best performance on average, but no one method performs consistently the best across all groups at a given classification level. We also found that combining the methods' outputs significantly improves the performance. Moreover, our new techniques to measure and visualize the methods' agreement with the CATH hierarchy, including the threshholded affinity graph, are useful beyond this work. In particular, they can be used to expose a similar composition of different classification groups in terms of structural fragments used by the method and thus provide an alternative demonstration of the continuous nature of the protein structure universe.

Secondary structure spatial conformation footprint: a novel method for fast protein structure comparison and classification.

BACKGROUND: Recently a new class of methods for fast protein structure comparison has emerged. We call the methods in this class projection methods as they rely on a mapping of protein structure into a high-dimensional vector space. Once the mapping is done, the structure comparison is reduced to distance computation between corresponding vectors. As structural similarity is approximated by distance between projections, the success of any projection method depends on how well its mapping function is able to capture the salient features of protein structure. There is no agreement on what constitutes a good projection technique and the three currently known projection methods utilize very different approaches to the mapping construction, both in terms of what structural elements are included and how this information is integrated to produce a vector representation. RESULTS: In this paper we propose a novel projection method that uses secondary structure information to produce the mapping. First, a diverse set of spatial arrangements of triplets of secondary structure elements, a set of structural models, is automatically selected. Then, each protein structure is mapped into a high-dimensional vector of "counts" or footprint, where each count corresponds to the number of times a given structural model is observed in the structure, weighted by the precision with which the model is reproduced. We perform the first comprehensive evaluation of our method together with all other currently known projection methods. CONCLUSION: The results of our evaluation suggest that the type of structural information used by a projection method affects the ability of the method to detect structural similarity. In particular, our method that uses the spatial conformations of triplets of secondary structure elements outperforms other methods in most of the tests.

Fast Algorithms for Structured Least Squares and Total Least Squares Problems.

We consider the problem of solving least squares problems involving a matrix M of small displacement rank with respect to two matrices Z 1 and Z 2. We develop formulas for the generators of the matrix M (H) M in terms of the generators of M and show that the Cholesky factorization of the matrix M (H) M can be computed quickly if Z 1 is close to unitary and Z 2 is triangular and nilpotent. These conditions are satisfied for several classes of matrices, including Toeplitz, block Toeplitz, Hankel, and block Hankel, and for matrices whose blocks have such structure. Fast Cholesky factorization enables fast solution of least squares problems, total least squares problems, and regularized total least squares problems involving these classes of matrices.

HOPE: a homotopy optimization method for protein structure prediction.

We use a homotopy optimization method, HOPE, to minimize the potential energy associated with a protein model. The method uses the minimum energy conformation of one protein as a template to predict the lowest energy structure of a query sequence. This objective is achieved by following a path of conformations determined by a homotopy between the potential energy functions for the two proteins. Ensembles of solutions are produced by perturbing conformations along the path, increasing the likelihood of predicting correct structures. Successful results are presented for pairs of homologous proteins, where HOPE is compared to a variant of Newton's method and to simulated annealing.

Asymptotically optimal quantum circuits for d-level systems.

Scalability of a quantum computation requires that the information be processed on multiple subsystems. However, it is unclear how the complexity of a quantum algorithm, quantified by the number of entangling gates, depends on the subsystem size. We examine the quantum circuit complexity for exactly universal computation on many d-level systems (qudits). Both a lower bound and a constructive upper bound on the number of two-qudit gates result, proving a sharp asymptotic of theta(d(2n)) gates. This closes the complexity question for all d-level systems (d finite). The optimal asymptotic applies to systems with locality constraints, e.g., nearest neighbor interactions.