Sesquiterpene lactone-based classification of three Asteraceae tribes: a study based on self-organizing neural networks applied to chemosystematics

This work describes an application of artificial neural networks on a small data set of sesquiterpene lactones (STLs) of three tribes of the family Asteraceae. Structurally different types of representative STLs from seven subtribes of the tribes Eupatorieae, Heliantheae and Vernonieae were selected as input data for self-organizing neural networks. Encoding the 3D molecular structures of STLs and their projection onto Kohonen maps allowed the classification of Asteraceae into tribes and subtribes. This approach allowed the evaluation of structural similarities among different sets of 3D structures of sesquiterpene lactones and their correlation with the current taxonomic classification of the family. Predictions of the occurrence of STLs from a plant species according to the taxa they belong to were also performed by the networks. The methodology used in this work can be applied to chemosystematic or chemotaxonomic studies of Asteraceae.     

A data-mining approach for multiple structural alignment of proteins

Comparing the 3D structures of proteins is an important but computationally hard problem in bioinformatics. In this paper, we propose studying the problem when much less information or assumptions are available. We model the structural alignment of proteins as a combinatorial problem. In the problem, each protein is simply a set of points in the 3D space, without sequence order information, and the objective is to discover all large enough alignments for any subset of the input. We propose a data-mining approach for this problem. We first perform geometric hashing of the structures such that points with similar locations in the 3D space are hashed into the same bin in the hash table. The novelty is that we consider each bin as a coincidence group and mine for frequent patterns, which is a well-studied technique in data mining. We observe that these frequent patterns are already potentially large alignments. Then a simple heuristic is used to extend the alignments if possible. We implemented the algorithm and tested it using real protein structures. The results were compared with existing tools. They showed that the algorithm is capable of finding conserved substructures that do not preserve sequence order, especially those existing in protein interfaces. The algorithm can also identify conserved substructures of functionally similar structures within a mixture with dissimilar ones. The running time of the program was smaller or comparable to that of the existing tools.     

ProDCoNN: Protein design using a convolutional neural network

Designing protein sequences that fold to a given three-dimensional (3D) structure has long been a challenging problem in computational structural biology with significant theoretical and practical implications. In this study, we first formulated this problem as predicting the residue type given the 3D structural environment around the C _α atom of a residue, which is repeated for each residue of a protein. We designed a nine-layer 3D deep convolutional neural network (CNN) that takes as input a gridded box with the atomic coordinates and types around a residue. Several CNN layers were designed to capture structure information at different scales, such as bond lengths, bond angles, torsion angles, and secondary structures. Trained on a very large number of protein structures, the method, called ProDCoNN (protein design with CNN), achieved state-of-the-art performance when tested on large numbers of test proteins and benchmark datasets.     

From spatial-data to 3D models of the developing human brain

Visualisation and interpretation of gene expression data have been crucial to advances in our understanding of mechanisms underlying early brain development. As most developmental processes involve complex changes in size, shape and structure, spatial-data can most readily provide information at multiple levels (cell type, cell location in relation to tissue organisation or body axes, etc.), that can be related to these complex changes. Although three-dimensional (3D) spatial-data are ideal, the restricted availability of suitable tissues makes it difficult to generate these for genes expressed at early human fetal stages. Mapping gene expression data to representative 3D models facilitates combinatorial analysis of multiple expression patterns but does not overcome the problems of sparsely sampled data in time and space. Here we describe software that allows 3D domains to be reconstructed by interpolating between sparse 2D gene expression patterns that have been mapped to 3D representative models of corresponding human developmental stages. A set of procedures are proposed to infer expression domains in these gaps. The procedures, which are connected in a serial way, include components clustering, components tracking, shape matching and points interpolation. Each procedure consists of a graphical user interface and a set of algorithms. Results on exemplar gene data are provided.     

Variations of the three-dimensional structure of the Escherichia coli ribosome in the range of overlap views. An application of the methods of multicone and local single-cone three-dimensional reconstruction.

Electron microscopic techniques are among the most important tools for obtaining structural information of biological specimens. However, the three-dimensional (3D) structural analysis of asymmetrical specimens that do not form crystalline sheets has traditionally presented serious methodological obstacles to its accomplishment. One of the fundamental questions to be addressed in this type of structural study is in what way, and to what degree, does the 3D structural conformation depend on the orientation of the specimen with respect to the electron microscopic support films. As a step in studying this problem, we have analyzed the variations of the 3D structure of the Escherichia coli 70S monosome by performing four different 3D reconstructions of the 70S monosome from subsets of images in the so-called overlap range of views. These subsets were selected according to a multivariate statistical analysis performed on the total population of overlap-range specimen images. A certain amount of structural variability exists among the 3D reconstructions, although many of the main morphological characteristics, as the relative orientation between the ribosomal subunits, remain unchanged. We have also generalized the random conical reconstruction technique (Radermacher, M., T. Wagenknecht, A. Verschoor, and J. Frank. 1987. J. Microsc. 146: 113-136) to include those cases where the specimen exhibits a rocking behavior with respect to the support. The resulting Multicone Reconstruction Technique has been applied to computer-generated images as well as the E. coli 70S monosome images from part of the overlap range of views.     

Electron tomography reveals diverse conformations of integrin alphaIIbbeta3 in the active state

We used electron tomography to determine the three-dimensional (3D) structure of integrin alphaIIbbeta3 in the active state. We found that we obtained better density maps when we reconstructed a 3D volume for each individual particle in the tilt series rather than to extract the particle-containing subvolumes from a 3D reconstruction of the entire specimen area. The 3D tomographic reconstructions of 100 particles revealed that activated alphaIIbbeta3 adopts many different conformations. An average of all the individual 3D reconstructions nicely accommodated the crystal structure of the alphaVbeta3 headpiece, confirming the locations assigned to the alpha- and beta-subunit in the density map. The most striking finding of our study is the structural flexibility of the lower leg of the beta-subunit as opposed to the conformational stability of the leg of the alpha-subunit. The good fit of the atomic structure of the betaI domain and the hybrid domain in the active state showed that the hybrid domain swings out, and most particles used for tomography are in the active state. Multivariate statistical analysis and classification applied to the set of 3D reconstructions revealed that more than 90% reconstructions are grouped into the classes that show the active state. Our results demonstrate that electron tomography can be used to classify complexes with a flexible structure such as integrins.     

Low-resolution density maps from atomic models: how stepping "back" can be a step "forward"

Atomic-resolution structures have had a tremendous impact on modern biological science. Much useful information also has been gleaned by merging and correlating atomic-resolution structural details with lower-resolution (15-40 A), three-dimensional (3D) reconstructions computed from images recorded with cryo-transmission electron microscopy (cryoTEM) procedures. One way to merge these structures involves reducing the resolution of an atomic model to a level comparable to a cryoTEM reconstruction. A low-resolution density map can be derived from an atomic-resolution structure by retrieving a set of atomic coordinates editing the coordinate file, computing structure factors from the model coordinates, and computing the inverse Fourier transform of the structure factors. This method is a useful tool for structural studies primarily in combination with 3D cryoTEM reconstructions. It has been used to assess the quality of 3D reconstructions, to determine corrections for the phase-contrast transfer function of the transmission electron microscope, to calibrate the dimensions and handedness of 3D reconstructions, to produce difference maps, to model features in macromolecules or macromolecular complexes, and to generate models to initiate model-based determination of particle orientation and origin parameters for 3D reconstruction.     

Efficient implementation of a filtered back-projection algorithm using a voxel-by-voxel approach

The large amount of image data necessary for high-resolution 3D reconstruction of macromolecular assemblies leads to significant increases in the computational time. One of the most time consuming operations is 3D density map reconstruction, and software optimization can greatly reduce the time required for any given structural study. The majority of algorithms proposed for improving the computational effectiveness of a 3D reconstruction are based on a ray-by-ray projection of each image into the reconstructed volume. In this paper, we propose a novel fast implementation of the "filtered back-projection" algorithm based on a voxel-by-voxel principle. Our version of this implementation has been exhaustively tested using both model and real data. We compared 3D reconstructions obtained by the new approach with results obtained by the filtered Back-Projections algorithm and the Fourier-Bessel algorithm commonly used for reconstructing icosahedral viruses. These computational experiments demonstrate the robustness, reliability, and efficiency of this approach.     

Low-Resolution Density Maps from Atomic Models: How Stepping “Back” Can Be a Step “Forward”

Atomic-resolution structures have had a tremendous impact on modern biological science. Much useful information also has been gleaned by merging and correlating atomic-resolution structural details with lower-resolution (15–40 Å), three-dimensional (3D) reconstructions computed from images recorded with cryo-transmission electron microscopy (cryoTEM) procedures. One way to merge these structures involves reducing the resolution of an atomic model to a level comparable to a cryoTEM reconstruction. A low-resolution density map can be derived from an atomic-resolution structure by retrieving a set of atomic coordinates editing the coordinate file, computing structure factors from the model coordinates, and computing the inverse Fourier transform of the structure factors. This method is a useful tool for structural studies primarily in combination with 3D cryoTEM reconstructions. It has been used to assess the quality of 3D reconstructions, to determine corrections for the phase-contrast transfer function of the transmission electron microscope, to calibrate the dimensions and handedness of 3D reconstructions, to produce difference maps, to model features in macromolecules or macromolecular complexes, and to generate models to initiate model-based determination of particle orientation and origin parameters for 3D reconstruction.     

Single particle reconstructions of the transferrin-transferrin receptor complex obtained with different specimen preparation techniques

The outcome of three-dimensional (3D) reconstructions in single particle electron microscopy (EM) depends on a number of parameters. We have used the well-characterized structure of the transferrin (Tf)-transferrin receptor (TfR) complex to study how specimen preparation techniques influence the outcome of single particle EM reconstructions. The Tf-TfR complex is small (290kDa) and of low symmetry (2-fold). Angular reconstitution from images of vitrified specimens does not reliably converge on the correct structure. Random conical tilt reconstructions from negatively stained specimens are reliable, but show variable degrees of artifacts depending on the negative staining protocol. Alignment of class averages from vitrified specimens to a 3D negative stain reference model using FREALIGN largely eliminated artifacts in the resulting 3D maps, but not completely. Our results stress the need for critical evaluation of structures determined by single particle EM.     

DynBench3D,a Web-Resource to Dynamically Generate Benchmark Sets of Large Heteromeric Protein Complexes

Multi-protein machines are responsible for most cellular tasks, and many efforts have been invested in the systematic identification and characterization of thousands of these macromolecular assemblies. However, unfortunately, the (quasi) atomic details necessary to understand their function are available only for a tiny fraction of the known complexes. The computational biology community is developing strategies to integrate structural data of different nature, from electron microscopy to X-ray crystallography, to model large molecular machines, as it has been done for individual proteins and interactions with remarkable success. However, unlike for binary interactions, there is no reliable gold-standard set of three-dimensional (3D) complexes to benchmark the performance of these methodologies and detect their limitations. Here, we present a strategy to dynamically generate non-redundant sets of 3D heteromeric complexes with three or more components. By changing the values of sequence identity and component overlap between assemblies required to define complex redundancy, we can create sets of representative complexes with known 3D structure (i.e., target complexes). Using an identity threshold of 20% and imposing a fraction of component overlap of < 0.5, we identify 495 unique target complexes, which represent a real non-redundant set of heteromeric assemblies with known 3D structure. Moreover, for each target complex, we also identify a set of assemblies, of varying degrees of identity and component overlap, that can be readily used as input in a complex modeling exercise (i.e., template subcomplexes). We hope that resources like this will significantly help the development and progress assessment of novel methodologies, as docking benchmarks and blind prediction contests did. The interactive resource is accessible at https://DynBench3D.irbbarcelona.org.     

Automated correlation of single particle tilt pairs for Random Conical Tilt and Orthogonal Tilt Reconstructions

One of the major methodological challenges in single particle electron microscopy is obtaining initial reconstructions which represent the structural heterogeneity of the dataset. Random Conical Tilt and Orthogonal Tilt Reconstruction techniques in combination with 3D alignment and classification can be used to obtain initial low-resolution reconstructions which represent the full range of structural heterogeneity of the dataset. In order to achieve statistical significance, however, a large number of 3D reconstructions, and, in turn, a large number of tilted image pairs are required. The extraction of single particle tilted image pairs from micrographs can be tedious and time-consuming, as it requires intensive user input even for semi-automated approaches. To overcome the bottleneck of manual selection of a large number of tilt pairs, we developed an algorithm for the correlation of single particle images from tilted image pairs in a fully automated and user-independent manner. The algorithm reliably correlates correct pairs even from noisy micrographs. We further demonstrate the applicability of the algorithm by using it to obtain initial references both from negative stain and unstained cryo datasets.     

Rule-based modeling and simulations of the inner kinetochore structure

Background

Combinatorial complexity is a central problem when modeling biochemical reaction networks, since the association of a few components can give rise to a large variation of protein complexes. Available classical modeling approaches are often insufficient for the analysis of very large and complex networks in detail. Recently, we developed a new rule-based modeling approach that facilitates the analysis of spatial and combinatorially complex problems. Here, we explore for the first time how this approach can be applied to a specific biological system, the human kinetochore, which is a multi-protein complex involving over 100 proteins.

Results

Applying our freely available SRSim software to a large data set on kinetochore proteins in human cells, we construct a spatial rule-based simulation model of the human inner kinetochore. The model generates an estimation of the probability distribution of the inner kinetochore 3D architecture and we show how to analyze this distribution using information theory. In our model, the formation of a bridge between CenpA and an H3 containing nucleosome only occurs efficiently for higher protein concentration realized during S-phase but may be not in G1. Above a certain nucleosome distance the protein bridge barely formed pointing towards the importance of chromatin structure for kinetochore complex formation. We define a metric for the distance between structures that allow us to identify structural clusters. Using this modeling technique, we explore different hypothetical chromatin layouts.

Conclusions

Applying a rule-based network analysis to the spatial kinetochore complex geometry allowed us to integrate experimental data on kinetochore proteins, suggesting a 3D model of the human inner kinetochore architecture that is governed by a combinatorial algebraic reaction network. This reaction network can serve as bridge between multiple scales of modeling. Our approach can be applied to other systems beyond kinetochores.     

Beyond the Twilight Zone: Automated prediction of structural properties of proteins by recursive neural networks and remote homology information

The prediction of 1D structural properties of proteins is an important step toward the prediction of protein structure and function, not only in the ab initio case but also when homology information to known structures is available. Despite this the vast majority of 1D predictors do not incorporate homology information into the prediction process. We develop a novel structural alignment method, SAMD, which we use to build alignments of putative remote homologues that we compress into templates of structural frequency profiles. We use these templates as additional input to ensembles of recursive neural networks, which we specialise for the prediction of query sequences that show only remote homology to any Protein Data Bank structure. We predict four 1D structural properties – secondary structure, relative solvent accessibility, backbone structural motifs, and contact density. Secondary structure prediction accuracy, tested by five‐fold cross‐validation on a large set of proteins allowing less than 25% sequence identity between training and test set and query sequences and templates, exceeds 82%, outperforming its ab initio counterpart, other state‐of‐the‐art secondary structure predictors (Jpred 3 and PSIPRED) and two other systems based on PSI‐BLAST and COMPASS templates. We show that structural information from homologues improves prediction accuracy well beyond the Twilight Zone of sequence similarity, even below 5% sequence identity, for all four structural properties. Significant improvement over the extraction of structural information directly from PDB templates suggests that the combination of sequence and template information is more informative than templates alone. Proteins 2009. © 2009 Wiley‐Liss, Inc.     

Statistical Analysis of Multiplex Brain Gene Expression Images

Analysis of variance (ANOVA) was employed to investigate 9,000 gene expression patterns from brains of both normal mice and mice with a pharmacological model of Parkinson's disease (PD). The data set was obtained using voxelation, a method that allows high-throughput acquisition of 3D gene expression patterns through analysis of spatially registered voxels (cubes). This method produces multiple volumetric maps of gene expression analogous to the images reconstructed in biomedical imaging systems. The ANOVA model was compared to the results from singular value decomposition (SVD) by using the first 42 singular vectors of the data matrix, a number equal to the rank of the ANOVA model. The ANOVA was also compared to the results from non-parametric statistics. Lastly, images were obtained for a subset of genes that emerged from the ANOVA as significant. The results suggest that ANOVA will be a valuable framework for insights into the large number of gene expression patterns obtained from voxelation.     

Histology far away from Flatland: 3D roller-coasting into grade-dependent angiogenetic patterns in oligodendrogliomas

Angiogenesis plays a key role in tumour progression, and undergoes structural changes associated to tumour biology itself. Although vessel density can be easily evaluated in brain tumours using a traditional immuno-histochemical approach, other parameters of conceptual/biological interest, such as the complex patterns of vascular growth, cannot be fully understood using a traditional bi-dimensional evaluation. We use here surgical specimens derived from oligodendrogliomas as a model for a novel elucidative 3D reconstruction of the grade-dependent vascular arborisation in brain tumours.     

Structure-based phylogenetic analysis of short-chain alcohol dehydrogenases and reclassification of the 17beta-hydroxysteroid dehydrogenase family.

Short-chain alcohol dehydrogenases (SCAD) constitute a large and diverse family of ancient origin. Several of its members play an important role in human physiology and disease, especially in the metabolism of steroid substrates (e.g., prostaglandins, estrogens, androgens, and corticosteroids). Their involvement in common human disorders such as endocrine-related cancer, osteoporosis, and Alzheimer disease makes them an important candidate for drug targets. Recent phylogenetic analysis of SCAD is incomplete and does not allow any conclusions on very ancient divergences or on a functional characterization of novel proteins within this complex family. We have developed a 3D structure-based approach to establish the deep-branching pattern within the SCAD family. In this approach, pairwise superpositions of X-ray structures were used to calculate similarity scores as an input for a tree-building algorithm. The resulting phylogeny was validated by comparison with the results of sequence-based algorithms and biochemical data. It was possible to use the 3D data as a template for the reliable determination of the phylogenetic position of novel proteins as a first step toward functional predictions. We were able to discern new patterns in the phylogenetic relationships of the SCAD family, including a basal dichotomy of the 17beta-hydroxysteroid dehydrogenases (17beta-HSDs). These data provide an important contribution toward the development of type-specific inhibitors for 17beta-HSDs for the treatment and prevention of disease. Our structure-based phylogenetic approach can also be applied to increase the reliability of evolutionary reconstructions in other large protein families.