Statistical significance of hierarchical multi-body potentials based on Delaunay tessellation and their application in sequence-structure alignment.

Statistical potentials based on pairwise interactions between C alpha atoms are commonly used in protein threading/fold-recognition attempts. Inclusion of higher order interaction is a possible means of improving the specificity of these potentials. Delaunay tessellation of the C alpha-atom representation of protein structure has been suggested as a means of defining multi-body interactions. A large number of parameters are required to define all four-body interactions of 20 amino acid types (20(4) = 160,000). Assuming that residue order within a four-body contact is irrelevant reduces this to a manageable 8,855 parameters, using a nonredundant dataset of 608 protein structures. Three lines of evidence support the significance and utility of the four-body potential for sequence-structure matching. First, compared to the four-body model, all lower-order interaction models (three-body, two-body, one-body) are found statistically inadequate to explain the frequency distribution of residue contacts. Second, coherent patterns of interaction are seen in a graphic presentation of the four-body potential. Many patterns have plausible biophysical explanations and are consistent across sets of residues sharing certain properties (e.g., size, hydrophobicity, or charge). Third, the utility of the multi-body potential is tested on a test set of 12 same-length pairs of proteins of known structure for two protocols: Sequence-recognizes-structure, where a query sequence is threaded (without gap) through the native and a non-native structure; and structure-recognizes-sequence, where a query structure is threaded by its native and another non-native sequence. Using cross-validated training, protein sequences correctly recognized their native structure in all 24 cases. Conversely, structures recognized the native sequence in 23 of 24 cases. Further, the score differences between correct and decoy structures increased significantly using the three- or four-body potential compared to potentials of lower order.     

Protein secondary structure assignment through Voronoï tessellation

We present a new automatic algorithm, named VoTAP (Vo ronoï T essellation A ssignment P rocedure), which assigns secondary structures of a polypeptide chain using the list of α‐carbon coordinates. This program uses three‐dimensional Voronoï tessellation. This geometrical tool associates with each amino acid a Voronoï polyhedron, the faces of which unambiguously define contacts between residues. Thanks to the face area, for the contacts close together along the primary structure (low‐order contacts) a distinction is made between strong and normal ones. This new definition yields new contact matrices, which are analyzed and used to assign secondary structures. This assignment is performed in two stages. The first one uses contacts between residues close together along the primary structure and is based on data collected on a bank of 282 well‐refined nonredundant structures. In this bank, associations were made between the prints defined by these low‐order contacts and the assignments performed by different automatic methods. The second step focuses on the strand assignment and uses contacts between distant residues. Comparison with several other automatic assignment methods are presented, and the influence of resolution on the assignment is investigated. Proteins 2004. © 2004 Wiley‐Liss, Inc.     

A new topological method to measure protein structure similarity

A method for the quantitative evaluation of structural similarity between protein pairs is developed that makes use of a Delaunay-based topological mapping. The result of the mapping is a three-dimensional array which is representative of the global structural topology and whose elements can be used to construe an integral scoring scheme. This scoring scheme was tested for its dependence on the protein length difference in a pairwise comparison, its ability to provide a reasonable means for structural similarity comparison within a family of structural neighbors of similar length, and its sensitivity to the differences in protein conformation. It is shown that such a topological evaluation of similarity is capable of providing insight into these points of interest. Protein structure comparison using the method is computationally efficient and the topological scores, although providing different information about protein similarity, correlate well with the distance root-mean-square deviation values calculated by rigid-body structural alignment.     

Thiessen polygons as a model for animal territory estimation

Thiessen polygons are often used to model territory characteristics. However, information about the quality of Thiessen polygon‐based estimates is currently lacking. We used published data to investigate the match between Thiessen polygons and mapped bird territories regarding territory size, shape and neighbourhood. Although territory sizes and the number of neighbours were strongly correlated between these two methods, both parameters were overestimated by the Thiessen polygons. Therefore, caution is required when Thiessen polygons are used as a model for absolute values and when the assumptions of Thiessen polygons, such as formation of discrete territories and a contiguous study area, are not met.     

Structural and dynamic roles of permanent water molecules in ligand molecular recognition by chicken liver bile acid binding protein

Chicken liver bile acid binding protein (cL-BABP) crystallizes with water molecules in its binding site. To obtain insights on the role of internal water, we performed two 100 ns molecular dynamics (MD) simulations in explicit solvent for cL-BABP, as apo form and as a complex with two molecules of cholic acid, and analyzed in detail the dynamics properties of all water molecules. The diffusion coefficients of the more persistent internal water molecules are significantly different from the bulk, but similar between the two protein forms. A different number of molecules and a different organization are observed for apo- and holo-cL-BABP. Most water molecules identified in the binding site of the apo-crystal diffuse to the bulk during the simulation. In contrast, almost all the internal waters of the holo-crystal maintain the same interactions with internal sidechains and ligands, which suggests they have a relevant role in protein-ligand molecular recognition. Only in the presence of these water molecules we were able to reproduce, by a classical molecular docking approach, the structure of the complex cL-BABP::cholic acid with a low ligand root mean square deviation (RMSD) with respect to its reference positioning. Literature data reported a conserved pattern of hydrogen bonds between a single water molecule and three amino acid residues of the binding site in a series of crystallized FABP. In cL-BABP, the interactions between this conserved water molecule and the three residues are present in the crystal of both apo- and holo-cL-BABP but are lost immediately after the start of molecular dynamics. Copyright (c) 2008 John Wiley & Sons, Ltd.     

Strategies and Decision-Support Tools for Optimizing Long-Term Groundwater Monitoring Plans—MAROS 2.0

Existing long-term groundwater monitoring programs can be optimized to increase their effectiveness/efficiency with the potential to generate considerable cost savings. The optimization can be achieved through an overall evaluation of conditions of the contaminant plume and the monitoring network, focused spatial and temporal sampling analyses, and automated and efficient management of data, analyses, and reporting. Version 2.0 of the Monitoring and Remediation Optimization System (MAROS) software, by integrating long-term monitoring analysis strategies and innovative optimization methods with a data management, processing, and reporting system, allows site managers to quickly and readily develop cost-effective long-term groundwater monitoring plans. The MAROS optimization strategy consists of a hierarchical combination of analysis methods essential to the decision-making process. Analyses are performed in three phases: 1) evaluating site information and historical monitoring data to obtain local concentration trends and an overview of the plume status; 2) developing optimal sampling plans for future monitoring at the site with innovative optimization methods; and 3) assessing the statistical sufficiency of the sampling plans to provide insights into the future performance of the monitoring program. Two case studies are presented to demonstrate the usefulness of the developed techniques and the rigor of the software.     

Residue packing in globular and intrinsically disordered proteins

Intrinsically disordered proteins (IDPs)/regions do not have well‐defined secondary and tertiary structures, however, they are functional and it is critical to gain a deep understanding of their residue packing. The shape distributions methodology, which is usually utilized in pattern recognition, clustering, and classification studies in computer science, may be adopted to study the residue packing of the proteins. In this study, shape distributions of the globular proteins and IDPs were obtained to shed light on the residue packing of their structures. The shape feature that was used is the sphericity of tetrahedra obtained by Delaunay Tessellation of points of Cα coordinates. Then the sphericity probability distributions were compared by using Principal Component Analysis. This computational structural study shows that the set of IDPs constitute a more diverse set than the set of globular proteins in terms of the geometrical properties of their network structures.     

Space allocation in Melanophila knoteki knoteki (Reitt.) var. hellenica (Obenberger) (Col., Buprestidae) in the attack of Greek fir [Abies cephalonica Loud. var. graeca (Fraas) Liu]: a pattern to process approach

The phloeo‐cambiophagous buprestid Melanophila knoteki knoteki (Reitt.) var. hellenica (Obenberger.) is not a primary factor of fir decline problem although the beetle substantially contributes to Greek fir Abies cephalonica Loud. var. graeca (Fraas) Liu mortality. By using mapping depiction of the exit holes of the insect on a set of fir trees located on a line transect in a randomized point‐centred quarter scheme and employing pattern analysis techniques we were able to reveal various scales of the infestation pattern. Four scales were recognized, two of them corresponding to the pattern of microsite selection on the bark of a fir tree. While the dispersed exit holes exhibited a statistically significant random dispersion on the bark, within each aggregation the pattern was uniform. The area of compartments created by Dirichlet partition approximated very well the sizes of the actual larval galleries. The Dirichlet tessellation of the bark space and the analysis of the parameter of the resulting partitions showed the predominance of the hexagonal conformation of the larval spaces when space was limited. When some exit holes were positioned close together it was found that they were directed away from each other so the resulting galleries were well separated. Several hypotheses are presented as to the mechanisms underpinning the observed patterns. The allocation of space is in accordance with the widely accepted ‘central place theory’ of W. Christaller, a general theory of pattern generated in the geographical dispersion of human settlements. The revealed pattern was also in accordance with the predictions of the theory of ‘central place foraging’ of R. H. MacArthur and the theory of ‘resource concentration hypothesis’ of R. Root.     

VoroMQA: Assessment of protein structure quality using interatomic contact areas

In the absence of experimentally determined protein structure many biological questions can be addressed using computational structural models. However, the utility of protein structural models depends on their quality. Therefore, the estimation of the quality of predicted structures is an important problem. One of the approaches to this problem is the use of knowledge‐based statistical potentials. Such methods typically rely on the statistics of distances and angles of residue‐residue or atom‐atom interactions collected from experimentally determined structures. Here, we present VoroMQA (Voronoi tessellation‐based Model Quality Assessment), a new method for the estimation of protein structure quality. Our method combines the idea of statistical potentials with the use of interatomic contact areas instead of distances. Contact areas, derived using Voronoi tessellation of protein structure, are used to describe and seamlessly integrate both explicit interactions between protein atoms and implicit interactions of protein atoms with solvent. VoroMQA produces scores at atomic, residue, and global levels, all in the fixed range from 0 to 1. The method was tested on the CASP data and compared to several other single‐model quality assessment methods. VoroMQA showed strong performance in the recognition of the native structure and in the structural model selection tests, thus demonstrating the efficacy of interatomic contact areas in estimating protein structure quality. The software implementation of VoroMQA is freely available as a standalone application and as a web server at http://bioinformatics.lt/software/voromqa . Proteins 2017; 85:1131–1145. © 2017 Wiley Periodicals, Inc.     

A new computational growth model for sea urchin skeletons

A new computational model has been developed to simulate growth of regular sea urchin skeletons. The model incorporates the processes of plate addition and individual plate growth into a composite model of whole-body (somatic) growth. A simple developmental model based on hypothetical morphogens underlies the assumptions used to define the simulated growth processes. The data model is based on a Delaunay triangulation of plate growth center points, using the dual Voronoi polygons to define plate topologies. A spherical frame of reference is used for growth calculations, with affine deformation of the sphere (based on a Young-Laplace membrane model) to result in an urchin-like three-dimensional form. The model verifies that the patterns of coronal plates in general meet the criteria of Voronoi polygonalization, that a morphogen/threshold inhibition model for plate addition results in the alternating plate addition pattern characteristic of sea urchins, and that application of the Bertalanffy growth model to individual plates results in simulated somatic growth that approximates that seen in living urchins. The model suggests avenues of research that could explain some of the distinctions between modern sea urchins and the much more disparate groups of forms that characterized the Paleozoic Era.