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.     

BetaDock: Shape-Priority Docking Method Based on Beta-Complex

Abstract

This paper presents an approach and a software, BetaDock, to the docking problem by putting the priority on shape complementarity between a receptor and a ligand. The approach is based on the theory of the β-complex. Given the Voronoi diagram of the receptor whose topology is stored in the quasi-triangulation, the β-complex corresponding to water molecule is computed. Then, the boundary of the β-complex defines the β-shape which has the complete proximity information among all atoms on the receptor boundary. From the β-shape, we first compute pockets where the ligand may bind. Then, we quickly place the ligand within each pocket by solving the singular value decomposition problem and the assignment problem. Using the conformations of the ligands within the pockets as the initial solutions, we run the genetic algorithm to find the optimal solution for the docking problem. The performance of the proposed algorithm was verified through a benchmark test and showed that BetaDock is superior to a popular docking software AutoDock 4.     

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.     

Quantitative delineation of how breathing motions open ligand migration channels in myoglobin and its mutants

Ligand migration and binding are central to the biological functions of many proteins such as myoglobin (Mb) and it is widely thought that protein breathing motions open up ligand channels dynamically. However, how a protein exerts its control over the opening and closing of these channels through its intrinsic dynamics is not fully understood. Specifically, a quantitative delineation of the breathing motions that are needed to open ligand channels is lacking. In this work, we present and apply a novel normal mode‐based method to quantitatively delineate what and how breathing motions open ligand migration channels in Mb and its mutants. The motivation behind this work springs from the observation that normal mode motions are closely linked to the breathing motions that are thought to open ligand migration channels. In addition, the method provides a direct and detailed depiction of the motions of each and every residue that lines a channel and can identify key residues that play a dominating role in regulating the channel. The all‐atom model and the full force‐field employed in the method provide a realistic energetics on the work cost required to open a channel, and as a result, the method can be used to efficiently study the effects of mutations on ligand migration channels and on ligand entry rates. Our results on Mb and its mutants are in excellent agreement with MD simulation results and experimentally determined ligand entry rates. Proteins 2015; 83:757–770. © 2015 Wiley Periodicals, Inc.     

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.     

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.     

基于Voronoi图的群落优势树种种内种间竞争

在浙江天目山国家级自然保护区内,选择典型常绿阔叶林设置样地,样地大小100m×100m。用全站仪测定每株树木坐标(x,y,z)。首先,用优势度分析法确定群落优势树种。其次,提出基于Voronoi图的V_Hegyi竞争指数,并对Hegyi、APA和V_Hegyi三种竞争指数进行比较分析。最后,采用V_Hegyi竞争指数分析常绿阔叶林的种内、种间竞争关系。结果表明:常绿阔叶林群落共有11个优势树种即细叶青冈(Cyclobalanopsis myrsinaefolia)、青冈(Cyclobalanopsis glauca)、短尾柯(Lithocarpus brevicau-datus)、豹皮樟(Litsea coreana)、白栎(Quercus fabri)、天目木姜子(Litsea auriculata)、黄连木(Pistacia chinensis)、榉树(Zelkovaschneideriana)、杉木(Cunninghamia lanceolata)、枫香(Liquidambar formosana)和黄檀(Dalbergia hupeana)。比较分析认为,V_Hegyi竞争指数既克服了用固定半径圆确定竞争单元的尺度不统一缺陷,又可进行种内、种间竞争分析,并保持竞争排序的稳定性,因此是优于Hegyi和APA的更合适的竞争指数,所以选择V_Hegyi竞争指数进行优势树种竞争分析。常绿阔叶林优势树种的种内竞争比种间竞争激烈。种内竞争最激烈的优势树种细叶青冈、青冈和短尾柯与其它优势树种的种间竞争强度也是最高的。反之,种内、种间竞争都较弱的优势树种包括豹皮樟、白栎、天目木姜子、黄连木、榉树、杉木、枫香和黄檀。多数优势树种存在1个主要竞争树种,很少有超过3个以上的情形。细叶青冈是群落最占优势的树种,具有最强烈的种内竞争。同时,也是所有其它优势树种的最大竞争者。     

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.