PocketPicker: analysis of ligand binding-sites with shape descriptors

Background Identification and evaluation of surface binding-pockets and occluded cavities are initial steps in protein structure-based drug design. Characterizing the active site's shape as well as the distribution of surrounding residues plays an important role for a variety of applications such as automated ligand docking or in situ modeling. Comparing the shape similarity of binding site geometries of related proteins provides further insights into the mechanisms of ligand binding. Results We present PocketPicker, an automated grid-based technique for the prediction of protein binding pockets that specifies the shape of a potential binding-site with regard to its buriedness. The method was applied to a representative set of protein-ligand complexes and their corresponding apo-protein structures to evaluate the quality of binding-site predictions. The performance of the pocket detection routine was compared to results achieved with the existing methods CAST, LIGSITE, LIGSITEcs, PASS and SURFNET. Success rates PocketPicker were comparable to those of LIGSITEcs and outperformed the other tools. We introduce a descriptor that translates the arrangement of grid points delineating a detected binding-site into a correlation vector. We show that this shape descriptor is suited for comparative analyses of similar binding-site geometry by examining induced-fit phenomena in aldose reductase. This new method uses information derived from calculations of the buriedness of potential binding-sites. Conclusions The pocket prediction routine of PocketPicker is a useful tool for identification of potential protein binding-pockets. It produces a convenient representation of binding-site shapes including an intuitive description of their accessibility. The shape-descriptor for automated classification of binding-site geometries can be used as an additional tool complementing elaborate manual inspections

MGOS: A library for molecular geometry and its operating system

The geometry of atomic arrangement underpins the structural understanding of molecules in many fields. However, no general framework of mathematical/computational theory for the geometry of atomic arrangement exists. Here we present "Molecular Geometry (MG)'' as a theoretical framework accompanied by "MG Operating System (MGOS)'' which consists of callable functions implementing the MG theory. MG allows researchers to model complicated molecular structure problems in terms of elementary yet standard notions of volume, area, etc. and MGOS frees them from the hard and tedious task of developing/implementing geometric algorithms so that they can focus more on their primary research issues. MG facilitates simpler modeling of molecular structure problems; MGOS functions can be conveniently embedded in application programs for the efficient and accurate solution of geometric queries involving atomic arrangements. The use of MGOS in problems involving spherical entities is akin to the use of math libraries in general purpose programming languages in science and engineering. (C) 2019 The Author(s). Published by Elsevier B.V

Shelling the Voronoi interface of protein-protein complexes predicts residue activity and conservation

The accurate description of protein-protein interfaces remains a challenging task. Traditional criteria, based on atomic contacts or changes in solvent accessibility, tend to over or underpredict the interface itself and cannot discriminate active from less relevant parts. A recent simulation study by Mihalek and co-authors (2007, JMB 369, 584-95) concluded that active residues tend to be `dry', that is, insulated from water fluctuations. We show that patterns of `dry' residues can, to a large extent, be predicted by a fast, parameter-free and purely geometric analysis of protein interfaces. We introduce the shelling order of Voronoi facets as a straightforward quantitative measure of an atom's depth inside an interface. We analyze the correlation between Voronoi shelling order, dryness, and conservation on a set of 54 protein-protein complexes. Residues with high shelling order tend to be dry; evolutionary conservation also correlates with dryness and shelling order but, perhaps not surprisingly, is a much less accurate predictor of either property. Voronoi shelling order thus seems a meaningful and efficient descriptor of protein interfaces. Moreover, the strong correlation with dryness suggests that water dynamics within protein interfaces may, in first approximation, be described by simple diffusion models

Exploring cavity dynamics in biomolecular systems

Background The internal cavities of proteins are dynamic structures and their dynamics may be associated with conformational changes which are required for the functioning of the protein. In order to study the dynamics of these internal protein cavities, appropriate tools are required that allow rapid identification of the cavities as well as assessment of their time-dependent structures. Results In this paper, we present such a tool and give results that illustrate the applicability for the analysis of molecular dynamics trajectories. Our algorithm consists of a pre-processing step where the structure of the cavity is computed from the Voronoi diagram of the van der Waals spheres based on coordinate sets from the molecular dynamics trajectory. The pre-processing step is followed by an interactive stage, where the user can compute, select and visualize the dynamic cavities. Importantly, the tool we discuss here allows the user to analyze the time-dependent changes of the components of the cavity structure. An overview of the cavity dynamics is derived by rendering the dynamic cavities in a single image that gives the cavity surface colored according to its time-dependent dynamics. Conclusion The Voronoi-based approach used here enables the user to perform accurate computations of the geometry of the internal cavities in biomolecules. For the first time, it is possible to compute dynamic molecular paths that have a user-defined minimum constriction size. To illustrate the usefulness of the tool for understanding protein dynamics, we probe the dynamic structure of internal cavities in the bacteriorhodopsin proton pump

Weighted persistent homology for biomolecular data analysis

In this paper, we systematically review weighted persistent homology (WPH) models and their applications in biomolecular data analysis. Essentially, the weight value, which reflects physical, chemical and biological properties, can be assigned to vertices (atom centers), edges (bonds), or higher order simplexes (cluster of atoms), depending on the biomolecular structure, function, and dynamics properties. Further, we propose the first localized weighted persistent homology (LWPH). Inspired by the great success of element specific persistent homology (ESPH), we do not treat biomolecules as an inseparable system like all previous weighted models, instead we decompose them into a series of local domains, which may be overlapped with each other. The general persistent homology or weighted persistent homology analysis is then applied on each of these local domains. In this way, functional properties, that are embedded in local structures, can be revealed. Our model has been applied to systematically studying DNA structures. It has been found that our LWPH based features can be used to successfully discriminate the A-, B-, and Z-types of DNA. More importantly, our LWPH based PCA model can identify two configurational states of DNA structure in ion liquid environment, which can be revealed only by the complicated helical coordinate system. The great consistence with the helical-coordinate model demonstrates that our model captures local structure variations so well that it is comparable with geometric models. Moreover, geometric measurements are usually defined in very local regions. For instance, the helical-coordinate system is limited to one or two basepairs. However, our LWPH can quantitatively characterize structure information in local regions or domains with arbitrary sizes and shapes, where traditional geometrical measurements fail.Comment: 27 pages; 18 figure

Geometric algorithms for cavity detection on protein surfaces

Macromolecular structures such as proteins heavily empower cellular processes or functions. These biological functions result from interactions between proteins and peptides, catalytic substrates, nucleotides or even human-made chemicals. Thus, several interactions can be distinguished: protein-ligand, protein-protein, protein-DNA, and so on. Furthermore, those interactions only happen under chemical- and shapecomplementarity conditions, and usually take place in regions known as binding sites. Typically, a protein consists of four structural levels. The primary structure of a protein is made up of its amino acid sequences (or chains). Its secondary structure essentially comprises -helices and -sheets, which are sub-sequences (or sub-domains) of amino acids of the primary structure. Its tertiary structure results from the composition of sub-domains into domains, which represent the geometric shape of the protein. Finally, the quaternary structure of a protein results from the aggregate of two or more tertiary structures, usually known as a protein complex. This thesis fits in the scope of structure-based drug design and protein docking. Specifically, one addresses the fundamental problem of detecting and identifying protein cavities, which are often seen as tentative binding sites for ligands in protein-ligand interactions. In general, cavity prediction algorithms split into three main categories: energy-based, geometry-based, and evolution-based. Evolutionary methods build upon evolutionary sequence conservation estimates; that is, these methods allow us to detect functional sites through the computation of the evolutionary conservation of the positions of amino acids in proteins. Energy-based methods build upon the computation of interaction energies between protein and ligand atoms. In turn, geometry-based algorithms build upon the analysis of the geometric shape of the protein (i.e., its tertiary structure) to identify cavities. This thesis focuses on geometric methods. We introduce here three new geometric-based algorithms for protein cavity detection. The main contribution of this thesis lies in the use of computer graphics techniques in the analysis and recognition of cavities in proteins, much in the spirit of molecular graphics and modeling. As seen further ahead, these techniques include field-of-view (FoV), voxel ray casting, back-face culling, shape diameter functions, Morse theory, and critical points. The leading idea is to come up with protein shape segmentation, much like we commonly do in mesh segmentation in computer graphics. In practice, protein cavity algorithms are nothing more than segmentation algorithms designed for proteins.Estruturas macromoleculares tais como as proteínas potencializam processos ou funções celulares. Estas funções resultam das interações entre proteínas e peptídeos, substratos catalíticos, nucleótideos, ou até mesmo substâncias químicas produzidas pelo homem. Assim, há vários tipos de interacções: proteína-ligante, proteína-proteína, proteína-DNA e assim por diante. Além disso, estas interações geralmente ocorrem em regiões conhecidas como locais de ligação (binding sites, do inglês) e só acontecem sob condições de complementaridade química e de forma. É também importante referir que uma proteína pode ser estruturada em quatro níveis. A estrutura primária que consiste em sequências de aminoácidos (ou cadeias), a estrutura secundária que compreende essencialmente por hélices e folhas , que são subsequências (ou subdomínios) dos aminoácidos da estrutura primária, a estrutura terciária que resulta da composição de subdomínios em domínios, que por sua vez representa a forma geométrica da proteína, e por fim a estrutura quaternária que é o resultado da agregação de duas ou mais estruturas terciárias. Este último nível estrutural é frequentemente conhecido por um complexo proteico. Esta tese enquadra-se no âmbito da conceção de fármacos baseados em estrutura e no acoplamento de proteínas. Mais especificamente, aborda-se o problema fundamental da deteção e identificação de cavidades que são frequentemente vistos como possíveis locais de ligação (putative binding sites, do inglês) para os seus ligantes (ligands, do inglês). De forma geral, os algoritmos de identificação de cavidades dividem-se em três categorias principais: baseados em energia, geometria ou evolução. Os métodos evolutivos baseiam-se em estimativas de conservação das sequências evolucionárias. Isto é, estes métodos permitem detectar locais funcionais através do cálculo da conservação evolutiva das posições dos aminoácidos das proteínas. Em relação aos métodos baseados em energia estes baseiam-se no cálculo das energias de interação entre átomos da proteína e do ligante. Por fim, os algoritmos geométricos baseiam-se na análise da forma geométrica da proteína para identificar cavidades. Esta tese foca-se nos métodos geométricos. Apresentamos nesta tese três novos algoritmos geométricos para detecção de cavidades em proteínas. A principal contribuição desta tese está no uso de técnicas de computação gráfica na análise e reconhecimento de cavidades em proteínas, muito no espírito da modelação e visualização molecular. Como pode ser visto mais à frente, estas técnicas incluem o field-of-view (FoV), voxel ray casting, back-face culling, funções de diâmetro de forma, a teoria de Morse, e os pontos críticos. A ideia principal é segmentar a proteína, à semelhança do que acontece na segmentação de malhas em computação gráfica. Na prática, os algoritmos de detecção de cavidades não são nada mais que algoritmos de segmentação de proteínas

Three-dimensional alpha shapes

Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is sometimes useful or required to compute what one might call the ``shape'' of the set. For that purpose, this paper introduces the formal notion of the family of $\alpha$-shapes of a finite point set in \Real^3. Each shape is a well-defined polytope, derived from the Delaunay triangulation of the point set, with a parameter \alpha \in \Real controlling the desired level of detail. An algorithm is presented that constructs the entire family of shapes for a given set of size $n$ in time $O(n^2)$, worst case. A robust implementation of the algorithm is discussed and several applications in the area of scientific computing are mentioned.Comment: 32 page