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

Highly Parallel Geometric Characterization and Visualization of Volumetric Data Sets

Volumetric 3D data sets are being generated in many different application areas. Some examples are CAT scans and MRI data, 3D models of protein molecules represented by implicit surfaces, multi-dimensional numeric simulations of plasma turbulence, and stacks of confocal microscopy images of cells. The size of these data sets has been increasing, requiring the speed of analysis and visualization techniques to also increase to keep up. Recent advances in processor technology have stopped increasing clock speed and instead begun increasing parallelism, resulting in multi-core CPUS and many-core GPUs. To take advantage of these new parallel architectures, algorithms must be explicitly written to exploit parallelism. In this thesis we describe several algorithms and techniques for volumetric data set analysis and visualization that are amenable to these modern parallel architectures. We first discuss modeling volumetric data with Gaussian Radial Basis Functions (RBFs). RBF representation of a data set has several advantages, including lossy compression, analytic differentiability, and analytic application of Gaussian blur. We also describe a parallel volume rendering algorithm that can create images of the data directly from the RBF representation. Next we discuss a parallel, stochastic algorithm for measuring the surface area of volumetric representations of molecules. The algorithm is suitable for implementation on a GPU and is also progressive, allowing it to return a rough answer almost immediately and refine the answer over time to the desired level of accuracy. After this we discuss the concept of Confluent Visualization, which allows the visualization of the interaction between a pair of volumetric data sets. The interaction is visualized through volume rendering, which is well suited to implementation on parallel architectures. Finally we discuss a parallel, stochastic algorithm for classifying stem cells as having been grown on a surface that induces differentiation or on a surface that does not induce differentiation. The algorithm takes as input 3D volumetric models of the cells generated from confocal microscopy. This algorithm builds on our algorithm for surface area measurement and, like that algorithm, this algorithm is also suitable for implementation on a GPU and is progressive

Festschrift zum 60. Geburtstag von Wolfgang Strasser

Die vorliegende Festschrift ist Prof. Dr.-Ing. Dr.-Ing. E.h. Wolfgang Straßer zu seinem 60. Geburtstag gewidmet. Eine Reihe von Wissenschaftlern auf dem Gebiet der Computergraphik, die alle aus der "Tübinger Schule" stammen, haben - zum Teil zusammen mit ihren Schülern - Aufsätze zu dieser Schrift beigetragen. Die Beiträge reichen von der Objektrekonstruktion aus Bildmerkmalen über die physikalische Simulation bis hin zum Rendering und der Visualisierung, vom theoretisch ausgerichteten Aufsatz bis zur praktischen gegenwärtigen und zukünftigen Anwendung. Diese thematische Buntheit verdeutlicht auf anschauliche Weise die Breite und Vielfalt der Wissenschaft von der Computergraphik, wie sie am Lehrstuhl Straßer in Tübingen betrieben wird. Schon allein an der Tatsache, daß im Bereich der Computergraphik zehn Professoren an Universitäten und Fachhochschulen aus Tübingen kommen, zeigt sich der prägende Einfluß Professor Straßers auf die Computergraphiklandschaft in Deutschland. Daß sich darunter mehrere Physiker und Mathematiker befinden, die in Tübingen für dieses Fach gewonnen werden konnten, ist vor allem seinem Engagement und seiner Ausstrahlung zu verdanken. Neben der Hochachtung vor den wissenschaftlichen Leistungen von Professor Straßer hat sicherlich seine Persönlichkeit einen entscheidenden Anteil an der spontanten Bereischaft der Autoren, zu dieser Festschrift beizutragen. Mit außergewöhnlich großem persönlichen Einsatz fördert er Studenten, Doktoranden und Habilitanden, vermittelt aus seinen reichen internationalen Beziehungen Forschungskontakte und schafft so außerordentlich gute Voraussetzungen für selbständige wissenschafliche Arbeit. Die Autoren wollen mit ihrem Beitrag Wolfgang Straßer eine Freude bereiten und verbinden mit ihrem Dank den Wunsch, auch weiterhin an seinem fachlich wie menschlich reichen und bereichernden Wirken teilhaben zu dürfen

Isosurface modelling of soft objects in computer graphics.

There are many different modelling techniques used in computer graphics to describe a wide range of objects and phenomena. In this thesis, details of research into the isosurface modelling technique are presented. The isosurface technique is used in conjunction with more traditional modelling techniques to describe the objects needed in the different scenes of an animation. The isosurface modelling technique allows the description and animation of objects that would be extremely difficult, or impossible to describe using other methods. The objects suitable for description using isosurface modelling are soft objects. Soft objects merge elegantly with each other, pull apart, bubble, ripple and exhibit a variety of other effects. The representation was studied in three phases of a computer animation project: modelling of the objects; animation of the objects; and the production of the images. The research clarifies and presents many algorithms needed to implement the isosurface representation in an animation system. The creation of a hierarchical computer graphics animation system implementing the isosurface representation is described. The scalar fields defining the isosurfaces are represented using a scalar field description language, created as part of this research, which is automatically generated from the hierarchical description of the scene. This language has many techniques for combining and building the scalar field from a variety of components. Surface attributes of the objects are specified within the graphics system. Techniques are described which allow the handling of these attributes along with the scalar field calculation. Many animation techniques specific to the isosurface representation are presented. By the conclusion of the research, a graphics system was created which elegantly handles the isosurface representation in a wide variety of animation situations. This thesis establishes that isosurface modelling of soft objects is a powerful and useful technique which has wide application in the computer graphics community

Towards Predictive Rendering in Virtual Reality

The strive for generating predictive images, i.e., images representing radiometrically correct renditions of reality, has been a longstanding problem in computer graphics. The exactness of such images is extremely important for Virtual Reality applications like Virtual Prototyping, where users need to make decisions impacting large investments based on the simulated images. Unfortunately, generation of predictive imagery is still an unsolved problem due to manifold reasons, especially if real-time restrictions apply. First, existing scenes used for rendering are not modeled accurately enough to create predictive images. Second, even with huge computational efforts existing rendering algorithms are not able to produce radiometrically correct images. Third, current display devices need to convert rendered images into some low-dimensional color space, which prohibits display of radiometrically correct images. Overcoming these limitations is the focus of current state-of-the-art research. This thesis also contributes to this task. First, it briefly introduces the necessary background and identifies the steps required for real-time predictive image generation. Then, existing techniques targeting these steps are presented and their limitations are pointed out. To solve some of the remaining problems, novel techniques are proposed. They cover various steps in the predictive image generation process, ranging from accurate scene modeling over efficient data representation to high-quality, real-time rendering. A special focus of this thesis lays on real-time generation of predictive images using bidirectional texture functions (BTFs), i.e., very accurate representations for spatially varying surface materials. The techniques proposed by this thesis enable efficient handling of BTFs by compressing the huge amount of data contained in this material representation, applying them to geometric surfaces using texture and BTF synthesis techniques, and rendering BTF covered objects in real-time. Further approaches proposed in this thesis target inclusion of real-time global illumination effects or more efficient rendering using novel level-of-detail representations for geometric objects. Finally, this thesis assesses the rendering quality achievable with BTF materials, indicating a significant increase in realism but also confirming the remainder of problems to be solved to achieve truly predictive image generation

New Models for High-Quality Surface Reconstruction and Rendering

The efficient reconstruction and artifact-free visualization of surfaces from measured real-world data is an important issue in various applications, such as medical and scientific visualization, quality control, and the media-related industry. The main contribution of this thesis is the development of the first efficient GPU-based reconstruction and visualization methods using trivariate splines, i.e., splines defined on tetrahedral partitions. Our methods show that these models are very well-suited for real-time reconstruction and high-quality visualizations of surfaces from volume data. We create a new quasi-interpolating operator which for the first time solves the problem of finding a globally C1-smooth quadratic spline approximating data and where no tetrahedra need to be further subdivided. In addition, we devise a new projection method for point sets arising from a sufficiently dense sampling of objects. Compared with existing approaches, high-quality surface triangulations can be generated with guaranteed numerical stability. Keywords. Piecewise polynomials; trivariate splines; quasi-interpolation; volume data; GPU ray casting; surface reconstruction; point set surface

New Models for High-Quality Surface Reconstruction and Rendering

The efficient reconstruction and artifact-free visualization of surfaces from measured real-world data is an important issue in various applications, such as medical and scientific visualization, quality control, and the media-related industry. The main contribution of this thesis is the development of the first efficient GPU-based reconstruction and visualization methods using trivariate splines, i.e., splines defined on tetrahedral partitions. Our methods show that these models are very well-suited for real-time reconstruction and high-quality visualizations of surfaces from volume data. We create a new quasi-interpolating operator which for the first time solves the problem of finding a globally C1-smooth quadratic spline approximating data and where no tetrahedra need to be further subdivided. In addition, we devise a new projection method for point sets arising from a sufficiently dense sampling of objects. Compared with existing approaches, high-quality surface triangulations can be generated with guaranteed numerical stability. Keywords. Piecewise polynomials; trivariate splines; quasi-interpolation; volume data; GPU ray casting; surface reconstruction; point set surface

Geometric modeling, simulation, and visualization methods for plasmid DNA molecules

Plasmid DNA molecules are a special type of DNA molecules that are used, among other applications, in DNA vaccination and gene therapy. These molecules are characterized by, when in their natural state, presenting a closed-circular conformation and by being supercoiled. The production of plasmid DNA using bacteria as hosts implies a purification step where the plasmid DNA molecules are separated from the DNA of the host and other contaminants. This purification process, and all the physical and chemical variations involved, such as temperature changes, may affect the plasmid DNA molecules conformation by uncoiling or even by open them, which makes them useless for therapeutic applications. Because of that, researchers are always searching for new purification techniques that maximize the amount of supercoiled plasmid DNA that is produced. Computer simulations and 3D visualization of plasmid DNA can bring many advantages because they allow researchers to actually see what can happen to the molecules under certain conditions. In this sense, it was necessary to develop reliable and accurate geometric models specific for plasmid DNA simulations. This dissertation presents a new assembling algorithm for B-DNA specifically developed for plasmid DNA assembling. This new assembling algorithm is completely adaptive in the sense that it allows researchers to assemble any plasmid DNA base-pair sequence along any arbitrary conformation that fits the length of the plasmid DNA molecule. This is specially suitable for plasmid DNA simulations, where conformations are generated by simulation procedures and there is the need to assemble the given base-pair sequence over that conformation, what can not be done by conventional predictive DNA assembling methods. Unlike traditional molecular visualization methods that are based on the atomic structure, this new assembling algorithm uses color coded 3D molecular surfaces of the nucleotides as the building blocks for DNA assembling. This new approach, not only reduces the amount of graphical objects and, consequently, makes the rendering faster, but also makes it easier to visually identify the nucleotides in the DNA strands. The algorithm used to triangulate the molecular surfaces of the nucleotides building blocks is also a novelty presented as part of this dissertation. This new triangulation algorithm for Gaussian molecular surfaces introduces a new mechanism that divides the atomic structure of molecules into boxes and spheres. This new space division method is faster because it confines the local calculation of the molecular surface to a specific region of influence of the atomic structure, not taking into account atoms that do not influence the triangulation of the molecular surface in that region. This new method also guarantees the continuity of the molecular surface. Having in mind that the aim of this dissertation is to present a complete set of methods for plasmid DNA visualization and simulation, it is also proposed a new deformation algorithm to be used for plasmid DNA Monte Carlo simulations. This new deformation algorithm uses a 3D polyline to represent the plasmid DNA conformation and performs small deformations on that polyline, keeping the segments length and connectivity. Experiments have been performed in order to compare this new deformation method with deformation methods traditionally used by Monte Carlo plasmid DNA simulations These experiments shown that the new method is more efficient in the sense that its trial acceptance ratio is higher and it converges sooner and faster to the elastic energy equilibrium state of the plasmid DNA molecule. In sum, this dissertation successfully presents an end-to-end set of models and algorithms for plasmid DNA geometric modelling, visualization and simulation