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The most popular molecular surface in molecular visualization is the solvent excluded surface (SES). It provides information about the accessibility of a biomolecule for a solvent molecule that is geometrically approximated by a sphere. During a period of almost four decades, the SES has served for many purposes – including visualization, analysis of molecular interactions and the
study of cavities in molecular structures. However, if one is interested in the surface that is accessible to a molecule whose shape differs significantly from a sphere, a different concept is necessary. To address this problem, we generalize the definition of the SES by replacing the probe sphere with the full geometry of the ligand defined by the arrangement of its van der Waals spheres. We call
the new surface ligand excluded surface (LES) and present an efficient, grid-based algorithm for its computation. Furthermore, we show that this algorithm can also be used to compute molecular cavities that could host the ligand molecule. We provide a detailed description of its implementation on CPU and GPU. Furthermore, we present a performance and convergence analysis and compare the LES for several molecules, using as ligands either water or small organic molecules.
Comets display with decreasing solar distance an increased emission of gas and dust particles, leading to the formation of the coma and tail. Spacecraft missions provide insight in the temporal and spatial variations of the dust and gas sources located on the cometary nucleus. For the case of comet 67P/Churyumov-Gerasimenko (67P/C-G), the long-term obser- vations from the Rosetta mission point to a homogeneous dust emission across the entire illuminated surface. Despite the homogeneous initial dis- tribution, a collimation in jet-like structures becomes visible. We propose that this observation is linked directly to the complex shape of the nucleus and projects concave topographical features into the dust coma. To test this hypothesis, we put forward a gas-dust description of 67P/C-G, where gravitational and gas forces are accurately determined from the surface mesh and the rotation of the nucleus is fully incorporated. The emerging jet-like structures persist for a wide range of gas-dust interactions and show a dust velocity dependent bending.
Ancient Egyptian papyri are often folded, rolled up or kept as small packages, sometimes even sealed. Physically unrolling or unfolding these packages might severely damage them. We demonstrate a way to get access to the hidden script without physical unfolding by employing computed tomography and mathematical algorithms for virtual unrolling and unfolding. Our algorithmic approaches are combined with manual interaction. This provides the necessary flexibility to enable the unfolding of even complicated and partly damaged papyrus packages. In addition, it allows us to cope with challenges posed by the structure of ancient papyrus, which is rather irregular, compared to other writing substrates like metallic foils or parchment. Unfolding of packages is done in two stages. In the first stage, we virtually invert the physical folding process step by step until the partially unfolded package is topologically equivalent to a scroll or a papyrus sheet folded only along one fold line. To minimize distortions at this stage, we apply the method of moving least squares. In the second stage, the papyrus is simply flattened, which requires the definition of a medial surface. We have applied our software framework to several papyri. In this work, we present the results of applying our approaches to mockup papyri that were either rolled or folded along perpendicular fold lines. In the case of the folded papyrus, our approach represents the first attempt to address the unfolding of such complicated folds.
Structural properties of molecules are of primary concern in many fields. This report provides a comprehensive overview on techniques that have been developed in the fields of molecular graphics and visualization with a focus on applications in structural biology. The field heavily relies on computerized geometric and visual representations of three-dimensional, complex, large and time-varying molecular structures. The report presents a taxonomy that demonstrates which areas of molecular visualization have already been extensively investigated and where the field is currently heading. It discusses visualizations for molecular structures, strategies for efficient display regarding image quality and frame rate, covers different aspects of level of detail and reviews visualizations illustrating the dynamic aspects of molecular simulation data. The survey concludes with an outlook on promising and important research topics to foster further success in the development of tools that help to reveal molecular secrets.
We compute trajectories of dust grains starting from a homogeneous surface activity-profile on a irregularly shaped cometary nucleus. Despite the initially homogeneous dust distribution a collimation in jet-like structures becomes visible. The fine structure is caused by concave topographical features with similar bundles of normal vectors. The model incorporates accurately determined gravitational forces, rotation of the nucleus, and gas-dust interaction. Jet-like dust structures are obtained for a wide range of gas-dust interactions. For the comet 67P/Churyumov-Gerasimenko, we derive the global dust distribution around the nucleus and find several areas of agreement between the homogeneous dust emission model and the Rosetta observation of dust jets, including velocity-dependent bending of trajectories.
In this report we review and structure the branch of molecular visualization that is concerned with the visual analysis of cavities in macromolecular protein structures. First the necessary background, the domain terminology, and the goals of analytical reasoning are introduced. Based on a comprehensive collection of relevant research works, we present a novel classification for cavity detection approaches and structure them into four distinct classes: grid-based, Voronoi-based, surface-based, and probe-based methods. The subclasses are then formed by their combinations. We match these approaches with corresponding visualization technologies starting with direct 3D visualization, followed with non-spatial visualization techniques that for example abstract the interactions between structures into a relational graph, straighten the cavity of interest to see its profile in one view, or aggregate the time sequence into a single contour plot. We also discuss the current state of methods for the visual analysis of cavities in dynamic data such as molecular dynamics simulations. Finally, we give an overview of the most common tools that are actively developed and used in the structural biology and biochemistry research. Our report is concluded by an outlook on future challenges in the field.
The analysis and visualization of nucleic acids (RNA and DNA) is playing an increasingly important role due to their fundamental importance for all forms of life and the growing number of known 3D structures of such molecules. The great complexity of these structures, in particular, those of RNA, demands interactive visualization to get deeper insights into the relationship between the 2D secondary structure motifs and their 3D tertiary structures. Over the last decades, a lot of research in molecular visualization has focused on the visual exploration of protein structures while nucleic acids have only been marginally addressed. In contrast to proteins, which are composed of amino acids, the ingredients of nucleic acids are nucleotides. They form structuring patterns that differ from those of proteins and, hence, also require different visualization and exploration techniques. In order to support interactive exploration of nucleic acids, the computation of secondary structure motifs as well as their visualization in 2D and 3D must be fast. Therefore, in this paper, we focus on the performance of both the computation and visualization of nucleic acid structure. We present a ray casting-based visualization of RNA and DNA secondary and tertiary structures, which enables for the first time real-time visualization of even large molecular dynamics trajectories. Furthermore, we provide a detailed description of all important aspects to visualize nucleic acid secondary and tertiary structures. With this, we close an important gap in molecular visualization.
The historical importance of ancient manuscripts is unique since they provide information about the heritage of ancient cultures. Often texts are hidden in rolled or folded documents. Due to recent impro- vements in sensitivity and resolution, spectacular disclosures of rolled hidden texts were possible by X-ray tomography. However, revealing text on folded manuscripts is even more challenging. Manual unfolding is often too risky in view of the fragile condition of fragments, as it can lead to the total loss of the document. X-ray tomography allows for virtual unfolding and enables non-destructive access to hid- den texts. We have recently demonstrated the procedure and tested unfolding algorithms on a mockup sample. Here, we present results on unfolding ancient papyrus packages from the papyrus collection of the Musée du Louvre, among them objects folded along approximately orthogonal folding lines. In one of the packages, the first identification of a word was achieved, the Coptic word for “Lord”.
One of the fundamental problems in neurobiological research is to understand how neural circuits generate behaviors in response to sensory stimuli. Elucidating such neural circuits requires anatomical and functional information about the neurons that are active during the processing of the sensory information and generation of the respective response, as well as an identification of the connections between these neurons. With modern imaging techniques, both morphological properties of individual neurons as well as functional information related to sensory processing, information integration and behavior can be obtained. Given the resulting information, neurobiologists are faced with the task of identifying the anatomical structures down to individual neurons that are linked to the studied behavior and the processing of the respective sensory stimuli. Here, we present a novel interactive tool that assists neurobiologists in the aforementioned task by allowing them to extract hypothetical neural circuits constrained by anatomical and functional data. Our approach is based on two types of structural data: brain regions that are anatomically or functionally defined, and morphologies of individual neurons.
Both types of structural data are interlinked and augmented with additional information. The presented tool allows the expert user to identify neurons using Boolean queries. The interactive formulation of these queries is supported by linked views, using, among other things, two novel 2D abstractions of neural circuits.
The approach was validated in two case studies investigating the neural basis of vision-based behavioral responses in zebrafish larvae. Despite this particular application, we believe that the presented tool will be of general interest for exploring hypotheses about neural circuits in other species, genera and taxa.
Our ability to grasp and understand complex phenomena is essentially based on recognizing structures and relating these to each other. For example, any meteorological description of a weather condition and explanation of its evolution recurs to meteorological structures, such as convection and circulation structures, cloud fields and rain fronts. All of these are spatiotemporal structures, defined by time-dependent patterns in the underlying fields. Typically, such a structure is defined by a verbal description that corresponds to the more or less uniform, often somewhat vague mental images of the experts.
However, a precise, formal definition of the structures or, more generally, concepts is often desirable, e.g., to enable automated data analysis or the development of phenomenological models. Here, we present a systematic approach and an interactive tool to obtain formal definitions of spatiotemporal structures. The tool enables experts to evaluate and compare different structure definitions on the basis of data sets with time-dependent fields that contain the respective structure. Since structure definitions are typically parameterized, an essential part is to identify parameter ranges that lead to desired structures in all time steps. In addition, it is important to allow a quantitative assessment of the resulting structures simultaneously. We demonstrate the use of the tool by applying it to two meteorological examples: finding structure definitions for vortex cores and center lines of temporarily evolving tropical cyclones.
Ideally, structure definitions should be objective and applicable to as many data sets as possible. However, finding such definitions, e.g., for the common atmospheric structures in meteorology, can only be a long-term goal. The proposed procedure, together with the presented tool, is just a first systematic approach aiming at facilitating this long and arduous way.