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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.
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.
An intuitive and sparse representation of the void space of porous materials supports the efficient analysis and visualization of interesting qualitative and quantitative parameters of such materials. We introduce definitions of the elements of this void space, here called pore space, based on its distance function, and present methods to extract these elements using the extremal structures of the distance function. The presented methods are implemented by an image processing pipeline that determines pore centers, pore paths and pore constrictions. These pore space elements build a graph that represents the topology of the pore space in a compact way. The representations we derive from μCT image data of realistic soil specimens enable the computation of many statistical parameters and, thus, provide a basis for further visual analysis and application-specific developments. We introduced parts of our pipeline in previous work. In this chapter, we present additional details and compare our results with the analytic computation of the pore space elements for a sphere packing in order to show the correctness of our graph computation.
Geometric morphometrics plays an important role in evolutionary studies. The state-of-the-art in this field are landmark-based methods. Since the landmarks usually need to be placed manually, only a limited number of landmarks are generally used to represent the shape of an anatomical structure. As a result, shape characteristics that cannot be properly represented by small sets of landmarks are disregarded.
In this study, we present a method that is free of this limitation. The method takes into account the whole shape of an anatomical structure, which is represented as a surface, hence the term ‘surface-based morphometrics’. Correspondence between two surfaces is established by defining a partitioning of the surfaces into homologous surface patches. The first step for the generation of a surface partitioning is to place landmarks on the surface. Subsequently, the landmarks are connected by curves lying on the surface. The curves, called ‘surface paths’, might either follow specific anatomical features or they can be geodesics, that is, shortest paths on the surface. One important requirement, however, is that the resulting surface path networks are topologically equivalent across all surfaces. Once the surface path networks have been defined, the surfaces are decomposed into patches according to the path networks.
This approach has several advantages. One of them is that we can discretize the surface by as many points as desired. Thus, even fine shape details can be resolved if this is of interest for the study. Since a point discretization is used, another advantage is that well-established analysis methods for landmark-based morphometrics can be utilized. Finally, the shapes can be easily morphed into one another, thereby greatly supporting the understanding of shape changes across all considered specimens.
To show the potential of the described method for evolutionary studies of biological specimens, we applied the method to the para-basisphenoid complex of the snake genus Eirenis. By using this anatomical structure as example, we present all the steps that are necessary for surface-based morphometrics, including the segmentation of the para-basisphenoid complex from micro-CT data sets. We also show some first results using statistical analysis as well as classification methods based on the presented technique.
When physical unfolding/unrolling of papyri is not possible or too dangerous for preserving the precious object, tomographic approaches may be the ap- propriate alternative. Requirements are the resolution and the contrast to distinguish writing and substrate. The steps to be performed are the following: (1) Select the object of interest (archaeological arguments, cultural back- ground of the object, etc.). (2) Find the proper physical procedure, especially with respect to contrast, take the tomographic data, e.g. by absorption x-ray tomography. (3) Apply mathematical unfolding transformations to the tomographic data, in order to obtain a 2d-planar reconstruction of text.
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.
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.
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 report concludes with an outlook on promising and important research topics to enable further success in advancing the knowledge about interaction of molecular structures.