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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.
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.
Introduction – Many biological structures show recurring tiling patterns on one structural level or the other. Current image acquisition techniques are able to resolve those tiling patterns to allow quantitative analyses. The resulting image data, however, may contain an enormous number of elements. This renders manual image analysis infeasible, in particular when statistical analysis is to be conducted, requiring a larger number of image data to be analyzed. As a consequence, the analysis process needs to be automated to a large degree. In this paper, we describe a multi-step image segmentation pipeline for the automated segmentation of the calcified cartilage into individual tesserae from computed tomography images of skeletal elements of stingrays.
Methods – Besides applying state-of-the-art algorithms like anisotropic diffusion smoothing, local thresholding for foreground segmentation, distance map calculation, and hierarchical watershed, we exploit a graph-based representation for fast correction of the segmentation. In addition, we propose a new distance map that is computed only in the plane that locally best approximates the calcified cartilage. This distance map drastically improves the separation of individual tesserae. We apply our segmentation pipeline to hyomandibulae from three individuals of the round stingray (Urobatis halleri), varying both in age and size.
Results – Each of the hyomandibula datasets contains approximately 3000 tesserae. To evaluate the quality of the automated segmentation, four expert users manually generated ground truth segmentations of small parts of one hyomandibula. These ground truth segmentations allowed us to compare the segmentation quality w.r.t. individual tesserae. Additionally, to investigate the segmentation quality of whole skeletal elements, landmarks were manually placed on all tesserae and their positions were then compared to the segmented tesserae. With the proposed segmentation pipeline, we sped up the processing of a single skeletal element from days or weeks to a few hours.