Library

Description: 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.

Description: This paper presents an algorithm called surfseek for selecting surfaces on the most visible features in direct volume rendering (DVR). The algorithm is based on a previously published technique (WYSIWYP) for picking 3D locations in DVR. The new algorithm projects a surface patch on the DVR image, consisting of multiple rays. For each ray the algorithm uses WYSIWYP or a variant of it to find the candidates for the most visible locations along the ray. Using these candidates the algorithm constructs a graph and computes a minimum cut on this graph. The minimum cut represents a visible and typically rather smooth surface. In the last step the selected surface is displayed. We provide examples for results using artificially generated and real-world data sets.

Description: The goal of visualization is to effectively and accurately communicate data. Visualization research has often overlooked the errors and uncertainty which accompany the scientific process and describe key characteristics used to fully understand the data. The lack of these representations can be attributed, in part, to the inherent difficulty in defining, characterizing, and controlling this uncertainty, and in part, to the difficulty in including additional visual metaphors in a well designed, potent display. However, the exclusion of this information cripples the use of visualization as a decision making tool due to the fact that the display is no longer a true representation of the data. This systematic omission of uncertainty commands fundamental research within the visualization community to address, integrate, and expect uncertainty information. In this chapter, we outline sources and models of uncertainty, give an overview of the state-of-the-art, provide general guidelines, outline small exemplary applications, and finally, discuss open problems in uncertainty visualization.

Description: Sensory-evoked signal flow, at cellular and network levels, is primarily determined by the synaptic wiring of the underlying neuronal circuitry. Measurements of synaptic innervation, connection probabilities and sub-cellular organization of synaptic inputs are thus among the most active fields of research in contemporary neuroscience. Methods to measure these quantities range from electrophysiological recordings over reconstructions of dendrite-axon overlap at light-microscopic levels to dense circuit reconstructions of small volumes at electron-microscopic resolution. However, quantitative and complete measurements at subcellular resolution and mesoscopic scales to obtain all local and long-range synaptic in/outputs for any neuron within an entire brain region are beyond present methodological limits. Here, we present a novel concept, implemented within an interactive software environment called NeuroNet, which allows (i) integration of sparsely sampled (sub)cellular morphological data into an accurate anatomical reference frame of the brain region(s) of interest, (ii) up-scaling to generate an average dense model of the neuronal circuitry within the respective brain region(s) and (iii) statistical measurements of synaptic innervation between all neurons within the model. We illustrate our approach by generating a dense average model of the entire rat vibrissal cortex, providing the required anatomical data, and illustrate how to measure synaptic innervation statistically. Comparing our results with data from paired recordings in vitro and in vivo, as well as with reconstructions of synaptic contact sites at light- and electron-microscopic levels, we find that our in silico measurements are in line with previous results.

Description: 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.