Ligand Excluded Surface: A New Type of Molecular Surface

Beta-complex versus Alpha-complex: Similarities and Dissimilarities

The beta-complex is a construct derived from the Voronoi diagram of spherical balls of arbitrary radii and has proven a powerful capability for proximity reasoning among spherical balls in three-dimensional space. Important applications related to molecular shapes in structural/computational molecular biology have been correctly, efficiently, and conveniently solved in the unified framework of the beta-complex and the Voronoi diagram. The beta-complex is a generalization of the ordinary alpha-complex. However, there are similarities and dissimilarities between the two complexes and it is necessary to correctly understand these similarities and dissimilarities to choose the right complex to solve application problems at hand. This paper presents the similarities and dissimilarities between these constructs and illustrates the consequence of the dissimilarity in application problems from both theoretical and practical points of view using examples of atomic arrangements.

Ellipsoidal Abstract and Illustrative Representations of Molecular Surfaces

Molecular visualization is often challenged with rendering of large molecular structures in real time. The key to LOD (level-of-detail), a classical technology, lies in designing a series of hierarchical abstractions of protein. In the paper, we improved the smoothness of transition for these abstractions by constructing a complete binary tree of a protein. In order to reduce the degree of expansion of the geometric model corresponding to the high level of abstraction, we introduced minimum ellipsoidal enveloping and some post-processing techniques. At the same time, a simple, ellipsoid drawing method based on graphics processing unit (GPU) is used that can guarantee that the drawing speed is not lower than the existing sphere-drawing method. Finally, we evaluated the rendering performance and effect on series of molecules with different scales. The post-processing techniques applied, diffuse shading and contours, further conceal the expansion problem and highlight the surface details.

Molecular Graphics: Bridging Structural Biologists and Computer Scientists

Visualization of molecular structures is one of the most common tasks carried out by structural biologists, typically using software, such as Chimera, COOT, PyMOL, or VMD. In this Perspective article, we outline how past developments in computer graphics and data visualization have expanded the understanding of biomolecular function, and we summarize recent advances that promise to further transform structural biology. We also highlight how progress in molecular graphics has been impeded by communication barriers between two communities: the computer scientists driving these advances, and the structural and computational biologists who stand to benefit. By pointing to canonical papers and explaining technical progress underlying new graphical developments in simple terms, we aim to improve communication between these communities; this, in turn, would help shape future developments in molecular graphics.

Geometric Detection Algorithms for Cavities on Protein Surfaces in Molecular Graphics: A Survey

Detecting and analyzing protein cavities provides significant information about active sites for biological processes (e.g., protein-protein or protein-ligand binding) in molecular graphics and modeling. Using the three-dimensional structure of a given protein (i.e., atom types and their locations in 3D) as retrieved from a PDB (Protein Data Bank) file, it is now computationally viable to determine a description of these cavities. Such cavities correspond to pockets, clefts, invaginations, voids, tunnels, channels, and grooves on the surface of a given protein. In this work, we survey the literature on protein cavity computation and classify algorithmic approaches into three categories: evolution-based, energy-based, and geometry-based. Our survey focuses on geometric algorithms, whose taxonomy is extended to include not only sphere-, grid-, and tessellation-based methods, but also surface-based, hybrid geometric, consensus, and time-varying methods. Finally, we detail those techniques that have been customized for GPU (Graphics Processing Unit) computing.

Real-Time Molecular Visualization Supporting Diffuse Interreflections and Ambient Occlusion

Today molecular simulations produce complex data sets capturing the interactions of molecules in detail. Due to the complexity of this time-varying data, advanced visualization techniques are required to support its visual analysis. Current molecular visualization techniques utilize ambient occlusion as a global illumination approximation to improve spatial comprehension. Besides these shadow-like effects, interreflections are also known to improve the spatial comprehension of complex geometric structures. Unfortunately, the inherent computational complexity of interreflections would forbid interactive exploration, which is mandatory in many scenarios dealing with static and time-varying data. In this paper, we introduce a novel analytic approach for capturing interreflections of molecular structures in real-time. By exploiting the knowledge of the underlying space filling representations, we are able to reduce the required parameters and can thus apply symbolic regression to obtain an analytic expression for interreflections. We show how to obtain the data required for the symbolic regression analysis, and how to exploit our analytic solution to enhance interactive molecular visualizations.