Tunnels and Voids in Molecules via Voronoi Diagram

Kim, Deok-Soo; Sugihara, Kōkichi

doi:10.1109/isvd.2012.25

Cited by 7 publications

(7 citation statements)

References 23 publications

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“…They extract clusters of Voronoi edges and vertices along which the probe can move and use them as skeletons of voids. A similar idea was presented by Kim and Sugihara [KS12]. They trim the whole diagram by atoms and use it to describe topological properties of voids and tunnels.…”

Section: Related Workmentioning

confidence: 97%

Interactive Analysis of Connolly Surfaces for Various Probes

Maňák

Jirkovsky

Kolingerová

2016

Computer Graphics Forum

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The Connolly surface defines the boundary between a molecular structure and its environment. Its shape depends on the radius of the probe used to inspect the structure. The exploration of surface features is of great interest among chemists because it helps them to better understand and describe processes in the molecular structure. To help chemists better explore these features, we have combined two things together: a fast extraction of Connolly surfaces from a Voronoi diagram of atoms and a fast visualization based on GPU ray casting. Not only the surface but also the volume description is provided by the diagram. This enables to distinguish surface cavities one from another and compute their properties, e.g. the approximate volume, the maximal filling sphere or the maximal probe that can escape from the cavity to the outer environment. Cavities can be filtered out by applying restrictions to these properties. Views behind the surface and surface clipping improve the perception of the complex internal structure. The surface is quickly recomputed for any probe radius, so interactive changes of the probe radius show the development of cavities, especially how and where they merge together or with the outer environment.The contour-buildup algorithm was parallelized for both CPU [LBPH10] and GPU [KGE11]. The CPU variant runs in

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Section: Related Workmentioning

confidence: 97%

Interactive Analysis of Connolly Surfaces for Various Probes

Maňák

Jirkovsky

Kolingerová

2016

Computer Graphics Forum

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“…ernet.in on the theory of alpha shapes and discrete flows in Delaunay triangulations. Kim et al [11,13] propose a definition of cavities based on an alternate representation of a set of atoms called beta shapes that faithfully captures proximity. Tools based on the above approach are available and widely used [2,14,12].…”

Section: Introductionmentioning

confidence: 99%

Extraction of Robust Voids and Pockets in Proteins

Sridharamurthy

Masood

Doraiswamy³

et al. 2016

Visualization in Medicine and Life Sciences III

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Voids and pockets in a protein refer to empty spaces that are enclosed by the protein molecule. Existing methods to compute, measure, and visualize the voids and pockets in a protein molecule are sensitive to inaccuracies in the empirically determined atomic radii. This paper presents a topological framework that enables robust computation and visualization of these structures. Given a fixed set of atoms, voids and pockets are represented as subsets of the weighted Delaunay triangulation of atom centers. A novel notion of (ε, π)-stable voids helps identify voids that are stable even after perturbing the atom radii by a small value. An efficient method is described to compute these stable voids for a given input pair of values (ε, π).

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“…reported on the cavity distribution in terms of their depth from the protein boundary . Kim and Sugihara reported an algorithm for recognizing molecular voids and tunnels with their topological structures using the Voronoi diagram of atoms and the beta‐complex …”

Section: Introductionmentioning

confidence: 99%

“…The accuracy and efficiency are proved from both mathematical and computational points of view. The method we describe in this article uses the idea initially proposed by Kim and Sugihara with the geometrical property computation adopting the beta‐decomposition algorithm reported in Ref. .…”

Section: Introductionmentioning

confidence: 99%

“…47 Kim and Sugihara reported an algorithm for recognizing molecular voids and tunnels with their topological structures using the Voronoi diagram of atoms and the beta-complex. 48 However, despite the fact that void recognition is essentially a problem in geometry, it is hard to find in these previous works any general and unified framework of geometrical theory on which to base one's analysis. Most previous studies have used a grid approach, enumerating sample points in the space in which the target molecule is placed.…”

Section: Introductionmentioning

confidence: 99%

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BetaVoid: Molecular voids via beta-complexes and Voronoi diagrams

et al. 2014

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Molecular external structure is important for molecular function, with voids on the surface and interior being one of the most important features. Hence, recognition of molecular voids and accurate computation of their geometrical properties, such as volume, area and topology, are crucial, yet most popular algorithms are based on the crude use of sampling points and thus are approximations even with a significant amount of computation. In this article, we propose an analytic approach to the problem using the Voronoi diagram of atoms and the beta-complex. The correctness and efficiency of the proposed algorithm is mathematically proved and experimentally verified. The benchmark test clearly shows the superiority of BetaVoid to two popular programs: VOIDOO and CASTp. The proposed algorithm is implemented in the BetaVoid program which is freely available at the Voronoi Diagram Research Center (http://voronoi.hanyang.ac.kr).

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Tunnels and Voids in Molecules via Voronoi Diagram

Cited by 7 publications

References 23 publications

Interactive Analysis of Connolly Surfaces for Various Probes

Interactive Analysis of Connolly Surfaces for Various Probes

Extraction of Robust Voids and Pockets in Proteins

BetaVoid: Molecular voids via beta-complexes and Voronoi diagrams

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