BetaMol: A Molecular Modeling, Analysis and Visualization Software Based on the Beta-Complex and the Quasi-Triangulation

Cho, Youngsong; Kim, Jae-Kwan; Ryu, Joonghyun; Won, Chung-In; Kim, Chong-Min; Kim, Donguk; Kim, Deok-Soo

doi:10.1299/jamdsm.6.389

Cited by 10 publications

(7 citation statements)

References 33 publications

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“…The values obtained in these samples should be the same as in the case of the proposed method. BetaMol [CKR*12] uses the aw‐Voronoi diagram of atoms to extract cavities [KCKS13]. Voroprot [OMV11] also uses the aw‐Voronoi diagram, but cavities are defined differently, so the results do not match.…”

Section: Experiments and Resultsmentioning

confidence: 99%

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Exploration of Empty Space among Spherical Obstacles via Additively Weighted Voronoi Diagram

Maňák

2016

Computer Graphics Forum

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Properties of granular materials or molecular structures are often studied on a simple geometric model – a set of 3D balls. If the balls simultaneously change in size by a constant speed, topological properties of the empty space outside all these balls may also change. Capturing the changes and their subsequent classification may reveal useful information about the model. This has already been solved for balls of the same size, but only an approximate solution has been reported for balls of different sizes. These solutions work on simplicial complexes derived from the dual structure of the ordinary Voronoi diagram of ball centers and use the mathematical concept of simplicial homology groups. If the balls have different radii, it is more appropriate to use the additively weighted Voronoi diagram (also known as the Apollonius diagram) instead of the ordinary diagram, but the dual structure is no longer a simplicial complex, so the previous approaches cannot be used directly. In this paper, a method is proposed to overcome this problem. The method works with Voronoi edges and vertices instead of the dual structure. Additional bridge edges are introduced to overcome disconnected cases. The output is a tree graph of events where cavities are created or merged during a simulated shrinking of the balls. This graph is then reorganized and filtered according to some criteria to get a more concise information about the development of the empty space in the model.

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Section: Experiments and Resultsmentioning

confidence: 99%

“…Comparison of the proposed method with BetaMol [CKR*12], Voroprot [OMV11] and the method based on alpha‐shapes [LEF*98]. Voroprot gives different results because it defines cavities differently.…”

Section: Experiments and Resultsmentioning

confidence: 99%

Exploration of Empty Space among Spherical Obstacles via Additively Weighted Voronoi Diagram

Maňák

2016

Computer Graphics Forum

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“…Using the beta-shape and the optimized shape descriptor, effective pockets can be efficiently recognized and used for the docking algorithm called the BetaDock [ 38 , 39 ]. The molecular graphics in this paper were created using BetaMol, a molecular modeling, visualization, and analysis program freely available from http://voronoi.hanyang.ac.kr/software.htm [ 40 ].…”

Section: Introductionmentioning

confidence: 99%

Optimal Ligand Descriptor for Pocket Recognition Based on the Beta-Shape

et al. 2015

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Structure-based virtual screening is one of the most important and common computational methods for the identification of predicted hit at the beginning of drug discovery. Pocket recognition and definition is frequently a prerequisite of structure-based virtual screening, reducing the search space of the predicted protein-ligand complex. In this paper, we present an optimal ligand shape descriptor for a pocket recognition algorithm based on the beta-shape, which is a derivative structure of the Voronoi diagram of atoms. We investigate six candidates for a shape descriptor for a ligand using statistical analysis: the minimum enclosing sphere, three measures from the principal component analysis of atoms, the van der Waals volume, and the beta-shape volume. Among them, the van der Waals volume of a ligand is the optimal shape descriptor for pocket recognition and best tunes the pocket recognition algorithm based on the beta-shape for efficient virtual screening. The performance of the proposed algorithm is verified by a benchmark test.

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“…in R 2 ), and 3) to help users extend their understanding to R 3 and motivate to use the BetaMol program [2], a molecular modeling, analysis, and visualization program for three-dimensional molecules. 4) In addition, this paper introduces two formal definitions: The dual mapping between the Voronoi diagram and the quasi-triangulation in R 2 and a new concept of the quasi-simplicial complex which we believe will play an important role in the theory in future.…”

Section: Introductionmentioning

confidence: 99%

Voronoi diagrams, quasi-triangulations, and beta-complexes for disks in R2: the theory and implementation in BetaConcept

Kim

Cho

Kim

et al. 2014

Journal of Computational Design and Engineering

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Voronoi diagrams are powerful for solving spatial problems among particles and have been used in many disciplines of science and engineering. In particular, the Voronoi diagram of three-dimensional spheres, also called the additively-weighted Voronoi diagram, has proven its powerful capabilities for solving the spatial reasoning problems for the arrangement of atoms in both molecular biology and material sciences. In order to solve application problems, the dual structure, called the quasi-triangulation, and its derivative structure, called the beta-complex, are frequently used with the Voronoi diagram itself. However, the Voronoi diagram, the quasi-triangulation, and the beta-complexes are sometimes regarded as somewhat difficult for ordinary users to understand. This paper presents the twodimensional counterparts of their definitions and introduce the BetaConcept program which implements the theory so that users can easily learn the powerful concept and capabilities of these constructs in a plane. The BetaConcept program was implemented in the standard C++ language with MFC and OpenGL and freely available at Voronoi Diagram Research Center (http://voronoi.hanyang.ac.kr).

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BetaMol: A Molecular Modeling, Analysis and Visualization Software Based on the Beta-Complex and the Quasi-Triangulation

Cited by 10 publications

References 33 publications

Exploration of Empty Space among Spherical Obstacles via Additively Weighted Voronoi Diagram

Exploration of Empty Space among Spherical Obstacles via Additively Weighted Voronoi Diagram

Optimal Ligand Descriptor for Pocket Recognition Based on the Beta-Shape

Voronoi diagrams, quasi-triangulations, and beta-complexes for disks in R2: the theory and implementation in BetaConcept

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