Tunnels and Voids in Molecules via Voronoi Diagrams and Beta-Complexes

Kim, Deok-Soo; Cho, Youngsong; Kim, Jae-Kwan; Sugihara, Kōkichi

doi:10.1007/978-3-642-41905-8_7

Cited by 11 publications

(11 citation statements)

References 32 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%

“…The aw‐Voronoi diagram has also been used for the detection of tunnels and cavities in proteins [KCKS13], for the computation, visualization and analysis of Connolly surfaces [RKC*05, RPK07, MJK16] and molecular paths [LBH11]. The method [RKC*05] also navigates a shrinking probe along diagram edges, but it does not handle disconnected cases.…”

Section: Related Workmentioning

confidence: 99%

“…The key difference is that the previous methods are not applicable to the problem if the balls have different radii, as in the case of molecular structures because the methods are not able to model uniform expansion/shrinking of nonuniform balls. Other methods that detect cavities via aw‐Voronoi diagrams or via their dual structures [KCKS13, KSS*14] require the probe radius to be specified prior to cavities detection, which is something that we really want to avoid in this paper.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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%

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

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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“…Equation implies that Vor Cmpl is obtained by trimming Vor with each atom in A O . It is known that the Voronoi complement and the space external to the molecule A O are homotopy equivalent . Therefore, they have an identical topological property and the structure of a Voronoi complement can be used to correctly recognize the structure of voids.…”

Section: Methodsmentioning

confidence: 99%

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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“…Then the paths connecting two user-specified points can be computed on the filtered graph. The utilization of AWVD for analysis of biomolecules was also proposed in [13], [21], [22] and implemented in tools BetaTunnel, BetaVoid and BetaMol. Another implementation of AWVD is the awVoronoi project following the approach described in [23].…”

Section: Related Workmentioning

confidence: 99%

CAVER: Algorithms for Analyzing Dynamics of Tunnels in Macromolecules

Pavelka¹,

Šebestová

Kozlíková³

et al. 2016

IEEE/ACM Trans. Comput. Biol. and Bioinf.

128

107

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The biological function of a macromolecule often requires that a small molecule or ion is transported through its structure. The transport pathway often leads through void spaces in the structure. The properties of transport pathways change significantly in time; therefore, the analysis of a trajectory from molecular dynamics rather than of a single static structure is needed for understanding the function of pathways. The identification and analysis of transport pathways are challenging because of the high complexity and diversity of macromolecular shapes, the thermal motion of their atoms, and the large amount of conformations needed to properly describe conformational space of protein structure. In this paper, we describe the principles of the CAVER 3.0 algorithms for the identification and analysis of properties of transport pathways both in static and dynamic structures. Moreover, we introduce the improved clustering solution for finding tunnels in macromolecules, which is included in the latest CAVER 3.02 version. Voronoi diagrams are used to identify potential pathways in each snapshot of a molecular dynamics trajectory and clustering is then used to find the correspondence between tunnels from different snapshots. Furthermore, the geometrical properties of pathways and their evolution in time are computed and visualized.

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Tunnels and Voids in Molecules via Voronoi Diagrams and Beta-Complexes

Cited by 11 publications

References 32 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

BetaVoid: Molecular voids via beta-complexes and Voronoi diagrams

CAVER: Algorithms for Analyzing Dynamics of Tunnels in Macromolecules

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