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Euclidean Voronoi diagrams of 3D spheres and applications to protein structure analysis

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Abstract

Despite its many important applications in various disciplines in sciences and engineering, the Euclidean Voronoi diagram for spheres in 3D space has not been studied as much as it deserves. In this paper, we present an algorithm to compute a Euclidean Voronoi diagram for 3D spheres and show how the diagram can be used in the analysis of protein structures.

Given an initial Voronoi vertex, the presented edge-tracing algorithm follows Voronoi edges until the construction is completed in O(mn) time in the worst-case, where m andn are the numbers of edges and spheres, respectively.

Once a Voronoi diagram for 3D atoms of a protein is computed, it is shown that the diagram can be used to efficiently and precisely analyze the spatial structure of the protein. It turns out that this capability of a Voronoi diagram can be crucial to solving several important problems remaining to be solved in structural biology.

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Authors and Affiliations

  1. Department of Industrial Engineering, Hanyang University, 17 Haengdangdong, Seongdonggu, 133-791, Seoul, South Korea

    Deok-Soo Kim

  2. Voronoi Diagram Research Center, Hanyang University, 17 Haengdangdong, Seongdonggu, 133-791, Seoul, South Korea

    Youngsong Cho & Donguk Kim

  3. National Genome Information Center, Korea Research Institute of Bioscience and Biotechnology, 52, Oundong, Yuseonggu, 305-333, Daejeon, South Korea

    Sangsoo Kim & Sung-Hoon Lee

  4. BioSystems Department, KAIST, 3731 Guseongdong, Yuseonggu, 305-701, Daejeon, South Korea

    Jonghwa Bhak

Authors
  1. Deok-Soo Kim
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  2. Youngsong Cho
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  3. Donguk Kim
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  4. Sangsoo Kim
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  5. Jonghwa Bhak
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  6. Sung-Hoon Lee
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Correspondence to Deok-Soo Kim.

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Kim, DS., Cho, Y., Kim, D. et al. Euclidean Voronoi diagrams of 3D spheres and applications to protein structure analysis. Japan J. Indust. Appl. Math. 22, 251–265 (2005). https://doi.org/10.1007/BF03167441

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  • DOI: https://doi.org/10.1007/BF03167441

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