Connolly Surface on an Atomic Structure via Voronoi Diagram of Atoms

One of the most important geometric structures of a protein is the Connolly surface of protein since a Connolly surface plays an important role in protein folding, docking, interactions between proteins, amongst other things. This paper presents an algorithm for precisely and efficiently computing the Connolly surface of a protein using a proposed geometric construct called β-shape based on the Voronoi diagram of atoms in the protein. Given the Voronoi diagram of atoms based on the Euclidean distance from the atom surfaces, the proposed algorithm first computes a β-shape with an appropriate probe. Then, the Connolly surface is computed by employing the blending operation on the atomic complex of the protein by the given probe.

Connolly Surface on an Atomic Structure via Voronoi Diagram of Atoms

One of the most important geometric structures of a protein is the Connolly surface of protein since a Connolly surface plays an important role in protein folding, docking, interactions between proteins, amongst other things. This paper presents an algorithm for precisely and efficiently computing the Connolly surface of a protein using a proposed geometric construct called β-shape based on the Voronoi diagram of atoms in the protein. Given the Voronoi diagram of atoms based on the Euclidean distance from the atom surfaces, the proposed algorithm first computes a β-shape with an appropriate probe. Then, the Connolly surface is computed by employing the blending operation on the atomic complex of the protein by the given probe. A preliminary version of this paper appeared in Proc. the 1st Korea-China Joint Conference on Geometric and Visual Computing. This work is supported by the Creative Research Initiative from the Ministry of Science and Technology, Korea. Joonghyun Ryu is a post-doctoral researcher in Voronoi Diagram Research Center (VDRC), Hanyang University, Korea. He received M.S. and Ph.D. degrees from Department of Industrial Engineering, Hanyang University, Korea in 1999 and 2002, respectively. Before joining the VDRC in 2004, he worked for Samsung SDS Co. Ltd., Korea developing commercial CAD/CAM software as a senior software engineer. His research interests are mainly in geometric modeling, computational geometry and optimization. Rhohun Park is currently enrolled in Master’s program at Department of Industrial Engineering, Hanyang University, Korea and works as a researcher at Voronoi Diagram Research Center, Hanyang University. He received the B.S. degree from Department of Industrial Engineering, Han-Kuk University of Foreign Language, Korea in 2004. His research interests are in geometric modeling and computational geometry. Deok-Soo Kim is a professor in Department of Industrial Engineering, Hanyang University, Korea. Before he joined the university in 1995, he worked at Applicon, USA, and Samsung Advanced Institute of Technology, Korea. He received the B.S. degree from Hanyang University, Korea, the M.S. degree from the New Jersey Institute of Technology, USA, and the Ph.D. degree from the University of Michigan, USA, in 1982, 1985 and 1990, respectively. His current research interests mainly lie in the theory and applications of Voronoi diagram while he has been interested in various geometric problems. He is current director of Voronoi Diagram Research Center supported by the Ministry of Science and Technology, Korea.