Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Connolly M L. Solvent-accessible surfaces of proteins and nucleic acids. Science, 1983, 221: 709–713.
Connolly M L. Analytical molecular surface calculation. Journal of Applied Crystallography, 1983, 16: 548–558.
Richards F M. Areas, volumes, packing and protein structure. Annu. Rev. Biophys. Bioeng., 1977, 6: 151–176.
Varshney A, Brooks F P Jr, Richardson D C. Defining, computing, and visualizing molecular interfaces. In Proc. 6th IEEE Visualization Conference, Atlanta, USA, Oct. 1995, pp.36–43.
Halperin I, Ma B, Wolfson H, Nussinov R. Principles of docking: An overview of search algorithms and a guide to scoring functions. PROTEINS: Structure, Function, and Genetics, 2002, 47: 409–443.
Lee B, Richards F M. The interpretation of protein structures: Estimation of static accessibility. Journal of Molecular Biology, 1971, 55: 379–400.
Sanner M F, Olson A J, Spehner J-C. Reduced surface: An efficient way to compute molecular surfaces. Biopolymers, 1996, 38(3): 305–320.
Halperin D, Overmars M H. Spheres, molecules, and hidden surface removal. In Proc. 10th ACM Symp. Computational Geometry, Stony Brook, NY, USA, June 1994, pp.113–122.
Varshney A, Brooks F P Jr, Wright W V. Computing smooth molecular surfaces. IEEE Computer Graphics and Applications, 1994, 14(5): 19–25.
Bajaj C L, Lee H Y, Merkert R, Pascucci V. NURBS based B-rep models for macromolecules and their properties. In Proc. 4th Symposium on Solid Modeling and Applications, Atlanta, USA, May 1997, pp.217–228.
Bajaj C L, Pascucci V, Shamir A, Holt R J, Netravali A N. Dynamic maintenance and visualization of molecular surfaces. Discrete Applied Mathematics, 2003, 127: 23–51.
Kim D-S, Cho Y, Kim D et al., Kim S, Bhak J, Lee S-H. Euclidean Voronoi diagram of 3D spheres and applications to protein structure analysis. In Proc. Int. Symp. Voronoi Diagrams in Science and Engineering, Tokyo, 2004, pp.137–144.
Kim D-S, Cho Y, Kim D. Euclidean Voronoi diagram of 3D balls and its computation via tracing edges. Computer-Aided Design, 2005, 37(13): 1412–1424.
Kim D-S, Cho C-H, Kim D, Cho Y. Recognition of docking sites on a protein using β-shape based on Voronoi diagram of atoms. Computer-Aided Design. (to appear)
Edelsbrunner H, Mücke E P. Three-dimensional alpha shapes. ACM Trans. Graphics, 1994, 13(1): 43–72.
Kim D-S, Cho C-H, Ryu J, Kim D. Three dimensional beta shapes. (submitted to Computer-Aided Design)
Author information
Authors and Affiliations
Corresponding author
Additional information
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.
Rights and permissions
About this article
Cite this article
Ryu, J., Park, R. & Kim, DS. Connolly Surface on an Atomic Structure via Voronoi Diagram of Atoms. J Comput Sci Technol 21, 255–260 (2006). https://doi.org/10.1007/s11390-006-0255-x
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s11390-006-0255-x