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Beta-decomposition for the volume and area of the union of three-dimensional balls and their offsets.
MedLine Citation:
PMID:  22396194     Owner:  NLM     Status:  Publisher    
Given a set of spherical balls, called atoms, in three-dimensional space, its mass properties such as the volume and the boundary area of the union of the atoms are important for many disciplines, particularly for computational chemistry/biology and structural molecular biology. Despite many previous studies, this seemingly easy problem of computing mass properties has not been well-solved. If the mass properties of the union of the offset of the atoms are to be computed as well, the problem gets even harder. In this article, we propose algorithms that compute the mass properties of both the union of atoms and their offsets both correctly and efficiently. The proposed algorithms employ an approach, called the Beta-decomposition, based on the recent theory of the beta-complex. Given the beta-complex of an atom set, these algorithms decompose the target mass property into a set of primitives using the simplexes of the beta-complex. Then, the molecular mass property is computed by appropriately summing up the mass property corresponding to each simplex. The time complexity of the proposed algorithm is O(m) in the worst case where m is the number of simplexes in the beta-complex that can be efficiently computed from the Voronoi diagram of the atoms. It is known in ℝ(3) that m = O(n) on average for biomolecules and m = O(n(2) ) in the worst case for general spheres where n is the number of atoms. The theory is first introduced in ℝ(2) and extended to ℝ(3) . The proposed algorithms were implemented into the software BetaMass and thoroughly tested using molecular structures available in the Protein Data Bank. BetaMass is freely available at the Voronoi Diagram Research Center web site. © 2012 Wiley Periodicals, Inc.
Deok-Soo Kim; Joonghyun Ryu; Hayong Shin; Youngsong Cho
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Publication Detail:
Type:  JOURNAL ARTICLE     Date:  2012-3-7
Journal Detail:
Title:  Journal of computational chemistry     Volume:  -     ISSN:  1096-987X     ISO Abbreviation:  -     Publication Date:  2012 Mar 
Date Detail:
Created Date:  2012-3-7     Completed Date:  -     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  9878362     Medline TA:  J Comput Chem     Country:  -    
Other Details:
Languages:  ENG     Pagination:  -     Citation Subset:  -    
Copyright Information:
Copyright © 2011 Wiley Periodicals, Inc.
Department of Industrial Engineering, Hanyang University, 17 Haengdang-dong, Seongdong-gu, Seoul 133-791, South Korea.
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