A 3D Molecular Surface Representation Supporting Neighborhood Queries 1 Thomas Seidl and Hans-Peter Kriegel Institute for Computer Science, University of Munich Leopoldstr. 11 B, D-80802 München, Germany email: { seidl | kriegel }@dbs.informatik.uni-muenchen.de Abstract: Applications in molecular biology more and more require geometric data man- agement along with physicochemical data handling. Thus, 3D structures and surfaces of molecules become basic objects in molecular databases. We propose the neighborhood query on graphs such as molecular surfaces as a fundamental query class concerning to- pological information on patch adjacency. Furthermore, we suggest a patch-based data structure, called the TriEdge structure, first, to efficiently support neighborhood query processing, and second, to save space in comparison to common 2D subdivision data structures such as the quad-edge structure or the doubly-connected edge list. In analogy to the quad-edge structure, the TriEdge structure has an algebraic interface and is imple- mented via complex pointers. However, we achieve a reduction of the space requirement by a factor of four. Finally, we investigate the time performance of our prototype which is based on an object-oriented database management system. Keywords: 3D molecular modeling, graphs in spatial databases, surface representation, neighborhood query, surface approximation, database systems in molecular biology. 1 Introduction The fundamental 3D objects in molecular biology and computational biochemistry are large molecules with several hundreds to thousands of atoms. There are various appli- cations that require access to the 3D structure of the molecules, as it is provided for pro- teins by the Brookhaven Protein Data Bank (PDB) [Ber 77]. Up to now, the PDB con- tains 3,000 proteins, enzymes, and viruses [PDB 95]. For each entry, along with infor- mation on the chemical structure of the protein, the 3D coordinates of its atoms are stored in a text file. In the last years, a new topic has been emerging in the area of protein engineering: the prediction of molecular interaction, called the docking problem. Several methods has been suggested to meet the one-to-one docking problem [Con 86], [BMH 92], [FNNW 93], [HT 94]: which constellation of two given proteins represents a stable complex? A constellation is the relative position of a molecule with respect to its dock- ing partner, and may be described by six parameters: three coordinates for translation in 3D space, and three Euler angles for rotation (cf. figure 1). Since all of these six degrees of freedom to compose two molecules together in 3D space are continuous, the constel- 1. This research was funded by the German Ministry for Research and Technology (BMFT) under grant no. 01 IB 307 B. The authors are responsible for the content of this paper. Proc. of the Fourth Int. Symposium on Large Spatial Databases (SSD ‘95), Portland, Maine, USA, Lecture Notes in Computer Science, Springer, 1995.