Xiong Wang, Jason T. L. Wang, Dennis Shasha, Bruce Shapiro, Sitaram Dikshitulu, Isidore Rigoutsos and Kaizhong Zhang
In this paper we present a method for discovering approximately common motifs (also known as active motifs) in three dimensional (3D) molecules. Each node in a molecule is represented by a 3D point in the Euclidean Space and each edge is represented by an undirected line segment connecting two nodes in the molecule. Motifs are rigid substructures which may occur in a molecule after allowing for an arbitrary number of rotations and translations as well as a small number (specified by the user) of node insert/delete operations in the motifs or the molecule. (We call this "approximate occurrence.") The proposed method combines the geometric hashing technique and block detection algorithms for undirected graphs. To demonstrate the utility of our algorithms, we discuss their applications to classifying three families of molecules pertaining to antibacterial sulfa drugs, anti-anxiety agents (benzodiazepines) and antiadrenergic agents (beta receptors). Experimental results indicate the good performance of our algorithms and the high quality of the discovered motifs.