Novel method to detect a motif of local structures in different protein conformations

In order to detect a motif of local structures in different protein conform ations, the Delaunay tessellation is applied to protein structures represen ted by C-alpha atoms only. By the Delaunay tessellation the interior space of the protein is uniquely divided up into Delaunay tetrahedra whose vertic es are the C-alpha atom positions. Some edges of the tetrahedra are virtual bonds connecting adjacent residues' C-alpha atoms along the polypeptide ch ain and others indicate interactions between residues nearest neighbouring in space. The rules are proposed to assign a code, i.e., a string of digits , to each tetrahedron to characterize the local structure constructed by th e vertex residues of one relevant tetrahedron and four surrounding it. Many sets comprised of the local structures with the same code are obtained fro m 293 proteins, each of which has relatively low sequence similarity with t he others, The local structures in each set are similar enough to each othe r to represent a motif, Some of them are parts of secondary or superseconda ry structures, and others are irregular, but definite structures. The metho d proposed here can find motifs of local structures in the Protein Data Ban k much more easily and rapidly than other conventional methods, because the y are represented by codes. The motifs detected in this method can provide more detailed information about specific interactions between residues in t he local structures, because the edges of the Delaunay tetrahedra are regar ded to express interactions between residues nearest neighbouring in space.