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In order to detect a motif of local structures in different protein conformations, the Delaunay tessellation is applied to protein structures represented by C(alpha) atoms only. By the Delaunay tessellation the interior space of the protein is uniquely divided up into Delaunay tetrahedra whose vertices are the C(alpha) atom positions. Some edges of the tetrahedra are virtual bonds connecting adjacent residues' C(alpha) atoms along the polypeptide chain 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 the vertex residues of one relevant tetrahedron and four surrounding it. Many sets comprised of the local structures with the same code are obtained from 293 proteins, each of which has relatively low sequence similarity with the others. The local structures in each set are similar enough to each other to represent a motif. Some of them are parts of secondary or supersecondary structures, and others are irregular, but definite structures. The method proposed here can find motifs of local structures in the Protein Data Bank much more easily and rapidly than other conventional methods, because they are represented by codes. The motifs detected in this method can provide more detailed information about specific interactions between residues in the local structures, because the edges of the Delaunay tetrahedra are regarded to express interactions between residues nearest neighbouring in space.

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