Structural alignment of proteins by a novel TOPOFIT method, as a superimposition of common volumes at a topomax point

Similarity of protein structures has been analyzed using three-dimensional Delaunay triangulation patterns derived from the backbone representation. It has been found that structurally related proteins have a common spatial invariant part, a set of tetrahedrons, mathematically described as a common spatial subgraph volume of the three-dimensional contact graph derived from Delaunay tessellation (DT). Based on this property of protein structures, we present a novel common volume superimposition (TOPOFIT) method to produce structural alignments. Structural alignments usually evaluated by a number of equivalent (aligned) positions (N^e) with corresponding root mean square deviation (RMSD). The superimposition of the DT patterns allows one to uniquely identify a maximal common number of equivalent residues in the structural alignment. In other words, TOPOFIT identifies a feature point on the RMSD N _e curve, a topomax point, until which the topologies of two structures correspond to each other, including backbone and interresidue contacts, whereas the growing number of mismatches between the DT patterns occurs at larger RMSD (N_e) after the topomax point. It has been found that the topomax point is present in all alignments from different protein structural classes; therefore, the TOPOFIT method identifies common, invariant structural parts between proteins. The alignments produced by the TOPOFIT method have a good correlation with alignments produced by other current methods. This novel method opens new opportunities for the comparative analysis of protein structures and for more detailed studies on understanding the molecular principles of tertiary structure organization and functionality. The TOPOFIT method also helps to detect conformational changes, topological differences in variable parts, which are particularly important for studies of variations in active/binding sites and protein classification.