The Analysis Of Protein Structure Symmetry With DRMSD Method

Proteins are fascinating molecules. For a protein to perform its function, it has to be folded into a three dimensional structure which then may be aggregated with other protein subunits to produce a bio-molecular machine or component. Protein structures are rarely built de novo, but, instead, they usually reuse a limited number of domains by the mechanisms of domain duplication, fusion, recombination, and divergence to meet the need of new functions. With many protein structures (now over 39,000 proteins) solved and a lot of experiments done over the past decade, it has been found that most of the proteins form symmetrical oligomeric complexes consisting of two or more identical subunits. Hence,symmetry seems to be a very important ingredient in understanding protein structures and functions. Since the protein structures which contain repeated structural elements often to a remarkable degree were solved, these substructures have been receiving increased attention and extensively studied.In addition, relationships between primary sequences and tertiary structures have been extensively investigated. To explain how an amino acid sequence codes its tertiary structure, our previous work tried to find the hidden symmetry in protein sequences when the tertiary structures are symmetric. It poses a question: how should a structure be treated as symmetric?In this paper, we present a method to detect the repetitive substructures by using the modified recurrence quantification analysis and Pearson correlation analysis. We choose that, if the value of distance root-mean-square deviation (dRMSD) between two substructures of one protein is not more than 3?, we treat the two are similar. We applied this method to the proteins of theβ-propellers, jelly rolls, and beta-trefoils and the results show that this method can detect the internal repetitive structures in proteins effectively, but also can identify their location easily.