Elucidating protein secondary structures using alpha-carbon recurrence quantifications

Secondary structures of proteins were studied by recurrence quantification analysis (RQA). High-resolution, 3-dimensional coordinates of alpha-carbon atoms comprising a set of 68 proteins were downloaded from the Protein Data Bank. By fine-tuning four recurrence parameters (radius, line, residue, separation), it was possible to establish excellent agreement between percent contribution of alpha-helix and beta-sheet structures determined independently by RQA and that of the DSSP algorithm (Define Secondary Structure of Proteins). These results indicate that there is an equivalency between these two techniques, which are based upon totally different pattern recognition strategies. RQA enhances qualitative contact maps by quantifying the arrangements of recurrent points of alpha carbons close in 3-dimensional space. For example, the radius was systematically increased, moving the analysis beyond local alpha-carbon neighborhoods in order to capture super-secondary and tertiary structures. However, differences between proteins could only be detected within distances up to about 6-11 A, but not higher. This result underscores the complexity of alpha-carbon spacing when super-secondary structures appear at larger distances. Finally, RQA-defined secondary structures were found to be robust against random displacement of alpha carbons upwards of 1 A. This finding has potential import for the dynamic functions of proteins in motion.