Multivariate analysis of a data matrix containing A-DNA and B-DNA dinucleoside monophosphate steps: Multidimensional Ramachandran plots for nucleic acids

A method to construct the equivalent of multidimensional Ramachandran plots for nucleic acids on the basis of singular value decomposition (SVD) is presented. For this purpose, a data matrix containing 244 DNA dinucleoside monophosphate steps, represented by nine torsion angles, was decomposed into a score and loading matrix. It is shown that biplots, containing both score points and loading vectors, provide a simple tool to interpret the principles of DNA class separation. Scores separate the data matrix into one A-DNA class, two different B-DNA classes, and one so-called crankshaft class. Loading vectors correlate torsion angles. The projections of scores on loading vectors indicate which torsion angles play a dominant role in DNA class separation. The results of the biplots are supported by (simple) physical interpretations. From a three-dimensional score space the nine original torsion angles can be reconstructed. Hence, the potential to create the multidimensional equivalent of a Ramachandran plot is available; that is, forbidden and accessible regions in the reduced space reflect these same regions in the nine-dimensional original space.