Abstract
The refinement of macromolecular structures is usually aided by prior stereochemical knowledge in the form of geometrical restraints. Such restraints are also used for the flexible sugar-phosphate backbones of nucleic acids. However, recent highly accurate structural studies of DNA suggest that the phosphate bond angles may have inadequate description in the existing stereochemical dictionaries. In this paper, we analyze the bonding deformations of the phosphodiester groups in the Cambridge Structural Database, cluster the studied fragments into six conformation-related categories and propose a revised set of restraints for the O-P-O bond angles and distances. The proposed restraints have been positively validated against data from the Nucleic Acid Database and an ultrahigh-resolution Z-DNA structure in the Protein Data Bank. Additionally, the manual classification of PO4 geometry is compared with geometrical clusters automatically discovered by machine learning methods. The machine learning cluster analysis provides useful insights and a practical example for general applications of clustering algorithms for automatic discovery of hidden patterns of molecular geometry. Finally, we describe the implementation and application of a public-domain web server for automatic generation of the proposed restraints.