title: An exact description of five-membered ring configurations. II. Applications to furanose rings in DNA and RNA, analysis of errors, and bond angle bending energy.
abstract: The method developed in Paper I (the preceding paper in this issue) for the exact parameterization of the five-atom furanose ring has been applied to rings in macromolecular structures. The data include coordinates for 322 rings in A- and B-form DNA; 60 rings in Z-form DNA; 29 rings in RNA molecules; and 53 rings in two specific DNA-protein complexes. Characteristic distributions of internal coordinates [q, P, S, gamma; (bj)] for the macromolecular data sets are found to be closely similar to the corresponding distributions for the small molecule data sets, even though the uncertainties in the atomic coordinates are larger for the larger molecules. To aid in the interpretation of such data rules of thumb are given. It is shown, analytically, that the distribution of the direction angle gamma is largely determined by the bond angle bending potential. This analytical result is fully confirmed by the data, which show that the average gamma value is roughly near 90 degrees. The experimentally observed gamma for each ring tends to fall near the theoretical gamma min calculated for it by minimizing the bond angle bending potential while holding the other internal parameters constant. Such unmistakable trends are discernible by considering large data sets using the full parameterization. The effects of uncertainties in the input Cartesian coordinates are treated, and it is shown that the new parameters S and gamma are more sensitive to error than are q and P, but that the uncertainties in S and gamma decrease when S is large. The Jacobian J of the transformation from Cartesian coordinates to the coordinates [q, P, S, gamma; (bj)] is calculated. The Jacobian, which can be used in statistical studies, aids in understanding the sampling of configuration space, the distribution of S values, and the propagation of error.
authors.affiliation: Public Health Research Institute, New York, NY 10016.
authors.forename: C J
authors.initials: CJ
authors.lastname: Marzec
authors.forename: L A
authors.initials: LA
authors.lastname: Day
mesh_terms: D004247:DNA / Q000737:chemistry*; D016206:Databases, Bibliographic; D008433:Mathematics; D008968:Molecular Conformation; D009690:Nucleic Acid Conformation; D009705:Nucleosides / Q000737:chemistry*; D012313:RNA / Q000737:chemistry*
chemical_list: D009705:Nucleosides; D012313:RNA; D004247:DNA