Advanced implication theory. Symmetry tables.

The MIF (multiple implication function) group symmetry was assigned to all 230 space groups. Knowledge of MIF symmetry allows the calculation of an asymmetric unit. A more accurate procedure for calculating MIFs has been developed.

A novel algorithm for calculation of Fourier and asymmetric units.

A new method is presented for determining asymmetric and Fourier units based on plane groups for all space groups. These units are specifically designed to improve the calculation of fast Fourier transforms compared with the units derived from asymmetric units in the International Tables for Crystallography, Vol. A.

Performance of phased rotation, conformation and translation function: accurate protein model building with tripeptidic and tetrapeptidic fragments.

The automatic building of protein structures with tripeptidic and tetrapeptidic fragments was investigated. The oligopeptidic conformers were positioned in the electron-density map by a phased rotation, conformation and translation function and refined by a real-space refinement. The number of successfully located fragments lay within the interval 75-95% depending on the resolution and phase quality.

Building of RNA and DNA double helices into electron density.

A method has been developed that automatically fits double-helical regions into the electron density of nucleic acid structures. Rigid fragments consisting of two Watson-Crick base pairs and three pairs of phosphate groups in the A-type or B-type conformation are positioned into the electron density by phased rotation and translation functions. The position and orientation of the localized double-helical fragments are determined by phased refinement.

Conformation families of protein fragments in multidimensional torsion-angle space.

Protein conformation families for automatic model building were determined for dipeptidic, tripeptidic, tetrapeptidic and pentapeptidic fragments. Mapping in n-dimensional conformational space (n = 2, 4 and 6), a conformation-generator method, a deletion-sorting process and a verification procedure were used to calculate the conformational preferences. Torsion angles were harvested from PDB structures with resolutions better than 1.

Accurate automatic protein models.

A method for automatic building of protein structures has been developed. The method is based on the concept of flexible structure units. A structure unit is a fragment (group) of about ten atoms that is positioned in the electron density by a phased rotation and translation function.

Automatic model building based on flexible fragment formalism. The case of high-resolution protein structures.

A concept of flexible fragments has been developed for automatic building of crystal structures. Six monopeptides were designed as search fragments in a phased rotation and translation function for protein building. Electron density in crystal and in molecular fragments is expanded in spherical harmonics and normalized spherical Bessel functions.

[N-(Carboxylatomethyl)aspartato(3-)](ethylenediamine)cobalt(III) trihydrate.

The mononuclear title complex, [Co(C(6)H(6)NO(6))(C(2)H(8)N(2))].3H(2)O, contains an octahedrally coordinated Co(III) atom. The N-(carboxymethyl)aspartate moiety is coordinated as a tetradentate ligand, providing an OONO-donor set and forming two trans five-membered chelate rings and one six-membered chelate ring.

Methodology and applications of automatic electron-density map interpretation by six-dimensional rotational and translational search for molecular fragments.

The electron density for a search fragment and for the crystal is expanded in the space of spherical harmonics Bessel functions. The fast rotation function is evaluated for each grid point to test if the fragment can be orientated there. For the best scoring points, the six-dimensional coordinates of the fragment are refined by the second-derivative block-diagonal procedure.