A method for automatic building of protein structures has been developed. The method is based on the concept of exible 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. The positions, orientations and internal torsion angles of all structure units are re®ned by a phased¯exible re®nement. Individual structure units are connected into polyalanine chains. The sequence is aligned by combined marker and rotamer methods. The side chains are built either by the marker method and a full conformational search or by the rotamer method. Side chains are independent structure units. The structure unit represents a generalized atom and the group model can be re®ned by the least-squares method. The protein model is built with an accuracy of about 0.2 A Ê at resolutions of 1.2±1.9 A Ê . Partial results can be obtained at resolutions of between 2.0 and 2.3 A Ê .

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. A fast rotation function, which is calculated at each grid point of the asymmetric unit, is used to find the fragment orientation. Position, orientation and internal torsion angles are refined. An algorithm for chain building is simplified using generalized atoms and virtual bonds. The structure is built from molecular structure units rather than from individual atoms. A polyalanine model is built with a high accuracy at resolutions 1.2-2.1 A.

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A method for studying conformation spaces in n dimensions has been developed. The method is used to calculate preferences of conformation families for the purpose of model building.

Methods for automatic structure determination [Pavel~fk (1988). Acta Cryst. A44, 724-729] have been extended by routines utilizing Patterson peaks and a new version of the XFPS computer program [Pavel-~fk, Rizzoli & Andreetti (1990). Univ. of Parma, Italy, and Komensky Univ., Bratislava, Czechoslovakia] has been developed. The results of test calculations were compared with those of SHELXS86 [Sheldrick (1986). Univ. of GSttingen, Germany]. About 80% of heavy-atom structures can be solved automatically.