Local similarity in organic crystals and the non-uniqueness of X-ray powder patterns

Two new concepts for molecular solids, 'local similarity' and 'boundary-preserving isometry', are defined mathematically and a theorem which relates these concepts is formulated. 'Locally similar' solids possess an identical short-range structure and a 'boundary-preserving isometry' is a new mathematical operation on a finite region of a solid that transforms mathematically a given solid to a locally similar one. It is shown further that the existence of such a 'boundary-preserving isometry' in a given solid has infinitely many 'locally similar' solids as a consequence. Chemical implications, referring to the similarity of X-ray powder patterns and patent registration, are discussed as well. These theoretical concepts, which are first introduced in a schematic manner, are proved to exist in nature by the elucidation of the crystal structure of some diketopyrrolopyrrole (DPP) derivatives with surprisingly similar powder patterns. Although the available powder patterns were not indexable, the underlying crystals could be elucidated by using the new technique of ab initio prediction of possible polymorphs and a subsequent Rietveld refinement. Further ab initio packing calculations on other molecules reveal that 'local crystal similarity' is not restricted to DPP derivatives and should also be exhibited by other molecules such as quinacridones. The 'boundary-preserving isometry' is presented as a predictive tool for crystal engineering purposes and attempts to detect it in crystals of the Cambridge Structural Database (CSD) are reported.

Protein three-dimensional structural databases: Domains, structurally aligned homologues and superfamilies

This paper reports the availability of a database of protein structural domains (DDBASE), an alignment database of homologous proteins (HOMSTRAD) and a database of structurally aligned superfamilies (CAMPASS) on the World Wide Web (WWW). DDBASE contains information on the organization of structural domains and their boundaries; it includes only one representative domain from each of the homologous families. This database has been derived by identifying the presence of structural domains in proteins on the basis of inter-secondary structural distances using the program DIAL [Sowdhamini & Blundell (1995), Protein Sci. 4, 506-520]. The alignment of proteins in superfamilies has been performed on the basis of the structural features and relationships of individual residues using the program COMPARER [Sali & Blundell (1990), J. Mol. Biol. 212, 403-428]. The alignment databases contain information on the conserved structural features in homologous proteins and those belonging to superfamilies. Available data include the sequence alignments in structure-annotated formats and the provision for viewing superposed structures of proteins using a graphical interface. Such information, which is freely accessible on the WWW, should be of value to crystallographers in the comparison of newly determined protein structures with previously identified protein domains or existing families.