The investigator and his colleagues are developing new theory and computational algorithms to improve and extend current methods for analysis of biological macromolecules and their assemblies by x-ray diffraction analysis. The new algorithms specifically target problems where the molecules are, or can be, oriented, but not crystallized. The number of such systems is large; including nucleic acids, muscle proteins, viruses, bacteriophages and some membrane proteins. These new algorithms will extend current methods to systems that are currently inaccessible, and will reduce the time and cost involved in such studies. The structural information obtained from such studies contributes to our understanding or the structure-function relationships in such systems. The manipulation of biological molecules and processes is fundamental to the prevention and treatment of disease, and to the development of new, and environmentally friendly, biomaterials. Success depends, however, on a detailed understanding of the structure of the molecules at the atomic level, and relationships to their behavior and properties. This project is concerned with new computational methods for studying the atomic structures of certain biological molecules using x-ray diffraction analysis. The approach is a synthesis of techniques from mathematics and modern computing, to model and analyze biological systems. The new algorithms being developed will broaden the scope, and improve the efficiency, of such investigations.