Topological and geometric analysis will be applied to closed duplex DNA in order to predict the effects of variations in extent and type of supercoiling upon the formation of local structural elements within specific regions of the duplex. In particular, the twist and writhe will be calculated for several possible DNA structural models, including interwound superhelices of various dimensions. Mathematically this involves the further development and use of the concept of a correspondence surface. Similar techniques will be applied to calculate the twist of special local structures, such as cruciforms, both perfect and containing various specific defects. The mathematical treatment will be extended further to determine the most probable configuration for catenated circular DNA molecules of various geometries. In order to test the results of the theoretical analyses, short oligonucleotide sequences will be synthesized chemically and cloned into appropriately constructed plasmid DNAs. The sequence of principal interest in this project is the palindrome, from which a cruciform can arise as a consequence of the torsional stress which accompanies ordered reduction in the topological linking number. The critical value of the topological linking number associated with duplex structural transistions will be determined by means of resolution of topoisomers in two dimensional gel electrophoresis. The results of systematic variation in the environmental conditions will be ascertained, including temperature, ionic strength, ion composition, and pH. The consequences of the introduction of specific defects in palindromic sequences will be determined. The topological and geometric calculations will be used in two ways: (1) to analyze the free energy changes associated with the formation of specific local structural elements and (2) to predict the effect upon the global properties of the DNA of topologically constrained alterations in local duplex structure. The results obtained here, along with a projected later extention to cloned oligoribonucleotides, will provide vital thermodynamic information for the prediction of secondary and tertiary structures.