This subproject is one of many research subprojects utilizing the resources provided by a Center grant funded by NIH/NCRR. The subproject and investigator (PI) may have received primary funding from another NIH source, and thus could be represented in other CRISP entries. The institution listed is for the Center, which is not necessarily the institution for the investigator. The proposed research applies and investigates graph polynomials in three closely related areas: string reconstructions, DNA constructs in biomolecular computing, and structural theory for the parameterized Tutte, topological Tutte, and generalized transition polynomials. I will be focusing my research on three topics, the first two involving applications of graph polynomials, and the last building theoretical foundations of graph polynomials. I will use relations among the interlace and generalized transition polynomials and various generalizations of the Tutte polynomial to address the general question of reconstructing strings of data from sets of substrings, a problem initially motivated by DNA sequencing. I will use the generalized transition and topological Tutte polynomials, results from cycle double coverings, and tools from topological graph theory to characterizing DNA constructs at the heart of combinatorial biomolecular computing. These applications are dependent on theoretical results concerning the properties and underlying algebraic structures of graph polynomials, so I will also continue on-going foundational work on the structural properties of a variety of graph and matroid functions. This research in the field of bioinformatics seeks theoretical information to inform critical areas of biomedical research. It will impact biomedical research by providing theoretical tools to facilitate the advancement of processes in DNA sequencing by hybridization and DNA nanostructures, and will lead to more efficient sequencing and construction techniques.
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