GRAPH POLYNOMIALS AND DNA STRUCTURES

绘制多项式和 DNA 结构图

• 批准号: 7381414
• 负责人: JOANNA ELLIS-MONAGHAN
• 金额: $ 6.18万
• 依托单位: UNIVERSITY OF VERMONT & ST AGRIC COLLEGE
• 依托单位国家: 美国
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-07-01 至 2007-06-30
• 项目状态: 已结题
• 来源: https://reporter.nih.gov/project-details/7381414
• 关键词: GRAPH; POLYNOMIALS; DNA; STRUCTURES

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.

该子项目是利用NIH/NCRR资助的中心赠款提供的资源的许多研究子项目之一。子弹和调查员（PI）可能已经从其他NIH来源获得了主要资金，因此可以在其他清晰的条目中代表。列出的机构适用于该中心，这不一定是调查员的机构。拟议的研究应用和研究了三个密切相关领域的多项式图：弦乐重建，生物分子计算中的DNA构建体以及参数化的Tutte，拓扑TUTTE和广义过渡多项式的结构理论。我将把研究重点放在三个主题上，即涉及图多项式应用的前两个主题，以及图形多项式的最后一个构建理论基础。我将利用交叉和广义的过渡多项式之间的关系以及TUTTE多项式的各种概括，以解决从基因组中重建数据字符串的一般问题，这是DNA测序最初动机的问题。我将使用广义的过渡和拓扑Tutte多项式，循环双重覆盖物以及拓扑图理论的工具来表征组合生物分子计算核心的DNA构建体。这些应用取决于图形多项式的属性和基础代数结构的理论结果，因此我还将继续继续进行有关多种图和矩阵函数的结构特性的基础工作。这项在生物信息学领域的研究寻求理论信息，以告知生物医学研究的关键领域。它将通过提供理论工具来影响生物医学研究，以促进通过杂交和DNA纳米结构在DNA测序中的进步，并将导致更有效的测序和构造技术。