GRAPH POLYNOMIALS AND DNA STRUCTURES

绘制多项式和 DNA 结构图

• 批准号: 7959872
• 负责人: JOANNA ELLIS-MONAGHAN
• 金额: $ 3.4万
• 依托单位: UNIVERSITY OF VERMONT & ST AGRIC COLLEGE
• 依托单位国家: 美国
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-07-01 至 2010-06-30
• 项目状态: 已结题
• 来源: https://reporter.nih.gov/project-details/7959872
• 关键词: Address; Affect; Area; Bioinformatics; Biological Process; Biological Products; Biomedical Research; Complex; Computational algorithm; Computer Retrieval of Information on Scientific Projects Database; DNA; DNA Sequence; DNA Structure; Data Set; Digital Computers; Foundations; Funding; Genetic; Grant; Graph; Heart; Institution; Lead; Methods; Nanostructures; Nanotechnology; Pharmacologic Substance; Property; Proteins; Reading; Research; Research Personnel; Resources; Source; Structure; Techniques; Time; United States National Institutes of Health; Vermont; Work; abstracting; combinatorial; improved; interest; nano; nanostructured; reconstruction; theories; tool

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. Abstract: 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 inform 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. Significance: This research in the field of bioinformatics seeks theoretical information to inform critical areas of biomedical research. The significance of this work will be manifest in its impact in two areas of bioinformatics: DNA sequencing by hybridization and the construction of DNA nanostructures pursuant to pharmaceutical applications and biomolecular computing. Both of these areas are of current critical interest in the field of bioinformatics. Improved methods for DNA sequencing will lead to more efficient identifications of DNA properties, and more efficient techniques for reading long strings of DNA. One of the current challenges in the highly promising area of biomolecular computing is encoding the mathematical concepts into DNA structures that then may be subject to biological processes which accomplish complex computational algorithms. The significance of this research is that it will provide theoretical tools for manifesting those mathematical structures as DNA nano-constructs which may then be subjected to biological processes that affect the necessary computations without the exponential time constraints of a digital computer. Furthermore, these DNA nano-structures, if rigidly constructed, have potential to be used as delivery mechanisms for other biological agents such as proteins within the body, as well other applications in the fast moving field of nano-technology.

该副本是利用众多研究子项目之一 由NIH/NCRR资助的中心赠款提供的资源。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。列出的机构是 对于中心，这不一定是调查员的机构。 摘要：拟议的研究应用并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，由循环双重覆盖物以及拓扑图理论的工具产生，以告知组合生物分子计算的核心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。 意义：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。这项工作的意义将在其在生物信息学的两个领域中的影响：通过杂交进行DNA测序以及根据药物应用和生物分子计算的DNA纳米结构的构建。这两个领域在生物信息学领域均具有目前的关键兴趣。改进的DNA测序方法将导致对DNA特性的更有效识别，以及更有效的技术来读取长链DNA的长字符串。在高度有希望的生物分子计算领域中，目前面临的挑战之一是将数学概念编码为DNA结构，这些概念可能会受到完成复杂计算算法的生物学过程。这项研究的意义在于，它将提供理论工具来表现这些数学结构为DNA纳米构造，然后可能会受到影响必要计算的生物学过程，而无需数字计算机的指数时间限制。此外，这些DNA纳米结构（如果结实构建）有可能用作其他生物学剂（例如体内蛋白质）的递送机制，以及在纳米技术快速移动领域中的其他应用。