Spatial Graphs and Their Application to Complex Molecular Structures

空间图及其在复杂分子结构中的应用

• 批准号: 1607744
• 负责人: Erica Flapan
• 金额: $ 19.7万
• 依托单位: Pomona College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-07-01 至 2022-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1607744&HistoricalAwards=false
• 关键词: Spatial; Graphs; Their; Application; Complex

The broad goal of this research project is to use the tools of topology and geometry to help molecular biologists and chemists better understand the structure and behavior of DNA, proteins, and complex synthetic molecules. The topological model under study would help molecular biologists by simplifying the analysis of the site-specific recombination mechanism for closed circular DNA molecules. The investigator also aims to identify the forms of knots, links, and non-planar graphs that arise in proteins, and to model how these complex structures may have occurred. This information may offer valuable insights into protein folding mechanisms and degradation pathways. Synthetic organic molecules are normally too small to see with an electron microscope; when chemists synthesize a complex structure they use data from nuclear magnetic resonance (NMR) spectroscopy to provide evidence that the molecular structure has a particular form. Since these structures are large enough to be somewhat flexible, both topology and geometry have to be taken into account when comparing the symmetry properties of the NMR data to those of a physical model. The investigator is working with organic chemists to identify different types of symmetries exhibited by complex structures and to design new structures with interesting symmetry properties. In contrast with knots and links, whose topology depends exclusively on their embedding in the three dimensional sphere, the intrinsic structure of some graphs can affect the topological properties of every embedding of the graph in a given three dimensional manifold. For example, some graphs have the property that for any embedding G of the graph in a three-manifold M, there is no orientation reversing homeomorphism of the pair (M,G). Such a graph is said to be intrinsically chiral in M. The investigator will work on characterizing which graphs are intrinsically chiral in the three-sphere and in other three-dimensional manifolds, as well as determining other properties of embedded graphs which are independent of the particular embedding of the graph. The project draws on three-manifold results including Jaco-Shalen and Johannson characteristic decompositions, Mostow's rigidity theorem, Thurstons' hyperbolization theorem, and the classification of Seifert manifolds, as well as techniques from knot theory and the theory of tangles.

该研究项目的广泛目标是使用拓扑学和几何学工具来帮助分子生物学家和化学家更好地理解DNA，蛋白质和复杂合成分子的结构和行为。正在研究的拓扑模型将有助于分子生物学家简化闭合环状DNA分子的位点特异性重组机制的分析。研究人员还旨在确定蛋白质中出现的结，链接和非平面图的形式，并对这些复杂结构如何发生进行建模。这些信息可能为蛋白质折叠机制和降解途径提供有价值的见解。合成的有机分子通常太小，无法用电子显微镜看到;当化学家合成复杂的结构时，他们使用核磁共振（NMR）光谱的数据来提供分子结构具有特定形式的证据。由于这些结构是足够大的是有点灵活，拓扑结构和几何形状都必须考虑到比较的NMR数据的对称性的物理模型。研究人员正在与有机化学家合作，以确定复杂结构所表现出的不同类型的对称性，并设计具有有趣对称性的新结构。与纽结和链环的拓扑完全取决于它们在三维球面中的嵌入相反，某些图的内在结构可以影响图在给定三维流形中的每个嵌入的拓扑性质。例如，一些图具有这样的性质，即对于图在三流形M中的任何嵌入G，不存在对（M，G）的方向反转同胚。这样的图被称为M中的固有手征图。研究人员将致力于表征哪些图形在三维球面和其他三维流形中具有内在手性，以及确定嵌入图形的其他属性，这些属性独立于图形的特定嵌入。该项目借鉴了三个流形的结果，包括M-Shalen和Johannson特征分解，Mostow的刚性定理，Thurstons的双曲化定理和塞弗特流形的分类，以及来自纽结理论和缠结理论的技术。