兰州大学机构库 >化学化工学院
病毒和DNA多面体的几何学和拓扑学
Alternative TitleThe geometry and topology of Virus and DNA polyhedra
胡广
Subtype博士
Thesis Advisor邱文元
2010-05-29
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name博士
Keyword多面体理论 纽结理论 多面体链环 病毒多面体 DNA多面体
Abstract本论文感兴趣的是几何学和拓扑学在理解化学和生命现象中的应用,特别是借助多面体理论和纽结理论去研究病毒衣壳和DNA三维多面体结构。本论文的主要内容包括以下三个部分。 I. 背景知识 在第一部分,我们将给读者介绍一些理论与实验的背景知识。理论知识包括多面体理论和纽结理论,它们为本论文的研究提供了必要的数学工具。而关于病毒多面体和DNA多面体的介绍不仅给我们提供了相关实验背景和研究目标,同时这些新颖的结构还激发着我们去发展新的方法和新的理论。 II. 病毒多面体的几何和拓扑结构 病毒结构包括两个部分,一个是携带遗传信息的DNA或者RNA基因组,另一个是保护这些基因的蛋白质衣壳。在这一章我们关注的是病毒衣壳的建筑学,尤其是具有二十面体对称性的病毒。结合几何学,图论和拓扑学中的方法,基于Goldberg多面体,我们构筑了一类新颖的具有二十面体对称性的几何体,它们可以用来解释一些病毒衣壳的结构。然后,利用“缠绕覆盖”的方法我们还可以得到它们相应的多面体链环,并且考察了包括手性和分支数在内的结构性质。此外,由于富勒烯和二十面体病毒具有相似的几何学原理,所以这个方法学可以推广到富勒烯分子的系统理论分析,以及与其相关的新奇多面体的分子设计上。 III. DNA多面体的几何和拓扑结构 在结构纳米技术中,DNA 分子已经被用于组装大量的复杂三维结构,特别是多面体结构。最近的这些实验进展为理论学家们带来了一个极大地挑战,即如何构筑理论模型去模拟DNA多面体的结构和组装过程。我们的研究主要集中在探讨多面体链环的构筑方法和结构规则上。根据实验结果,首先提出了几种不同的构建方法,且构筑了一些形形色色的多面体链环。基于这些模型,我们进一步寻找一些有用的纽结不变量去刻画DNA纳米结构的复杂性。如果把DNA链看成两条反平行的纽带,这些不变量就包括交叉点数,unknotting 数和辫子指数。而如果将DNA 多面体索烃嵌入到相应的曲面上,亏格数和Seifert 环数就成为两个有用的不变量。此外,我们还借助了这些不变量去描述DNA 多面体的欧拉定理,和酶作用引起的拓扑转换。
Other AbstractThe thesis interested in applications of geometry and topology to understand chemical and biological phenomena, in particular applying polyhedral theory and knot theory to viral capsids and DNA three-dimensional nanocages. The general outline of this thesis consists of three parts. I Background In a first part, we will introduce the reader some theoretical and experimental background. The theoretical knowledge includes polyhedral theory and knot theory, which provides the necessary mathematical tools for this thesis’ research. The DNA polyhedra and virus polyhedra not only provides us with the relevant experimental background and research objectives, but also inspire us to develop new methods and new theory for their novel structures. II. The geometrical and topological structures of viral capsids Viruses consist two structural components, DNA or RNA genomes that carry genetic information, and protein capsids that protect these genes. In particular, my attention focuses on the understanding of the architecture of viral capsids, especially viruses with icosahedral symmetry. Combining the method coming form the geometry, graph theory and topology, a kind of novel geometrical objects with icosahedral symmetry, which are considered to explain some viral capsids, have been constructed based on Goldberg polyhedra. Then applying the “tangle-covering” method, their related polyhedral links have also been built and some structural properties including chirality and component numbers have been investigated. Moreover, fullerenes and icosahedral virus share the underlying geometry, and therefore this methodology could also be extended to the systematic theoretical study and the molecular design of novel models of fullerene and related polyhedra. III. The geometrical and topological properties of DNA nanostructures In structural nanotechnology, the DNA molecule has been employed to assemble a large variety of three dimensional structures which have connectivity of polyhedra. Given these recent experimental advances, it would provide a nice challenge to construct theoretical models that can describe the organization and self-assembly of DNA nanostructures. It has been proposed that polyhedral links are reasonable mathematical models for DNA polyhedra. This suggests that techniques coming from knot theory have potential applications in investigating the physico-chemical properties of these DNA nanostructures. My research is focus on the construction metho...
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/238242
Collection化学化工学院
Recommended Citation
GB/T 7714
胡广. 病毒和DNA多面体的几何学和拓扑学[D]. 兰州. 兰州大学,2010.
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