Construction And Topological Characteristics Of DNA Polyhedral Links With Odd Tangles

As the bearer of the genes, DNA plays an important part in the survival and reproduction of humanity. Moreover, DNA is also used as basic materials to assemble some novel structures like polyhedrons which are hardly achieved by the traditional strategies. While this new field evokes the interests of many scientists, it calls on a new theoretical model to analyze and characterize the unique structures and synthetic process.The thesis includes the following three parts:1. The part of the research background includes experimental background and theoretical basis. To depict these novel and complex structures, knot theory and topology have been proved to be useful tools, so the related information is introduced. DNA molecules have been used to build a variety of nanoscale structures and devices like DNA polyhedral links, the advantage and procedures to assemble these structures by DNA are presented.2. DNA polyhedral links and new Euler’s formula were put forward to deal with this challenge. By the application of mathematic instruments like topology and knot theory, different models to depict the DNA polyhedrons are unified and the computation of new Euler’s characteristics of different models are converted into the computation of new Euler’s characteristics of odd tangle polyhedral links.3. We present a new method to construct DNA polyhedral links of a given polyhedron based on truncation and topological transformation. This approach could finally solve the problem of computation of new Euler’s characteristics and provide a theoretical guide to the DNA polyhedral design.4. Since people have gained great success in the manipulation of DNA in lab, if we could use the technique developed for DNA in its counterpart—protein, the potential effect will be overwhelming. General analysis on the feasibility is conducted and the possible procedure of the synthesis of protein in lab with the assistance of DNA is predicted.