Study The Self-assemble Mechanisms Of DNA Polyhedra Based On Topological Models

The thesis focused on applications of geometrical and topological methods to depict and understand structures, characters and assemble mechanisms of DNA polyhedra. Our aims is to provide more novel polyhedral molecular to candidate and new guilding principles for chemists.In general, DNA is considered as carriers that possess genetic information. However, all is overturned with the birth of the first DNA polyhedra. It is not simple genetic information carrier any longer, but is regarded as ideal raw material to build nano-structures. Then, various DNA architectures have been produced in labs.The developments of experiments require theoretical researches follow their steps as well. However, our traditional chemical theory cannot keep pace with the experiments. Therefore, it is new challenge to seek new theoretical models to simulate these novel structures. The polyhedral links is born in response to the proper time and conditions. Regardless of thickness of DNA strands and then a series of DNA polyhedral links can be constructed to simulate DNA polyhedra. We can understand the self-assemble mechanisms of DNA polyhedra well by studying these polyhedral links.To study the self-assemble mechanisms of DNA polyhedra based on polyhedral link models, three ways must be paid attention, there are:the number of strands that is required to construct a DNA polyhedron; the number of components that is required to construct a DNA polyhedron; secrets behind DNA polyhedra and molecular design. The exploration of these three cases is the clue of my thesis, all our study is around these centers.I Strands numberEach edge of the majority of known DNA polyhedra is covered by a helix with even half-turns, in other words, each face is covered by a single DNA strand, so a DNA polyhedron is composed of F (F is the total number of faces) strands. However, it is very alluring to synthesize DNA polyhedra with the least strands number. We successfully constructed DNA Sierpinski links, DNA Sierpinski knots, DNA n-order pyramids and prisms by introducing odd half-turn edges.II Components numberThe majority of DNA polyhedra consists several components no matter branched junctions or n-point stars are used. In the earlier, some scientists wanted to reduce components number of a DNA polyhedron to the limitation.However, it is never be realized. The palindromic sequences is a kind of sequences with special symmetry. The required components number will be reduce to the limitation if replace general sequences with such ones. If a polyhedron is made of n kind of faces, then the limitation of component number is n.III Molecular designThe majority of DNA polyhedra meet an elegant formula, which connects the crossing number, Seifert circles and components number. All these polyhedral molecules are homeomorphic to a sphere, so their genus are zero.However, it is new challenge to design polyhedral structures with higher genus. A series of novel molecules are designed by introducing odd half-turn edges, crossed vertex junctions and surfaces.Our work is just an elementary exploration of DNA nanostructures, the future work will be harder and more important. It is hoped that our results can provide more novel candidates for chemists and can be realized and applied in practice.