标题：A Topological Approach to Assembling Strands-Based DNA Tetrahedra
作者：Liu, Shuya; Guo, Luxuan; Bai, Hui; Hao, Jincheng
作者机构：[Liu, Shuya; Guo, Luxuan; Bai, Hui; Hao, Jincheng] Shandong Univ, Sch Chem & Chem Engn, Jinan 250018, Shandong, Peoples R China.
通讯作者地址：[Hao, JC]Shandong Univ, Sch Chem & Chem Engn, Jinan 250018, Shandong, Peoples R China.
来源：MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY
摘要：With the rapid development of DNA nanotechnology, DNA polyhedra have been reported and widely applied in chemical biology, analytical chemistry, medicine and materials science. Our goal in this paper is to determine all permissible topological structures for DNA tetrahedra with double-helical edges, which have been partially realized by multiple appropriately designed oligonucleotides. Here four types of oriented twist tangles with even or odd number are designed as basic building blocks to assemble tetrahedral links as the mathematical models for DNA tetrahedra. As a result, there are a total of 26 different link types to be identified from all generated tetrahedral links. Each type includes infinite many tetrahedral links by changing the number of building blocks on each edge. Furthermore, the chirality of these links is discussed and all determined by calculating some invariants such as crossing number, twist number and HOMELY polynomial. In particular, four achiral tetrahedral links are firstly given by employing the association of tetrahedral link diagrams and their dual link diagrams. Our work provides a list of candidates for further synthesized DNA tetrahedra with required topological structures.