The calculation of topological structures of strands-based DNA trigonal bipyramids.

With the rapid development of DNA nanotechnology, strands-based DNA polyhedra have been reported and widely applied in chemical biology, drug delivery and materials science. A fundamental problem is to determine which topological structures such a DNA polyhedron will allow. Our goal in this paper is to determine all permissible nontrivial topological structures for DNA trigonal bipyramids with double-helical edges, which have been partially realized by one-step self-assembly of multiple DNA single-strands designed rationally. Here oriented trigonal bipyramid links (OTB links) are constructed as the mathematical models for DNA trigonal bipyramids and are further classified into 451 link types. In this process, an OTBL program is designed in the Python programming language to generate all OTB link diagrams and also to remove the same topological structures produced by the rotational symmetry of trigonal bipyramid. Our result gives a list of candidates for further synthesized DNA trigonal bipyramid prisms with required topological structures.