## Abstract

Cage structures engineered from nucleic acids are of interest in nanotechnology, for example as a means of drug delivery (Destito et al 2007). Until now, most experimentally realized DNA cages have crystallographic symmetry, such as the shape of a cube (Chen and Seeman 1991 Nature 350 631-3), a tetrahedron (Goodman et al 2005 Science 310 1661-5), an octahedron (Shih et al 2004 Nature 427 618-21) or a truncated octahedron (Zhang and Seeman 1994 J. Am. Chem. Soc. 116 1661-9). Two examples of cages with non-crystallographic symmetry, a dodecahedron and a buckyball, have been realized recently (He et al 2008 Nature 452 198-201). A characteristic feature of these realizations is the fact that the cages are built from a number of identical building blocks called tiles: 20 for the case of the dodecahedron, and 60 for the case of the buckyball. We derive here a blueprint for the organization of nucleic acid in a dodecahedral cage such that the final product has a minimal number of strands. In particular, we show that a dodecahedral cage can be realized in terms of only two circular DNA molecules. We focus on the dodecahedral cage, because the volume to surface ratio of such a cage is larger than that of its crystallographic counterparts given the same fixed radial distance of the polyhedral vertices from the centre of the structure, whilst still requiring a smaller complexity than the truncated icosahedron (buckyball). We therefore expect that the dodecahedral DNA cages discussed here may be of interest in further applications in nanotechnology.

Original language | English |
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Article number | 304043 |

Number of pages | 14 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 41 |

Issue number | 30 |

DOIs | |

Publication status | Published - 1 Aug 2008 |

## Keywords

- BRANCHED JUNCTIONS
- BUILDING-BLOCKS
- NANODEVICES
- OCTAHEDRON