A New Euler's Formula for DNA Polyhedra

作者：Hu, Guang^*; Qiu, Wen-Yuan; Ceulemans, Arnout

来源：PLos One, 2011, 6(10): e26308.

DOI：10.1371/journal.pone.0026308

• MOLECULAR DESIGN
• ARCHITECTURE
• TOPOLOGY

DNA polyhedra are cage-like architectures based on interlocked and interlinked DNA strands. We propose a formula which unites the basic features of these entangled structures. It is based on the transformation of the DNA polyhedral links into Seifert surfaces, which removes all knots. The numbers of components mu, of crossings c, and of Seifert circles s are related by a simple and elegant formula: s+mu = c+2. This formula connects the topological aspects of the DNA cage to the Euler characteristic of the underlying polyhedron. It implies that Seifert circles can be used as effective topological indices to describe polyhedral links. Our study demonstrates that, the new Euler's formula provides a theoretical framework for the stereo-chemistry of DNA polyhedra, which can characterize enzymatic transformations of DNA and be used to characterize and design novel cages with higher genus.

• 出版日期2011-10-17
• 单位功能有机分子化学国家重点实验室; 兰州大学