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A New Euler's Formula for DNA Polyhedra

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  • Guang Hu
  • Wen-Yuan Qiu
  • Arnout Ceulemans

Abstract

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 , of crossings , and of Seifert circles are related by a simple and elegant formula: . 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.

Suggested Citation

  • Guang Hu & Wen-Yuan Qiu & Arnout Ceulemans, 2011. "A New Euler's Formula for DNA Polyhedra," PLOS ONE, Public Library of Science, vol. 6(10), pages 1-6, October.
    • Handle: RePEc:plo:pone00:0026308
    DOI: 10.1371/journal.pone.0026308
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    References listed on IDEAS

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    1. Shawn M. Douglas & Hendrik Dietz & Tim Liedl & Björn Högberg & Franziska Graf & William M. Shih, 2009. "Self-assembly of DNA into nanoscale three-dimensional shapes," Nature, Nature, vol. 459(7245), pages 414-418, May.
    2. Yu He & Tao Ye & Min Su & Chuan Zhang & Alexander E. Ribbe & Wen Jiang & Chengde Mao, 2008. "Hierarchical self-assembly of DNA into symmetric supramolecular polyhedra," Nature, Nature, vol. 452(7184), pages 198-201, March.
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