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Constructions of DNA and polypeptide cages based on plane graphs and odd crossing π-junctions

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  • Cheng, Xiao-Sheng
  • Deng, Qingying
  • Diao, Yuanan

Abstract

The constructions of three-dimensional synthetic DNA and polypeptide structures with a single closed DNA strand and polypeptide chain are mathematically based on strong traces of polyhedral graphs. However, a method developed for constructing such a DNA and polypeptide structure may impose additional restrictions on the types of strong traces and polyhedral graphs. In this paper, we show that strong traces for certain 2-connected plane graphs (allowed to have multiple edges) can be obtained using thickened graphs (sometimes called ribbon graphs) constructed with only two types of junctions : 0-crossing junction and special d(v)-crossing junction (called π-junction), where d(v) is the degree of the vertex v at which the d(v)-crossing junction is to be placed. The π-junctions are only applicable to vertices with odd degrees (≥3). We characterize the 2-connected plane graphs to which our approach can be applied and provide a brief guideline for the implementation of our method. This approach provides the theory, as well as a set of candidates, for designing and constructing stable DNA and polypeptide molecules needing only a method capable of creating the 0-crossing and π-junctions in a 2-connected plane graph.

Suggested Citation

  • Cheng, Xiao-Sheng & Deng, Qingying & Diao, Yuanan, 2023. "Constructions of DNA and polypeptide cages based on plane graphs and odd crossing π-junctions," Applied Mathematics and Computation, Elsevier, vol. 443(C).
    • Handle: RePEc:eee:apmaco:v:443:y:2023:i:c:s0096300322008414
    DOI: 10.1016/j.amc.2022.127773
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    References listed on IDEAS

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    1. Tomohisa Sawada & Yuuki Inomata & Koya Shimokawa & Makoto Fujita, 2019. "A metal–peptide capsule by multiple ring threading," Nature Communications, Nature, vol. 10(1), pages 1-8, December.
    2. Evelyn Auyeung & Ting I. N. G. Li & Andrew J. Senesi & Abrin L. Schmucker & Bridget C. Pals & Monica Olvera de la Cruz & Chad A. Mirkin, 2014. "DNA-mediated nanoparticle crystallization into Wulff polyhedra," Nature, Nature, vol. 505(7481), pages 73-77, January.
    3. Tomohisa Sawada & Ami Saito & Kenki Tamiya & Koya Shimokawa & Yutaro Hisada & Makoto Fujita, 2019. "Metal–peptide rings form highly entangled topologically inequivalent frameworks with the same ring- and crossing-numbers," Nature Communications, Nature, vol. 10(1), pages 1-7, December.
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