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Topological chirality of a type of DNA and protein polyhedral links

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Abstract

Polyhedral links, interlinked and interlocked architectures, have been proposed for the description and characterization of DNA and protein polyhedra. In this paper, we study the topological chirality of a type of DNA polyhedral links constructed by the strategy of “n-point stars” and a type of protein polyhedral links constructed by “three-cross curves and untwisted double-line” covering. Furthermore, we prove that links corresponding to bipartite plane graphs have antiparallel orientations, and under these orientations, their writhes are not zero. As a result, the type of double crossover DNA polyhedral links are topologically chiral. We also prove that the unoriented link corresponding to a connected, even, bipartite plane graph always has self-writhe 0. Using the Jones polynomial for unoriented links we derive two simple criteria for chirality of unoriented alternating links with self-writhe 0. By applying this criterion we show that 3-regular protein polyhedral links are also topologically chiral. Topological chirality always implies chemical chirality, hence the corresponding DNA and protein polyhedra are all chemically chiral. Our chiral criteria may be used to detect the topological chirality of more complicated DNA and protein polyhedral links that may be synthesized by chemists and biologists in the future.

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Acknowledgments

We thank Assistant Professor Weiling Yang and Dr. Jun Ge for reading the paper. This work was supported by the grants from the National Natural Science Foundation of China (Nos. 11271307 and 11101174) and from Natural Science Foundation of Fujian Province of China (No. 2012J01019).

Conflict of interest

The authors declare that they have no conflict of interest.

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Authors and Affiliations

  1. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, Fujian, People’s Republic of China

    Xian’an Jin & Xiao-Sheng Cheng

  2. Department of Mathematics, Huizhou University, Huizhou, 516007, Guangdong, People’s Republic of China

    Xiao-Sheng Cheng

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  1. Xian’an Jin
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  2. Xiao-Sheng Cheng
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Correspondence to Xiao-Sheng Cheng.

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Jin, X., Cheng, XS. Topological chirality of a type of DNA and protein polyhedral links. J Math Chem 53, 1791–1807 (2015). https://doi.org/10.1007/s10910-015-0520-8

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  • DOI: https://doi.org/10.1007/s10910-015-0520-8

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