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DNA origami words, graphical structures and their rewriting systems

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Abstract

We classify rectangular DNA origami structures according to their scaffold and staples organization by associating a graphical representation to each scaffold folding. Inspired by well studied Temperley–Lieb algebra, we identify basic modules that form the structures. The graphical description is obtained by ‘gluing’ basic modules one on top of the other. To each module we associate a symbol such that gluing of modules corresponds to concatenating the associated symbols. Every word corresponds to a graphical representation of a DNA origami structure. A set of rewriting rules defines equivalent words that correspond to the same graphical structure. We propose two different types of basic module structures and corresponding rewriting rules. For each type, we provide the number of all possible structures through the number of equivalence classes of words. We also give a polynomial time algorithm that computes the shortest word for each equivalence class.

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Acknowledgements

This research was (partially) supported by the Grants NSF DMS-1800443/1764366 and the Southeast Center for Mathematics and Biology, an NSF-Simons Research Center for Mathematics of Complex Biological Systems, under National Science Foundation Grant No. DMS-1764406, Simons Foundation Grant No.594594, and Incheon National University (International Cooperative) Research Grant in 2020.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of South Florida, 4202 E. Fowler Ave., Tampa, FL, 33620, USA

    James Garrett, Nataša Jonoska & Masahico Saito

  2. Department of Computer Science and Engineering, Incheon National University, 119 Academy-Ro, Yeonsu-Gu, Incheon, 22012, Republic of Korea

    Hwee Kim

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  1. James Garrett
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  2. Nataša Jonoska
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  3. Hwee Kim
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  4. Masahico Saito
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Correspondence to Hwee Kim.

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Garrett, J., Jonoska, N., Kim, H. et al. DNA origami words, graphical structures and their rewriting systems. Nat Comput 20, 217–231 (2021). https://doi.org/10.1007/s11047-020-09825-z

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  • DOI: https://doi.org/10.1007/s11047-020-09825-z

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