Abstract
We initiate an algebraic approach to study DNA origami structures. We identify two types of basic building blocks and describe a DNA origami structure by their composition. These building blocks are taken as generators of a monoid, called the origami monoid, and motivated by the well studied Temperley-Lieb algebras, we identify a set of relations that characterize the origami monoid. We present several observations about Green’s relations for the origami monoid and study the relations to a direct product of Jones monoids, which is a morphic image of an origami monoid.
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Acknowledgment
This work is partially supported by NIH R01GM109459, and by NSF’s CCF-1526485 and DMS-1800443. This research was also partially supported by 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 and Simons Foundation Grant No. 594594.
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Garrett, J., Jonoska, N., Kim, H., Saito, M. (2019). Algebraic Systems Motivated by DNA Origami. In: Ćirić, M., Droste, M., Pin, JÉ. (eds) Algebraic Informatics. CAI 2019. Lecture Notes in Computer Science(), vol 11545. Springer, Cham. https://doi.org/10.1007/978-3-030-21363-3_14
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DOI: https://doi.org/10.1007/978-3-030-21363-3_14
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