Abstract
DNA sequences are prone to creating secondary structures by folding back on themselves by non-specific hybridization of its nucleotides. The formation of large stem-length secondary structures makes the sequences chemically inactive towards synthesis and sequencing processes. Furthermore, in DNA computing, other constraints like homopolymer run length also introduce complications. In this paper, our goal is to tackle the problems due to the creation of secondary structures in DNA sequences along with constraints such as not having a large homopolymer run length. This paper presents families of DNA codes with secondary structures of stem length at most two and homopolymer run length at most four. We identified \(\mathbb {Z}_{11}\) as an ideal structure to construct DNA codes to avoid the above problems. By mapping the error-correcting codes over \(\mathbb {Z}_{11}\) to DNA nucleotides, we obtained DNA codes with rates 0.5765 times the corresponding code rate over \(\mathbb {Z}_{11}\), including some new secondary structure-free and better-performing codes for DNA-based data storage and DNA computing purposes.
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References
Church, G.M., Gao, Y., Kosuri, S.: Next-generation digital information storage in DNA. Science 337(6102), 1628–1628 (2012)
Goldman, N., Bertone, P., Chen, S., Dessimoz, C., LeProust, E.M., Sipos, B., Birney, E.: Towards practical, high-capacity, low maintenance information storage in synthesized DNA. Nature (2013)
Yazdi, S.M.H.T., Kiah, H.M., Garcia-Ruiz, E., Ma, J., Zhao, H., Milenkovic, O.: DNA-based storage: trends and methods. IEEE Trans. on Molecular, Biological and Multi-Scale Communications 1(3), 230–248 (2015). https://doi.org/10.1109/TMBMC.2016.2537305
Tuan, T.N., Cai, K., Kiah, H.M., Dao, D.T., Schouhamer Immink, K.A.: On the Design of Codes for DNA Computing: Secondary Structure Avoidance Codes. arXiv e-prints: arXiv-2302 (2023)
Marathe, A., Codon, A.E., Corn, R.M.: On combinatorial DNA word design. J. Comput. Biol. 8(3), 201–219 (2004)
Benerjee, K.G., Banerjee, A.: On DNA codes with multiple constraints. IEEE Commun. Lett. https://doi.org/10.1109/LCOMM.2020.3029071
Limbachiya, D., Benerjee, K.G., Rao, B., Gupta, M.K.: On DNA codes using the ring \(Z_4 + wZ_4\). In: Proceedings of the IEEE International Symposium on Information Theory (ISIT), Vail, CO, USA, pp. 2401–2405 (2018)
Rykov, V.V., Macula, A.J., Torney, D.C., White, P.S.: DNA sequences and quaternary cyclic codes. In: Proceedings of the IEEE International Symposium on Information Theory (ISIT), Washington, DC, USA, USA, pp. 248–248 (2001)
International Human Genome Sequencing Consortium: initial sequencing and analysis of the human genome. Nature 409(6822), 860–921 (2001)
Kim, Y.S., Kim, S.H.: New construction of DNA codes with constant-GC contents from binary sequences with ideal correlation. In: Proceedings of the IEEE International Symposium on Information Theory (ISIT), St. Petersburg, Russia, pp. 1569–1573 (2011)
Milenkovic, O., Kashyap, N.: On the design of codes for DNA computing. In: Ytrehus (ed.) Coding and Cryptography. Berlin, Heidelberg: Springer Berlin Heidelberg, pp. 100–119 (2006)
Zuker, M., Sankoff, D.: RNA secondary structures and their prediction. Bulletin of Mathematical Biology 46(4), 591–621 (1984). ISSN 0092-8240, https://doi.org/10.1016/S0092-8240(84)80062-2
Nussinov, R., Jacobson, A.B.: Fast algorithm for predicting the secondary structure of single-stranded RNA. Natl. Acad. Sci. 77(11), 6309–6313 (1980)
Clote, P., Backofen, R.: Computational molecular biology: an introduction. Wiley Series in Mathematical and Computational Biology, Hoboken, New Jersey, US (2000)
Mishra, P., Bhaya, C., Pal, A.K., Singh, A.K.: Compressed DNA coding using minimum variance Huffman tree. IEEE Commun. Lett. 24(8), 1602–1606 (2020). https://doi.org/10.1109/LCOMM.2020.2991461
Limbachiya, D., Gupta, M.K., Aggarwal, V.: Family of constrained codes for archival DNA data storage. IEEE Commun. Lett. 22(10), 1972–1975 (2018). https://doi.org/10.1109/LCOMM.2018.2861867
Acknowledgements
The authors would like to sincerely thank the referees for a meticulous reading of this manuscript, and for valuable suggestions which helped to create an improved final version. Some part of this paper was done during the visit of Prof Abhay Kumar Singh to Prof Udaya Parampalli, School of Computing and Information Systems, The University of Melbourne, Parkville, Australia in September 2023. Prof Abhay Kumar Singh expresses gratitude to the School of Computing and Information Systems at The University of Melbourne, Parkville, Australia for their hospitality and support during discussions on DNA-constrained codes.
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Bhoi, S.S., Parampalli, U. & Singh, A.K. Construction of DNA codes with multiple constrained properties. Cryptogr. Commun. (2024). https://doi.org/10.1007/s12095-024-00718-x
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DOI: https://doi.org/10.1007/s12095-024-00718-x