Struktur Aljabar untuk Barisan Kodon dari Asam Deoksiribonukleat (DNA)

Nabila Nurmala Hasan; Edi Kurniadi; Nurul Gusriani

doi:10.24198/jmi.v21.n2.67778.213-228

Struktur Aljabar untuk Barisan Kodon dari Asam Deoksiribonukleat (DNA)

Nabila Nurmala Hasan, Edi Kurniadi, Nurul Gusriani

Abstract

This article discusses the algebraic structure of codon sequences as a representation of DNA nitrogen base sets in mathematical terms. The study aims to prove what algebraic structures are obtained for codon sequences from DNA bases. The methods used include qualitative research methods in the form of literature studies and quantitative research methods in the form of experiments on DNA base sets. In mathematical notation, the nitrogen bases of DNA can be collected in a set and connected into algebraic structures through a bijective mapping on the Galois field of order 4. This results in the set B being viewed as a Galois field of order 4. Additionally, DNA base triplets or codons can be represented in mathematical form. Furthermore, these codons are bijectively mapped onto the Galois field of order 64, so that the resulting algebraic structure is a field. The result of this study show that the codon sequences have an algebraic structure in the form of a one-dimensional vector space over the Galois field on the codon. For further research, the Lie structure in codon can be investigated through the construction of its Lie brackets, where this vector space is a necessary condition for Lie algebras.

Keywords

DNA, Codon, Galois Field, Vector Space, Dimension.

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References

J. D. WATSON and F. H. C. CRICK. “Molecular Structure of Nucleic Acids: A Structure for Deoxyribose Nucleic Acid”. inNature: 171.4356 (april 1953), pages 737–738. issn: 0028-0836. doi: 10.1038/171737a0. url: https://www.nature.com/articles/

a0.

Isah Aisah and Nurul Ulla. “Grup Kuosien Sebagai Representasi Dari Kode Genetik Standar Berdasarkan Kimia Nukleotida”. inJurnal Matematika Integratif : 13.1 (2017), page 35. issn: 1412-6184. doi: 10.24198/jmi.v13i1.11412.

Muhammad Arsyad and Putranto Hadi. “Konstruksi Kode DNA dan Implementasinya Menggunakan Python”. in8: (2025), pages 377–384.

Isah Aisah, Fujia Nur Fadilah and Moch Suyudi. “Aplikasi Logika Matematika pada Aljabar Untaian DNA dalam Proses Hibridisasi Application of Mathematical Logic on DNA Strand Algebra In Hybridization”. inSigma-Mu.: 9.2 (2017), pages 1–8.

Isah Aisah, Edi Kurniadi and Ema Carnia. “Representasi Mutasi Kode Genetik Standar Berdasarkan Basa Nukleotida”. inJurnal Matematika Integratif : 11.1 (2015), page 25. issn: 1412-6184. doi: 10.24198/jmi.v11i1.9399.

H.A. Aleem, D.H. Green and Ferda Mavituna. “Representing the Genetic Code as a Function on a Galois Field Using the Reed-Muller Expansion”. in2009 39th International Symposium on Multiple-Valued Logic: (2009), pages 356–361. doi: 10.1109/ISMVL. 2009.59. url: https://api.semanticscholar.org/CorpusID:21198048%20http: //ieeexplore.ieee.org/document/5010425/.

Haitao Yang and Weixian Xi. “Nucleobase-Containing Polymers: Structure, Synthesis, and Applications”. inPolymers: 9.12 (december 2017), page 666. issn: 2073-4360. doi: 10.3390/polym9120666. url: https://www.mdpi.com/2073-4360/9/12/666.

Robersy S´anchez, Ricardo Grau and Eberto Morgado. “A novel Lie algebra of the genetic code over the Galois field of four DNA bases”. inMathematical Biosciences: 202.1 (2006), pages 156–174. issn: 00255564. doi: 10.1016/j.mbs.2006.03.017.

Robersy Sanchez andothers. “A New DNA Sequences Vector Space on a Genetic Code Galois Field”. inMatch: 54.1 (december 2004), pages 3–28. issn: 03406253. doi: doi.org/10.48550/arXiv.q-bio/0412019. arXiv: 0412019 [q-bio]. url: http://arxiv.

org/abs/q-bio/0412019.

Joseph Gallian. Contemporary Abstract Algebra. Boca Raton: Chapman and Hall/CRC, march 2025, pages 1–635. isbn: 9781003488026. doi: 10.1201/9781003488026. url: https://www.taylorfrancis.com/books/9781003488026.

DOI: https://doi.org/10.24198/jmi.v21.n2.67778.213-228