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On Conjugation Partitions of Sets of Trinucleotides
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Applied Mathematics·Volume 03 (2012)·Pages 107–112·Published 4 January 2012·DOI10.4236/am.2012.31017
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Abstract
We prove that a trinucleotide circular code is self-complementary if and only if its two conjugated classes are complement of each other. Using only this proposition, we prove that if a circular code is self-complementary then either both its two conjugated classes are circular codes or none is a circular code.
KeywordsTrinucleotideConjugated TrinucleotidesCodeCircular CodeSelf-Complementary Circular CodeComplementary Circular Codes
- J. Berstel and D. Perrin, “Theory of Codes, Vol. 117, (Pure and Applied Mathematics),” Academic Press, London, 1985.
- J.-L. Lassez, “Circular codes and synchronization,” International Journal of Computer & Information Sciences, Vol. 5, 1976, pp. 201-208.
- F. H. C. Crick, J. S. Griffith and L. E. Orgel, “Codes without commas,” Proceedings of the National Academy of Sciences of the USA, Vol. 43, 1957, pp. 416-421. doi:10.1073/pnas.43.5.416
- S. W. Golomb, B. Gordon and L. R. Welch, “Comma-Free codes,” Canadian Journal of Mathematics, Vol. 10, No. 2, 1958, pp. 202-209. doi:10.4153/CJM-1958-023-9
- S. W. Golomb, L. R. Welch and M. Delbrück, “Construction and Properties of Comma-Free Codes,” Biologiske Meddel Danske Vidensk Selsk, Vol. 23, 1958, pp. 1-34.
- D. G. Arquès and C. J. Michel, “A Complementary Circular Code in the Protein Coding Genes,” Journal of Theoretical Biology, Vol. 182, No. 1, 1996, pp. 45-58. doi:10.1006/jtbi.1996.0142
- A. J. Koch and J. Lehman, “About A symmetry of the Genetic Code,” Journal of Theoretical Biology, Vol. 189, No. 2, 1997, pp. 171-174. doi:10.1006/jtbi.1997.0503
- M.-P. Béal and J. Senellart, “On the Bound of the Synchronization Delay of a Local Automaton,” Theoretical Computer Science, Vol. 205, No. 1-2, 1998, pp. 297-306. doi:10.1016/S0304-3975(98)80011-X
- F. Bassino, “Generating Function of Circular Codes,” Advances in Applied Mathematics, Vol. 22, No. 1, 1999, pp. 1-24. doi:10.1006/aama.1998.0613
- N. ?tambuk, “On Circular Coding Properties of Gene and Protein Sequences,” Croatica Chemica Acta, Vol. 72, No. 4, 1999, pp. 999-1008.
- R. Jolivet and F. Rothen, “Peculiar Symmetry of DNA Sequences and Evidence Suggesting Its Evolutionary Origin in a Primeval Genetic Code,” First European Workshop Exo-/Astro-Biology, Noordwijk, 21-23 May 2001, pp. 173- 176.
- G. Frey and C. J. Michel, “Circular Codes in Archaeal Genomes,” Journal of Theoretical Biology, Vol. 223, No. 4, 2003, pp. 413-431. doi:10.1016/S0022-5193(03)00119-X
- C. Nikolaou and Y. Almirantis, “Mutually Symmetric and Complementary Triplets: Difference in Their Use Distinguish Systematically between Coding and Non-Coding Genomic Sequences,” Journal of Theoretical Biology, Vol. 223, No. 4, 2003, pp. 477-487. doi:10.1016/S0022-5193(03)00123-1
- E. E. May, M. A. Vouk, D. L. Bitzer and D. I. Rosnick, “An Error-COrrecting Framework for Genetic Sequence Analysis,” Journal of the Franklin Institute, Vol. 341, No. 1-2, 2004, pp. 89-109. doi:10.1016/j.jfranklin.2003.12.009