On Conjugation Partitions of Sets of Trinucleotides
Lorenzo Bussoli, Christian J. Michel, Giuseppe Pirillo
DOI: 10.4236/am.2012.31017   PDF    HTML   XML   5,709 Downloads   8,648 Views   Citations


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.

Share and Cite:

L. Bussoli, C. Michel and G. Pirillo, "On Conjugation Partitions of Sets of Trinucleotides," Applied Mathematics, Vol. 3 No. 1, 2012, pp. 107-112. doi: 10.4236/am.2012.31017.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] J. Berstel and D. Perrin, “Theory of Codes, Vol. 117, (Pure and Applied Mathematics),” Academic Press, London, 1985.
[2] J.-L. Lassez, “Circular codes and synchronization,” International Journal of Computer & Information Sciences, Vol. 5, 1976, pp. 201-208.
[3] 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
[4] 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
[5] 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.
[6] 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
[7] 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
[8] 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
[9] 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
[10] N. ?tambuk, “On Circular Coding Properties of Gene and Protein Sequences,” Croatica Chemica Acta, Vol. 72, No. 4, 1999, pp. 999-1008.
[11] 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.
[12] 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
[13] 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
[14] 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
[15] G. Frey and C. J. Michel, “Identification of Circular Codes in Bacterial Genomes and Their Use in a Factorization Method for Retrieving the Reading Frames of Genes,” Computational Biology and Chemistry, Vol. 30, No. 2, 2006, pp. 87-101. doi:10.1016/j.compbiolchem.2005.11.001
[16] J.-L. Lassez, R. A. Rossi and A. E. Bernal, “Crick’s Hypothesis Revisited: The Existence of a Universal Coding Frame,” Proceedings of the 21st International Conference on Advanced Information Networking and Applications Workshops/Symposia (AINA'07), Niagara Falls, Vol. 2, 21-23 May 2007, pp. 745-751.
[17] G. Pirillo, “A characterization for a Set of Trinucleotides to be a Circular Code,” In: C. Pellegrini, P. Cerrai, P. Freguglia, V. Benci and G. Israel, Eds., Determinism, Holism, and Complexity, Kluwer, Boston, 2003.
[18] C. J. Michel, G. Pirillo and M. A. Pirillo, “Varieties of Comma-Free Codes,” Computers & Mathematics with Applications, Vol. 55, No. 5, 2008, pp. 989-996. doi:10.1016/j.camwa.2006.12.091
[19] G. Pirillo, “A Hierarchy for Circular Codes,” Theoretical Informatics and Applications, Vol. 42, No. 4, 2008, pp. 717-728.
[20] M. V. José, T. Govezensky, J. A. García and J. R. Bobadilla, “On the Evolution of the Standard Genetic Code: Vestiges of Critical Scale Invariance from the RNA World in Current Prokaryote Genomes,” PLoS ONE, Vol. 4, No. 2, 2009, p. e4340. doi:10.1371/journal.pone.0004340
[21] G. Pirillo, “Some Remarks on Prefix and Suffix Codes,” Pure Mathematics and Applications, Vol. 19, No. 2-3, 2008, pp. 53-60.
[22] G. Pirillo, “Non Sharing Border Codes,” Advances in Applied Mathematics, Vol. 3, No. 2, 2010, pp. 215-223.
[23] L. Bussoli, C. J. Michel and G. Pirillo, “On Some Forbidden Configurations for Self-Complementary Trinucleotide Circular Codes,” Journal for Algebra Number Theory Academia, Vol. 2, 2011, pp. 223-232.
[24] G. Pirillo and M. A. Pirillo, “Growth Function of Self-Complementary Circular Codes,” Biology Forum, Vol. 98, 2005, pp. 97-110.
[25] C. J. Michel, G. Pirillo and M. A. Pirillo, “A Relation between Trinucleotide Comma-Free Codes and Trinucleotide Circular Codes,” Theoretical Computer Science, Vol. 401, No. 1-3, 2008, pp. 17-25. doi:10.1016/j.tcs.2008.02.049

Copyright © 2023 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.