Table of Contents
ISRN Biomathematics
Volume 2013, Article ID 538631, 8 pages
http://dx.doi.org/10.1155/2013/538631
Research Article

Dinucleotide Circular Codes

1Equipe de Bioinformatique Théorique, BFO, LSIIT, UMR 7005, Université de Strasbourg, Pôle API, 300 Boulevard Sébastien Brant, 67400 Illkirch, France
2Istituto di Analisi dei Sistemi ed Informatica “Antonio Ruberti”, Consiglio Nazionale delle Ricerche and Dipartimento di Matematica, “Ulisse Dini” Università di Firenze, Viale Morgagni 67/A, 50134 Firenze, Italy
3Université de Marne-la-Vallée, 5 boulevard Descartes, 77454 Marne-la-Vallée Cedex 2, France

Received 12 October 2012; Accepted 12 December 2012

Academic Editors: J. Chow, M. Jose, M. R. Roussel, and J. H. Wu

Copyright © 2013 Christian J. Michel and Giuseppe Pirillo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. Berstel and D. Perrin, Theory of Codes, Academic Press, London, UK, 1985.
  2. J. L. Lassez, “Circular codes and synchronization,” International Journal of Computer and Information Sciences, vol. 5, no. 2, pp. 201–208, 1976. View at Publisher · View at Google Scholar · View at Scopus
  3. F. H. C. Crick, J. S. Griffith, and L. E. Orgel, “Codes without commas,” Proceedings of the National Academy of Sciences, vol. 43, pp. 416–421, 1957. View at Publisher · View at Google Scholar
  4. S. W. Golomb, B. Gordon, and L. R. Welch, “Comma-free codes,” Canadian Journal of Mathematics, vol. 10, pp. 202–209, 1958. View at Publisher · View at Google Scholar
  5. S. W. Golomb, L. R. Welch, and M. Delbrück, “Construction and properties of comma-free codes,” Biologiske Meddelelser, Kongelige Danske Videnskabernes Selskab, vol. 23, no. 9, 1958. View at Google Scholar
  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, pp. 45–58, 1996. View at Publisher · View at Google Scholar · View at Scopus
  7. A. J. Koch and J. Lehmann, “About a symmetry of the genetic code,” Journal of Theoretical Biology, vol. 189, no. 2, pp. 171–174, 1997. View at Publisher · View at Google Scholar · View at Scopus
  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, pp. 297–306, 1998. View at Google Scholar · View at Scopus
  9. F. Bassino, “Generating functions of circular codes,” Advances in Applied Mathematics, vol. 22, no. 1, pp. 1–24, 1999. View at Publisher · View at Google Scholar · View at Scopus
  10. R. Jolivet and F. Rothen, “Peculiar symmetry of DNA sequences and evidence suggesting its evolutionary origin in a primeval genetic code,” in Proceedings of the 1st European Workshop in Exo-/Astro-Biology, P. Ehrenfreund, O. Angerer, and B. Battrick, Eds., ESA SP-496, pp. 173–176, Noordwijk, The Netherlands. View at Scopus
  11. G. Frey and C. J. Michel, “Circular codes in archaeal genomes,” Journal of Theoretical Biology, vol. 223, no. 4, pp. 413–431, 2003. View at Publisher · View at Google Scholar · View at Scopus
  12. C. Nikolaou and Y. Almirantis, “Mutually symmetric and complementary triplets: differences in their use distinguish systematically between coding and non-coding genomic sequences,” Journal of Theoretical Biology, vol. 223, no. 4, pp. 477–487, 2003. View at Publisher · View at Google Scholar · View at Scopus
  13. G. Pirillo, “A characterization for a set of trinucleotides to be a circular code,” in Determinism, Holism, and Complexity, C. Pellegrini, P. Cerrai, P. Freguglia, V. Benci, and G. Israel, Eds., Kluwer Academic Publisher, New York, NY, USA, 2003. View at Google Scholar
  14. G. Pirillo and M. A. Pirillo, “Growth function of self-complementary circular codes,” Biology Forum, vol. 98, no. 1, pp. 97–110, 2005. View at Google Scholar · View at Scopus
  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, pp. 87–101, 2006. View at Publisher · View at Google Scholar · View at Scopus
  16. J. L. Lassez, R. A. Rossi, and A. E. Bernal, “Crick's hypothesis revisited: the existence of a universal coding frame,” in Proceedings of the 21st International Conference on Advanced Information Networking and Applications Workshops (AINAW '07), pp. 745–751, Niagara Falls, Canada, May 2007. View at Publisher · View at Google Scholar
  17. C. J. Michel, G. Pirillo, and M. A. Pirillo, “Varieties of comma-free codes,” Computers and Mathematics with Applications, vol. 55, no. 5, pp. 989–996, 2008. View at Publisher · View at Google Scholar · View at Scopus
  18. 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, pp. 17–26, 2008. View at Publisher · View at Google Scholar · View at Scopus
  19. G. Pirillo, “A hierarchy for circular codes,” RAIRO-Theoretical Informatics and Applications, vol. 42, no. 4, pp. 717–728, 2008. View at Publisher · View at Google Scholar · View at Scopus
  20. G. Pirillo, “Some remarks on prefix and suffix codes,” Pure Mathematics and Applications, vol. 19, pp. 53–60, 2008. View at Google Scholar
  21. C. J. Michel and G. Pirillo, “Identification of all trinucleotide circular codes,” Computational Biology and Chemistry, vol. 34, no. 2, pp. 122–125, 2010. View at Publisher · View at Google Scholar · View at Scopus
  22. G. Pirillo, “Non sharing border codes,” The Advances in Applied Mathematics and Mechanics, vol. 3, pp. 215–223, 2010. View at Google Scholar
  23. C. J. Michel and G. Pirillo, “Strong trinucleotide circular codes,” International Journal of Combinatorics, vol. 2011, Article ID 659567, 14 pages, 2011. View at Publisher · View at Google Scholar
  24. 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, pp. 223–232, 2011. View at Google Scholar
  25. D. L. Gonzalez, S. Giannerini, and R. Rosa, “Circular codes revisited: a statistical approach,” Journal of Theoretical Biology, vol. 275, no. 1, pp. 21–28, 2011. View at Publisher · View at Google Scholar
  26. L. Bussoli, C. J. Michel, and G. Pirillo, “On conjugation partitions of sets of trinucleotides,” Applied mathematics, vol. 3, pp. 107–112, 2012. View at Google Scholar
  27. C. J. Michel, G. Pirillo, and M. A. Pirillo, “A classification of 20-trinucleotide circular codes,” Information and Computation, vol. 212, pp. 55–63, 2012. View at Publisher · View at Google Scholar
  28. M. Burset, I. A. Seledtsov, and V. V. Solovyev, “Analysis of canonical and non-canonical splice sites in mammalian genomes,” Nucleic Acids Research, vol. 28, no. 21, pp. 4364–4375, 2000. View at Google Scholar · View at Scopus
  29. S. M. Mount, “A catalogue of splice junction sequences,” Nucleic Acids Research, vol. 10, no. 2, pp. 459–472, 1982. View at Google Scholar · View at Scopus
  30. A. Bird, “The dinucleotide CG as a genomic signalling module,” Journal of Molecular Biology, vol. 409, no. 1, pp. 47–53, 2011. View at Publisher · View at Google Scholar
  31. F. Gebhardt, K. S. Zänker, and B. Brandt, “Modulation of epidermal growth factor receptor gene transcription by a polymorphic dinucleotide repeat in intron 1,” Journal of Biological Chemistry, vol. 274, no. 19, pp. 13176–13180, 1999. View at Publisher · View at Google Scholar · View at Scopus
  32. H. Buerger, J. Packeisen, A. Boecker et al., “Allelic length of a CA dinucleotide repeat in the egfr gene correlates with the frequency of amplifications of this sequence—first results of an inter-ethnic breast cancer study,” Journal of Pathology, vol. 203, no. 1, pp. 545–550, 2004. View at Publisher · View at Google Scholar · View at Scopus
  33. A. L. Schmidt and V. Mitter, “Microsatellite mutation directed by an external stimulus,” Mutation Research, vol. 568, no. 2, pp. 233–243, 2004. View at Publisher · View at Google Scholar · View at Scopus
  34. H. Cuppens, W. Lin, M. Jaspers et al., “Polyvariant mutant cystic fibrosis transmembrane conductance regulator genes: the polymorphic (TG)m locus explains the partial penetrance of the T5 polymorphism as a disease mutation,” Journal of Clinical Investigation, vol. 101, no. 2, pp. 487–496, 1998. View at Google Scholar · View at Scopus
  35. J. Rozenski, P. F. Crain, and J. A. McCloskey, “The RNA modification database: 1999 update,” Nucleic Acids Research, vol. 27, no. 1, pp. 196–197, 1999. View at Publisher · View at Google Scholar · View at Scopus