Abstract
New developments are presented in the framework of the model introduced bythe authors in References [1, 2] and in which nucleotides as well ascodons are classified in crystal bases of the quantum group U q(sl(2) ⊕ sl (2)) in the limit q → 0. An operator whichgives the correspondence between the amino-acids and the codons isobtained for any known genetic code. The free energy released by basepairing of dinucleotides as well as the relative hydrophilicity andhydrophobicity of the dinucleosides are also computed. For the vertebrateseries, a universal behaviour in the ratios of codon usage frequencies isput in evidence and is shown to fit nicely in our model. Then a firstattempt to represent the mutations relative to the deletion of apyrimidine by action of a suitable crystal spinor operator is proposed.Finally recent theoretial descriptions are reviewed and compared with ourmodel.PACS number: 87.10.+e, 02.10.-v
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Frappat, L., Sciarrino, A. and Sorba, P.: A crystal base for the genetic code, Phys. Lett. A 250 (1998), 214 and physics/9801027.
Frappat, L., Sciarrino, A. and Sorba, P.: Symmetry and codon usage correlations in the genetic code, Phys. Lett. A 259 (1999), 339 and physics/9812041.
Singer, M. and Berg, P.: Genes and Genomes, Editions Vigot, Paris 1992.
Kashiwara, M.: Crystallizing the q-analogue of universal enveloping algebras, Commun. Math. Phys. 133 (1990), 249.
Bashford, J. D. and Jarvis, P. D.: The genetic code as a periodic table: algebraic aspects, physics/0001066, to appear in BioSystems.
Mathews, D. H., Sabina, J., Zucker, M. and Turner, D. H.: J. Mol. Biol. 288 (1999), 911.
Weber, A. L. and Lacey, J. C.: Genetic code correlations: amino-acids and their anticodon nucleotides, J. Mol. Evol. 11 (1978), 199.
Jemcyck, J. R.: The genetic code as a periodic table, J. Mol. Evol. 11 (1978), 211.
Chiusano, M. L., Frappat, L., Sciarrino, A. and Sorba, P.: Codon usage correlations and Crystal Basis model of the genetic code, preprint LAPTH-736/99, DSF-Th-17/99.
Nakamura, Y., Gojobori, T. and Ikemura, T.: Nucleic Acids Res. 26 (1998), 334. Duret, L. and Mouchiroud, D.: Expression pattern and, surprisingly, gene length shape codon usage in Caenorhabditis, Drosophila, and Arabidopsis, Proc. Natl. Acad. Sci. USA 96 (1999), 4482.
Bagnoli, F. and Liò, P.: Selection, mutations and codon usage in a bacterial model, J. Theor. Biol. 173 (1995), 271.
Jestin, J. L. and Kempf, A.: Chain termination codons and polymerase-induced frameshift mutations, FEBS Letters 419 (1997), 153.
Marotta, V. and Sciarrino, A.: Tensor operator and Wigner-Eckart theorem for Uq→0(sl(2)), preprint DSF-T-43/98, math.QA/9811143, submitted to J. Math. Phys.
Hornos, J. E. and Hornos, Y.: Algebraic model for the evolution of the genetic code, Phys. Rev. Lett. 71 (1993), 4401.
Forger,M., Hornos, Y. and Hornos, J.E.: Global aspects in the algebraic approach in the genetic code, Phys. Rev. E 56 (1997), 7078.
Kent, R. D., Schlesinger, M. and Wybourne, B. G.: On algebraic approach to the genetic code, in: B. P. Corney, R. Delbourgo and P. D. Jarvis (eds.), Proc. XXII Int. Coll. on Group Theoretical Methods in Physics, International Press, Boston, 1999, pp. 152.
Bashford, J. D., Tsohantjis, I. and Jarvis, P. D.: Codon and nucleotide assignments in a supersymmetric model of the genetic code, Phys. Lett. A 233 (1997), 481 and A supersymmetric model for the evolution of the genetic code, Proc. Nat. Acad. Sci. USA 95 (1998), 987.
Forger, M. and Sachse, S.: Lie Superalgebras and the Multiplet Structure of the Genetic Code I: Codons Representations, II: Branching Schemes, math-ph/9808001 and math-ph/9905017.
Rumer, Yu. B.: Systematization of the Codons of Genetic Code, Translated from Doklady Akademi Nauk SSSR 167, N.6, 1966, pp. 1393-1394 and Systematization of the Codons of Genetic Code, Translated from Doklady Akademi Nauk SSSR 187, N.4, 1969, pp. 937–938.
Konopel'chenko, B. G. and Rumer, Yu. B.: Classification of Codons in the Genetic Code, Translated from Doklady Akademi Nauk SSSR 223, N.2, 1975, pp. 471–474.
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Frappat, L., Sciarrino, A. & Sorba, P. Crystalizing the Genetic Code. Journal of Biological Physics 27, 1–34 (2001). https://doi.org/10.1023/A:1011874407742
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DOI: https://doi.org/10.1023/A:1011874407742