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Bulletin of Mathematical Biology

, Volume 67, Issue 1, pp 1–14 | Cite as

A genetic code Boolean structure. I. The meaning of Boolean deductions

  • Robersy SánchezEmail author
  • Eberto Morgado
  • Ricardo Grau
Article

Abstract

This paper proposes a genetic code Boolean structure derived from hydrogen bond numbers and chemical types of bases, purines and pyrimidines. It shows that in such Boolean structure, deductions comprise physico-chemical meaning. In particular, codons with adenine as a second base coding to hydrophilic amino acids are not deductible from codons with uracil in the same position, which code to hydrophobic amino acids. Boolean deductions could help us describe the gene evolution process. For instance, most of the reported mutations that confer drug resistance to the HIV protease gene correspond to deductions. What is more, in the human beta-globin gene a similar situation appears where most of the single codon mutations correspond to Boolean deductions from the respective wild-type codon.

Keywords

Codon Boolean Algebra Genetic Code Indinavir Solvent Accessible Surface Area 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Alf-Steinberger, C., 1969. The genetic code and error transmission. Proc. Natl. Acad. Sci. USA 64, 584–591.CrossRefGoogle Scholar
  2. Balakrishnan, J., 2002. Symmetry scheme for amino acid codons. Phys. Rev. E 65, 021912–021915.Google Scholar
  3. Bashford, J.D., Jarvis, P.D., 2000. The genetic code as a periodic table. Biosystems 57, 147–161.CrossRefGoogle Scholar
  4. Bashford, J.D., Tsohantjis, I., Jarvis, P.D., 1998. A supersymmetric model for the evolution of the genetic code. Proc. Natl. Acad. Sci. USA 95, 987–992.CrossRefGoogle Scholar
  5. Beland, P., Allen, T.F., 1994. The origin and evolution of the genetic code. J. Theor. Biol. 170, 359–365.CrossRefGoogle Scholar
  6. Bertman, M.O., Jungck, J.R., 1979. Group graph of the genetic code. J. Hered. 70, 379–384.Google Scholar
  7. Birkhoff, G., MacLane, S., 1941. A Survey of Modern Algebra. The Macmillan Company, New York.zbMATHGoogle Scholar
  8. Chothia, C., 1974. Hydrophobic bonding and accessible surface area in proteins. Nature 248, 338–339.CrossRefGoogle Scholar
  9. Crick, F.H.C., 1968. The origin of the genetic code. J. Mol. Biol. 38, 367–379.CrossRefGoogle Scholar
  10. Epstein, C.J., 1966. Role of the amino-acid ‘code’ and of selection for conformation in the evolution of proteins. Nature 210, 25–28.Google Scholar
  11. Friedman, S.M., Weinstein, I.B., 1964. Lack of fidelity in the translation of ribopolynucleotides. Proc. Natl. Acad. Sci. USA 52, 988–996.CrossRefGoogle Scholar
  12. Gillis, D., Massar, S., Cerf, N.J., Rooman, M., 2001. Optimality of the genetic code with respect to protein stability and amino acid frequencies. Genome Biol. 2, research0049.1-research0049.12.Google Scholar
  13. Grantham, R., 1974. Amino acid difference formula to help explain protein evolution. Science 185, 862–864.Google Scholar
  14. He, M., Petoukhov, S.V., Ricci, P.E., 2004. Genetic code, Hamming distance and stochastic matrices, Bull. Math. Biol. (in press).Google Scholar
  15. Jimńez-Montaño, M.A., de la Mora-Basanet, C.R., Poschel, T., 1996. The hypercube structure of the genetic code explains conservative and non-conservative amino acid substitutions in vivo and in vitro. Biosystems 39, 117–125.CrossRefGoogle Scholar
  16. Jiménez-Montaño, M.A., 1999. Protein evolution drives the evolution of the genetic code and vice versa. Biosystems 54, 47–64.CrossRefGoogle Scholar
  17. Karasev, V.A., Stefanov, V.E., 2001. Topological nature of the genetic code. J. Theor. Biol. 209, 303–317.CrossRefGoogle Scholar
  18. Karplus, P.A., 1997. Hydrophobicity regained. Protein Sci. 6, 1302.CrossRefGoogle Scholar
  19. Lehmann, J., 2000. Physico-chemical constraints connected with the coding properties of the genetic system. J. Theor. Biol. 202, 129–144.CrossRefGoogle Scholar
  20. Parker, J., 1989. Errors and alternatives in reading the universal genetic code. Microbiol. Rev. 53, 273–298.Google Scholar
  21. Robin, D., Knight, R.D., Freeland, S.J., Landweber, L.F., 1999. Selection, history and chemistry: the three faces of the genetic code. Trends Biochem. Sci. 24, 241–247.CrossRefGoogle Scholar
  22. Rose, G.D., Geselowitz, A.R., Lesser, G.J., Lee, R.H., Zehfus, M.H., 1985. Hydrophobicity of amino acid residues in globular proteins. Science 229, 834–838.Google Scholar
  23. Siemion, I.Z., Siemion, P.J., Krajewski, K., 1995. Chou-Fasman conformational amino acid parameters and the genetic code. Biosystems 36, 231–238.CrossRefGoogle Scholar
  24. Stambuk, N., 2000. Universal metric properties of the genetic code. Croatica Chem. Acta 73, 1123–1139.Google Scholar

Copyright information

© Society for Mathematical Biology 2005

Authors and Affiliations

  • Robersy Sánchez
    • 1
    Email author
  • Eberto Morgado
    • 2
  • Ricardo Grau
    • 3
  1. 1.Biotechnology GroupResearch Institute of Tropical Roots, Tuber Crops and Banana (INIVIT)Santo Domingo, Villa ClaraCuba
  2. 2.Faculty of Mathematics, Physics and ComputationCentral University of Las VillasVilla ClaraCuba
  3. 3.Center of Studies on InformaticsCentral University of Las VillasVilla ClaraCuba

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