Boolean Algebraic Structures of the Genetic Code: Possibilities of Applications

  • Ricardo Grau
  • Maria del C. Chavez
  • Robersy Sanchez
  • Eberto Morgado
  • Gladys Casas
  • Isis Bonet
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4366)


Authors had reported before two dual Boolean algebras to understand the underlying logic of the genetic code structure. In such Boolean structures, deductions have physico-chemical meaning. We summarize here that these algebraic structures can help us to describe the gene evolution process. Particularly in the experimental confrontation, it was found that most of the mutations of several proteins correspond to deductions in these algebras and they have a small Hamming distance related to their respective wild type. Two applications of the corresponding codification system in bioinformatics problems are also shown. The first one is the classification of mutations in a protein. The other one is related with the problem of detecting donors and acceptors in DNA sequences. Besides, pure mathematical models, Statistical techniques (Decision Trees) and Artificial Intelligence techniques (Bayesian Networks) were used in order to show how to accomplish them to solve these knowledge-discovery practical problems.


Genetic code Boolean algebra mutant sequence analysis  splice site prediction decision trees Bayesian networks 


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  1. 1.
    Crick, F.H.C.: The Origin of the Genetic Code. J. Mol. Biol. 38(3), 367–379 (1968)CrossRefGoogle Scholar
  2. 2.
    Freeland, S., Hurst, L.: The Genetic Code is One in a Million. J. Mol. Evol. 47(3), 238–248 (1998)CrossRefGoogle Scholar
  3. 3.
    Alf-Steinberger, C.: The Genetic Code and Error Transmission. Proc. Natl. Acad. Sci. USA 64(2), 584–591 (1969)CrossRefGoogle Scholar
  4. 4.
    Swanson, R.: A Unifying Concept for the Amino Acid Code. Bull. Math. Biol. 46(2), 187–203 (1984)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Sanchez, R., Grau, R., Morgado, E.: A Genetic Code Boolean Structure I. Meaning of Boolean Deductions. Bull. Math. Biol. 67, 1–14 (2005)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Sanchez, R., Grau, R., Morgado, E.: The Genetic Code Boolean Lattice, MATCH Commun. Math. Comput. Chem. 52, 29–46 (2004)zbMATHGoogle Scholar
  7. 7.
    Sánchez, R., Grau, R., Morgado, E.: Genetic Code Boolean Algebras. WSEAS Transactions on Biology and Biomedicine 1, 190–197 (2004)Google Scholar
  8. 8.
    Friedman, S.M., Weinstein, I.B.: Lack of Fidelity in the Translation of Ribopolynucleotides. Proc. Natl. Acad. Sci. 52, 988–996 (1964)CrossRefGoogle Scholar
  9. 9.
    Parker, J.: Errors and Alternatives in Reading the Universal Ggenetic Code. Microbiol. Rev. 53(3), 273–298 (1989)Google Scholar
  10. 10.
    Rose, R.E., et al.: Human Immunodeficiency Virus Type 1 Biral Background Plays a Major Role in Development of Resistance to Protease Inhibitors. Proc. Natl. Acad. Sci. 93(4), 1648–1653 (1996)CrossRefGoogle Scholar
  11. 11.
    Kim, B., Hathaway, T.R., Loeb, L.A.: Human Immunodeficiency Virus Reverse Transcriptase Functional Mutants Obtained by Random Mutagenesis Coupled with Genetic Selection in Escherichia Coli. J. Biol. Chem. 271(9), 4872–4878 (1996)CrossRefGoogle Scholar
  12. 12.
    Chávez, M.C., Rodr’iguez, L.O.: Bayshell, Software para crear redes Bayesianas e inferir evidencias en la misma, Registro de Software CENDA, 09358-9358, mayo (2002), Published in
  13. 13.
    Castillo, E., Gutiérrez, J.M., Hadi, A.S.: Expert Systems and Probabilistic Network Models. Springer, New York (1996)zbMATHGoogle Scholar
  14. 14.
    Stuart, R., Norvig, P.: Inteligencia Artificial: Un Enfoque Moderno. Prentice Hall, México (1996)Google Scholar
  15. 15.
    Williams, W.L., Wilson, R.C., Hancock, E.R.: Multiple Graph Matching with Bayesian Inference. Pattern Recognition Lett. 38, 11–13 (1998)Google Scholar
  16. 16.
    Hunter, L.: Planning to Learn About Protein Structure. In: Hunter, L. (ed.) Artificial Intelligence and Molecular Biology, AAAI Press, Cambridge (2003)Google Scholar
  17. 17.
    Grau, R., et al.: Algunas Aplicaciones de la Estructura Booleana del Código Genético. Revista Cubana de Ciencias Informáticas, vol. 1, 16-30 (2006)Google Scholar
  18. 18.
    Chavez, M.C., et al.: Statistical Learning Bayesian Networks from of Protein Database of Mutants. In: Proceedings of First International Workshop on Bioinformatics Cuba-Flanders 2006, Santa Clara, Cuba (2006)Google Scholar
  19. 19.
    Degroeve, S., et al.: Predicting Splice Sites from High-Dimensional Local Context Representations. Bioinformatics 21(8), 1332–1338 (2005)CrossRefGoogle Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Ricardo Grau
    • 1
  • Maria del C. Chavez
    • 1
  • Robersy Sanchez
    • 2
  • Eberto Morgado
    • 1
  • Gladys Casas
    • 1
  • Isis Bonet
    • 1
  1. 1.Center of Studies on Informatics, Central University of Las Villas, Santa Clara, CP 54830Cuba
  2. 2.Research Institute of Tropical Roots, Tuber Crops and Banana (INIVIT), Biotechnology Group, Santo DomingoCuba

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