Acta Biotheoretica

, Volume 54, Issue 1, pp 27–42 | Cite as

A Novel Algebraic Structure of the Genetic Code Over the Galois Field of Four DNA Bases

  • Robersy SánchezEmail author
  • Ricardo Grau


A novel algebraic structure of the genetic code is proposed. Here, the principal partitions of the genetic code table were obtained as equivalent classes of quotient spaces of the genetic code vector space over the Galois field of the four DNA bases. The new algebraic structure shows strong connections among algebraic relationships, codon assignment and physicochemical properties of amino acids. Moreover, a distance function defined between the codon binary representations in the vector space was demonstrated to have a linear behavior respect to physical variables such as the mean of amino acids interaction energies in proteins. It was also noticed that the distance between wild type and mutant codons approach to smaller values in mutational variants of four genes, i.e., human phenylalanine hydroxylase, human β-globin, HIV-1 protease and HIV-1 reverse transcriptase. These results strongly suggest that deterministic rules must be involved in the genetic code origin.

Key words

genetic code vector space genetic code algebra genetic code Lie algebra gene mutation 


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Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Research Institute of Tropical Roots, Tuber Crops and Banana (INIVIT)Biotechnology GroupSanto DomingoCuba
  2. 2.Center of Studies on InformaticsCentral University of Las VillasCuba
  3. 3.Santa Clara 1Cuba

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