Journal of Mathematical Biology

, Volume 51, Issue 4, pp 431–457 | Cite as

Gene algebra from a genetic code algebraic structure

  • R. SanchezEmail author
  • E. Morgado
  • R. Grau


By considering two important factors involved in the codon-anticodon interactions, the hydrogen bond number and the chemical type of bases, a codon array of the genetic code table as an increasing code scale of interaction energies of amino acids in proteins was obtained. Next, in order to consecutively obtain all codons from the codon AAC, a sum operation has been introduced in the set of codons. The group obtained over the set of codons is isomorphic to the group (Z64, +) of the integer module 64. On the Z64-algebra of the set of 64 N codon sequences of length N, gene mutations are described by means of endomorphisms f:(Z64) N →(Z64) N . Endomorphisms and automorphisms helped us describe the gene mutation pathways. For instance, 77.7% mutations in 749 HIV protease gene sequences correspond to unique diagonal endomorphisms of the wild type strain HXB2. In particular, most of the reported mutations that confer drug resistance to the HIV protease gene correspond to diagonal automorphisms of the wild type. What is more, in the human beta-globin gene a similar situation appears where most of the single codon mutations correspond to automorphisms. Hence, in the analyses of molecular evolution process on the DNA sequence set of length N, the Z64-algebra will help us explain the quantitative relationships between genes.

Key words or phrases

Gene algebra Genetic code algebra Molecular evolution process 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Research Institute of Tropical Roots, Tuber Crops and Banana (INIVIT)Biotechnology groupSanto DomingoCuba
  2. 2.Faculty of Mathematics Physic and ComputationCentral University of Las VillasCuba
  3. 3.Center of Studies on InformaticsCentral University of Las VillasCuba

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