RESEARCH ARTICLE


Free Triplet Conjecture and Equivalence Classes Derived Using Group Theory



Zhang Dakun*, Song Guozhi, Huang Cui
School of Computer Science and Software Engineering, Tianjin Polytechnic University, Tianjin300387, China


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Creative Commons License
© 2015 Dakun et al.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: (https://creativecommons.org/licenses/by/4.0/legalcode). This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at School of Computer Science and Software Engineering, Tianjin Polytechnic University, Tianjin 300387, China; Tel: +86 13752392145; E-mail: zhangdakun2013@163.com


Abstract

All proteins are made up of 20 different amino acids which contain 4 kinds of nucleotides . Three consecutive nucleotides on the gene, called triplet codons, are used to code an amino acid, and 64 triplet codons comprise the genetic code table. Central dogma (DNA-RNA-protein) has been acknowledged, but the process and mechanism of mRNA passing through the nuclear membrane still require further investigation. For these two problems mentioned above, this paper proposed a conjecture of nucleotide free triplet and obtained 20 equivalence classes of mapping from free triplet vertex set to nucleotide set using group theory. Whether the four numbers 3, 4, 20 and 64 have relevance are taken into consideration here. Subsequently, the numbers 3, 4, 20 and 64 were connected together which was important for the analysis of triplet code and protein composition.

Keywords: DNA/mRNA/protein, equivalence class, free triplet, group theory, nucleotide.