The biological distinction between the base positions in the codon, the chemical types of bases (purine and pyrimidine) and their hydrogen bond number have been the most relevant codon properties used in the genetic code analysis. Now, these properties have Hence, in the analyses of molecular evolution process on the DNA sequence set of length N, the Z 64 -algebra will help us explain the quantitative relationships between genes.
Starting from the four DNA bases order in the Boolean lattice, a novel Lie Algebra of the genetic code is proposed. Here, the main 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 assignments and physicochemical properties of amino acids. Moreover, a distance defined between codons expresses a physicochemical meaning. It was also noticed that the distance between wild type and mutant codons tends to be small in mutational variants of four genes: human phenylalanine hydroxylase, human beta-globin, HIV-1 protease and HIV-1 reverse transcriptase. These results strongly suggest that deterministic rules in genetic code origin must be involved.
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