Algebraic principle of natural bases from the standard genetic code degeneracy

Abstract

The symmetry and group in degeneracy of the standard genetic code (SGC) have been studied. However, the core role of equations of degree n with one unknown between symmetry and group theory has been ignored. In this study, algebraic concept was employed to abstract all genetic codons in the SGC table into equations of degree n with one unknown, and the bases in the third position of nucleotide triplets are these equations solutions. Basing upon the analysis of natural bases permutation groups and natural bases as the unit roots, some results were found that the characteristics of solvable groups imply the amount of natural bases, the relation between the first two bases in nucleotide triplets is the algebraic multiplication binary operation, and natural bases have the significance of complex number. These results gave natural bases the significance of number in the complex plane, and clarified the amount and operation in the mathematical sense, which would contribute to understand the origin and evolution of genetic code.