A mathematical model and the functional relationship of three-base codons in the complex plane

The biological mechanisms of gene expression have been studied in-depth. A relatively systematic theory has been formed. In order to better analyze and understand the process of gene expression, the group model described in the complex plane is employed in this paper to construct a mathematical model of the gene information carrier, three-base codons. With this model, the function that describes the relationship between codons encoding the same amino acid has been defined, which is useful to investigate the influence of gene mutations on protein synthesis.