The constraints between amino acids influence the unequal distribution of codons and protein sequence evolution.

Four nucleotides (A, U, C and G) constitute 64 codons at free combination but 64 codons are unequally assigned to 21 items (20 amino acids plus one stop). About 500 amino acids are known but only 20 are selected to make up the proteins. However, the relationships between amino acid and codon and between 20 amino acids have been unclear. In this paper, we studied the relationships between 20 amino acids in 33 species and found there were three constraints between 20 amino acids, such as the relatively stable mean carbon and hydrogen (C : H) ratios (0.50), similarity interactions between the constituent ratios of amino acids, and the frequency of amino acids according with Poisson distribution under certain conditions. We demonstrated that the unequal distribution of 64 codons and the choice of amino acids in molecular evolution would be constrained to remain stable C : H ratios. The constituent ratios and frequency of 20 amino acids in a species or a protein are two determinants of protein sequence evolution, so this finding showed the constraints between 20 amino acids played an important role in protein sequence evolution.