A study of the purine/pyrimidine codon occurrence with a reduced centered variable and an evaluation compared to the frequency statistic.

With the three-letter alphabet [R,Y,N] (R = purine, Y = pyrimidine, N = R or Y), there are 26 codons (NNN being excluded): RNN,...,NNY (six codons at two unspecified bases N), RRN,...,NYY (12 codons at one unspecified base N), RRR,...,YYY (eight specified codons). A statistical methodology that uses the codon frequency and a reduced centered variable leads to similar results for a codon occurrence study, regardless of gene function and regardless of a particular protein coding gene taxonomic population. Therefore, this variable can be considered a new codon usage index, whose use removes certain nonsignificant results found with the frequency statistic. This methodology identifies the common and rare codons (i.e., the codons having the highest and lowest occurrence) and leads to a model of codon evolution at three successive states: RNN, then RNY, and finally RYY. Some biological relations between this model and the YRY(N)6YRY preferential occurrence are also presented.