Effective number of codons
Effective number of codons (ENC) is a measure for assessing codon usage
bias. The ENC value ranges from 20 (maximum bias, i.e. only one codon is
used to encode an amino acid) to 61 (minimum bias, i.e. codons are used
randomly)36,37. In contrast to the RSCU value, the ENC
value characterizes the overall codon usage bias for a gene/genome.
The calculation of codon homozygosity (Fk ) for
all amino acids having synonymous codons, which is required to calculate
the ENC value, was carried out according to the following equations (5):
\(S=\ \sum_{i=1}^{k}{\left(\frac{n_{i}}{n}\right)^{2};\ \ \ \ \ F_{k}=\frac{nS-1}{n-1}}\) (5),
where ni is the occurrence of the k -codon
for the i -amino acid; n is the total number of codons for
the i -amino acid; k is the number of codons for thei -amino acid (k = 2, 3, 4, 6). In this work,ni and n were represented by the average
values for Hsp60 sequences of 17 phyla excluding Viruses and
Platyhelminthes (Supplementary, GC-content and ENC).
The ENC values were calculated for 17 phyla according to equations (6):
\(ENC=2+\frac{9}{F_{2}}+\frac{1}{F_{3}}+\frac{5}{F_{4}}+\frac{3}{F_{6}};\ \ \ \ \ \text{ENC}_{\exp}=2.5+s+\frac{29.5}{s^{2}+{(1-s)}^{2}}\) (6)
where 2 is a sum of F for Met and Trp, since these amino
acid residues have no synonymous codons; F2/3/4/6is an average Fk for those amino acid residues
that have k synonymous codons. The ENCexpvalue is the expected ENC value for various GC contents at the third
synonymous codon position (GC3 content) in the Hsp60
gene for 17 phyla. Here, s is the given value of
GC3 content (Supplementary, GC-content and ENC). The
data obtained were used to construct the Nc-plot, where the ENC values
are presented as a scatter plot, and the ENCexpvalues are presented as a solid curve. Gene codons are unbiased if the
corresponding point is on the expected curve38.