Towards a resolution on the inherent methodological weakness of the "effective number of codons used by a gene"

Recently Anders Fuglsang provided a modified way for calculating N(c) when biased discrepancy is present in a gene [Biochem. Biophys. Res. Commun. 317 (2004) 957]. Instead of taking the average codon homozygosity for each synonymous family type (as proposed by Wright) [Gene 87 (1990) 23] Fuglsang considered codon homozygosity of each amino acid individually. Marsashi and Najafabadi [Biochem. Biophys. Res. Commun. 324 (2004) 1] in their recent article demonstrated that the readjustment for overestimation at the level of individual amino acids results in loss of considerable amount of information. Immediately after the publication of Marsashi and Najafabadi, Fuglsang proposed that codon homozygosities can be calculated based on the classical population genetics [Biochem. Biophys. Res. Commun. 327 (2005) 1]. Though Fuglsang's approach is a novel one, it fails when any of the amino acids are absent in a gene. However, the inherent cause of overestimation at the level of individual amino acids is still obscured in the literature. Here in this communication we have presented a general condition where effective number of codons is overestimated using Wright's formula and also we propose a new way to calculate N(c), which is independent of amino acid composition.