Gaussian-distributed codon frequencies of genomes

DNA encodes protein primary structure using 64 different codons to specify 20 different amino acids and a stop signal. Frequencies of codon occurrence when ordered in descending sequence provide a global characterization of a genomes preference (bias) for using the different codons of the redundant genetic code. Whereas frequency/rank relations have been described by empirical relations, here we propose a statistical model in which two different forms of codon usage co-exist in a genome. We investigate whether such a model can account for the range of codon usages observed in a large set of genomes from different taxa. The differences in frequency/rank relations across these genomes can be expressed in a single parameter, the proportion of the two codon compartments. One compartment uses different codons with weak bias according to a Gaussian distribution of frequency, the other uses different codons with strong bias. In prokaryotic genomes both compartments appear to be present in a wide range of proportions, whereas in eukaryotic genomes the compartment with Gaussian distribution tends to dominate. Codon frequencies that are Gaussian-distributed suggest that many evolutionary conditions are involved in shaping weakly-biased codon usage, whereas strong bias in codon usage suggests dominance of few evolutionary conditions.