Conspiracy in bacterial genomes

The rank ordered distribution of the codon usage frequencies for 109 eubacteria and 14 archaea is best fitted by a three-parameter function which is the sum of a constant, an exponential and a linear term in the rank n. The parameters depend (two parabolically) from the total GC content. The rank ordered distribution of the amino acids is fitted by a straight line. The Shannon entropy computed over all the codons is well fitted by a parabola in the GC content, while the partial entropies computed over subsets of the codons show peculiar different behavior. Moreover, the sum of the codon usage frequencies over particular sets, e.g. with C and A (respectively G and U) as ith nucleotide, show a clear linear dependence from the GC content, exhibiting a conspiracy effect.