  The distribution functions of the codon usage probabilities, computed over
all the available GenBank data, for 40 eukaryotic biological species and 5
chloroplasts, do not follow a Zipf law, but are best fitted by the sum of a
constant, an exponential and a linear function in the rank of usage. For
mitochondriae the analysis is not conclusive. A quantum-mechanics-inspired
model is proposed to describe the observed behaviour. These functions are
characterized by parameters that strongly depend on the total GC content of the
coding regions of biological species. It is predicted that the codon usage is
the same in all exonic genes with the same GC content. The Shannon entropy for
codons, also strongly depending on the exonic GC content, is computed.
