  The nature of the quantitative distribution of the 64 DNA codons in the human
genome has been an issue of debate for over a decade. Some groups have proposed
that the quantitative distribution of the DNA codons ordered as a
rank-frequency plot follows a well-known power law called Zipf's law. Others
have shown that the DNA codon distribution is best fitted to an exponential
function. However, the reason for such scaling behavior has not yet been
addressed. In the present study, we demonstrate that the nonlinearity of the
DNA codon distribution is a direct consequence of the frequency recurrence of
the codon usage (i.e., the repetitiveness of codon usage frequencies at the
whole genome level). We discover that if frequency recurrence is absent from
the human genome, the frequency of occurrence of codons scales linearly with
the codon rank. We also show that DNA codons of both low and high frequency of
occurrence in the genome are best fitted by an exponential function and provide
strong evidence to suggest that the coding region of the human genome does not
follow Zipf's law. Information-theoretic methods and entropy calculations are
applied to the DNA codon distribution and a new approach, called the lariat
method, is proposed to quantitatively analyze the DNA codon distribution in
Homo sapiens.
