Statistical properties of DNA sequences revisited: the role of inverse bilateral symmetry in bacterial chromosomes

Herein it is shown that in order to study the statistical properties of DNA sequences in bacterial chromosomes it suffices to consider only one half of the chromosome because they are similar to its corresponding complementary sequence in the other half. This is due to the inverse bilateral symmetry of bacterial chromosomes. Contrary to the classical result that DNA coding regions of bacterial genomes are purely uncorrelated random sequences, here it is shown, via a renormalization group approach, that DNA random fluctuations of single bases are modulated by log-periodic variations. Distance series of triplets display long-range correlations in each half of the intact chromosome and in protein-coding sequences, or both long-range correlations and log-periodic modulations along the whole chromosome. Hence scaling analyses of distance series of DNA sequences have to consider the functional units of bacterial chromosomes.