Addendum to the paper “ Codon usage domains over bacterial chromosomes ”

An issue left unexplained in the paper [1] is the striking quantitative difference between E. coli and B. subtilis. This is clearly visible in Fig. 6 of [1], where it is shown the probability that two genes at distance l belong to the same cluster of codon usage. Clusters are characterized by a similar codon bias and were identified using a novel information-based clustering method. While both curves decay on distances sizably longer than what could be accounted by operons, B. subtilis curve manifestly features much longer correlations. It is hard to develop a biologically well-founded explanation for such a striking difference between the two organisms. This observation and discussions with Dr. Morten Kloster (Princeton Univ.) spurred us to reconsider the issue and further pursue our analysis of the clusters. The purpose of this addendum is to describe this analysis, which allows us to point out an incorrect statement made in the paper [1], and provide an explanation for the aforementioned difference between the two organisms. The conclusion is that clusters of B. subtilis and E. coli not biased in GC content display now the same behaviour, with correlations of codons usage of the same order, roughly three times the length of the average operon. Contrary to what was previously stated, the GC content of the various clusters is not quite homogeneous and the correct values are reported in Table A1.