Narrow Results

Series of coding sequence lengths extracted from the chromosome of Bacillus subtilis were subjected to detrended fluctuation analysis (DFA). The non-linear characteristic of the DFA plot was interpreted in terms of short-range correlation. The analysis was performed on series consisting of the whole chromosome coding sequences, as well as on the leading and lagging strands. These were compared to the same series subjected to a randomization procedure. The series were divided into two halves, which also revealed different short-range characteristics. Similar results were noticed for seven strains of Escherichia coli. Therefore, the short-range correlation characteristics are sensitive to species and strains and could be used for comparative investigations of microbial genome organization.

Previous investigation of the length of coding sequence lengths (CDS) in the bacterial circular chromosome revealed short range correlation in the series of these data. We have further analyzed the averaged periodograms of these series and we found that the organization of CDS can be well described by first-order autoregressive processes. This involves interaction between the neighboring terms. The autoregressive analysis may have great potential in modeling various physical and biological processes like light emission of galaxies, protein organization, cell flickering, cognitive processes and perhaps others.

Many models of genome rearrangement involve operations that are self-inverse, and hence generate a group acting on the space of genomes. This gives a correspondence between genome arrangements and the elements of a group, and consequently, between evolutionary paths and walks on the Cayley graph. Many common methods for phylogenetic reconstruction rely on calculating the minimal distance between two genomes; this omits much of the other information available from the Cayley graph. In this paper, we begin an exploration of some of this additional information, in particular describing the phylogeny as a Steiner tree within the Cayley graph, and exploring the “interval” between two genomes. While motivated by problems in systematic biology, many of these ideas are of independent group-theoretic interest.