ABSTRACT
The task of the quartet puzzling problem is to find a best-fitting binary X-tree for a finite n-set from confidence values for the 3n4 binary trees with exactly four leaves from X, its fitness being measured by the sum of the confidence values of all "induced" four-leaves subtrees. We describe a method for finding an exact solution of this problem by integer linear programming. Similar procedures can also be used for finding, e.g. best-fitting "circular" networks. A crucial problem in this context is, of course, how to obtain the input confidence values for the quartet trees. We propose to use inner products of rate-matrix diagonals calculated for pairs of taxa and present the trees resulting from applying our approach to two data sets of up to 36 mitochondrial sequences of mammals including an outgroup.
ABSTRACT
BACKGROUND: Although the organisation of the bacterial chromosome is an area of active research, little is known yet on that subject. The difficulty lies in the fact that the system is dynamic and difficult to observe directly. The advent of massive hybridisation techniques opens the way to further studies of the chromosomal structure because the genes that are co-expressed, as identified by microarray experiments, probably share some spatial relationship. The use of several independent sets of gene expression data should make it possible to obtain an exhaustive view of the genes co-expression and thus a more accurate image of the structure of the chromosome. RESULTS: For both Bacillus subtilis and Escherichia coli the co-expression of genes varies as a function of the distance between the genes along the chromosome. The long-range correlations are surprising: the changes in the level of expression of any gene are correlated (positively or negatively) to the changes in the expression level of other genes located at well-defined long-range distances. This property is true for all the genes, regardless of their localisation on the chromosome. We also found short-range correlations, which suggest that the location of these co-expressed genes corresponds to DNA turns on the nucleoid surface (14-16 genes). CONCLUSION: The long-range correlations do not correspond to the domains so far identified in the nucleoid. We explain our results by a model of the nucleoid solenoid structure based on two types of spirals (short and long). The long spirals are uncoiled expressed DNA while the short ones correspond to coiled unexpressed DNA.
