Using Ciliate Operations to Construct Chromosome Phylogenies

Whole genome sequencing has revealed several examples where genomes of different species are related by permutation. The number of certain types of rearrangements needed to transform one permuted list into another can measure the distance between such lists. Using an algorithm based on three basic DNA editing operations suggested by a model for ciliate micro nuclear decryption, this study defines the distance between two permutations to be the number of ciliate operations the algorithm performs during such a transformation. Combining well-known clustering methods with this distance function enables one to construct corresponding phylogenies. These ideas are illustrated by exploring the phylogenetic relationships among the chromosomes of eight fruitfly (drosophila) species, using the well-known UPGMA algorithm on the distance function provided by the ciliate operations. Over evolutionary time “local” DNA editing events such as nucleotide substitutions, deletions or insertions diversify the set of DNA sequences present in organisms. Results of whole genome sequencing suggest that also “global” DNA editing events diversify these DNA sequences. Consider two species S1 and S2 with a common ancestor whose genome was organized over n linear chromosomes. A geneG of the ancestor was inherited as gene G1 by species S1 and as gene G2 by species S2. G1 and G2 are orthologous genes, or simply orthologs. Assume that the species S1 and S2 each also has n chromosomes, and that for each ancestral chromosome i, the orthologs of any ancestral gene on chromosome i are also in the descendant species S1 and S2 on the corresponding chromosome i. This assumption is known, in the context of certain fruitfly species, as the Muller hypothesis. In this paper we shall assume the Muller hypothesis for our applications. It may happen that the order in which orthologs on chromosome i appear in species S1 is different from the order in which they appear in species S2. In this case chromosome i in each of these two species can be partitioned into a number, say k, of synteny blocks: A synteny block is a maximal list of adjacent orthologous Date: January 6, 2014. 2000 Mathematics Subject Classification. 05E15, 20B99, 92-08, 92D15, 92D99.