Phylogenetic Reconstruction from Genome Order Data

Abstract

Abstract The growing number of complete mapped genome maps has enabled the extraction of phylogenetic information from global rearrangements over the whole genome, rather than just local nucleotide or amino acid patterns. Each genome is encoded as a permutation of the set of common genes. The distance, or amount of divergence, between two genomes can be estimated under a number of models; we use the breakpoint distance model because of its generality and ease of calculation. The breakpoint distance between two permutations is equal to the number of pairs of objects (genes) that are adjacent in one permutation but not the other. We wish to construct Steiner trees for genomes under the breakpoint distance. This problem is NP-hard for just three genomes: making both the breakpoint Steiner tree problem, and the fixed topology breakpoint Steiner problem NP-hard. In practice, however, the three genome case can be solved for moderate sized genomes by using a transformation to the Travelling Salesman Problem. We show how techniques employed to solve TSP can be extended to solve the fixed topology breakpoint Steiner tree problem.