Genome rearrangement based on reversals that preserve conserved intervals

The order of genes in the genomes of species can change during evolution and can provide information about their phylogenetic relationship. An interesting method to infer the phylogenetic relationship from the gene orders is to use different types of rearrangement operations and to find possible rearrangement scenarios using these operations. One of the most common rearrangement operations is reversals, which reverse the order of a subset of neighbored genes. In this paper, we study the problem to find the ancestral gene order for three species represented by their gene orders. The rearrangement scenario should use a minimal number of reversals and no other rearrangement operations. This problem is called the Median problem and is known to be NP-complete. In this paper, we describe a heuristic algorithm for finding solutions to the Median problem that searches for rearrangement scenarios with the additional property that gene groups should not be destroyed by reversal operations. The concept of conserved intervals for signed permutations is used to describe such gene groups. We show experimentally, for different types of test problems, that the proposed algorithm produces very good results compared to other algorithms for the Median problem. We also integrate our reversal selection procedure into the well-known MGR and GRAPPA algorithms and show that they achieve a significant speedup while obtaining solutions of the same quality as the original algorithms on the test problems.