Genomic Distances under Deletions and Insertions

Abstract

As more and more genomes are sequenced, evolutionary biologists are becoming increasingly interested in evolution at the level of whole genomes, in scenarios in which the genome evolves through insertions, deletions, and movements of genes along its chromosomes. In the mathematical model pioneered by Sankoff and others, a unichromosomal genome is represented by a signed permutation of a multi-set of genes; Hannenhalli and Pevzner showed that the edit distance between two signed permutations of the same set can be computed in polynomial time when all operations are inversions. El-Mabrouk extended that result to allow deletions and a limited form of insertions (which forbids duplications). In this paper we extend El-Mabrouk's work to handle duplications as well as insertions and present an alternate framework for computing (near) minimal edit sequences involving insertions, deletions, and inversions. We derive an error bound for our polynomial-time distance computation under various assumptions and present preliminary experimental results that suggest that performance in practice may be excellent, within a few percent of the actual distance.

Some Algorithmic Challenges in Genome-Wide Ortholog Assignment

“…El-Mabrouk [19] developed an approach to reconstructing the ancestor of a modern genome by minimizing the number of duplication transpositions and reversals. The work in [20][21] proposed methods that attempt to find one-to-one gene correspondence between gene families based on conserved segments. Very recently, Swenson et al [22] presented some algorithmic results on the cycle splitting problem in a combinatorial framework similar to the one introduced in [8][9][10].…”

A Framework for Orthology Assignment from Gene Rearrangement Data

“…(In absence of this constraint, of course, the most parsimonious edit sequence is almost always that which deletes the entire genome G 1 as a single operation, then insert the entire genome G 2 , an absurd scenario.) Once that identification has been made, the algorithms of ElMabrouk [9] and of our group [8,12,17,18] can complete the work of finding one ore more parsimonious edit sequences.…”

“…A good choice of orthologies can reduce the required number of deletions (or duplications)-this is the main focus of the cover-based method [12,17]. It can also reduce the number of required inversions by grouping them properly: this is the focus of this paper.…”

“…Sankoff [14] first addressed this problem with his introduction of exemplars, in which he suggested identifying a single gene within each family (the exemplar) on the basis of a parsimonious criterion (using the fewest rearrangements) and discarding all others. Our group provided an alternate approach in which a correspondence is established between gene families on the basis of conserved segments [12,17]; our results suggested that considering all members of a gene family yields better results than keeping only exemplars, but were limited in that the assignment of orthologs did not take into account any rearrangement structure beyond conserved segments. In this paper, we remedy this problem by providing an optimization framework derived from the breakpoint graph (the basic structure behind the last decade of work in gene rearrangements [10]) in which to phrase the problem; we give preliminary theoretical results in support of our framework.…”

Duplication-Loss Genome Alignment: Complexity and Algorithm

“…The case of strings being permutations (i.e. each gene family with a single representative in each genome) has been largely considered by the genome rearrangement community for pairwise comparison (for example [3,8,10,13]) or multiple comparison in a phylogenetic framework (for example [4,12,14,15]). An extra degree of difficulty is introduced in the case of strings containing multiple gene copies.…”