Some Algorithmic Challenges in Genome-Wide Ortholog Assignment

Abstract

Genome-scale assignment of orthologous genes is a fundamental and challenging problem in computational biology and has a wide range of applications in comparative genomics, functional genomics, and systems biology. Many methods based on sequence similarity, phylogenetic analysis, chromosomal syntenic information, and genome rearrangement have been proposed in recent years for ortholog assignment. Although these methods produce results that largely agree with each other, their results may still contain significant differences. In this article, we consider the recently proposed parsimony approach for assigning orthologs between closely related genomes based on genome rearrangement, which essentially attempts to transform one genome into another by the smallest number of genome rearrangement events including reversal, translocation, fusion, and fission, as well as gene duplication events. We will highlight some of the challenging algorithmic problems that arise in the approach including (i) minimum common substring partition, (ii) signed reversal distance with duplicates, and (iii) signed transposition distance with duplicates. The most recent progress towards the solution of these problems will be reviewed and some open questions will be posed. We will also discuss some possible extensions of the approach to the simultaneous comparison of multiple genomes.

Analysis of Gene Order Evolution Beyond Single-Copy Genes

“…Other approaches maximize the number of genes matched in each family [29,3]. A more general method allowing all gene copies to be kept, and accounting for reversals, translocations, fusions and fissions, has been developed and implemented in the MSOAR software [46,68,104]. Finding the most parsimonious rearrangement process transforming one genome into another constructs, as a byproduct, the list of orthologous gene pairs.…”

Issues in the Reconstruction of Gene Order Evolution

“…Incorporating this fact into the mathematics of genome comparison and genome reconstruction complicates the formulation of problems and inevitably worsens their complexity. For this introductory essay, therefore, we will keep largely to the single-copy genes case, and leave it to the reader to explore the voluminous literature (starting with [22]) that attempts to generalize to the multicopy case. We will touch on the latter occasionally, especially in Section 4 on genome halving, a context where there are exactly two copies of each gene.…”

“…A typical problem involves ambiguous homology or paralogy, due to WGD and other duplication processes, leading to the risk of matching up inappropriate pairs of genes as orthologs in the two genomes [22] . These problems tend to artifactually disrupt long runs of consecutive genes in both genomes, and increase the number of shorter runs, often consisting of only one or two genes.…”

“…We will characterize genomes as gene orders, and often use the terms interchangeably. We will not delve further into the separate question of identifying genes within a genome, though we will have to address aspects of the question of how to treat spatially dispersed multicopy or paralogous genes in one genome with respect to their homologous counterparts in another genome, a problem which is discussed in depth by Tao Jiang elsewhere in this issue [22] .…”

Reversal Distances for Strings with Few Blocks or Small Alphabets

“…More precisely, the reversal diameter of strings of length n is n − max a∈Σ #(a) where #(a) denotes the number of occurrences of letter a in either input string. Signed String Reversal Distance has applications in the identification of orthologous genes across two genomes [5,10,12]. Signed String Reversal Distance is NP-hard if each letter occurs at most twice [5] and for binary signed strings [13].…”