Combinatorics of Genome Rearrangements

Abstract

A comprehensive survey of a rapidly expanding field of combinatorial optimization, mathematically oriented but offering biological explanations when required. From one cell to another, from one individual to another, and from one species to another, the content of DNA molecules is often similar. The organization of these molecules, however, differs dramatically, and the mutations that affect this organization are known as genome rearrangements. Combinatorial methods are used to reconstruct putative rearrangement scenarios in order to explain the evolutionary history of a set of species, often formalizing the evolutionary events that can explain the multiple combinations of observed genomes as combinatorial optimization problems. This book offers the first comprehensive survey of this rapidly expanding application of combinatorial optimization. It can be used as a reference for experienced researchers or as an introductory text for a broader audience. Genome rearrangement problems have proved so interesting from a combinatorial point of view that the field now belongs as much to mathematics as to biology. This book takes a mathematically oriented approach, but provides biological background when necessary. It presents a series of models, beginning with the simplest (which is progressively extended by dropping restrictions), each constructing a genome rearrangement problem. The book also discusses an important generalization of the basic problem known as the median problem, surveys attempts to reconstruct the relationships between genomes with phylogenetic trees, and offers a collection of summaries and appendixes with useful additional information.

Duplication, Rearrangement and Reconciliation: A Follow-Up 13 Years Later

“…It is only in the early eighties that formal models of gene order evolution were investigated again, after a nearly 50 year hiatus [15], mainly following Sankoff's efforts [16,17]. As for today, despite significant progress, the considered models for gene order evolution are still not reaching the sophistication of those for sequence evolution [18] (see also Chapter 7 in this volume).…”

O(1)-Time Unsorting by Prefix-Reversals in a Boustrophedon Linked List

“…The minimum number of reversals needed to sort a particular permutation is known as sorting by reversals. This problem arises in biology when determining hereditary distance [1,6]. In burnt pancake sorting [4] and signed sorting by reversals [9], each pancake or element has two distinct sides; the boustrophedon linked list is an analogous data structure (except individual nodes are unaware of their orientation).…”

Issues in the Reconstruction of Gene Order Evolution

“…The mathematical details of some of the work discussed here appears in [23], while the field of combinatorics and algorithms for genome rearrangement is the topic of an excellent survey volume by Fertin et al [24] In the next section, we sketch various kinds of genomes and how they are formalized as well as the basic chromosomal rearrangement processes and how they are defined mathematically. This leads to various concepts of genomic distance.…”