Gene Maps Linearization Using Genomic Rearrangement Distances

Abstract

A preliminary step to most comparative genomics studies is the annotation of chromosomes as ordered sequences of genes. Different genetic mapping techniques often give rise to different maps with unequal gene content and sets of unordered neighboring genes. Only partial orders can thus be obtained from combining such maps. However, once a total order O is known for a given genome, it can be used as a reference to order genes of a closely related species characterized by a partial order P . Our goal is to find a linearization of P that is as close as possible to O, in term of a given genomic distance. We first prove NP-completeness complexity results considering the breakpoint and the common interval distances. We then focus on the breakpoint distance and give a dynamic programming algorithm whose running time is exponential for general partial orders, but polynomial when the partial order is derived from a bounded number of genetic maps. A time-efficient greedy heuristic is then given for the general case and is empirically shown to produce solutions within 10% of the optimal solution, on simulated data. Applications to the analysis of grass genomes are presented.

Pseudo Boolean Programming for Partially Ordered Genomes

“…Following the example of [4], we have tested our algorithms on simulated data to assess the performance of our programs for different parameters inherent to partial orders. The rationale for this choice is two-fold.…”

“…the number of adjacencies between T 1 and T 2 is maximized among all linear extensions of P 1 and P 2 . Note that problems MCIL-1PO, MAL-1PO and MAL-2PO have been proved to be NP-hard in [4].…”

“…Unfortunately, concerning the number of adjacencies, the number of common intervals and the reversal distance, finding a linear extension that optimizes one of these measures between this extension and a given total order is NP-hard [4,6]. In this paper, we first present an approach to compute a linear extension of a partially ordered genome with respect to a given totally ordered genome without duplicated genes.…”

“…We also extend our approach and consider the problem of comparing two partially ordered genomes with respect to the number of adjacencies. After presenting our three algorithms, we evaluate our method by using the same simulated data as in [4]. This paper is organized as follows.…”

Issues in the Reconstruction of Gene Order Evolution

“…Comparison of DAGs for genome comparison are generally hard problems [53] , but considerable work has been done on heuristics [51][52] , approximations [54] and generalizations [53] . …”