Evolution of Genome Organization by Duplication and Loss: An Alignment Approach

Abstract

Abstract. We present a comparative genomics approach for inferring ancestral genome organization and evolutionary scenarios, based on a model accounting for content-modifying operations. More precisely, we focus on comparing two ordered gene sequences with duplicated genes that have evolved from a common ancestor through duplications and losses; our model can be grouped in the class of "Block Edit" models. From a combinatorial point of view, the main consequence is the possibility of formulating the problem as an alignment problem. On the other hand, in contrast to symmetrical metrics such as the inversion distance, duplications and losses are asymmetrical operations that are applicable to one of the two aligned sequences. Consequently, an ancestral genome can directly be inferred from a duplication-loss scenario attached to a given alignment. Although alignments are a priori simpler to handle than rearrangements, we show that a direct approach based on dynamic programming leads, at best, to an efficient heuristic. We present an exact pseudo-boolean linear programming algorithm to search for the optimal alignment along with an optimal scenario of duplications and losses. Although exponential in the worst case, we show low running times on real datasets as well as synthetic data. We apply our algorithm in a phylogenetic context to the evolution of stable RNA (tRNA and rRNA) gene content and organization in Bacillus genomes. Our results lead to various biological insights, such as rates of ribosomal RNA proliferation among lineages, their role in altering tRNA gene content, and evidence of tRNA class conversion.

Duplication-Loss Genome Alignment: Complexity and Algorithm

“…The Duplication-Loss Alignment Problem: We introduced in [11] the concept of "Feasible" Labeled Alignment of two genomes X and Y , and showed the oneto-one correspondence between the set of such alignments and the set of all possible "visible" evolutionary histories from a common ancestor A to X and Y . Definitions on alignments are given below, and illustrated in Figure 1.…”

“…Most of the methods used for comparing two genomes with duplicates (reviewed in [6,7,9]) rely mainly on rearrangement events. Contrariwise, we considered in [11], an evolutionary model restricted to content-modifying operations, and more specifically to duplications and losses. We showed that this model is required to study the evolution of certain gene families, such as Transfer RNAs (tRNAs).…”

“…From a combinatorial point of view, the main consequence of ignoring rearrangements is the fact that gene organization is preserved, which allows reformulating the comparison of two genomes as a Duplication-Loss Alignment problem: find an alignment minimizing the cost of duplications and losses. As in [11], we consider in this paper the cost of an alignment to be the number of underlying segmental duplications (duplication of a string of adjacent genes) and single losses (loss of a single gene). Although alignments are a priori simpler to handle than rearrangements, we showed in [11] that a direct approach based on dynamic programming leads, at best, to an efficient heuristic, and we rather developed an exact pseudo-boolean linear programming algorithm.…”

“…As in [11], we consider in this paper the cost of an alignment to be the number of underlying segmental duplications (duplication of a string of adjacent genes) and single losses (loss of a single gene). Although alignments are a priori simpler to handle than rearrangements, we showed in [11] that a direct approach based on dynamic programming leads, at best, to an efficient heuristic, and we rather developed an exact pseudo-boolean linear programming algorithm. This algorithm is however exponential in the worst case, preventing from being applicable to relatively large genomes (more than 200 genes).…”

“…The way to solve the Minimum Label Alignment problem, as well as its complexity, were left open in [11]. We show in Section 4 that it is APX-hard, even if the number of occurrences of a gene inside a genome is bounded by 5.…”