Double Cut and Join with Insertions and Deletions

Abstract

Many approaches to compute the genomic distance are still limited to genomes with the same content, without duplicated markers. However, differences in the gene content are frequently observed and can reflect important evolutionary aspects. While duplicated markers can hardly be handled by exact models, when duplicated markers are not allowed, a few polynomial time algorithms that include genome rearrangements, insertions and deletions were already proposed. In an attempt to improve these results, in the present work we give the first linear time algorithm to compute the distance between two multichromosomal genomes with unequal content, but without duplicated markers, considering insertions, deletions and double cut and join (DCJ) operations. We derive from this approach algorithms to sort one genome into another one also using DCJ operations, insertions and deletions. The optimal sorting scenarios can have different compositions and we compare two types of sorting scenarios: one that maximizes and one that minimizes the number of DCJ operations with respect to the number of insertions and deletions. We also show that, although the triangle inequality can be disrupted in the proposed genomic distance, it is possible to correct this problem adopting a surcharge on the number of non-common markers. We use our method to analyze six species of Rickettsia, a group of obligate intracellular parasites, and identify preliminary evidence of clusters of deletions.

Comparative genomics meets topology: a novel view on genome median and halving problems

“…For example, analysis of non-orientable surfaces (such as Klein bottle) seems to be relevant to the double distance problem asking for a maximal cycle decomposition of the contracted breakpoint graph of a given all-duplicated genome and an ordinary genome. Also, embedded graphs on surfaces with boundaries (holes) can be related to models including genome rearrangements along with gene insertions and deletions [29, 30]. …”

Fast ancestral gene order reconstruction of genomes with unequal gene content

“…The DCJ-indel distance between A and B is the minimum number of DCJs and indels required to transform A into B , and it is denoted as d DCJ ind( A,B ). This distance can also be found in polynomial time, using two different approaches (Compeau [20] and Braga et al [21]). Here, we use Compeau’s approach, which is based creating prosthetic chromosomes [22] in each genome, formed by the unique genes of the other, creating two new genomes with the same gene content.…”

Genomic distance under gene substitutions

“…We analyze genomes with unequal content, but without duplicated markers and extend the results given in [6] to develop a linear time algorithm that exactly computes the genomic distance with substitutions and DCJ operations. The objective of this model is to provide a parsimonious genomic distance to handle genomes free of duplicated markers, that in practice is a lower bound to the real genomic distances.…”

“…Insertions and deletions can be shortly called indels . In [4], the operations allowed are inversions and indels, while the models given in [5] and [6] consider indels and the double cut and join (DCJ) operation [7], that is able to represent most large scale mutation events in genomes, such as inversions, translocations, fusions and fissions. The mentioned approaches assign the same weight to all rearrangement operations, including indels, regardless of the size of the affected regions and the particular types of the operations.…”

“…In the remainder of this section we introduce some concepts given in [1] and [6] and define the operation that substitutes markers in a genome - these are the basis of the method that we will present here.…”