Incorporating intergenic regions into reversal and transposition distances with indels

Alexandrino, Alexsandro Oliveira; Oliveira, André Rodrigues; Dias, Ulisses; Dias, Zanoni

doi:10.1142/s0219720021400114

Cited by 10 publications

(4 citation statements)

References 11 publications

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“… 2009 ; Alexandrino et al. 2021 ). Broadly, breakpoints are the regions in the genome around which rearrangements have occurred.…”

Section: Cuts and Breakpointsmentioning

confidence: 99%

Rearrangement Events on Circular Genomes

Stevenson,

Terauds,

Sumner

2023

Bull Math Biol

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Early literature on genome rearrangement modelling views the problem of computing evolutionary distances as an inherently combinatorial one. In particular, attention is given to estimating distances using the minimum number of events required to transform one genome into another. In hindsight, this approach is analogous to early methods for inferring phylogenetic trees from DNA sequences such as maximum parsimony—both are motivated by the principle that the true distance minimises evolutionary change, and both are effective if this principle is a true reflection of reality. Recent literature considers genome rearrangement under statistical models, continuing this parallel with DNA-based methods, with the goal of using model-based methods (for example maximum likelihood techniques) to compute distance estimates that incorporate the large number of rearrangement paths that can transform one genome into another. Crucially, this approach requires one to decide upon a set of feasible rearrangement events and, in this paper, we focus on characterising well-motivated models for signed, uni-chromosomal circular genomes, where the number of regions remains fixed. Since rearrangements are often mathematically described using permutations, we isolate the sets of permutations representing rearrangements that are biologically reasonable in this context, for example inversions and transpositions. We provide precise mathematical expressions for these rearrangements, and then describe them in terms of the set of cuts made in the genome when they are applied. We directly compare cuts to breakpoints, and use this concept to count the distinct rearrangement actions which apply a given number of cuts. Finally, we provide some examples of rearrangement models, and include a discussion of some questions that arise when defining plausible models.

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“… 2009 ; Alexandrino et al. 2021 ). Broadly, breakpoints are the regions in the genome around which rearrangements have occurred.…”

Section: Cuts and Breakpointsmentioning

confidence: 99%

Rearrangement Events on Circular Genomes

Stevenson,

Terauds,

Sumner

2023

Bull Math Biol

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show abstract

“…The subset of permutations on [n] which satisfy (1) forms a subgroup of S [n] (the group of permutations on [n]), namely the hyperoctahedral group, which we denote as H n . This extension means we can write σ simply as 1 2 3 4 5 1 4 3 5 2 , or in one-row notation as [14352], remembering that its action on the remaining elements of [n] is given by Equation (1). We of course have a natural embedding of S n as a subgroup of H n , obtained by extending each permutation in S n via the above process.…”

Section: Genomes and Rearrangements As Permutationsmentioning

confidence: 99%

“…Since the number of regions n is encoded in the symmetry element z, this model can be written in the same way for any number of regions n > 2. These rearrangement actions can be allowed to occur with equal probability by simply assigning 1 2 to each action, or they can be given different weights. For example, there is some evidence of smaller inversions being more prevalent compared to larger inversions [10,19], and this can be modelled by assigning the 1-and 2-region inversions the probabilities 2 3 and 1 3 , for example.…”

Section: Example 43 (One and Two Region Inversions) A Model Containin...mentioning

confidence: 99%

“…While the specific position labels themselves are less important in the circular case (since positions can be rotated/flipped around without altering the genome) the cut set does describe a configuration of cuts around the genome. Breakpoints have a number of different definitions in the literature, some of which are specific to particular symmetries or other assumptions [26,15,1]. In this section we provide a definition of a breakpoint for circular genomes that is analogous to the set of cuts.…”

Section: Breakpointsmentioning

confidence: 99%

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Rearrangement Events on Circular Genomes

Stevenson¹,

Terauds²,

Sumner³

2022

Preprint

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Early literature on genome rearrangement modelling views the problem of computing evolutionary distances as an inherently combinatorial one. In particular, attention was given to estimating distances using the minimum number of events required to transform one genome into another. In hindsight, this approach is analogous to early methods for inferring phylogenetic trees from DNA sequences such as maximum parsimony-both are motivated by the principle that the true distance minimises evolutionary change, and both are effective if this principle is a true reflection of reality. Recent literature considers genome rearrangement under statistical models, continuing this parallel with DNA-based methods; the goal here is to use model-based methods (for example maximum likelihood techniques) to compute distance estimates that incorporate the large number of rearrangement paths that can transform one genome into another. Crucially, this approach requires one to decide upon a set of feasible rearrangement events and, in this paper, we focus on characterising well-motivated models for signed, uni-chromosomal circular genomes, where the number of regions remains fixed. Since rearrangements are often mathematically described using permutations, we isolate the sets of permutations representing rearrangements that are biologically reasonable in this context, for example inversions and translocations. We provide precise mathematical expressions for these rearrangements, and then describe them in terms of the set of cuts made in the genome when they are applied. We directly compare cuts to breakpoints, and use this concept to count the distinct rearrangement actions which apply a given number of cuts. Finally, we provide some examples of rearrangement models, and include a discussion of some questions that arise when defining plausible models.

show abstract