Counting Sorting Scenarios and Intermediate Genomes for the Rank Distance

Zanetti, João Paulo Pereira; Chindelevitch, Leonid; Meidânis, João

doi:10.1007/978-3-030-18174-1_10

Cited by 3 publications

(8 citation statements)

References 22 publications

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“…In a series of recent papers [8,7,9,10,11], our group has proposed the representation of genomes as square, 0-1, sparse matrices and the use of rank distance to study genome evolution by large-scale events. Our matrix representation relies on a previous step consisting of the definition of homologous or evolutionarily corresponding regions in the genomes being compared.…”

Section: Representing Genomes As Matricesmentioning

confidence: 99%

Fast median computation for symmetric, orthogonal matrices under the rank distance

Meidânis

Chindelevitch

2021

Linear Algebra and its Applications

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Section: Representing Genomes As Matricesmentioning

confidence: 99%

Fast median computation for symmetric, orthogonal matrices under the rank distance

Meidânis

Chindelevitch

2021

Linear Algebra and its Applications

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“…Such operations are called basic because any other operation can be written as a sum of cuts, joins, and double swaps. For the purpose of this text, it suffices to know that cuts and joins have weight 1, and double swaps have weight 2 (for more details, refer to [65]). Given genomes A and B, a sorting scenario with orign A and target B is a sequence of operations leading from A to B with minimum weight.…”

Section: Chapter 5 Conclusionmentioning

confidence: 99%

“…There are, however, results regarding the counting of optimal scenarios under the DCJ model that consider such recombinations [5] as well as results that do not encompass them [5,39]. In 2019, Zanetti et al [65] produced analogous results for the rank distance and showed that different types of chromosomes are not recombined while sorting one genome into another, which favored the derivation of results for the genomic sorting problem.…”

Section: Chapter 1 Introductionmentioning

confidence: 99%

“…We also present in the appendix a contribution to the results regarding the enumeration of sorting scenarios under the rank distance. In [65], the authors provide formulas to count such scenarios for each component of the breakpoint graph. In particular, the formula that counts sorting scenarios for paths is a recurrence relation that is unlikely to have a closed form, but it does have a closed form for scenarios of minimum and maximum length.…”

Section: Chapter 1 Introductionmentioning

confidence: 99%

“…In particular, the formula that counts sorting scenarios for paths is a recurrence relation that is unlikely to have a closed form, but it does have a closed form for scenarios of minimum and maximum length. Although we provide a bijective proof of this result in [65], we leave registered in this text an algebraic proof for scenarios of maximum length.…”

Section: Chapter 1 Introductionmentioning

confidence: 99%

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Extensions and applications of the genomic rank distance

Peres Oliveira

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Firstly, I am grateful to my family, especially my mother, for supporting me through this whole trajectory.I am very grateful to my advisor, João Meidanis, for his patience and continuous support. Even though I doubted myself several times, João has always pushed me forward and cared for me greatly; I was fortunate to have an amazing advisor by my side. I am also grateful to the Institute of Computing and the University of Campinas for providing us with an outstanding faculty and an stimulating environment.This project was funded by grant #2020/00740-8, São Paulo Research Foundation (FAPESP). We are very grateful to FAPESP for funding our research in the past two years. ResumoSob uma perspectiva computacional, genomas podem ser modelados como uma coleção de segmentos orientados, comumente denominados blocos sintênicos, que representam regiões conservadas ao longo da evolução. Tais regiões são suscetíveis a mutações em larga escala -conhecidas como rearranjos de genomas -que permutam os blocos sintênicos em diferentes configurações. Ao longo dos anos, diversos modelos de distância baseados em rearranjos foram desenvolvidos a fim de calcular eficientemente a distância evolutiva entre genomas. Dentre eles, a distância de posto baseia-se na modelagem de genomas como matrizes e na utilização do posto como métrica de distância. A distância de posto é a sucessora da distância algébrica, um modelo de distância que representa genomas como permutações e é fundamentado na teoria de grupos de permutação.Recentemente, a distância de posto foi estendida para abarcar eventos de inserção e remoçãoindels. Embora existam algoritmos eficientes para calcular o posto nesse contexto, muitos resultados da teoria matricial para rearranjo de genomas ainda são fundamentados em noções de teoria de grupos de permutação. Em adição, os resultados são em grande parte teóricos, e pouco se conhece sobre a aplicabilidade biológica dessa extensão da distância de posto.Neste trabalho, consolidamos e expandimos os resultados recentes referentes à extensão da distância de posto que considera eventos de indel. Em particular, introduzimos uma estrutura de dados denominada grafo de colunas a fim de elaborar fórmulas mais simples para calcular o posto em tempo linear. Este ferramental permitiu que a teoria matricial para rearranjo de genomas e algoritmos derivados fossem simplificados consideravelmente. Em adição, realizamos experimentos em inferência filogenética utilizando dados simulados e genomas reais para averiguar a aplicabilidade biológica da distância de posto. Nossos resultados atestam que a distância de posto é competitiva quando comparada com a distância DCJ-Indel, um método estado-da-arte em rearranjo de genomas. Finalmente, apresentamos uma contribuição para o estudo de enumeração de cenários de ordenação sob a distância de posto.

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Generalizations of the genomic rank distance to indels

et al. 2023

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Motivation The rank distance model, introduced by Zanetti et al. (2016), represents genome rearrangements in multi-chromosomal genomes as matrix operations, which allows the reconstruction of parsimonious histories of evolution by rearrangements. We seek to generalize this model by allowing for genomes with different gene content, to accommodate a broader range of biological contexts. We approach this generalization by using a matrix representation of genomes. This leads to simple distance formulas and sorting algorithms for genomes with different gene contents, but without duplications. Results We generalize the rank distance to genomes with different gene content in two different ways. The first approach adds insertions, deletions, and the substitution of a single extremity to the basic operations. We show how to efficiently compute this distance. To avoid genomes with incomplete markers, our alternative distance, the rank-indel distance, only uses insertions and deletions of entire chromosomes. We construct phylogenetic trees with our distances and the DCJ-Indel distance for simulated data and real prokaryotic genomes, and compare them against reference trees. For simulated data, our distances outperform the DCJ-Indel distance using the Quartet metric as baseline. This suggests that rank distances are more robust for comparing distantly related species. For real prokaryotic genomes, all rearrangement-based distances yield phylogenetic trees that are topologically distant from the reference (65% similarity with Quartet metric), but are able to cluster related species within their respective clades and distinguish the Shigella strains as the farthest relative of the E. coli strains, a feature not seen in the reference tree. Availability Code and instructions available at https://github.com/meidanis-lab/rank-indel. Supplementary information Supplementary data are available at Bioinformatics online.

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Counting Sorting Scenarios and Intermediate Genomes for the Rank Distance

Cited by 3 publications

References 22 publications

Fast median computation for symmetric, orthogonal matrices under the rank distance

Fast median computation for symmetric, orthogonal matrices under the rank distance

Extensions and applications of the genomic rank distance

Generalizations of the genomic rank distance to indels

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