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DOI: 10.4230/LIPIcs.WABI.2023.22

Bridging Disparate Views on the DCJ-Indel Model for a Capping-Free Solution to the Natural Distance Problem

Authors: Leonard Bohnenkämper

Published in: LIPIcs, Volume 273, 23rd International Workshop on Algorithms in Bioinformatics (WABI 2023)

Abstract

One of the most fundamental problems in genome rearrangement is the (genomic) distance problem. It is typically formulated as finding the minimum number of rearrangements under a model that are needed to transform one genome into the other. A powerful multi-chromosomal model is the Double Cut and Join (DCJ) model. While the DCJ model is not able to deal with some situations that occur in practice, like duplicated or lost regions, it was extended over time to handle these cases. First, it was extended to the DCJ-indel model, solving the issue of lost markers. Later ILP-solutions for so called natural genomes, in which each genomic region may occur an arbitrary number of times, were developed, enabling in theory to solve the distance problem for any pair of genomes. However, some theoretical and practical issues remained unsolved. On the theoretical side of things, there exist two disparate views of the DCJ-indel model, motivated in the same way, but with different conceptualizations that could not be reconciled so far. On the practical side, while the solutions for natural genomes typically perform well on telomere to telomere resolved genomes, they have been shown in recent years to quickly loose performance on genomes with a large number of contigs or linear chromosomes. This has been linked to a particular technique increasing the solution space superexponentially named capping. Recently, we introduced a new conceptualization of the DCJ-indel model within the context of another rearrangement problem. In this manuscript, we will apply this new conceptualization to the distance problem. In doing this, we uncover the relation between the disparate conceptualizations of the DCJ-indel model. We are also able to derive an ILP solution to the distance problem that does not rely on capping and therefore significantly improves upon the performance of previous solutions for genomes with high numbers of contigs while still solving the problem exactly. To the best of our knowledge, our approach is the first allowing for an exact computation of the DCJ-indel distance for natural genomes with large numbers of linear chromosomes. We demonstrate the performance advantage as well as limitations in comparison to an existing solution on simulated genomes as well as showing its practical usefulness in an analysis of 11 Drosophila genomes.

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Leonard Bohnenkämper. Bridging Disparate Views on the DCJ-Indel Model for a Capping-Free Solution to the Natural Distance Problem. In 23rd International Workshop on Algorithms in Bioinformatics (WABI 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 273, pp. 22:1-22:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bohnenkamper:LIPIcs.WABI.2023.22,
  author =	{Bohnenk\"{a}mper, Leonard},
  title =	{{Bridging Disparate Views on the DCJ-Indel Model for a Capping-Free Solution to the Natural Distance Problem}},
  booktitle =	{23rd International Workshop on Algorithms in Bioinformatics (WABI 2023)},
  pages =	{22:1--22:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-294-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{273},
  editor =	{Belazzougui, Djamal and Ouangraoua, A\"{i}da},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2023.22},
  URN =		{urn:nbn:de:0030-drops-186484},
  doi =		{10.4230/LIPIcs.WABI.2023.22},
  annote =	{Keywords: Comparative Genomics, Genome Rearrangement, Double-Cut-And-Join, Indels, Integer Linear Programming, Capping}
}

Document

DOI: 10.4230/LIPIcs.WABI.2022.6

Constructing Founder Sets Under Allelic and Non-Allelic Homologous Recombination

Authors: Konstantinn Bonnet, Tobias Marschall, and Daniel Doerr¹

Published in: LIPIcs, Volume 242, 22nd International Workshop on Algorithms in Bioinformatics (WABI 2022)

Abstract

Homologous recombination between the maternal and paternal copies of a chromosome is a key mechanism for human inheritance and shapes population genetic properties of our species. However, a similar mechanism can also act between different copies of the same sequence, then called non-allelic homologous recombination (NAHR). This process can result in genomic rearrangements - including deletion, duplication, and inversion - and is underlying many genomic disorders. Despite its importance for genome evolution and disease, there is a lack of computational models to study genomic loci prone to NAHR. In this work, we propose such a computational model, providing a unified framework for both (allelic) homologous recombination and NAHR. Our model represents a set of genomes as a graph, where human haplotypes correspond to walks through this graph. We formulate two founder set problems under our recombination model, provide flow-based algorithms for their solution, and demonstrate scalability to problem instances arising in practice.

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Konstantinn Bonnet, Tobias Marschall, and Daniel Doerr¹. Constructing Founder Sets Under Allelic and Non-Allelic Homologous Recombination. In 22nd International Workshop on Algorithms in Bioinformatics (WABI 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 242, pp. 6:1-6:23, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bonnet_et_al:LIPIcs.WABI.2022.6,
  author =	{Bonnet, Konstantinn and Marschall, Tobias and Doerr¹, Daniel},
  title =	{{Constructing Founder Sets Under Allelic and Non-Allelic Homologous Recombination}},
  booktitle =	{22nd International Workshop on Algorithms in Bioinformatics (WABI 2022)},
  pages =	{6:1--6:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-243-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{242},
  editor =	{Boucher, Christina and Rahmann, Sven},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2022.6},
  URN =		{urn:nbn:de:0030-drops-170403},
  doi =		{10.4230/LIPIcs.WABI.2022.6},
  annote =	{Keywords: founder set reconstruction, variation graph, pangenomics, NAHR, homologous recombination}
}

Document

DOI: 10.4230/LIPIcs.WABI.2022.13

A Linear Time Algorithm for an Extended Version of the Breakpoint Double Distance

Authors: Marília D. V. Braga, Leonie R. Brockmann, Katharina Klerx, and Jens Stoye

Published in: LIPIcs, Volume 242, 22nd International Workshop on Algorithms in Bioinformatics (WABI 2022)

Abstract

Two genomes over the same set of gene families form a canonical pair when each of them has exactly one gene from each family. A genome is circular when it contains only circular chromosomes. Different distances of canonical circular genomes can be derived from a structure called breakpoint graph, which represents the relation between the two given genomes as a collection of cycles of even length. Then, the breakpoint distance is equal to n-c_2, where n is the number of genes and c_2 is the number of cycles of length 2. Similarly, when the considered rearrangements are those modeled by the double-cut-and-join (DCJ) operation, the rearrangement distance is n-c, where c is the total number of cycles. The distance problem is a basic unit for several other combinatorial problems related to genome evolution and ancestral reconstruction, such as median or double distance. Interestingly, both median and double distance problems can be solved in polynomial time for the breakpoint distance, while they are NP-hard for the rearrangement distance. One way of exploring the complexity space between these two extremes is to consider a σ_k distance, defined to be n-(c_2+c_4+…+c_k), and increasingly investigate the complexities of median and double distance for the σ₄ distance, then the σ₆ distance, and so on. While for the median much effort was done in our and in other research groups but no progress was obtained even for the σ₄ distance, for solving the double distance under σ₄ and σ₆ distances we could devise linear time algorithms, which we present here.

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Marília D. V. Braga, Leonie R. Brockmann, Katharina Klerx, and Jens Stoye. A Linear Time Algorithm for an Extended Version of the Breakpoint Double Distance. In 22nd International Workshop on Algorithms in Bioinformatics (WABI 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 242, pp. 13:1-13:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

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@InProceedings{braga_et_al:LIPIcs.WABI.2022.13,
  author =	{Braga, Mar{\'\i}lia D. V. and Brockmann, Leonie R. and Klerx, Katharina and Stoye, Jens},
  title =	{{A Linear Time Algorithm for an Extended Version of the Breakpoint Double Distance}},
  booktitle =	{22nd International Workshop on Algorithms in Bioinformatics (WABI 2022)},
  pages =	{13:1--13:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-243-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{242},
  editor =	{Boucher, Christina and Rahmann, Sven},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2022.13},
  URN =		{urn:nbn:de:0030-drops-170472},
  doi =		{10.4230/LIPIcs.WABI.2022.13},
  annote =	{Keywords: Comparative genomics, genome rearrangement, breakpoint distance, double-cut-and-join (DCJ) distance, double distance}
}

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Bridging Disparate Views on the DCJ-Indel Model for a Capping-Free Solution to the Natural Distance Problem

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Constructing Founder Sets Under Allelic and Non-Allelic Homologous Recombination

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A Linear Time Algorithm for an Extended Version of the Breakpoint Double Distance

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