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DOI: 10.4230/LIPIcs.WABI.2021.18

Genome Halving and Aliquoting Under the Copy Number Distance

Authors: Ron Zeira, Geoffrey Mon, and Benjamin J. Raphael

Published in: LIPIcs, Volume 201, 21st International Workshop on Algorithms in Bioinformatics (WABI 2021)

Abstract

Large-scale genome rearrangements occur frequently in species evolution and cancer evolution. While the computation of evolutionary distances is tractable for balanced rearrangements, such as inversions and translocations, computing distances involving duplications and deletions is much more difficult. In the recently proposed Copy Number Distance (CND) model, a genome is represented as a Copy Number Profile (CNP), a sequence of integers, and the CND between two CNPs is the length of a shortest sequence of deletions and amplifications of contiguous segments that transforms one CNP into the other. In addition to these segmental events, genomes also undergo global events such as Whole Genome Duplication (WGD) or polyploidization that multiply the entire genome content. These global events are common and important in both species and cancer evolution. In this paper, we formulate the genome halving problem of finding a closest preduplication CNP that has undergone a WGD and evolved into a given CNP under the CND model. We also formulate the analogous genome aliquoting problem of finding the closest prepolyploidzation CNP under the CND distance. We give a linear time algorithm for the halving distance and a quadratic time dynamic programming algorithm for the aliquoting distance. We implement these algorithms and show that they produce reasonable solutions on simulated CNPs.

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Ron Zeira, Geoffrey Mon, and Benjamin J. Raphael. Genome Halving and Aliquoting Under the Copy Number Distance. In 21st International Workshop on Algorithms in Bioinformatics (WABI 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 201, pp. 18:1-18:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{zeira_et_al:LIPIcs.WABI.2021.18,
  author =	{Zeira, Ron and Mon, Geoffrey and Raphael, Benjamin J.},
  title =	{{Genome Halving and Aliquoting Under the Copy Number Distance}},
  booktitle =	{21st International Workshop on Algorithms in Bioinformatics (WABI 2021)},
  pages =	{18:1--18:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-200-6},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{201},
  editor =	{Carbone, Alessandra and El-Kebir, Mohammed},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2021.18},
  URN =		{urn:nbn:de:0030-drops-143711},
  doi =		{10.4230/LIPIcs.WABI.2021.18},
  annote =	{Keywords: Genome rearrangements, Copy number distance, Whole genome duplication, polyploidization, genome halving distance, genome aliquoting distance}
}

Document

DOI: 10.4230/LIPIcs.CPM.2016.16

A Linear-Time Algorithm for the Copy Number Transformation Problem

Authors: Ron Shamir, Meirav Zehavi, and Ron Zeira

Published in: LIPIcs, Volume 54, 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)

Abstract

Problems of genome rearrangement are central in both evolution and cancer. Most evolutionary scenarios have been studied under the assumption that the genome contains a single copy of each gene. In contrast, tumor genomes undergo deletions and duplications, and thus the number of copies of genes varies. The number of copies of each gene along a chromosome is called its copy number profile. Understanding copy number profile changes can assist in predicting disease progression and treatment. To date, questions related to distances between copy number profiles gained little scientific attention. Here we focus on the following fundamental problem, introduced by Schwarz et al. (PLOS Comp. Biol., 2014): given two copy number profiles, u and v, compute the edit distance from u to v, where the edit operations are segmental deletions and amplifications. We establish the computational complexity of this problem, showing that it is solvable in linear time and constant space.

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Ron Shamir, Meirav Zehavi, and Ron Zeira. A Linear-Time Algorithm for the Copy Number Transformation Problem. In 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 54, pp. 16:1-16:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{shamir_et_al:LIPIcs.CPM.2016.16,
  author =	{Shamir, Ron and Zehavi, Meirav and Zeira, Ron},
  title =	{{A Linear-Time Algorithm for the Copy Number Transformation Problem}},
  booktitle =	{27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)},
  pages =	{16:1--16:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-012-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{54},
  editor =	{Grossi, Roberto and Lewenstein, Moshe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2016.16},
  URN =		{urn:nbn:de:0030-drops-60789},
  doi =		{10.4230/LIPIcs.CPM.2016.16},
  annote =	{Keywords: Genome Rearrangement, Copy Number}
}

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Genome Halving and Aliquoting Under the Copy Number Distance

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A Linear-Time Algorithm for the Copy Number Transformation Problem

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