Complexity and algorithms for copy-number evolution problems

Background Cancer is an evolutionary process characterized by the accumulation of somatic mutations in a population of cells that form a tumor. One frequent type of mutations is copy number aberrations, which alter the number of copies of genomic regions. The number of copies of each position along...

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Published in:	Algorithms for molecular biology Vol. 12; no. 1; pp. 13 - 11
Main Authors:	El-Kebir, Mohammed, Raphael, Benjamin J., Shamir, Ron, Sharan, Roded, Zaccaria, Simone, Zehavi, Meirav, Zeira, Ron
Format:	Journal Article
Language:	English
Published:	London BioMed Central 16.05.2017 Springer Nature B.V BMC
Subjects:	Aberration Algorithms Bioinformatics Biomedical and Life Sciences Cancer Cellular and Medical Topics Children Chromosomes Complexity Computational Biology/Bioinformatics Computer simulation Computing time Copy number Copy-number variant Diagnosis Dynamic programming Evolutionary algorithms Genes Graph theory Leaves Life Sciences Maximum parsimony Mutation Phylogenetics Phylogeny Physiological Prognosis Quality assessment Selected papers from WABI 2016 Somatic mutation Somatic mutation Phylogeny Maximum parsimony Copy-number variant Cancer
ISSN:	1748-7188, 1748-7188
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Abstract	Background Cancer is an evolutionary process characterized by the accumulation of somatic mutations in a population of cells that form a tumor. One frequent type of mutations is copy number aberrations, which alter the number of copies of genomic regions. The number of copies of each position along a chromosome constitutes the chromosome’s copy-number profile. Understanding how such profiles evolve in cancer can assist in both diagnosis and prognosis. Results We model the evolution of a tumor by segmental deletions and amplifications, and gauge distance from profile a to b by the minimum number of events needed to transform a into b . Given two profiles, our first problem aims to find a parental profile that minimizes the sum of distances to its children. Given k profiles, the second, more general problem, seeks a phylogenetic tree, whose k leaves are labeled by the k given profiles and whose internal vertices are labeled by ancestral profiles such that the sum of edge distances is minimum. Conclusions For the former problem we give a pseudo-polynomial dynamic programming algorithm that is linear in the profile length, and an integer linear program formulation. For the latter problem we show it is NP-hard and give an integer linear program formulation that scales to practical problem instance sizes. We assess the efficiency and quality of our algorithms on simulated instances. Availability https://github.com/raphael-group/CNT-ILP
AbstractList	Background Cancer is an evolutionary process characterized by the accumulation of somatic mutations in a population of cells that form a tumor. One frequent type of mutations is copy number aberrations, which alter the number of copies of genomic regions. The number of copies of each position along a chromosome constitutes the chromosome’s copy-number profile. Understanding how such profiles evolve in cancer can assist in both diagnosis and prognosis. Results We model the evolution of a tumor by segmental deletions and amplifications, and gauge distance from profile a to b by the minimum number of events needed to transform a into b . Given two profiles, our first problem aims to find a parental profile that minimizes the sum of distances to its children. Given k profiles, the second, more general problem, seeks a phylogenetic tree, whose k leaves are labeled by the k given profiles and whose internal vertices are labeled by ancestral profiles such that the sum of edge distances is minimum. Conclusions For the former problem we give a pseudo-polynomial dynamic programming algorithm that is linear in the profile length, and an integer linear program formulation. For the latter problem we show it is NP-hard and give an integer linear program formulation that scales to practical problem instance sizes. We assess the efficiency and quality of our algorithms on simulated instances. Availability https://github.com/raphael-group/CNT-ILP Cancer is an evolutionary process characterized by the accumulation of somatic mutations in a population of cells that form a tumor. One frequent type of mutations is copy number aberrations, which alter the number of copies of genomic regions. The number of copies of each position along a chromosome constitutes the chromosome's copy-number profile. Understanding how such profiles evolve in cancer can assist in both diagnosis and prognosis.BACKGROUNDCancer is an evolutionary process characterized by the accumulation of somatic mutations in a population of cells that form a tumor. One frequent type of mutations is copy number aberrations, which alter the number of copies of genomic regions. The number of copies of each position along a chromosome constitutes the chromosome's copy-number profile. Understanding how such profiles evolve in cancer can assist in both diagnosis and prognosis.We model the evolution of a tumor by segmental deletions and amplifications, and gauge distance from profile [Formula: see text] to [Formula: see text] by the minimum number of events needed to transform [Formula: see text] into [Formula: see text]. Given two profiles, our first problem aims to find a parental profile that minimizes the sum of distances to its children. Given k profiles, the second, more general problem, seeks a phylogenetic tree, whose k leaves are labeled by the k given profiles and whose internal vertices are labeled by ancestral profiles such that the sum of edge distances is minimum.RESULTSWe model the evolution of a tumor by segmental deletions and amplifications, and gauge distance from profile [Formula: see text] to [Formula: see text] by the minimum number of events needed to transform [Formula: see text] into [Formula: see text]. Given two profiles, our first problem aims to find a parental profile that minimizes the sum of distances to its children. Given k profiles, the second, more general problem, seeks a phylogenetic tree, whose k leaves are labeled by the k given profiles and whose internal vertices are labeled by ancestral profiles such that the sum of edge distances is minimum.For the former problem we give a pseudo-polynomial dynamic programming algorithm that is linear in the profile length, and an integer linear program formulation. For the latter problem we show it is NP-hard and give an integer linear program formulation that scales to practical problem instance sizes. We assess the efficiency and quality of our algorithms on simulated instances.CONCLUSIONSFor the former problem we give a pseudo-polynomial dynamic programming algorithm that is linear in the profile length, and an integer linear program formulation. For the latter problem we show it is NP-hard and give an integer linear program formulation that scales to practical problem instance sizes. We assess the efficiency and quality of our algorithms on simulated instances.https://github.com/raphael-group/CNT-ILP.AVAILABILITYhttps://github.com/raphael-group/CNT-ILP. Background Cancer is an evolutionary process characterized by the accumulation of somatic mutations in a population of cells that form a tumor. One frequent type of mutations is copy number aberrations, which alter the number of copies of genomic regions. The number of copies of each position along a chromosome constitutes the chromosome’s copy-number profile. Understanding how such profiles evolve in cancer can assist in both diagnosis and prognosis. Results We model the evolution of a tumor by segmental deletions and amplifications, and gauge distance from profile $\mathbf {a}$ to $\mathbf {b}$ by the minimum number of events needed to transform $\mathbf {a}$ into $\mathbf {b}$. Given two profiles, our first problem aims to find a parental profile that minimizes the sum of distances to its children. Given k profiles, the second, more general problem, seeks a phylogenetic tree, whose k leaves are labeled by the k given profiles and whose internal vertices are labeled by ancestral profiles such that the sum of edge distances is minimum. Conclusions For the former problem we give a pseudo-polynomial dynamic programming algorithm that is linear in the profile length, and an integer linear program formulation. For the latter problem we show it is NP-hard and give an integer linear program formulation that scales to practical problem instance sizes. We assess the efficiency and quality of our algorithms on simulated instances. Availability https://github.com/raphael-group/CNT-ILP Abstract Background Cancer is an evolutionary process characterized by the accumulation of somatic mutations in a population of cells that form a tumor. One frequent type of mutations is copy number aberrations, which alter the number of copies of genomic regions. The number of copies of each position along a chromosome constitutes the chromosome’s copy-number profile. Understanding how such profiles evolve in cancer can assist in both diagnosis and prognosis. Results We model the evolution of a tumor by segmental deletions and amplifications, and gauge distance from profile $$\mathbf {a}$$ a to $$\mathbf {b}$$ b by the minimum number of events needed to transform $$\mathbf {a}$$ a into $$\mathbf {b}$$ b . Given two profiles, our first problem aims to find a parental profile that minimizes the sum of distances to its children. Given k profiles, the second, more general problem, seeks a phylogenetic tree, whose k leaves are labeled by the k given profiles and whose internal vertices are labeled by ancestral profiles such that the sum of edge distances is minimum. Conclusions For the former problem we give a pseudo-polynomial dynamic programming algorithm that is linear in the profile length, and an integer linear program formulation. For the latter problem we show it is NP-hard and give an integer linear program formulation that scales to practical problem instance sizes. We assess the efficiency and quality of our algorithms on simulated instances. Availability https://github.com/raphael-group/CNT-ILP Cancer is an evolutionary process characterized by the accumulation of somatic mutations in a population of cells that form a tumor. One frequent type of mutations is copy number aberrations, which alter the number of copies of genomic regions. The number of copies of each position along a chromosome constitutes the chromosome's copy-number profile. Understanding how such profiles evolve in cancer can assist in both diagnosis and prognosis. We model the evolution of a tumor by segmental deletions and amplifications, and gauge distance from profile [Formula: see text] to [Formula: see text] by the minimum number of events needed to transform [Formula: see text] into [Formula: see text]. Given two profiles, our first problem aims to find a parental profile that minimizes the sum of distances to its children. Given profiles, the second, more general problem, seeks a phylogenetic tree, whose leaves are labeled by the given profiles and whose internal vertices are labeled by ancestral profiles such that the sum of edge distances is minimum. For the former problem we give a pseudo-polynomial dynamic programming algorithm that is linear in the profile length, and an integer linear program formulation. For the latter problem we show it is NP-hard and give an integer linear program formulation that scales to practical problem instance sizes. We assess the efficiency and quality of our algorithms on simulated instances. https://github.com/raphael-group/CNT-ILP.
ArticleNumber	13
Author	Zeira, Ron Raphael, Benjamin J. Sharan, Roded El-Kebir, Mohammed Zaccaria, Simone Zehavi, Meirav Shamir, Ron
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Keywords	Somatic mutation Phylogeny Maximum parsimony Copy-number variant Cancer
Language	English
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Snippet	Background Cancer is an evolutionary process characterized by the accumulation of somatic mutations in a population of cells that form a tumor. One frequent... Cancer is an evolutionary process characterized by the accumulation of somatic mutations in a population of cells that form a tumor. One frequent type of... Background Cancer is an evolutionary process characterized by the accumulation of somatic mutations in a population of cells that form a tumor. One frequent... Abstract Background Cancer is an evolutionary process characterized by the accumulation of somatic mutations in a population of cells that form a tumor. One...
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SubjectTerms	Aberration Algorithms Bioinformatics Biomedical and Life Sciences Cancer Cellular and Medical Topics Children Chromosomes Complexity Computational Biology/Bioinformatics Computer simulation Computing time Copy number Copy-number variant Diagnosis Dynamic programming Evolutionary algorithms Genes Graph theory Leaves Life Sciences Maximum parsimony Mutation Phylogenetics Phylogeny Physiological Prognosis Quality assessment Selected papers from WABI 2016 Somatic mutation
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Title	Complexity and algorithms for copy-number evolution problems
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