Mohammed El-Kebir1,2, Benjamin J Raphael1,2, Ron Shamir3, Roded Sharan3, Simone Zaccaria1,2,4, Meirav Zehavi3, Ron Zeira3. 1. Department of Computer Science, Princeton University, Princeton, NJ 08540 USA. 2. Department of Computer Science, Center for Computational Molecular Biology, Brown University, Providence, RI 02912 USA. 3. School of Computer Science, Tel Aviv University, Tel Aviv, Israel. 4. Dipartimento di Informatica Sistemistica e Comunicazione (DISCo), Univ. degli Studi di Milano-Bicocca, Milan, Italy.
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 [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. 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.
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 [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. 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.
Entities:
Keywords:
Cancer; Copy-number variant; Maximum parsimony; Phylogeny; Somatic mutation
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