Complexity and algorithms for copy-number evolution problems
2017
Mohammed El-Kebir | Benjamin J. Raphael | Ron Shamir | Roded Sharan | Simone Zaccaria | Meirav Zehavi | Ron Zeira
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
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