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 are 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 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. 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. We assess the efficiency and quality of our algorithms on simulated instances.
CITATION STYLE
El-Kebir, M., Raphael, B. J., Shamir, R., Sharan, R., Zaccaria, S., Zehavi, M., & Zeira, R. (2016). Copy-number evolution problems: Complexity and algorithms. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9838 LNCS, pp. 137–149). Springer Verlag. https://doi.org/10.1007/978-3-319-43681-4_11
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