Copy-Number Evolution Problems: Complexity and Algorithms Conference Paper uri icon

abstract

  • 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‚Äôs 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 \(\mathbf {a}\) 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. 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.

publication date

  • January 1, 2016