1
|
Frohn M. On the approximability of the fixed-tree balanced minimum evolution problem. OPTIMIZATION LETTERS 2021; 15:2321-2329. [PMID: 33425038 PMCID: PMC7778423 DOI: 10.1007/s11590-020-01677-x] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 04/13/2020] [Accepted: 11/30/2020] [Indexed: 06/12/2023]
Abstract
The Fixed-Tree BMEP (FT-BMEP) is a special case of the Balanced Minimum Evolution Problem (BMEP) that consists of finding the assignment of a set of n taxa to the n leaves of a given unrooted binary tree so as to minimize the BMEP objective function. Deciding the computational complexity of the FT-BMEP has been an open problem for almost a decade. Here, we show that a few modifications to Fiorini and Joret's proof of the NP -hardness of the BMEP suffice to prove the general NP -hardness of the FT-BMEP as well as its strong inapproximability.
Collapse
Affiliation(s)
- Martin Frohn
- CORE, Université Catholique de Louvain, Voie du Roman Pays 34, 1348 Louvain-la-Neuve, Belgium
| |
Collapse
|
2
|
Abstract
Rapid advances in high-throughput sequencing and a growing realization of the importance of evolutionary theory to cancer genomics have led to a proliferation of phylogenetic studies of tumour progression. These studies have yielded not only new insights but also a plethora of experimental approaches, sometimes reaching conflicting or poorly supported conclusions. Here, we consider this body of work in light of the key computational principles underpinning phylogenetic inference, with the goal of providing practical guidance on the design and analysis of scientifically rigorous tumour phylogeny studies. We survey the range of methods and tools available to the researcher, their key applications, and the various unsolved problems, closing with a perspective on the prospects and broader implications of this field.
Collapse
Affiliation(s)
- Russell Schwartz
- Department of Biological Sciences and Computational Biology Department, Carnegie Mellon University, Pittsburgh, Pennsylvania 15217, USA
| | - Alejandro A Schäffer
- Computational Biology Branch, National Center for Biotechnology Information, National Institutes of Health, Bethesda, Maryland 20892, USA
| |
Collapse
|
3
|
Gertz EM, Chowdhury SA, Lee WJ, Wangsa D, Heselmeyer-Haddad K, Ried T, Schwartz R, Schäffer AA. FISHtrees 3.0: Tumor Phylogenetics Using a Ploidy Probe. PLoS One 2016; 11:e0158569. [PMID: 27362268 PMCID: PMC4928784 DOI: 10.1371/journal.pone.0158569] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2016] [Accepted: 06/19/2016] [Indexed: 01/03/2023] Open
Abstract
Advances in fluorescence in situ hybridization (FISH) make it feasible to detect multiple copy-number changes in hundreds of cells of solid tumors. Studies using FISH, sequencing, and other technologies have revealed substantial intra-tumor heterogeneity. The evolution of subclones in tumors may be modeled by phylogenies. Tumors often harbor aneuploid or polyploid cell populations. Using a FISH probe to estimate changes in ploidy can guide the creation of trees that model changes in ploidy and individual gene copy-number variations. We present FISHtrees 3.0, which implements a ploidy-based tree building method based on mixed integer linear programming (MILP). The ploidy-based modeling in FISHtrees includes a new formulation of the problem of merging trees for changes of a single gene into trees modeling changes in multiple genes and the ploidy. When multiple samples are collected from each patient, varying over time or tumor regions, it is useful to evaluate similarities in tumor progression among the samples. Therefore, we further implemented in FISHtrees 3.0 a new method to build consensus graphs for multiple samples. We validate FISHtrees 3.0 on a simulated data and on FISH data from paired cases of cervical primary and metastatic tumors and on paired breast ductal carcinoma in situ (DCIS) and invasive ductal carcinoma (IDC). Tests on simulated data show improved accuracy of the ploidy-based approach relative to prior ploidyless methods. Tests on real data further demonstrate novel insights these methods offer into tumor progression processes. Trees for DCIS samples are significantly less complex than trees for paired IDC samples. Consensus graphs show substantial divergence among most paired samples from both sets. Low consensus between DCIS and IDC trees may help explain the difficulty in finding biomarkers that predict which DCIS cases are at most risk to progress to IDC. The FISHtrees software is available at ftp://ftp.ncbi.nih.gov/pub/FISHtrees.
Collapse
MESH Headings
- Biomarkers, Tumor/genetics
- Breast Neoplasms/genetics
- Breast Neoplasms/pathology
- Carcinoma, Ductal, Breast/genetics
- Carcinoma, Ductal, Breast/pathology
- Carcinoma, Intraductal, Noninfiltrating/genetics
- Carcinoma, Intraductal, Noninfiltrating/pathology
- Databases, Genetic
- Female
- Humans
- In Situ Hybridization, Fluorescence/methods
- Ploidies
- Uterine Cervical Neoplasms/genetics
- Uterine Cervical Neoplasms/pathology
Collapse
Affiliation(s)
- E. Michael Gertz
- Computational Biology Branch, National Center for Biotechnology Information, U.S. National Institutes of Health, Bethesda, MD, United States of America
| | - Salim Akhter Chowdhury
- Computational Biology Department, Carnegie Mellon University, Pittsburgh, PA, United States of America
- Carnegie Mellon/University of Pittsburgh Joint Ph.D. Program in Computational Biology, Pittsburgh, PA, United States of America
| | - Woei-Jyh Lee
- Computational Biology Branch, National Center for Biotechnology Information, U.S. National Institutes of Health, Bethesda, MD, United States of America
| | - Darawalee Wangsa
- Section of Cancer Genomics, Genetics Branch, Center for Cancer Research, National Cancer Institute, U.S. National Institutes of Health, Bethesda, MD, United States of America
| | - Kerstin Heselmeyer-Haddad
- Section of Cancer Genomics, Genetics Branch, Center for Cancer Research, National Cancer Institute, U.S. National Institutes of Health, Bethesda, MD, United States of America
| | - Thomas Ried
- Section of Cancer Genomics, Genetics Branch, Center for Cancer Research, National Cancer Institute, U.S. National Institutes of Health, Bethesda, MD, United States of America
| | - Russell Schwartz
- Computational Biology Department, Carnegie Mellon University, Pittsburgh, PA, United States of America
- Department of Biological Sciences, Carnegie Mellon University, Pittsburgh, PA, United States of America
| | - Alejandro A. Schäffer
- Computational Biology Branch, National Center for Biotechnology Information, U.S. National Institutes of Health, Bethesda, MD, United States of America
| |
Collapse
|