Copy number evolution with weighted aberrations in cancer

Abstract

Motivation Copy number aberrations (CNAs), which delete or amplify large contiguous segments of the genome, are a common type of somatic mutation in cancer. Copy number profiles, representing the number of copies of each region of a genome, are readily obtained from whole-genome sequencing or microarrays. However, modeling copy number evolution is a substantial challenge, because different CNAs may overlap with one another on the genome. A recent popular model for copy number evolution is the copy number distance (CND), defined as the length of a shortest sequence of deletions and amplifications of contiguous segments that transforms one profile into the other. In the CND, all events contribute equally; however, it is well known that rates of CNAs vary by length, genomic position and type (amplification versus deletion). Results We introduce a weighted CND that allows events to have varying weights, or probabilities, based on their length, position and type. We derive an efficient algorithm to compute the weighted CND as well as the associated transformation. This algorithm is based on the observation that the constraint matrix of the underlying optimization problem is totally unimodular. We show that the weighted CND improves phylogenetic reconstruction on simulated data where CNAs occur with varying probabilities, aids in the derivation of phylogenies from ultra-low-coverage single-cell DNA sequencing data and helps estimate CNA rates in a large pan-cancer dataset. Availability and implementation Code is available at https://github.com/raphael-group/WCND. Supplementary information Supplementary data are available at Bioinformatics online.

Single-cell genomic variation induced by mutational processes in cancer

“…1j ). Analysis of cell-to-cell pairwise haplotype-specific copy number (HSCN) distances 20 , 25 found that TP53 −/− induced a 3.9-fold (SA906a) and 1.9-fold (SA906b) increase in cell-to-cell divergence, BRCA2 −/− induced a 4.5-fold (SA1055) and 2.6-fold (SA1056) increase and BRCA1 −/− induced a 13.7-fold increase (Fig. 1k ; P < 10 −10 ) relative to pairwise distances in wild-type cells.…”

Treatment-mediated selection of lethal prostate cancer clones defined by copy number architectures

“…Thirdly, we used autosome copy number transition points to define the relationships of metastases and confirmed a common clone of origin in lethal metastases and the original diagnostic biopsy. Similar approaches have been described previously (35,36) but our report describes a scalable analysis pipeline that can be implemented in whole-genome sequencing data of variable coverage and from samples of variable quality. Moreover, the patient-unique transition points common to both biopsy and autopsy sample types could be leveraged for tracking of metastatic clones throughout the patient's duration of disease.…”

CNETML: Maximum likelihood inference of phylogeny from copy number profiles of spatio-temporal samples

“…It has been extended to allow weights on CNAs of different position, size, and type (duplication/deletion) [35] and WGD [9, 36]. The weighted versions of both models allow the estimation of CNA rates in term of event probabilities [17, 35], but mutation rates by calendar time cannot be estimated. A few CNP-based methods use the finite sites models, or continuous-time Markov chains, which have good theoretical properties and are frequently used to model nucleotide changes [37].…”

“…This model deals with horizontal dependencies caused by overlapping CNAs and hence is less likely affected by convergent evolution. It has been extended to allow weights on CNAs of different position, size, and type (duplication/deletion) [35] and WGD [9, 36]. The weighted versions of both models allow the estimation of CNA rates in term of event probabilities [17, 35], but mutation rates by calendar time cannot be estimated.…”