A zero-agnostic model for copy number evolution in cancer

Abstract

Motivation: New low-coverage single-cell DNA sequencing technologies enable the measurement of copy number profiles from thousands of individual cells within tumors. From this data, one can infer the evolutionary history of the tumor by modeling transformations of the genome via copy number aberrations. A widely used model to infer such copy number phylogenies is the copy number transformation (CNT) model in which a genome is represented by an integer vector and a copy number aberration is an event that either increases or decreases the number of copies of a contiguous segment of the genome. The CNT distance between a pair of copy number profiles is the minimum number of events required to transform one profile to another. While this distance can be computed efficiently, no efficient algorithm has been developed to find the most parsimonious phylogeny under the CNT model. Results: We introduce the zero-agnostic copy number transformation (ZCNT) model, a simplification of the CNT model that allows the amplification or deletion of regions with zero copies. We derive a closed form expression for the ZCNT distance between two copy number profiles and show that, unlike the CNT distance, the ZCNT distance forms a metric. We leverage the closed-form expression for the ZCNT distance and an alternative characterization of copy number profiles to derive polynomial time algorithms for two natural relaxations of the small parsimony problem on copy number profiles. While the alteration of zero copy number regions allowed under the ZCNT model is not biologically realistic, we show on both simulated and real datasets that the ZCNT distance is a close approximation to the CNT distance. Extending our polynomial time algorithm for the ZCNT small parsimony problem, we develop an algorithm, Lazac, for solving the large parsimony problem on copy number profiles. We demonstrate that Lazac outperforms existing methods for inferring copy number phylogenies on both simulated and real data.

Evolution-Aware Deep Reinforcement Learning for Single-Cell DNA Copy Number Calling

“…2d), we find that DeepCopy better matched the true number of unique profiles with a Pearson correlation of r = 0.98 and a median percentage error of 6.92% compared to SIGNALS ( r = − 0.28 and 110%) and CHISEL ( r = − 0.59 and 110%). Fourth, we utilized the copy number profiles inferred by each method to construct a phylogenetic tree as described in Section 4.4, defining the parsimony score as the number of CNA events on this tree using the zero-agnostic copy number transformation (ZCNT) distance [34]. For the shown simulation instance in Fig.…”

“…To calculate a tree on the set of cells, we calculate a CNA distance between the copy number profiles of pairs of cells and then apply neighbor-joining. Specifically, we slightly modify the zero-agnostic copy number transformation (ZCNT) distance to include whole genome duplication [34]. The original copy number transformation (CNT) distance from a haploid copy number profile P ∈ N L to copy number profile P ′ ∈ N L is the minimum number of CNA events required to transform P into P ′ [59].…”

NestedBD: Bayesian inference of phylogenetic trees from single-cell copy number profiles under a birth-death model

“…A possible explanation of this observation is that for small numbers of CNAs (Low), there is weak signal for MP and NJ to recover the tree, and for a large number of events (High), the overlap of CNAs resulting in more challenging patterns for these two methods. While such trend is less applicable to Lazac, potentially due to the ability of the proposed ZCNT distance to account for bin dependencies [ 33 ], NestedBD maintains the highest accuracy under most complex scenarios.…”

“…Recently developed methods focus on clonal tree inference, such as CONET [ 26 ] and SCICoNE [ 25 ], infer an evolutionary tree with nodes defined by CNA events jointly with breakpoints. Methods that aim to build a full binary tree, such as those reported in [ 29 , 33 , 66 ], infer a phylogenetic tree and reconstruct the ancestral copy number events to provide an estimate on the number of CNA events. These methods, however, do not provide information on the times of nodes and relative mutation rates per unit time per branch as NestedBD does.…”

“…Furthermore, these two methods are run in a way that assumes independence among the bins. Additionally, we have included a comparison with Lazac [ 33 ], a state-of-the-art method for inferring copy number phylogenies because it has been extensively benchmarked against various methods, demonstrating its effectiveness in copy number phylogeny inference. We found that NestedBD infers more accurate tree topologies than the other methods on the simulated data.…”