Implications of non-uniqueness in phylogenetic deconvolution of bulk DNA samples of tumors

Consensus Tree Under the Ancestor-Descendant Distance is NP-Hard

Due to uncertainty in tumor phylogeny inference from sequencing data, many methods infer multiple, equally plausible phylogenies for the same cancer. To summarize the solution space T of tumor phylogenies, consensus tree methods seek a single best representative tree S under a specified pairwise tree distance function. One such distance function is the ancestor-descendant (AD) distance [Formula: see text] , which equals the size of the symmetric difference of the transitive closures of the edge sets [Formula: see text] and [Formula: see text] . Here, we show that finding a consensus tree S for tumor phylogenies T that minimizes the total AD distance [Formula: see text] is NP-hard.

A common methodological phylogenomics framework for intra-patient heteroplasmies to infer SARS-CoV-2 sublineages and tumor clones

BACKGROUND

All diseases containing genetic material undergo genetic evolution and give rise to heterogeneity including cancer and infection. Although these illnesses are biologically very different, the ability for phylogenetic retrodiction based on the genomic reads is common between them and thus tree-based principles and assumptions are shared. Just as the different frequencies of tumor genomic variants presupposes the existence of multiple tumor clones and provides a handle to computationally infer them, we postulate that the different variant frequencies in viral reads offers the means to infer multiple co-infecting sublineages.

RESULTS

We present a common methodological framework to infer the phylogenomics from genomic data, be it reads of SARS-CoV-2 of multiple COVID-19 patients or bulk DNAseq of the tumor of a cancer patient. We describe the Concerti computational framework for inferring phylogenies in each of the two scenarios.To demonstrate the accuracy of the method, we reproduce some known results in both scenarios. We also make some additional discoveries.

CONCLUSIONS

Concerti successfully extracts and integrates information from multi-point samples, enabling the discovery of clinically plausible phylogenetic trees that capture the heterogeneity known to exist both spatially and temporally. These models can have direct therapeutic implications by highlighting "birth" of clones that may harbor resistance mechanisms to treatment, "death" of subclones with drug targets, and acquisition of functionally pertinent mutations in clones that may have seemed clinically irrelevant. Specifically in this paper we uncover new potential parallel mutations in the evolution of the SARS-CoV-2 virus. In the context of cancer, we identify new clones harboring resistant mutations to therapy.

Distinguishing linear and branched evolution given single-cell DNA sequencing data of tumors

Background

Cancer arises from an evolutionary process where somatic mutations give rise to clonal expansions. Reconstructing this evolutionary process is useful for treatment decision-making as well as understanding evolutionary patterns across patients and cancer types. In particular, classifying a tumor’s evolutionary process as either linear or branched and understanding what cancer types and which patients have each of these trajectories could provide useful insights for both clinicians and researchers. While comprehensive cancer phylogeny inference from single-cell DNA sequencing data is challenging due to limitations with current sequencing technology and the complexity of the resulting problem, current data might provide sufficient signal to accurately classify a tumor’s evolutionary history as either linear or branched.

Results

We introduce the Linear Perfect Phylogeny Flipping (LPPF) problem as a means of testing two alternative hypotheses for the pattern of evolution, which we prove to be NP-hard. We develop Phyolin, which uses constraint programming to solve the LPPF problem. Through both in silico experiments and real data application, we demonstrate the performance of our method, outperforming a competing machine learning approach.

Conclusion

Phyolin is an accurate, easy to use and fast method for classifying an evolutionary trajectory as linear or branched given a tumor’s single-cell DNA sequencing data.

Moss enables high sensitivity single-nucleotide variant calling from multiple bulk DNA tumor samples

Intra-tumor heterogeneity renders the identification of somatic single-nucleotide variants (SNVs) a challenging problem. In particular, low-frequency SNVs are hard to distinguish from sequencing artifacts. While the increasing availability of multi-sample tumor DNA sequencing data holds the potential for more accurate variant calling, there is a lack of high-sensitivity multi-sample SNV callers that utilize these data. Here we report Moss, a method to identify low-frequency SNVs that recur in multiple sequencing samples from the same tumor. Moss provides any existing single-sample SNV caller the ability to support multiple samples with little additional time overhead. We demonstrate that Moss improves recall while maintaining high precision in a simulated dataset. On multi-sample hepatocellular carcinoma, acute myeloid leukemia and colorectal cancer datasets, Moss identifies new low-frequency variants that meet manual review criteria and are consistent with the tumor's mutational signature profile. In addition, Moss detects the presence of variants in more samples of the same tumor than reported by the single-sample caller. Moss' improved sensitivity in SNV calling will enable more detailed downstream analyses in cancer genomics.

Detecting evolutionary patterns of cancers using consensus trees

MOTIVATION

While each cancer is the result of an isolated evolutionary process, there are repeated patterns in tumorigenesis defined by recurrent driver mutations and their temporal ordering. Such repeated evolutionary trajectories hold the potential to improve stratification of cancer patients into subtypes with distinct survival and therapy response profiles. However, current cancer phylogeny methods infer large solution spaces of plausible evolutionary histories from the same sequencing data, obfuscating repeated evolutionary patterns.

RESULTS

To simultaneously resolve ambiguities in sequencing data and identify cancer subtypes, we propose to leverage common patterns of evolution found in patient cohorts. We first formulate the Multiple Choice Consensus Tree problem, which seeks to select a tumor tree for each patient and assign patients into clusters in such a way that maximizes consistency within each cluster of patient trees. We prove that this problem is NP-hard and develop a heuristic algorithm, Revealing Evolutionary Consensus Across Patients (RECAP), to solve this problem in practice. Finally, on simulated data, we show RECAP outperforms existing methods that do not account for patient subtypes. We then use RECAP to resolve ambiguities in patient trees and find repeated evolutionary trajectories in lung and breast cancer cohorts.

AVAILABILITY AND IMPLEMENTATION

https://github.com/elkebir-group/RECAP.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Reconstructing tumor evolutionary histories and clone trees in polynomial-time with SubMARine

Tumors contain multiple subpopulations of genetically distinct cancer cells. Reconstructing their evolutionary history can improve our understanding of how cancers develop and respond to treatment. Subclonal reconstruction methods cluster mutations into groups that co-occur within the same subpopulations, estimate the frequency of cells belonging to each subpopulation, and infer the ancestral relationships among the subpopulations by constructing a clone tree. However, often multiple clone trees are consistent with the data and current methods do not efficiently capture this uncertainty; nor can these methods scale to clone trees with a large number of subclonal populations.

Here, we formalize the notion of a partially-defined clone tree (partial clone tree for short) that defines a subset of the pairwise ancestral relationships in a clone tree, thereby implicitly representing the set of all clone trees that have these defined pairwise relationships. Also, we introduce a special partial clone tree, the Maximally-Constrained Ancestral Reconstruction (MAR), which summarizes all clone trees fitting the input data equally well. Finally, we extend commonly used clone tree validity conditions to apply to partial clone trees and describe SubMARine, a polynomial-time algorithm producing the subMAR, which approximates the MAR and guarantees that its defined relationships are a subset of those present in the MAR. We also extend SubMARine to work with subclonal copy number aberrations and define equivalence constraints for this purpose. Further, we extend SubMARine to permit noise in the estimates of the subclonal frequencies while retaining its validity conditions and guarantees. In contrast to other clone tree reconstruction methods, SubMARine runs in time and space that scale polynomially in the number of subclones.

We show through extensive noise-free simulation, a large lung cancer dataset and a prostate cancer dataset that the subMAR equals the MAR in all cases where only a single clone tree exists and that it is a perfect match to the MAR in most of the other cases. Notably, SubMARine runs in less than 70 seconds on a single thread with less than one Gb of memory on all datasets presented in this paper, including ones with 50 nodes in a clone tree. On the real-world data, SubMARine almost perfectly recovers the previously reported trees and identifies minor errors made in the expert-driven reconstructions of those trees.

The freely-available open-source code implementing SubMARine can be downloaded at https://github.com/morrislab/submarine.

Cancer cells accumulate mutations over time and consist of genetically distinct subpopulations. Their evolutionary history (as represented by tumor phylogenies) can be inferred from bulk cancer genome sequencing data. Current tumor phylogeny reconstruction methods have two main issues: they are slow, and they do not efficiently represent uncertainty in the reconstruction.

To address these issues, we developed SubMARine, a fast algorithm that summarizes all valid phylogenies in an intuitive format. SubMARine solved all reconstruction problems in this manuscript in less than 70 seconds, orders of magnitude faster than other methods. These reconstruction problems included those with up to 50 subclones; problems that are too large for other algorithms to even attempt. SubMARine achieves these result because, unlike other algorithms, it performs its reconstruction by identifying an upper-bound on the solution set of trees and the amount of noise in the estimates of the subclonal frequencies. In the vast majority of cases we checked, i. e. an extensive noise-free simulation, a lung cancer and a prostate cancer dataset, this upper bound is tight: when only a single solution exists, SubMARine converges to it every time. When multiple solutions exist, our algorithm correctly recovers the uncertain relationships in 71% of cases.

In addition to solving these two major challenges, we introduce some useful new concepts for and open research problems in the field of tumor phylogeny reconstruction. Specifically, we formalize the concept of a partial clone tree which provides a set of constraints on the solution set of clone trees; and provide a complete set of conditions under which a partial clone tree is valid. These conditions guarantee that all trees in the solution set satisfy the constraints implied by the partial clone tree.

Quantifying the influence of mutation detection on tumour subclonal reconstruction

Whole-genome sequencing can be used to estimate subclonal populations in tumours and this intra-tumoural heterogeneity is linked to clinical outcomes. Many algorithms have been developed for subclonal reconstruction, but their variabilities and consistencies are largely unknown. We evaluate sixteen pipelines for reconstructing the evolutionary histories of 293 localized prostate cancers from single samples, and eighteen pipelines for the reconstruction of 10 tumours with multi-region sampling. We show that predictions of subclonal architecture and timing of somatic mutations vary extensively across pipelines. Pipelines show consistent types of biases, with those incorporating SomaticSniper and Battenberg preferentially predicting homogenous cancer cell populations and those using MuTect tending to predict multiple populations of cancer cells. Subclonal reconstructions using multi-region sampling confirm that single-sample reconstructions systematically underestimate intra-tumoural heterogeneity, predicting on average fewer than half of the cancer cell populations identified by multi-region sequencing. Overall, these biases suggest caution in interpreting specific architectures and subclonal variants.

PhyDOSE: Design of follow-up single-cell sequencing experiments of tumors

The combination of bulk and single-cell DNA sequencing data of the same tumor enables the inference of high-fidelity phylogenies that form the input to many important downstream analyses in cancer genomics. While many studies simultaneously perform bulk and single-cell sequencing, some studies have analyzed initial bulk data to identify which mutations to target in a follow-up single-cell sequencing experiment, thereby decreasing cost. Bulk data provide an additional untapped source of valuable information, composed of candidate phylogenies and associated clonal prevalence. Here, we introduce PhyDOSE, a method that uses this information to strategically optimize the design of follow-up single cell experiments. Underpinning our method is the observation that only a small number of clones uniquely distinguish one candidate tree from all other trees. We incorporate distinguishing features into a probabilistic model that infers the number of cells to sequence so as to confidently reconstruct the phylogeny of the tumor. We validate PhyDOSE using simulations and a retrospective analysis of a leukemia patient, concluding that PhyDOSE's computed number of cells resolves tree ambiguity even in the presence of typical single-cell sequencing errors. We also conduct a retrospective analysis on an acute myeloid leukemia cohort, demonstrating the potential to achieve similar results with a significant reduction in the number of cells sequenced. In a prospective analysis, we demonstrate the advantage of selecting cells to sequence across multiple biopsies and that only a small number of cells suffice to disambiguate the solution space of trees in a recent lung cancer cohort. In summary, PhyDOSE proposes cost-efficient single-cell sequencing experiments that yield high-fidelity phylogenies, which will improve downstream analyses aimed at deepening our understanding of cancer biology.

ClonArch: visualizing the spatial clonal architecture of tumors

MOTIVATION

Cancer is caused by the accumulation of somatic mutations that lead to the formation of distinct populations of cells, called clones. The resulting clonal architecture is the main cause of relapse and resistance to treatment. With decreasing costs in DNA sequencing technology, rich cancer genomics datasets with many spatial sequencing samples are becoming increasingly available, enabling the inference of high-resolution tumor clones and prevalences across different spatial coordinates. While temporal and phylogenetic aspects of tumor evolution, such as clonal evolution over time and clonal response to treatment, are commonly visualized in various clonal evolution diagrams, visual analytics methods that reveal the spatial clonal architecture are missing.

RESULTS

This article introduces ClonArch, a web-based tool to interactively visualize the phylogenetic tree and spatial distribution of clones in a single tumor mass. ClonArch uses the marching squares algorithm to draw closed boundaries representing the presence of clones in a real or simulated tumor. ClonArch enables researchers to examine the spatial clonal architecture of a subset of relevant mutations at different prevalence thresholds and across multiple phylogenetic trees. In addition to simulated tumors with varying number of biopsies, we demonstrate the use of ClonArch on a hepatocellular carcinoma tumor with ∼280 sequencing biopsies. ClonArch provides an automated way to interactively examine the spatial clonal architecture of a tumor, facilitating clinical and biological interpretations of the spatial aspects of intra-tumor heterogeneity.

AVAILABILITY AND IMPLEMENTATION

https://github.com/elkebir-group/ClonArch.