The Bourque distances for mutation trees of cancers

Weighted centroid trees: a general approach to summarize phylogenies in single-labeled tumor mutation tree inference

MOTIVATION

Tumor trees, which depict the evolutionary process of cancer, provide a backbone for discovering recurring evolutionary processes in cancer. While they are not the primary information extracted from genomic data, they are valuable for this purpose. One such extraction method involves summarizing multiple trees into a single representative tree, such as consensus trees or supertrees.

RESULTS

We define the "weighted centroid tree problem" to find the centroid tree of a set of single-labeled rooted trees through the following steps: (i) mapping the given trees into the Euclidean space, (ii) computing the weighted centroid matrix of the mapped trees, and (iii) finding the nearest mapped tree (NMTP) to the centroid matrix. We show that this setup encompasses previously studied parent-child and ancestor-descendent metrics as well as the GraPhyC and TuELiP consensus tree algorithms. Moreover, we show that, while the NMTP problem is polynomial-time solvable for the adjacency embedding, it is NP-hard for ancestry and distance mappings. We introduce integer linear programs for NMTP in different setups where we also provide a new algorithm for the case of ancestry embedding called 2-AncL2, that uses a novel weighting scheme for ancestry signals. Our experimental results show that 2-AncL2 has a superior performance compared to available consensus tree algorithms. We also illustrate our setup's application on providing representative trees for a large real breast cancer dataset, deducing that the cluster centroid trees summarize reliable evolutionary information about the original dataset.

AVAILABILITY AND IMPLEMENTATION

https://github.com/vasei/WAncILP.

Oncotree2vec - a method for embedding and clustering of tumor mutation trees

MOTIVATION

Understanding the genomic heterogeneity of tumors is an important task in computational oncology, especially in the context of finding personalized treatments based on the genetic profile of each patient's tumor. Tumor clustering that takes into account the temporal order of genetic events, as represented by tumor mutation trees, is a powerful approach for grouping together patients with genetically and evolutionarily similar tumors and can provide insights into discovering tumor subtypes, for more accurate clinical diagnosis and prognosis.

RESULTS

Here, we propose oncotree2vec, a method for clustering tumor mutation trees by learning vector representations of mutation trees that capture the different relationships between subclones in an unsupervised manner. Learning low-dimensional tree embeddings facilitates the visualization of relations between trees in large cohorts and can be used for downstream analyses, such as deep learning approaches for single-cell multi-omics data integration. We assessed the performance and the usefulness of our method in three simulation studies and on two real datasets: a cohort of 43 trees from six cancer types with different branching patterns corresponding to different modes of spatial tumor evolution and a cohort of 123 AML mutation trees.

AVAILABILITY AND IMPLEMENTATION

https://github.com/cbg-ethz/oncotree2vec.

The k-Robinson-Foulds Dissimilarity Measures for Comparison of Labeled Trees

Understanding the mutational history of tumor cells is a critical endeavor in unraveling the mechanisms that drive the onset and progression of cancer. Modeling tumor cell evolution with labeled trees motivates researchers to develop different measures to compare labeled trees. Although the Robinson-Foulds (RF) distance is widely used for comparing species trees, its applicability to labeled trees reveals certain limitations. This study introduces the k-RF dissimilarity measures, tailored to address the challenges of labeled tree comparison. The RF distance is succinctly expressed as n-RF in the space of labeled trees with n nodes. Like the RF distance, the k-RF is a pseudometric for multiset-labeled trees and becomes a metric in the space of 1-labeled trees. By setting k to a small value, the k-RF dissimilarity can capture analogous local regions in two labeled trees with different size or different labels.

A weighted distance-based approach for deriving consensus tumor evolutionary trees

MOTIVATION

The acquisition of somatic mutations by a tumor can be modeled by a type of evolutionary tree. However, it is impossible to observe this tree directly. Instead, numerous algorithms have been developed to infer such a tree from different types of sequencing data. But such methods can produce conflicting trees for the same patient, making it desirable to have approaches that can combine several such tumor trees into a consensus or summary tree. We introduce The Weighted m-Tumor Tree Consensus Problem (W-m-TTCP) to find a consensus tree among multiple plausible tumor evolutionary histories, each assigned a confidence weight, given a specific distance measure between tumor trees. We present an algorithm called TuELiP that is based on integer linear programming which solves the W-m-TTCP, and unlike other existing consensus methods, allows the input trees to be weighted differently.

RESULTS

On simulated data we show that TuELiP outperforms two existing methods at correctly identifying the true underlying tree used to create the simulations. We also show that the incorporation of weights can lead to more accurate tree inference. On a Triple-Negative Breast Cancer dataset, we show that including confidence weights can have important impacts on the consensus tree identified.

AVAILABILITY

An implementation of TuELiP and simulated datasets are available at https://bitbucket.org/oesperlab/consensus-ilp/src/main/.