A Multi-labeled Tree Edit Distance for Comparing "Clonal Trees" of Tumor Progression

We introduce a new edit distance measure between a pair of "clonal trees", each representing the progression and mutational heterogeneity of a tumor sample, constructed by the use of single cell or bulk high throughput sequencing data. In a clonal tree, each vertex represents a specific tumor clone, and is labeled with one or more mutations in a way that each mutation is assigned to the oldest clone that harbors it. Given two clonal trees, our multi-labeled tree edit distance (MLTED) measure is defined as the minimum number of mutation/label deletions, (empty) leaf deletions, and vertex (clonal) expansions, applied in any order, to convert each of the two trees to the maximal common tree. We show that the MLTED measure can be computed efficiently in polynomial time and it captures the similarity between trees of different clonal granularity well. We have implemented our algorithm to compute MLTED exactly and applied it to a variety of data sets successfully. The source code of our method can be found in: https://github.com/khaled-rahman/leafDelTED

A Multi-Labeled Tree Dissimilarity Measure for Comparing “Clonal Trees” of Tumor Progression

We introduce a new dissimilarity measure between a pair of “clonal trees”, each representing the progression and mutational heterogeneity of a tumor sample, constructed by the use of single cell or bulk high throughput sequencing data. In a clonal tree, each vertex represents a specific tumor clone, and is labeled with one or more mutations in a way that each mutation is assigned to the oldest clone that harbors it. Given two clonal trees, our multi-labeled tree dissimilarity (MLTD) measure is defined as the minimum number of mutation/label deletions, (empty) leaf deletions, and vertex (clonal) expansions, applied in any order, to convert each of the two trees to the maximum common tree. We show that the MLTD measure can be computed efficiently in polynomial time and it captures the similarity between trees of different clonal granularity well

The Bourque Distances for Mutation Trees of Cancers

Mutation trees are rooted trees of arbitrary node degree in which each node is labeled with a mutation set. These trees, also referred to as clonal trees, are used in computational oncology to represent the mutational history of tumours. Classical tree metrics such as the popular Robinson - Foulds distance are of limited use for the comparison of mutation trees. One reason is that mutation trees inferred with different methods or for different patients often contain different sets of mutation labels. Here, we generalize the Robinson - Foulds distance into a set of distance metrics called Bourque distances for comparing mutation trees. A connection between the Robinson - Foulds distance and the nearest neighbor interchange distance is also presented

The generalized Robinson-Foulds distance for phylogenetic trees

The Robinson-Foulds (RF) distance, one of the most widely used metrics for comparing phylogenetic trees, has the advantage of being intuitive, with a natural interpretation in terms of common splits, and it can be computed in linear time, but it has a very low resolution, and it may become trivial for phylogenetic trees with overlapping taxa, that is, phylogenetic trees that share some but not all of their leaf labels. In this article, we study the properties of the Generalized Robinson-Foulds (GRF) distance, a recently proposed metric for comparing any structures that can be described by multisets of multisets of labels, when applied to rooted phylogenetic trees with overlapping taxa, which are described by sets of clusters, that is, by sets of sets of labels. We show that the GRF distance has a very high resolution, it can also be computed in linear time, and it is not (uniformly) equivalent to the RF distance.This research was partially supported by the Spanish Ministry of Science, Innovation and Universitiesand the European Regional Development Fund through project PGC2018-096956-B-C43 (FEDER/MICINN/AEI), and by the Agency for Management of University and Research Grants (AGAUR) throughgrant 2017-SGR-786 (ALBCOM).Peer ReviewedPostprint (published version

A Rearrangement Distance for Fully-Labelled Trees

The problem of comparing trees representing the evolutionary histories of cancerous tumors has turned out to be crucial, since there is a variety of different methods which typically infer multiple possible trees. A departure from the widely studied setting of classical phylogenetics, where trees are leaf-labelled, tumoral trees are fully labelled, i.e., every vertex has a label. In this paper we provide a rearrangement distance measure between two fully-labelled trees. This notion originates from two operations: one which modifies the topology of the tree, the other which permutes the labels of the vertices, hence leaving the topology unaffected. While we show that the distance between two trees in terms of each such operation alone can be decided in polynomial time, the more general notion of distance when both operations are allowed is NP-hard to decide. Despite this result, we show that it is fixed-parameter tractable, and we give a 4-approximation algorithm when one of the trees is binary

On Two Measures of Distance Between Fully-Labelled Trees

The last decade brought a significant increase in the amount of data and a variety of new inference methods for reconstructing the detailed evolutionary history of various cancers. This brings the need of designing efficient procedures for comparing rooted trees representing the evolution of mutations in tumor phylogenies. Bernardini et al. [CPM 2019] recently introduced a notion of the rearrangement distance for fully-labelled trees motivated by this necessity. This notion originates from two operations: one that permutes the labels of the nodes, the other that affects the topology of the tree. Each operation alone defines a distance that can be computed in polynomial time, while the actual rearrangement distance, that combines the two, was proven to be NP-hard. We answer two open question left unanswered by the previous work. First, what is the complexity of computing the permutation distance? Second, is there a constant-factor approximation algorithm for estimating the rearrangement distance between two arbitrary trees? We answer the first one by showing, via a two-way reduction, that calculating the permutation distance between two trees on n nodes is equivalent, up to polylogarithmic factors, to finding the largest cardinality matching in a sparse bipartite graph. In particular, by plugging in the algorithm of Liu and Sidford [ArXiv 2020], we obtain an ??(n^{4/3+o(1}) time algorithm for computing the permutation distance between two trees on n nodes. Then we answer the second question positively, and design a linear-time constant-factor approximation algorithm that does not need any assumption on the trees

Tumoreen eboluzioko datuen simulazioa eta bistaraketa

Cancer is a collection of genetic diseases based on the uncontrollable division of cells and their spreading into surrounding tissues, caused by changes in DNA. This process leads to the overcrowding of altered cells that form a mass known as tumor. Nevertheless, all cells in a particular tumor do not have the same characteristics as tumors are formed by diverse clones with different mutations, and therefore different properties and behaviour. As a consequence, this intratumoral heterogeneity entails a problem in regard to the diagnosis and medical treatments that can help to manage the disease, potentially resulting in the failure of therapies and the possible propagation of carcinogenic cells to other organs or tissues, which is known as metastasis. Therefore, the development of methods to study the intratumoral heterogeneity are a hot research topic. This project aims at providing a tool to help researchers to easily simulate tumor data and analyze the results of their approaches for studying the composition and the evolutionary history of tumors

Single-Cell Lineage Tracing Of Cancer Metastasis

The underpinnings of cancer metastasis remain poorly understood, in part due to a lack of tools for probing their emergence at high resolution. Here we present macsGESTALT, an inducible CRISPR-Cas9-based lineage recorder with highly efficient single-cell capture of both transcriptional and phylogenetic information. Applying macsGESTALT to a mouse model of metastatic pancreatic cancer, we recover ~380,000 CRISPR target sites and reconstruct dissemination of ~28,000 single cells across multiple metastatic sites. We find cells occupy a continuum of epithelial-to-mesenchymal transition (EMT) states. Metastatic potential peaks in rare, late-hybrid EMT states, which are aggressively selected from a predominately epithelial ancestral pool. The gene signatures of these late-hybrid EMT states are predictive of reduced survival in both human pancreatic and lung cancer patients, highlighting their relevance to clinical disease progression. Finally, we observe evidence for in vivo propagation of S100 family gene expression across clonally distinct metastatic subpopulations