A multi-labeled tree dissimilarity measure for comparing “clonal trees” of tumor progression

Abstract

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.

Distance Measures for Tumor Evolutionary Trees

“…A difference in a vertex with many descendants should then contribute more to a distance measure than one in a vertex with few descendants, since it affects more clonal populations. Thus, a tumor evolution distance measure that simply counts the differences between trees (often referred to as a tree edit distance, as proposed by [28,30], and others) does not address the impact any given label change may have. A distance measure should assign different weights to disagreements in different locations in order to appropriately address the relationship between topology and mutation labeling.…”

“…Clustering trees inferred from different patients can also be used to identify shared evolutionary patterns. We compare our distance measures to MLTED [28], the four distance measures introduced in [20] (ancestor-descendant, parentchild, clonal, and path distances), and triplet distance [33] (a modified version of a distance designed for phylogenetic trees, described in A.4) using a clustering scenario on both simulated datasets.…”

“…On the OncoLib dataset, we applied CASet ∪ , CASet ∩ , DISC ∪ , DISC ∩ , and MLTED [28] when doing hierarchical clustering. Figure 6 shows heatmaps of all pairwise tree distances for the five tree families A-E and the average silhouette score for five clusters, which all but one method identified as the optimal hierarchical clustering cut (CASet ∩ had an optimal cut at three clusters).…”

“…Furthermore, the mutations in a tumor evolutionary tree are inherited by all descendant tumor populations, creating a complex underlying relationship between topology and mutation labeling. In addition, nodes in tumor evolutionary trees may contain multiple labels (indicating mutations whose order of appearance cannot be readily identified) whereas nodes in a traditional phylogeny contain only one label each [20,28]. There is then a critical need for specially calibrated distance methods that account for the intricacies of tumor evolutionary trees.…”

“…Several simple distance measures described by [20] generalized earlier ad hoc approaches that relied on the existence of a ground truth tree [2][3][4], but were not the focus of that work, and their effectiveness was not analyzed in depth. Another recently proposed approach called MLTED uses an edit distance-based measure focused on handling multi-labeled nodes to count the minimum number of moves to convert both trees into a specific common tree [28]. However, this distance measure does not explicitly consider that mutation labels are inherited by all descendant populations.…”