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.
Highlights
According to the clonal theory of cancer evolution [1], cancer originates from a single cell which had acquired a set of mutations that provide it proliferative advantage compared to the neighboring healthy cells
Cancer cells acquire new mutations and some of them might accumulate a set of mutations conferring further selective advantage or disadvantage compared to the other cells
In this work we focus on trees built by the use of single nucleotide variants (SNVs), which represent the most widely used type of mutations in reconstructing trees of tumor evolution [2]
Summary
According to the clonal theory of cancer evolution [1], cancer originates from a single cell which had acquired a set of mutations that provide it proliferative advantage compared to the neighboring healthy cells. Multi-labeled tree dissimilarity is the first polynomial time computable dissimilarity measure for vertex unordered trees.1 We have devised and implemented an algorithm to compute MLTD and applied it to a number of synthetic and real data sets to compare trees inferred by some of the available tumor history reconstruction methods with success.
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