Fig 1.
Lineage trees inferred by different methods on a single-cell dataset from a muscle-invasive bladder tumor.
Nodes in these trees represent clones (i.e., inferred, evolutionary genomes ancestral to the observed single-cell genomes). For the methods generating trees over samples, and not the clones, colored nodes represent samples. Blue nodes represent clones containing only normal cells, orange nodes represent clones containing only cancer cells, and brown nodes represent clones containing both normal and cancer cells. Text within the nodes indicates the identification number of the assigned sample cell(s) to the corresponding clone. White nodes represent nodes with no observed sample.
Table 1.
Comparison of reconstruction of ground truth lineage tree from data simulated by OncoNEM, showing the distance between the inferred trees and the ground truth for all methods across eight lineage trees.
Each cell represents average of tree distance measure for ten different simulated datasets. The best results among all the methods for each evolutionary tree are shown in bold. The variance of the values are represented in brackets.
Fig 2.
Comparison of the methods for single-cell lineage tree reconstruction on simulated tumor data.
Note that in case of the lineage tree reconstruction error (A), lower values show a better reconstruction. On the other hand, the split similarity measure represents (B) similarity between the reconstructed tree and the ground truth tree, making higher values favorable.
Fig 3.
Robustness of Scelestial to variation in the properties of ground truth lineage trees in terms of sample distance in the trees between the inferred and ground truth trees.
Fig 4.
Robustness of Scelestial to variation in the properties of ground truth lineage trees in terms of topological similarity between the inferred and ground truth trees.
Table 2.
Comparison of single-cell phylogenetic trees reconstruction methods on real single-cell genomic datasets.
Fig 5.
Lineage tree inferred by the different methods on a single-cell dataset from the first colorectal cancer patient.
Fig 6.
Lineage tree inferred by the different methods on a single-cell dataset from the second colorectal cancer patient.
Fig 7.
Run time comparison in relation to the number of samples and sites.
Fig 8.
Comparison of methods with respect to running time and lineage tree reconstruction error.
For the results obtained from different execution of a method a confidence ellipsoid is calculated and shown as the shaded area around the resulting points. The confidence interval is calculated under the assumption of normal distribution of the points in the two dimensional diagram.
Fig 9.
The details of the Scelestial algorithm.
The inputs to the Scelestial algorithm are a) a set of sequences S, b) the degree of restriction of the restricted Steiner tree k. The value k represents the size of trees to be considered as potential improvement for the tree T (details in Section 3.5.1). An example is shown at the right side of each step. The input sequences S are “CAC”, “GAG”, “GCC”, and “XAC” (“X” represents a missing value). In step 1 the tree T is initialized with the minimum spanning tree of the input sequences S. The edge lengths represent the cost of the edge according to the Scelestial’s cost function (see Section 3.5.5). In step 2 an example of a subset of sequences for K is highlighted in the picture. In step 2A a tree τ over leaf nodes K is shown. In step 2B bridges are highlighted as red edges between input sequences. In step 2C the result of adding tree τ to the current tree T is shown. In this example the bridges shown in step 2B are removed and two edges between nodes K corresponding to bridges are added. For each bridge an edge between the two nodes from K which their path passed through the edge is added. The new costs are defined as it is shown in step 2C. In step 3, the trees τ are added to the tree with their corresponding internal nodes. In step 4 lowest cost imputation of sample nodes are added to the tree, in the sample place as input sequences.