Fig 1.
Overview of the proposed method.
(A) Example of cancer evolution. A founder cell is established after a normal cell acquires several passenger mutations and driver mutations (founder SSNVs), and sub-clones evolve by acquiring progressor SSNVs. Each color (purple, orange, dark blue, light blue, and green) of circles represents different sub-clones. (B) Example of a cancer evolutionary tree in the case of (A). A root and its immediate node represent the normal cell and founder cell, respectively. Subsequent nodes indicate sub-clones and edge lengths indicate the number of SSNVs acquired in the sub-clones. (C) Example of the registration of a tree. To resolve (p1)–(p4) for comparison of the evolutionary trees, a sufficiently large bifurcated tree is constructed, which is the reference tree (note that we have omitted bifurcation from the root for clearer visualization). The tree topologies and attributes are mapped to the reference tree beginning with those with the largest depths to those with the smallest depths. In the case of a tie, the sub-trees are mapped from those with the largest edge lengths. Zero-length edges are regarded as degenerated edges (dashed lines). Edge lengths are normalized by the sum of all edge lengths within tumors. The resulting trees can be represented as edge length vectors zi. (D) Clustering cancer evolutionary trees to summarize the evolutionary history of cancer for each patient. The trees are reconstructed based on the VAFs and then n cancer sub-clonal evolutionary trees are divided into K subgroups based on tree topologies and edge attributes. Through the registration, n evolutionary trees can be represented as m-dimensional n vectors in Euclidean space, and a standard clustering algorithm can be applied.
Fig 2.
Classes of cancer evolutionary trees in the simulations.
Simulation I: Five classes of tree topologies were considered: monoclonal (MC), polyclonal-low (PL), polyclonal-middle (PM), polyclonal-high (PH), and mutator-phenotype (MT). Simulation II: Three classes of edge lengths of the tree are considered: trunk accumulation (TR), branched accumulation (BR), and balanced accumulation (BL). Simulation III: Nine classes of trees are considered: polyclonal-low trunk accumulation (PL-TR), polyclonal-low balanced accumulation (PL-BL), polyclonal-low branch accumulation (PL-BR), polyclonal-middle trunk-accumulation (PM-TR), polyclonal-middle balanced-accumulation (PM-BL), polyclonal-middle branch-accumulation (PM-BR), polyclonal-high trunk accumulation (PH-TR), polyclonal-high balanced accumulation (PH-BL), and polyclonal-high branch accumulation (PH-BR)
Fig 3.
Each row of panels represents the simulation type (simulation I, II, and III), and each column represents the external clustering validation indices: purity (PR), normalized mutual information (NMI), and Rand index (RI). The horizontal axis of each graph is the variance parameter defined in S1 Text, and the vertical axis is the external validation index. The bold lines and the bands indicate the mean and 95% confidence interval of the index for 100 replicates of each dataset.
Table 1.
Clustering result of the ccRCC dataset.
Fig 4.
(A-1) Three clusters of the ccRCC dataset. The x-axis and y-axis are the lower dimensions reconstructed by CMDS. Clusters 1 (green) and 2 (orange) reflect drug-sensitive evolution and parallel evolution, respectively; we cannot provide a valid interpretation for cluster 3 (purple) at present. (B-1) Sub-clonal diversity plot of the ccRCC dataset. The x-axis and y-axis are the fraction of accumulated SSNVs and the number of sub-clones, respectively. Each color corresponds to the clusters shown in (A). Expansions in cluster 1 occurred with x = 0.6; (i.e., the proportion of SSNVs in the trunk is 60%). This result is in contrast to that obtained for cluster 2 (x = 0.2) and cluster 3 (x = 0.1). Trees in cluster 2 show gradual growth of sub-clonal diversity curves, indicating that these sub-clones acquire a relatively large fraction of SSNVs. The sub-clones independently evolve in spatially distinct regions [21]. (A-2) Two clusters in the NSCLC dataset. Clusters 1 (green) and 2 (orange) reflect the non-recurrent and recurrent group, respectively. Only case 270 and case 356 were misclassified to clusters 1 and 2, respectively. (B-2) Sub-clonal diversity plot of the NSCLC dataset. Each color corresponds to the clusters shown in (A-2). (A-3) Two clusters in the ccRCC and NSCLC datasets combined. Clusters 1 (green) and 2 (orange) represent the cancer types NSCLC and ccRCC, respectively. (B-3) Sub-clonal diversity plot of the ccRCC and NSCLC datasets.
Table 2.
Clustering result of the NSCLC dataset.
Table 3.
Clustering result of the ccRCC and NSCLC datasets.