Fig 1.
Defining Distance Metrics on Lineage Based Tree Structures.
(A) Cell lineages can be expressed as binary trees, with parent, sibling, and child cells relationship reflected in node topology. C. elegans has a naming convention that allows for direct comparisons between cells in distinct lineages. Here we show schematics of two lineages with different topologies, corresponding to embryos “X” and “Y.” The canonical names of the cells are shown either next to or at the end of the corresponding edges. Lineage tracing data also provides information about how long each cell persists between when it is “born” through division and when it divides itself. The numerical values next to each edge indicate these cell cycle times in this schematic. (B) The tree edit distance describes the topological differences between trees by counting the number of additive/subtractive operations required to transform one tree into another. In the case of C. elegans lineage trees, this corresponds to the size of the symmetric difference between the set of nodes present in one embryo vs. another. (C) The intersection branch distance is the Euclidean or L2 norm between measurements associated with shared nodes or edges of trees, disregarding topological differences between trees by only considering nodes/edges present in both trees. (D) The union branch distance is the Euclidean or L2 norm between values on the union set of nodes or edges between trees. Nodes or edges that are absent from one tree in any comparison are given a 0 value.
Fig 2.
Summation of Cycle Times into Birth Times Suppresses Variation.
(A) A comparison between the birth time of each cell (calculated as the sum of cell cycle times of each cell’s ancestors) in two wild type C. elegans embryos. (B) Comparison between birth times calculated from two randomly shuffled wild type embryos, where each cell is assigned another random cell’s birth time from within the lineage of the same embryo. Note that a significant correlation in birth times exists even in this shuffled data. (C) Comparison between shuffled cell cycle times rather than birth times. In this case, there is no correlation, as would be expected. (D) Comparison between the cell cycle times of each cell in two wild type embryos. Note that the same two embryos were used for all comparisons in panels A-D.
Fig 3.
The Branch Distance Reveals previously undetected Batch Effects in WT Embryo Cell Cycle Timing.
(A) Heatmap showing the union branch distance calculated between each pair of wild type embryos in the dataset. The ordering of embryos was sorted based on their assignment to two clusters computed using hierarchical clustering. (B) Heatmap showing the R2 in cell cycle times between all pairs of WT embryos, sorted as in (A). (C) The slope calculated between cell cycle times between all pairs of WT embryos, sorted as in (A).
Fig 4.
The union branch distance reveals Heterogeneity in RNAi Cell Cycle Timing Coordination.
(A) Heatmap showing the union branch distance between all 30 WT embryos and 1322 RNAi Embryos in the dataset. Embryos were hierarchically clustered and sorted into 4 clusters shown along the axes of the heatmap, with WT embryos visible as a “white block” in cluster 3. (B) i. Distribution of the tree edit distance between 6 SUF-1 embryos and 30 WT embryos. ii. Distribution of the intersection branch distance between 6 SUF-1 embryos and 30 WT embryos. iii. Distribution of the tree edit distance between 10 SKR-2 embryos and 30 WT embryos. iv. Distribution of the intersection branch distance between 10 SKR-2 embryos and 30 WT embryos. (C) Comparison between the tree edit distance and intersection branch distance for each of the 1322 RNAi embryos relative to a single WT reference embryo.
Fig 5.
Branch Distance reveals structure in the AB lineage.
A) Heatmap showing the intersection branch distance between every pair of sublineages in every pair of 21 wild type embryos. B) Illustration of the first two Notch signaling events in the early AB lineage. C) Heatmap showing a zoomed in view of the intersection branch distance between the 21 wild type embryos for each pair of AB-derived sublineages. Colormap is scaled from 0 to the max intersection branch distances between same-generation AB sublineages. D) Heatmap showing a zoomed in view of the intersection branch distance between AB-derived sublineages of 6 embryos treated with RNAi against glp-1 for each pair of AB-derived sublineages. Colormap is scaled from 0 to the max intersection branch distances between same-generation AB sublineages. E) Distributions of intersection branch distances between subsets of AB-derived sublineages in WT embryos and embryos treated with RNAi against glp-1. P-values calculated using 106 iterations of a permutation test.
Fig 6.
Evidence for cell fate control over cell cycle timing.
A) Illustration of the transformation heuristic. For each WT destination lineage (black dots) a diameter D is calculated as the maximum intragroup intersection branch distance. The transformation efficiency is then defined as the fraction of WT destination lineages that fall within diameter D of each RNAi origin lineage (colored squares). In some cases, the transformation efficiency is 0 but the RNAi lineage has WT origin neighbors (green square) suggesting that the RNAi perturbed lineage maintained its original fate in terms of cell cycle timing. In other cases, this value is 0 and the RNAi origin lineage has no WT neighbors (orange square) suggesting that the RNAi perturbed lineage has both lost its original fate and failed to acquire the pattern of cell cycle timing of the destination lineage. In a minority of cases the RNAi origin lineage is within D of 1 or more WT destination sublineages and a transformation efficiency is reported (magenta square). B) Histogram of the number of WT destination neighbors that homeotically transformed RNAi lineages have, using the heuristic defined in A. C) Histogram of the number of new WT neighbors that perturbed RNAi lineages have. D) Heatmaps representing the transformation heuristic in A. for homeotically transformed lineages with at least 1 WT destination neighbor. The genes that induce these transformations and functions are listed alongside the corresponding heatmap of transformation.
Fig 7.
The Generalized Branch Distance recapitulates structure in lineage coordination.
(A) Heatmap showing the intersection branch distance calculated between pairs of wild type AB8 lineages (B) Heatmap showing the generalized branch distance calculated between pairs of wild type AB8 lineages (C) Heatmap showing the percentage of cells in the lineage of one embryo that map to cells in a different position in the lineage of another embryo under the alignment produced by the generalized branch distance in (B).