# Developmental scRNASeq Trajectories in Gene- and Cell-State Space--The Flatworm Example
## 3 Results
### Development along Branched Trees  
The unbranched pt approach applied in the previous subsection sorts the cells along one dimension independent of the cell type. A more realistic computational approach is provided by URD [40]. It splits the pt path of planarian tissue development into a tree-like, multibranched one. The algorithm applies diffusion-like random walks to search for graphs through cellular states. The obtained trajectory starts with a common trunk of neoblast cells for early pseudotime values at pt \(<\) 0.6 (blue color in Figure 5A,B). Subsequently it divides into tissue-specific branches at pt \(>\) 0.6 (yellow to red). Notably, the multibranched tree obtained by means of the URD algorithm reproduces the differentiated cell types identified by independent methods in the original publication [29]. Different visualizations of URD branching in terms of a 3D cell cloud (Figure 5A), of a path-tree or t-SNE plots (Figure 5B) enable inspection of paths under different perspectives. The tree describes differentiation into more than thirty final tissue types via 13 progenitor populations (Figure 5C). Initial stemness states stratify into a variety of neoblast and progenitor cells such as gut and early epidermal progenitors at pt = 0. Subsequently, the main branch splits the trajectory into sub-branches describing differentiation into tissues such as parenchymal, neuronal, proto-nephridial, and diverse epidermal and gut cells. Further branching separates late epidermal progenitors, pigment and epidermis cells, muscle body and muscle pharynx cells, and npp-18 and oft+ cell neurons. The profiling of spot gene expression along the different sub-branches using URD-pseudotime (pt) as argument shows the decline of expression of the stem cell module \"N\" and the gain of the expression of the spot-modules referring to differentiated tissues as expected (Figure 5D). Differentiation proceeds rather step-wise which concerns variance of the data than continuously at different pt-values ranging from about pt = 0.1 (epidermal tissue) and 0.2 (muscle) to 0.5 (neurons) which suggests switching of the cellular machinery from stemness programs into programs of differentiated cells almost without intermediate expression states. Some tissues show indications of intermediate states (e.g., muscle, epidermis) in terms of more smooth transitions between undifferentiated source and differentiated sink states. Next, we made use of previous stratification of planarian genes into 48 clusters of co-expressed genes, which were assigned to different tissues and tissue-combinations [29]. The tree in Figure 5E illustrates the obtained hierarchy and maps marker genes taken from [29] into the SOM. In general, one observes that genes upregulated in several tissues (upper part of the tree) locate more in the middle part of the SOM and of the intended trajectories while marker genes for single tissues are found in and near the respective tissue-related spots detected in our analysis. Overall, the spread of genes is relatively large, presumably because the number of 48 clusters used in [29] is insufficient to resolve the expression patterns underlying tissue differentiation. On the other hand, the location of part of the tissue markers slightly away from the sink nodes presumably reflects also the fact that they are activated in transition states as progenitors of more than one tissue type as visualized in the tree (Figure 5E). Tissue markers of our spot-analysis are listed in Figure 5E and Table 1. In summary, multi-branched pseudotime approaches such as URD provide an overview of tissue differentiation by sorting the cells into differentiation paths based on their mutual similarity relations. Figure 5: Branched pseudotime analysis of planarian tissue development. (**A**) URD plot [40] of branched differentiation in 3D is shown in two projections. The pseudotime is calculated as the average  
number of diffusion steps required to reach each cell from the root cell (neoblast 1) [40]. (**B**) Pseudotime coloring of t-SNE plot and URD-branching tree.