Figure 4. Multipotential fate associations between immature retinal ganglion cells (RGCs) and terminal types inferred via optimal transport.

(a) Extreme models of diversification at single-cell resolution. Multipotential fate associations in a transcriptionally defined cluster (ellipse) could arise from a mixture of unipotential RGCs (left) or from multipotential RGCs (right). (b) Distributions of potential P across immature RGCs by age showing that restriction increases with age. (c) Inter- and intra-cluster variation of potential by age. At each age, variation in the potential values is shown for each transcriptomically defined cluster at that age. Dots denote the average potential, and dotted lines depict the standard deviation for cells within each cluster. (d–h) Uniform Manifold Approximation and Projection (UMAP) projections of embryonic day (E)13 (d), E14 (e), E16 (f), postnatal day (P)0 (g), and P5 (h) RGCs as in Figure 2, but with individual cells colored by their inferred potential. Potential of all RGCs at P56 = 1. The colorbar on the lower right is common to all panels, and values are thresholded at P = 20.

Figure 4—figure supplement 1. Variations in Waddington optimal transport (WOT)-inferred temporal couplings and tests across variations in hyperparameters.

(a) Variations in WOT-inferred temporal couplings (${\Pi }_{ij}$) at the level of cells and clusters to changes in the set of highly variable genes (HVGs) used for computing transport maps. Four sets of features were tested corresponding to the top 800, 1100, 1400, and 1800 HVGs based on our previously described Poisson-Gamma model (Liu et al., 2018). Using these sets, we inferred four corresponding transport maps at each of the five age pairs embryonic day (E)13–E14, E14–E16, E16–postnatal day (P0), P0–P5, and P5–P56. The entropic regularization hyperparameter $ϵ$ (see panels b, c) was held constant at a value 2^–7 in these tests. At each age pair, we computed the Pearson correlation coefficient (PCC) between estimated temporal couplings for every older cell (column of the transport map $\mathrm{\Pi }$) across each pairwise combination of the four transport maps, towards a total of six combinations. These are indicated as red dots and lines (mean ± SD). We then grouped (summed) the rows of the transport map by transcriptomic cluster at the younger age, such that each element of the new matrix indicates cell (column)–cluster (row) couplings. The PCC values of these couplings were computed for each older cell (column) within each pairwise combination of the four transport maps and are indicated as green dots and lines (mean ± SD). Finally, we grouped (summed) both the rows and columns of the transport map by transcriptomic cluster at either age to obtain a matrix of cluster–cluster couplings. The PCC values of these couplings were computed for each older cluster within each pairwise combination of the four transport maps and are indicated as blue dots and lines (mean ± SD). We find that the cell–cell couplings increase in robustness at later ages, but the cell–cluster and cluster–cluster couplings are quite robust (correlation >0.6). (b) Variations in WOT-inferred temporal couplings at the level of cells and clusters as in panel (a), but to changes in the entropic regularization $ϵ$. Six values were used (2^–8 , 2^–7 , 2^–6, 2^–5, 2^–4, 2^–3) with increasing values corresponding to more transport maps with decreasingly localized (or increasingly distributed) couplings. At each age pair, six transport maps are computed and PCC values for cell–cell, cell–cluster, and cluster–cluster couplings are computed as in panel (a) for each of the 15 transport map pairs. Here too, the cluster–cluster and cell–cluster couplings show higher stability, although at later stages higher values of $ϵ$ exhibit loss of stability even at the cluster–cluster level (see panel c). (c) Heatmap showing cluster–cluster PCC values for P5–P56 transport maps inferred using different values of the entropic regularization parameter, epsilon (rows and columns). Loss of stability occurs at higher values of the entropic regularization, consistent with panel (b). Based on this, we used ε = 2^–7 to calculate the results shown in Figure 4.

Figure 4—figure supplement 2. Temporal correspondences between transcriptomic clusters evaluated using Waddington optimal transport (WOT).

(a–e) Average temporal couplings at the level of clusters. Panels correspond to the pairs embryonic day (E14)–E13 (a), E16–E14 (b), postnatal day (P0)–E16 (c), P5–P0 (d), and P56–P5 (e), respectively. In each case, the WOT-inferred transport map was grouped along rows and columns based on transcriptomic cluster, and the elements were summed within each group. The resulting matrix was normalized such that each row sums to 100%. These matrices strongly resemble those in Figure 3d–h, as confirmed by the high values of the Pearson correlation coefficient (top, all P ≥ 0.92).