(1111). In most trajectories, particularly during intermediate time steps (2222), curvature becomes negative, indicating the oversquashing phenomenon, characteristic of Bridges. In contrast, regions with positive curvature (3333) predominantly appear in Stromal and Neural cell types, suggesting excessive connectivity, characteristic of Hubs.
The concept of "bridges" and "hubs" in curvature in this work is really interesting to me. It suggests that you can identify places along a developmental trajectory where fate transitions are narrowed vs. robust and redundant. Have you considered applying this metric to scRNA-seq datasets focused on tumor progression, e.g. something like Liu et al. 2024? I wonder if you could predict what cell populations are likely to undergo critical state transitions during the development of tumors and identify therapeutically relevant cell populations to target.