Hodge Laplacians and Trajectory Inference with PHLOWER accepted in Nature Methods

Thrilled to share PHLOWER, which uses Hodge Laplacians to build trajectory-level embedding for inferring complex cellular differentiation trees from multimodal (RNA+ATAC) single-cell data (https://www.nature.com/articles/s41592-025-02870-5). Hodge Laplacian (HL) is a generalisation of a graph Laplacian used for clustering/pseudo-time estimation. Spectral decomposition of HL creates embeddings on the edge or trajectory space (cell differentiation events or paths) representing these processes more naturally. PHLOWER was evaluted on an extensive Dynverse based benchmark improving the inference of cell differentiation trees in particular for complex and large cell differentiation trees.

To study and improve Kkdney organoid protocols, we generated parallel RNA and ATAC single cell of kidney organoids. PHLOWER inferred tree recapitulates temporal and cellular differentiation events and predicts bona-fide regulators controlling epithelial, stromal and off-target neuronal cells. We used previous results to improve kidney organoids by perturbing TFs predicted to be regulating off-target neuronal/muscle cells. This improves kidney organoid maturation showing the ability of PHLOWER to uncover regulators in cell differentiation systems.

Amazing work by Mingbo Cheng, Jitske Jansen with Vincent Grande, Katharina Charlotte Reimer, MD, James Nagai, Martin Grasshoff and co-lead by Christoph Kuppe, Michael Schaub and Rafael Kramann, MD, PhD