PHLOWER - Single cell trajectory analysis using Decomposition of the Hodge Laplacian

Multi-modal single-cell sequencing, which captures changes in chromatin and gene expression in the same cells, is a game changer in the study of gene regulation in cellular differentiation processes. Computational trajectory analysis is a key computational task for inferring differentiation trees from this single-cell data, though current methods struggle with complex, multi-branching trees and multi-modal data. To address this, PHLOWER leverages simplicial complexes and Hodge Laplacian decomposition to infer trajectory embeddings. These natural representations of cell differentiation facilitate the estimation of their underlying differentiation trees. We evaluate PHLOWER through benchmarking with multi-branching differentiation trees and using novel kidney organoid multi-modal and spatial single-cell data. These demonstrate the power of PHLOWER in both the inference of complex trees and the identification of transcription factors regulating off-target cells in kidney organoids.