Abstract
Computational trajectory analysis is a key computational task for inferring differentiation trees from this single-cell data. An open challenge is the prediction of complex and multi-branching trees from multimodal data. To address these challenges, we present PHLOWER (decomposition of the Hodge Laplacian for inferring trajectories from flows of cell differentiation), which leverages the harmonic component of the Hodge decomposition on simplicial complexes to infer trajectory embeddings from single-cell multimodal data. 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 kidney organoid multimodal 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. Thus, PHLOWER enables inference of complex branching trajectories and prediction of transcriptional regulators by leveraging multimodal data.