Fig. 3: Delineating transcriptome-wise progression with manifold-consistent kinetic genes using GraphVelo.

a Schematitc of transcritional events mislead RNA velocity estimation in the phase portrait by standard approaches. Left: for genes exhibiting rapid degradation, the cells appear above the steady state line on the phase portrait, whereas the true velocity is negative. Right: For genes exhibiting transcription burst, the transcription rate abruptly increases at intermediate states, leading to a steady state line whose slope is overestimated. b Schematic of manifold-consistent score calculation for robustly estimated velocity genes. c The projected velocity field from GraphVelo are consistent with the erythroid differentiation by using all highly variable genes. d The correlation between GraphVelo vector field-based pseudotime and embryo time for erythroid lineage cells. Spearman correlation coefficients are shown. e GO enrichment analyses of top ranked MacK genes. f The phase portrait of two transcription burst genes (Smim1, Hba-x). g Scatter plots of: i) velocities estimated by scVelo, ii) refined velocities by GraphVelo, and iii) mature mRNA expression of transcription burst genes (Smim1, Hba-x). Cells were colored by corresponding velocity, and mature mRNA abundance, respectively, and visualized on the UMAP representation. h Gene regulatory cascade unraveled by GraphVelo-based vector field analyses that drives cell lineage commitment. Gene set enrichment was performed using one-sided Fisher’s exact test, Benjamini–Hochberg correction. Adjusted p-values represent FDR-corrected significance of gene set enrichment. i Activation of Gata1 inhibitor TF Spi1 lead to reversed velocity flows in gastrulation erythroid maturation investigated through in silico perturbation analyses on GraphVelo-based vector field. j Velocities derived from GraphVelo for the branching lineage in the hematopoiesis development and projected onto a pre-defined TSNE embedding. Directions of the projected cell velocities on TSNE are in agreement with the reported differentiation directions. k Terminal states identified by CellRank based on Markov chain formulation derived from GraphVelo velocities. l Phase portrait, velocity estimated by scVelo, refined velocity by GraphVelo, and gene expression of mature mRNA of identified rapid degradation genes (NPR3, ANGPT1). The cells were colored by the palantir pseudotime³¹ in the phase portrait. The box plots showed cell-specific \({{{\boldsymbol{\gamma }}}}\) for cells divided into bins according to pseudotime ordering in the phase protrait. The number of cells within each time bins from early to late is 653, 650, 654, 657, 657, respectively. Boxplots indicate median (middle line), first and third quartiles (box), and the upper whisker extends from the edges to the largest value no further than 1.5 × IQR (interquartile range) from the quartiles and the lower whisker extends from the edge to the smallest value at most 1.5 × IQR of the edge, while data beyond the end of the whiskers are outlying points that are plotted individually. Source data are provided as a Source Data file.