Fig. 4: Inferring state trajectories through time-resolved measurements.

a, The RealTimeKernel combines across time-point transitions from WOT¹⁵ with within-time-point transitions from gene expression similarity to account for the asynchrony observed in many cellular processes. All views are combined in a single transition matrix. b, By including within-time-point information, the RealTimeKernel enables recovering more granular state transitions; WOT only considers transitions between consecutive time points. c, UMAP embedding of pharyngeal organ development³⁷ (n = 55,044 cells) colored by embryonic day (E; left) and original cell type annotation (right; cTEC, mTEC, UBB); gray color encodes early, uncommitted cells. d, Using the RealTimeKernel, CellRank 2 correctly identifies 10 out of 11 terminal states. The black outline highlights mTECs and potential precursor cells. e,f, Fate probabilities toward the mTEC terminal state (left) and top 20 lineage-correlated genes identified (right) based on the RealTimeKernel (e) or WOT’s pullback distribution (f). We highlight TFs in yellow and known mTEC development genes in green. CellRank 2 identifies putative drivers by correlating fate probabilities with gene expression, WOT by comparing high- and low-probability cells.