a, Maturation progression of granule neurons in the mouse hippocampus dataset is approximated by pseudotime (estimated with a principal curve). b, For a pair of example genes (rows), the plots show unspliced and spliced gene expression profiles along the pseudotime (left panels), empirically estimated smoothed pseudotime derivative of the observed gene expression and the estimated RNA velocity (middle panels), as well as the relationship between spliced and unspliced expression (right panel). The velocity estimates for the two chosen genes are highly correlated with the empirically observed derivative, indicating accurate velocity estimation. c, The majority (75%) of the genes that were differentially regulated along the pseudotime trajectory showed a positive correlation with the empirical expression derivative. The distribution of such genes is split according to three classes of trajectory-associated genes as shown in d. By contrast, velocity estimates for genes that were not differentially expressed along the pseudotime trajectory did not show such correlation (grey). Incorporating information about co-regulated genes into velocity estimation using gene kNN clustering (see Supplementary Note 1) can significantly boost the accuracy of the velocity predictions (lower panel). d, Trajectory-associated genes were classified as early, transient and late, according to their peak expression time. x axis, cells ordered by pseudotime; y axis, genes ordered by their peak expression time. e, The genes that were well-correlated in terms of their spliced expression patterns with Ptprg, also showed a high correlation of their velocity estimates with Ptprg. To assess the degree of consistency of the velocities of co-regulated genes, we introduced a measure of velocity coordination for a given gene, as a difference between the mean correlations of the velocity estimates of the co-regulated genes and the velocity estimates of all genes. The two quantities being compared are shown for Ptprg with dotted vertical lines: grey, mean velocity correlation with all genes; red, mean velocity correlation with top co-regulated genes. Velocity coordination provides an unbiased measure of quality for velocity estimates. f, Velocities of co-regulated genes were correlated. Distribution of gene velocity coordination values is shown for genes that had co-regulated genes (that is, the genes that had well-correlated gene neighbours in terms of their spliced expression pattern, green), as well as for the genes that did not have enough co-regulated genes (without neighbours, grey). g, Co-regulated genes that had high velocity coordination tended to have high correlation with the empirical derivatives. Spearman correlation coefficient is shown. h–k, Velocity performance during maturation of pyramidal neurons (h). Genes differentially expressed during maturation had high correlation of velocity with empirical derivative (i), co-regulated genes tended to have correlated velocity estimates (j) and the degree of velocity coordination was associated with its correlation with empirical derivative (k). l, m, Velocity performance during chromaffin differentiation. p–s, Velocity performance during maturation of oligodendrocytes. Number of top co-regulated genes analysed for velocity correlation: 200 (g), 150 (k, o, s).