Fig 1.
An overview of RNA velocity analysis steps in the κ-velo and eco-velo workflow.
Fig 2.
Visualisation of simulated velocities with linear and nonlinear projection methods.
A. Velocities projected on PCA embedding. The blue outline highlights a region of high velocity variation and the red outline shows a low-variance, high-velocity region. The arrows in the PCA linear projection capture both the plasticity in direction and magnitude of the velocities. B. Velocities projected on PCA embedding by scVelo. scVelo smoothes the velocities as artefact of the projection method, thereby losing the information on cell state velocities variation as illustrated in the cells outlined in blue. scVelo also loses the information of vector length as shown in the cells outlined in red. C. Summary of velocity projection using the Nyström method D-E. Velocities projected by Nyström-projection method shown on PCA in (D) and t-SNE in (E).
Fig 3.
Scaling of gene-wise velocity components.
A. If the gene-wise velocities are incorrectly scaled the high-dimensional velocity vector will change direction (displacement angle θ). B. We propose to use cell densities as a proxy of time. For a same time interval, the displacement in u will be proportional to a gene’s speed. This allows us to relate velocities across genes and solve the scale invariance problem. C. To validate κ-velo, we simulate splicing kinetics scaled by a scaling factor κ and evaluate how well the factors are recovered. D. We compare the κ-velo and scVelo velocities to the true velocities for two genes with different speeds. The high-dimensional velocity vectors are normalised to have equal variance for ease of comparison. E. The high-dimensional vector is projected on the first two principal components to evaluate differences between true velocities and recovered velocities. We return the change in direction (cosine similarity) and length (difference in vector norm) (Note J in S1 Appendix) for κ-velo and scVelo. To make the length comparable, the vectors are variance-normalised. Note the log-scale for frequency.
Fig 4.
κ-velo on pancreas endocrinogenesis.
A. Range of splicing rate β estimated by scVelo (in red) and κ-velo (in blue). B. Examples of fast and slow genes, selected according to κβ. Learned kinetics are shown by blue (upregulation) and orange (downregulation) curves. C. Velocities from κ-velo projected onto a UMAP embedding using κ-velo projection. D. Velocities from scVelo projected onto the same UMAP embedding using κ-velo projection. E. Embedded velocities as returned by scVelo. For ease of comparison, plotting style was matched to (C) and (D). F-G. Quantitative comparison of the projected velocities from κ-velo (A) and scVelo (E) on the low dimensional embedding. We return the norm of the errors in F and the cosine similarity in G.
Fig 5.
A. UMAP embedding with cells coloured for stemness score. B. κ-velo-recovered velocities projected onto UMAP embedding of the cells using Nyström projection. C. Velocities from scVelo projected onto the same UMAP embedding plotted using scVelo’s velocity stream plot. D-F. Recovered dynamics in u-s portrait and expression UMAP of two fast genes Fcnb in D and Ermap in E and one slow gene Pum2 in F.
Fig 6.
Eco-velo as an alternative to computationally costly reaction rate parameter recovery.
A. Under certain conditions, a cell’s unspliced state will represent the cell’s future spliced state. To infer velocities, we look for the first MNN between a cell’s unspliced counts and other cells’ spliced counts. We draw an arrow from the cell to the identified MNN. B. We validate eco-velo on simulation and visualise the resulting velocities on t-SNE. C. eco-velo on pancreas endocrinogenesis.