Fig. 1: Refining RNA velocity by tangent space projection and transforming between representations using GraphVelo.

a Workflow of RNA velocity-based analyses incoporating GraphVelo. Note GraphVelo takes any form of RNA velocity (i.e., not just splicing-based velocity) as input, and the kNN neighborhood is defined in the full state space (e.g., by both scRNAseq and scATACseq in multi-omics data). b Schematic of tangent space projection and velocity transformation between homeomophic manifolds. Left: RNA velocity vectors are projected onto the tangent space defined by the discretized local manifold of neighborhood cell samples. Right: GraphVelo allows for transformation of velocity vectors from a manifold embeded in a higher dimensional space \(({{{\mathcal{M}}}})\) to that in a lower-dimensional space \((\aleph )\), and vice versa. c The process of minimizing the loss function of tangent space projection. Noisy velocity vectors (left) generated by adding random components orthogonal to those sampled from an analytical 2D manifold were projected back onto the 2D manifold, resulting in smooth velocity vectors that lie in the tangent space (right). d GraphVelo allows whole genome velocity inference based on the robustly estimated MacK genes (see also Fig. 3). Velocities of genes undergoing variable kinetic rates, such as rapid degradation or transcription burst, are difficult to be correctly inferred by other methods, but can be inferred robustly with GraphVelo. e Virus infection dynamics and underlying host-virus interaction mechanisms uncovered by GraphVelo (see also Fig. 4). Upper: pathways involved in host-virus interactions were identified using GraphVelo. Lower: GraphVelo predicted reversed trajectory of viral infection in response to in silico perturbations of viral factors. f GraphVelo provides a consistent view of epigenetic and transcription dynamics (see also Fig. 5). Upper: GraphVelo analyses on multi-omics data revealed that most cell-cycle dependent genes showed decoupling between transcription dynamics and chromatin accessibility change dynamics. Lower: Effective dose-response curves reconstructed from multi-omics data revealed pioneer transcription factors increased chromatin accessibility then transcription of targe genes.