RNA Velocity

RNA velocity exploits the intron-exon architecture of eukaryotic gene expression. When a gene is activated, unspliced pre-mRNA (containing introns) is transcribed first, followed by a lag before mature spliced mRNA appears. By quantifying the ratio of unspliced to spliced reads for each gene in each cell, the method infers whether transcription is being induced (positive velocity) or repressed (negative velocity). This ratio acts as a molecular timestamp, projecting each cell into a future transcriptional state along a differentiation trajectory.

The core mathematical framework plots each gene's unspliced (u) vs. spliced (s) counts across all cells. In a steady-state system, the ratio u/s is constant. Deviations from this equilibrium form a characteristic 'phase portrait':

• Induction phase: High u, low s — the gene is being turned on.
• Repression phase: Low u, high s — the gene is being shut down. The steady-state ratio (γ/β), where γ is the splicing rate and β is the degradation rate, defines the expected equilibrium line. The residual distance of each cell from this line determines its instantaneous velocity vector.

The steady-state model assumes all genes share a common splicing rate, which fails during rapid state transitions. Dynamical RNA velocity (scVelo) fits a full likelihood-based model to each gene's splicing dynamics, solving for cell-specific latent time rather than a global equilibrium. This captures:

• Transcription rate (α): The rate of unspliced mRNA production.
• Splicing rate (β): The rate of intron removal.
• Degradation rate (γ): The rate of spliced mRNA decay. This approach resolves complex trajectories with multiple branching points and convergent fates that steady-state models flatten.

Raw velocity vectors are high-dimensional and noisy. To project them onto a low-dimensional embedding (e.g., UMAP), a velocity graph is constructed. This graph computes cosine similarity between each cell's velocity vector and the displacement vectors to its k-nearest neighbors. The resulting transition probability matrix defines a Markov chain where edges represent the likelihood of a cell transitioning to a neighboring state. This matrix is used to:

• Project velocity arrows onto the embedding.
• Simulate random walks to predict terminal fates.
• Compute root and end-point probabilities for lineage tracing.

While pseudotime orders cells along a trajectory based on transcriptomic similarity, latent time from dynamical velocity models reconstructs the actual internal clock of the differentiation process. Latent time assigns each cell a continuous value representing its position along the gene-shared transcriptional dynamics, independent of the manifold geometry. This resolves directional ambiguity — distinguishing a cell moving toward a fate from one moving away — and aligns cells from different branches onto a common temporal axis for comparative analysis of gene cascades.

RNA velocity is increasingly paired with other modalities to validate and enrich trajectory predictions:

• Lineage tracing: CRISPR barcodes provide ground-truth clonal relationships to benchmark velocity directionality.
• ATAC-seq: Chromatin accessibility dynamics reveal the regulatory logic preceding transcriptional bursts.
• Spatial transcriptomics: Velocity fields projected onto tissue coordinates predict migration paths and spatial differentiation gradients.
• Metabolic labeling: 4-thiouridine (4sU) pulse-chase experiments directly measure nascent RNA, providing an orthogonal validation of velocity estimates.