RNA Velocity

The core mathematical engine predicts future gene expression by solving a system of ordinary differential equations. The model estimates transcription rate (α), splicing rate (β), and degradation rate (γ) for each gene independently.

• Unspliced mRNA serves as a proxy for nascent transcription
• Spliced mRNA represents the mature, functional transcript pool
• The phase portrait of spliced vs. unspliced counts reveals the instantaneous rate of change
• A positive velocity indicates upregulation; negative velocity indicates repression

Each gene's transcriptional dynamics are visualized as a phase portrait—a scatter plot of unspliced (u) against spliced (s) counts across all cells. The deviation from the steady-state equilibrium line defines the velocity vector.

• Cells above the equilibrium line are in the induction phase (transcriptional burst)
• Cells below the line are in the repression phase (mRNA decay)
• The slope of the equilibrium line equals the ratio of degradation to splicing rates (γ/β)
• Arrows on UMAP or t-SNE embeddings project these gene-level velocities into a low-dimensional representation

Two distinct modeling frameworks exist for estimating RNA velocity parameters, each with different assumptions and computational requirements.

• Steady-state model (velocyto): Assumes transcriptional equilibrium and fits a linear regression to the extreme quantiles of the phase portrait. Computationally fast but fails for transient populations
• Dynamical model (scVelo): Solves the full differential equation using an expectation-maximization algorithm, recovering a latent time variable. Captures transient states and convergent differentiation paths
• The dynamical model resolves the directionality ambiguity inherent in steady-state approximations

The dynamical RNA velocity framework reconstructs an intrinsic cellular clock called latent time, which orders cells along a differentiation trajectory based on their transcriptional kinetics rather than transcriptomic similarity.

• Latent time aligns cells from multiple lineages onto a common temporal scale
• It correctly positions cells that share similar expression profiles but are on divergent paths
• This metric resolves the terminal state convergence problem where pseudotime methods fail
• Enables identification of driver genes that initiate lineage commitment decisions

Cell-to-cell transition probabilities are encoded in a velocity graph—a directed, weighted nearest-neighbor graph where edges represent the likelihood of a cell transitioning toward its neighbors.

• Cosine similarity between the velocity vector and the displacement vector to each neighbor determines edge weights
• The graph is used to project velocities onto low-dimensional embeddings for visualization
• Markov chain simulations on the velocity graph predict terminal fate probabilities
• Enables identification of lineage drivers and commitment points without prior biological knowledge

RNA velocity analysis predicts the ultimate differentiation fate of progenitor cells by propagating transition probabilities through the velocity graph to identify absorption states.

• Random walk simulations starting from each cell estimate the probability of reaching each terminal state
• Commitment bias quantifies how strongly a cell is directed toward a specific lineage
• This approach identifies bifurcation points where lineage decisions occur
• Applied in hematopoiesis to map hematopoietic stem cell differentiation into erythroid, myeloid, and lymphoid branches

The fundamental distinction that makes RNA velocity possible. Spliced mRNA counts represent mature transcripts ready for translation, while unspliced mRNA counts capture nascent transcripts still containing introns. The ratio between these two species provides a temporal derivative of gene expression.

• Spliced: Reads mapping exclusively to exons
• Unspliced: Reads spanning exon-intron boundaries
• The balance indicates whether a gene is being activated (high unspliced) or repressed (low unspliced)

A quantitative measure of a cell's progression along a continuous biological process, inferred from transcriptomic similarity rather than real clock time. RNA velocity vectors are often projected onto pseudotime trajectories to validate the directionality of differentiation.

• Diffusion pseudotime: Uses random-walk distances on a nearest-neighbor graph
• Monocle: Employs reversed graph embedding to learn a principal tree
• RNA velocity provides an arrow of time that orients pseudotime trajectories

The computational reconstruction of dynamic biological paths, such as developmental lineages, by ordering cells based on transcriptomic similarity. RNA velocity adds a directional vector field to these otherwise undirected graphs.

• Partition-based graph abstraction (PAGA): Coarse-grains trajectories while preserving topology
• Slingshot: Identifies global lineage structure using minimum spanning trees
• Velocity-informed trajectories resolve branching points with higher confidence than static methods

Mathematical transformation of high-dimensional single-cell data into a lower-dimensional space for visualization and noise reduction. RNA velocity vectors are computed in high-dimensional gene space but visualized on t-SNE or UMAP embeddings.

• PCA: Linear reduction used as a preprocessing step before velocity estimation
• UMAP: Preserves global structure better than t-SNE for velocity projection
• Velocity arrows on UMAP plots show the predicted future state of each cell neighborhood

A sparse numerical matrix where rows represent genes and columns represent cell barcodes. RNA velocity requires two count matrices: one for spliced reads and one for unspliced reads, both generated from the same alignment data.

• Loom format: Efficient file format for storing spliced/unspliced matrices
• AnnData layers: Scanpy stores spliced and unspliced counts in separate .layers
• The velocity model fits a ratio of unspliced to spliced change over time

Computational models that map regulatory relationships between transcription factors and their target genes. RNA velocity can be extended to dynamical GRN inference by modeling how transcription factor expression changes drive downstream target velocity.

• scVelo dynamical mode: Recovers transcription rates, splicing rates, and degradation rates
• CellRank: Combines velocity with lineage tracing to estimate fate probabilities
• Latent time inferred from velocity aligns cells along a shared differentiation clock