RNA Velocity

RNA in the nucleus is first transcribed as a pre-mRNA

which still contains introns (non-coding sequences)

Before the mRNA can be exported and translated, several processing steps must occur:

5' capping

3' poly-A tail addition

RNA splicing — removal of introns to yield the mature, spliced mRNA

Critically, there is a time lag between transcription and splicing.

The unspliced (pre-mRNA) transcript exists in the cell for a measurable window before becoming the mature spliced form.

Simple model (spliced mRNA only):

dS/dt ​= α−γS

Extended model (capturing unspliced → spliced dynamics):

dU/dt = a - BU

dS/dt = BU - yS

U = unspliced transcript concentration

• SS S = spliced transcript concentration

• β\beta β = RNA processing (splicing) rate

  • γ\gamma γ = degradation rate (gene-specific)

Key simplifying assumptions:

β (processing rate) is constant across all genes

γ (degradation rate) is gene-specific

S>U (more spliced than unspliced)

Gene is being downregulated (ΔS<0)

U>S (more unspliced than spliced)

Gene is being upregulated (ΔS>0)

U ≈ S

Gene is at steady state

These plots of U vs S are called

phase portraits

The line y=x serves as a boundary:

cells above it are upregulating that gene; cells below it are downregulating.

A key practical question: standard scRNA-seq uses poly-dT capture beads

(targeting the poly-A tail of processed mRNA)

Internal poly-A stretches in introns

introns may contain short poly-A sequences that are captured by the beads

Lysis captures nuclear contents

when cells are lysed, nuclear pre-mRNA is released along with cytoplasmic mRNA

Empirically, 17–23% of reads in common platforms (inDrop, 10x Chromium, Smart-seq)

are intronic, making this feasible.

RNA velocity uses the U/S ratio

to

predict the future expression state of each cell.

For multiple genes simultaneously:

Compute the residual (deviation from steady-state ratio) for each gene

From those residuals, compute ΔS\Delta S

ΔS — the expected change in spliced abundance

This gives a predicted future expression profile for the cell

Project the current and predicted states onto a low-dimensional embedding (e.g., PCA, UMAP/t-SNE)

Draw an arrow from the current position to the predicted future position

Do this for every cell

you get a velocity field showing the flow of cell states.

Validation: Circadian Rhythm Data

The approach was validated on bulk RNA-seq data of circadian rhythm genes sampled at 3-hour intervals.

At time t the unspliced abundance of a gene predicts

the spliced abundance at time t+1

This held consistently

across multiple timepoints

Phase portraits of circadian genes showed

the expected cyclical dynamics

Applied to myoblast differentiation (known differentiation trajectory: progenitor → intermediate → myocyte):

Marker genes for progenitors showed negative unspliced residuals in later cell states → expression is declining

Marker genes for mature cells showed positive unspliced residuals in earlier cell states → expression is about to rise

Velocity arrows were computed and overlaid on PCA (PC1 vs PC2) and then on t-SNE embeddings

and generally pointed in the expected direction of differentiation.

Velocities computed in PCA space vs. t-SNE/UMAP space can

give discordant results

Apparent bifurcations in t-SNE may not

be visible in PCA

It can be hard to interpret arrows

in non-linear embeddings confidently

Compute velocity using genes that

contribute most to PC1 and PC2

Project in PCA

space

This allows a cleaner statement:

"these cells are activating the transcriptional program associated with [cell type]" without overinterpreting specific cell-to-cell transitions

RNA velocity applied to hippocampal neuron data

showed sequential bifurcations into many neuron subtypes

Arrows formed coherent

flow fields at scale

Starting from random positions in the graph and following velocity arrows

can infer trajectory roots without prior knowledge

This addresses a key limitation of pseudotime methods (e.g., Monocle)

which required manual selection of root cells

Similarly, endpoints of trajectories

can be identified computationally

The embedding sensitivity caveat is also worth remembering

the lecturer clearly views this as the main practical pitfall. The same velocity data can look like a clean linear trajectory in PCA and a bifurcation in UMAP, and these aren't trivially reconcilable.