RNA velocity of single cells

scRNA-seq captures a static snapshot of gene expression

making it difficult to study time-resolved processes like embryogenesis or tissue regeneration

differentiation occurs on timescales of hours to days,

which is comparable to the typical mRNA half-life

Therefore, the relative abundance of nascent (unspliced) vs. mature (spliced) mRNA encodes information about the direction and rate of transcriptional change

without needing metabolic labeling or time-course experiments

RNA velocity

the time derivative of the gene expression state; a high-dimensional vector predicting the future state of individual cells on a timescale of hours

All common scRNA-seq protocols use

oligo-dT primers to enrich for polyadenylated mRNA

Despite this, examining SMART-seq2, STRT/C1, inDrop, and 10x Chromium datasets

15–25% of reads contained unspliced intronic sequences

Origins of intronic reads:

Mostly from secondary priming positions within intronic regions

In 10x Chromium: also abundant discordant priming from intronic polyT sequences,

possibly generated during PCR amplification from first-strand cDNA

Correlation of intronic with exonic counts

these represent unspliced precursor mRNAs

Metabolic labeling validation: 4sU labeling of HEK293 cells (5, 15, 30 min exposure) followed by oligo-dT-primed STRT sequencing

83% of genes showed expression time courses consistent with simple first-order kinetics, confirming unspliced reads = nascent mRNA

ds/dt = βu − γs

α = transcription rate (production of unspliced mRNA)

β = splicing rate (unspliced → spliced; set to 1 by convention)

γ = degradation rate of spliced mRNA

u = unspliced mRNA count

s = spliced mRNA count

RNA velocity = ds/dt =

the first time derivative of spliced mRNA abundance

When α is constant,

system approaches steady state asymptotically

At steady state: u = γs

fixed-slope relationship in phase portrait space

γ captures:

degradation rate, splicing rate, ratio of intronic/exonic lengths, number of internal priming sites

u > γs

gene is being induced → positive velocity → cell moving toward higher expression

u < γs

gene is being repressed → negative velocity → cell moving toward lower expression

Velocity = 0

at steady state (cells on the diagonal)

Key Property of γ

Examined across Tabula Muris dataset (48 cell types, 8,385 genes)

Most genes show a single fixed γ

across widely different cell types and tissues (high Pearson correlation of spliced/unspliced counts across cell types)

~11% of genes show distinct slopes in different tissue subsets, suggesting

tissue-specific alternative splicing (Alt. splicing confirmed for Sept9, Sgk1) or tissue-specific degradation rates

Double-γ genes estimated by regression

mixture modeling (EM, R package flexmix)

γ fit performed using regression on extreme expression quantiles

(robust even when most cells are outside steady state)

Alternative: structure-based γ fit — uses gene structural parameters to predict γ, then uses k most correlated genes to adjust M-value (M = log₂[u_observed / u_steady-state]) and re-estimate γ

corrects for genes exclusively observed far from equilibrium

For large/noisy datasets, read counts pooled across k nearest cell neighbors

before γ estimation to reduce technical noise

Different k values used per dataset

(e.g., k=500 for hippocampus, k=90 for oligodendrocytes)

Joint PCA embedding:

observed and extrapolated states jointly embedded in PCA space; arrows show direction of travel

Projection onto existing embeddings (t-SNE):

extrapolated state compared to similarity with neighboring cells; velocity arrows reflect where a cell would most likely go

Locally averaged vector fields (grid visualization)

for large datasets; Gaussian smoothing on a regular grid

Cells can have RNA velocities along

multiple independent components simultaneously (differentiation, maturation, proliferation)

A cell with no apparent velocity in one embedding may still have substantial velocity

in an unvisualized subspace

Validation 1: Mouse Liver Circadian Cycle (Bulk RNA-seq)

Examined bulk RNA-seq time course of mouse liver circadian cycle (24h)

Unspliced mRNA at each time point consistently more similar to

spliced mRNA of the next time point

Circadian genes showed expected excess of unspliced RNA during

upregulation, deficit during downregulation

Solving differential equations for each gene

velocity arrows on PCA correctly captured expected direction of circadian progression

Validation 2: Mouse Chromaffin Cell Differentiation (SMART-seq2)

System: Schwann cell precursors (SCPs) differentiating into chromaffin cells (neuroendocrine cells of adrenal medulla); direction of differentiation can be validated by lineage tracing

Phase portraits showed expected deviations from steady-state in many genes

Serpine2: repressed in SCPs → below steady-state line → negative velocity

Chga: induced in chromaffin cells → above steady-state line → positive velocity

Velocity vectors correctly showed general movement

toward chromaffin fate

Also captured:

movement toward and away from intermediate bridge state

Captured cell cycle dynamics involved in chromaffin

differentiation (in PCA and dedicated cell-cycle gene analysis)

Metabolic labeling:

spliced/unspliced ratio changes detectable after 10–100 minutes (τ distribution, Fig. 2g mode at ~10–20 min for most genes)

Based on EdU pulse labeling of chromaffin progenitor cells:

effective extrapolation 2.5–3.8 hours into the future

Consistent with ability to resolve

cell-cycle events

Predictive timescale depends on

curvature of the expression manifold (linear extrapolation)

Longer timescales accessible by tracing a sequence of small

extrapolation steps on the observed manifold

Application 1: Developing Mouse Hippocampus (10x Chromium)

Cell types identified (by known marker genes):

Radial glia (Hes1+, Hopx+) — identified as root/origin

Neuroblasts → three neuronal lineages:

Dentate gyrus granule neurons

Pyramidal neurons: Subiculum, CA1, CA2, CA3, Hilus (five fields)

Astrocytes (Aqp4+)

Oligodendrocyte precursors (OPCs, Pdgfra+)

Markov random walk model on velocity field

automatically identified root (radial glia) and terminal states (all lineage endpoints)

Confirmed fate mapping showing radial glia as true origin

of hippocampal lineage tree

Two paths from radial glia: direct

astrocytes (no cell division) OR → pre-OPC → narrow passage → OPCs

Narrow passage

moment of commitment to oligodendrocyte lineage

A cell in the narrow passage

overwhelmingly likely to become OPC

A cell in pre-OPC state: as likely to remain in pre-OPC state

true commitment requires passing through the narrow passage

Fate choice at this level is non-deterministic

tilting of gene expression, followed by lock-in of final fate via TF feedback loops

Neuronal fate choice example:

Two adjacent neuroblasts at branching point between CA and granule fates

Current gene expression states are neighbors

similar transcriptomes

But their futures are already tilted toward different fates

distinguished by activation of Prox1

Consistent with known biology: Prox1 required for granule neuron formation; Prox1 deletion

neuroblasts adopt pyramidal neuron fate instead

Granule neurons of dentate gyrus first split

from hippocampus proper

Second split: subiculum/CA1 vs. CA2–4

consistent with major anatomical subdivisions

Pdgfra (OPC marker):

positive velocity in pre-OPCs, neutral in OPCs (induction then maintenance)

Igfbpl1 (neuroblast):

positive velocity from radial glia to neuroblasts, negative going from neuroblasts to main neuronal branches

Application 2: Human Embryonic Forebrain (10x Chromium)

System: radial glia → neuroblast → immature neuron → neuron (glutamatergic, expressing SLC17A7/VGLUT1)

Strong velocity pattern originating from

proliferating progenitor state (radial glia)

Proceeding through intermediate neuroblast stages

to mature glutamatergic neurons

Pseudotime ordering by principal curve

(using velocity field to determine direction)

Layered spatial expression in tissue corresponded closely to

pseudotemporal distribution in scRNA-seq data

Confirmed

unspliced mRNAs consistently precede spliced mRNAs during both up- and down-regulation

Observed both fast and slow kinetics:

Fast: RNASEH2B — little difference between unspliced and spliced RNAs

Slow (burst + overshoot): DCX, ELAVL4, STMN2 — initial rapid burst of transcription, then reduced sustained level; spliced transcripts follow with a noticeably delayed trajectory

"Dynamic induction with overshooting" proposed to help quickly induce genes with slow degradation kinetics

first time demonstrated in human embryos

Velocity toward/from stem cell states was detectable for a limited set of genes (e.g., Lgr5)

but genome-wide stem cell dynamics were confounded by cell cycle.

Velocity estimates robust to:

Variation of model parameters

Gene subsampling

Cell subsampling

Most sensitive parameter

size of the neighborhood used in visualization of velocity in pre-defined embeddings

75% of differentially expressed genes along pseudotime trajectories showed positive correlation

between velocity estimates and empirically observed expression derivatives

Velocity coordination metric:

genes well-correlated in spliced expression also show correlated velocity estimates → serves as unbiased quality measure

Genes observed exclusively far from equilibrium

(→ structure-based γ correction helps)

Uneven contribution of

non-coding transcripts

Alternative splicing leading to multiple γ

rates across measured populations

No metabolic labeling or time course required

velocity inferred from a single static snapshot

Platform-agnostic

works on SMART-seq2, STRT/C1, inDrop, and 10x Chromium

Tree orientation without prior knowledge

root and terminal states identified automatically via Markov random walk on velocity field

Single-cell resolution fate decisions

reveals early tilting of fate at individual cell level, distinguishing neighbors already committed to different fates

Manifold learning algorithms that simultaneously fit a manifold and the kinetics on that manifold

based on RNA velocity; already applied to whole-organism development