Physical-time grounding

中文導讀

這頁講為什麼多數 RNA velocity 方法的時間軸不是真正的 physical time。從 splicing kinetics ODE 出發,snapshot data 只能定出 β/γ 這類 ratio,定不了 absolute timescale——把時間跟所有 rate 一起 rescale,觀測到的 (u, s) 分布不變,所以 latent time 充其量是 ordinal、不是 metric。要 break 這個 degeneracy 得靠外部 anchor,例如 metabolic labeling 或 real-time series。RegVelo 補的是 GRN/mechanistic 那條軸, physical-time grounding 這條沒動到——正是 FlowVelo 要切的點。

Definition

The degree to which an inferred temporal coordinate — latent time, pseudotime, or a velocity magnitude — corresponds to absolute physical time (real units such as hours or days) rather than to a dimensionless ordering of cell states. A method is metrically grounded if equal intervals of its time axis correspond to equal real durations everywhere; it is only ordinally grounded if it merely recovers the correct sequence of states.

This is the central evaluative axis for RNA velocity methods in this wiki.

Why it is hard: the splicing ODE and its scale degeneracy

The single-gene model underlying splicing-kinetics-ode is

du/dt = α(t) − β·u          (unspliced)
ds/dt = β·u − γ·s           (spliced)

with α transcription, β splicing, γ degradation rates. From a snapshot we observe many cells as points sampled along the (u, s) phase trajectory.

The induction steady state is u_ss = α/β, s_ss = α/γ, so the steady-state relation between spliced and unspliced depends only on the ratio β/γ (this is exactly what the scVelo steady-state estimator fits — the slope identifies γ with β normalised to 1). Equivalently, rescaling time to τ = β·t leaves the dynamics depending only on α/β and γ/β. The common scale β — the factor that converts the latent axis into real time — is free.

Consequences:

• Direction is identifiable. The velocity vector v = ds/dt = β·u − γ·s points the right way in expression space regardless of the scale.
• Absolute timescale is not. Because β is unconstrained by snapshot data, the magnitude of v and the spacing of latent time are known only up to a global (and, if rates vary along the trajectory, locally varying) factor.

So pure snapshot scRNA-seq can recover the shape and direction of a trajectory but not its duration. Physical-time grounding therefore requires information that snapshot data does not contain.

What can break the degeneracy

• Metabolic labeling (metabolic-labeling: scEU-seq, sci-fate, scNT-seq): a known labeling window Δt separates newly-synthesised from pre-existing RNA and pins the absolute rates → real-time grounding.
• True time-series with known sampling times.
• A calibrated reference clock (e.g. a known cell-cycle duration, or a FUCCI-anchored phase axis) — note this calibrates one process, not the whole manifold. VeloCycle (velocycle-2024) is the worked example: on the cell cycle (a closed 1D periodic manifold of known period), it expresses velocity in mean-half-life units and scales by measured average half-lives to obtain a cell-cycle period in hours — validated against live imaging and EdU. This is the rate–time degeneracy broken by a measured rate rather than a labeling Δt.
• A measured absolute rate (e.g. an average mRNA half-life): converts relative (“per-half-life”) velocity to real units. This is VeloCycle’s anchor, distinct from labeling.

Method scorecard

Method	Time axis	Rate scale	External anchor	Verdict
velocyto (2018 origin)	local physical rate; extrapolation in hours	ratio γ (β≡1), labeling pins step	EdU / metabolic labeling	physically grounded origin
scVelo (steady-state / dynamical)	ordinal latent time	ratios only (β≡1)	none	ungrounded
veloVI	ordinal latent time	relative	none	ungrounded
RegVelo	ordinal latent time, FUCCI-correlated	α made regulation-dependent; β, γ still relative	none	mechanistically grounded, temporally ungrounded
GraphVelo	refines velocity, not time; pseudotime ordinal	magnitude preserved but inherited; α, γ relaxed	none of its own	manifold-consistent, scale-preserving but scale-inheriting
ddHodge	ordinal potential (+ acceleration)	inherited (relative)	none of its own	geometry-preserving; adds potency + acceleration axes
TopoVelo	metric-by-assumption (20 h gene-cycle convention)	expression time assumed; space real (μm)	partial: μm + live-imaging migration-rate match	closest to physical units; timescale imported, not identified
veloVI	ordinal latent time (+ uncertainty + applicability test)	relative	none (names labeling as the missing anchor)	ungrounded, but honest about whether velocity is trustworthy
VeloCycle	METRIC on the cell cycle — period in hours	broken by a measured half-life (rpmh→h)	known periodicity + measured half-lives + live-imaging/EdU validation	metric & experimentally validated (first of its kind); scoped to periodic processes
dynamo	can be metric	absolute when labels present	metabolic labels (optional)	grounded with labeling
FlowVelo	target: metric	target: absolute / physically interpretable	(lab objective)	the gap this work aims to close

NOTE: RegVelo’s strongest time validation is a Spearman ≈ 0.68 between latent time and the FUCCI score — an ordinal check. It certifies the ordering, not the metric spacing. RegVelo never claims physical-time grounding; this is a limitation only relative to our objective. See regvelo-physical-time-critique.

NOTE: TopoVelo is the most physical-time-relevant ingested method and a sharp test case. It reports cell migration velocity in μm/hour that matches live-cell imaging — but it does not break the snapshot scale degeneracy. The spatial scale is measured (μm); the temporal scale is assumed (the convention that a gene’s induction/repression cycle takes 20 h). So it is metric-by-assumption plus an external spatial check, not data-driven metric time. This splits the problem usefully: space can be anchored, but absolute time still needs its own signal — exactly FlowVelo’s question. See spatial-velocity.

Grounding was present at the origin (then lost)

A correction to the naïve “velocity was never physical” story: the 2018 origin (velocyto) did anchor velocity to physical time — it calibrated the extrapolation step to hours using EdU / metabolic labeling, and validated direction against the circadian clock. The snapshot-only scVelo dynamical model then relabeled the axis as ordinal latent-time and dropped the anchor; dynamo later re-introduced labeling. So physical-time grounding is partly a regression to recover, not a feature never had — which is precisely JianhuaXing’s narrative (xing-hu-regvelo-debate) and a clean motivation for FlowVelo.

The recovery now has a worked example — from the origin’s own author. GioeleLaManno, lead author of velocyto-2018, returns with VeloCycle (velocycle-2024, with FelixNaef): a manifold-constrained Bayesian model that, on the cell cycle, reaches metric time in hours and validates it directly against live-imaging microscopy and EdU — the first direct experimental validation of RNA velocity in real (not pseudo) time. It does so without metabolic labeling, by exploiting (a) the cell cycle’s known periodicity (a closed 1D manifold) and (b) a measured average half-life to scale the rate. This closes the origin→regression→recovery loop and qualifies the wiki’s headline claim: the temporal axis is no longer uniformly open — it is solved on periodic / known-geometry processes with a measured rate scale, and still open for general developmental trajectories (non-periodic, unknown geometry). That sharper statement is the honest framing for FlowVelo: extend VeloCycle’s recipe (constrained geometry + a rate anchor) beyond the cell cycle.

Author-level corroboration

This wiki’s thesis is not idiosyncratic. JianhuaXing (dynamo / GraphVelo PI), unprompted, states it more strongly: latent time is a geometric reaction coordinate, unrelated to physical time, and scVelo silently swapped the physically defined 2018 velocity for a “pseudo-velocity” (xing-hu-regvelo-debate). The broader velocity-skepticism cluster (LiorPachter, GennadyGorin) attacks the same gap from the biophysics/normalization side. Use these as ideas (not verbatim quotes) when motivating FlowVelo; keep the framing measured (see the caveats in regvelo-physical-time-critique).

Open questions / research hooks

• VeloCycle solved the periodic case — can it generalize? It reaches validated metric time on a known-period, closed 1D manifold. What is the analog for an open, non-periodic developmental trajectory, whose geometry and “period” are not known a priori?
• Can a flow-matching or optimal-transport formulation carry a physically interpretable time without ingesting labels — or, à la VeloCycle, with only a measured average rate (half-life) instead of a labeling Δt?
• If β, γ drift along a trajectory, even a labeled anchor calibrates only locally — how should a global metric time be defined and validated? (VeloCycle sidesteps this by letting speed ω(φ) vary while keeping β, γ constant — is that the right split?)
• What is the minimal external signal (one labeled timepoint? a single known duration? one measured half-life?) sufficient to make snapshot-inferred dynamics metric?

Related pages

RNA velocity · splicing-kinetics-ode · latent-time · grn-informed-velocity · spatial-velocity · manifold-consistent-velocity · potential-landscape · metabolic-labeling · RegVelo · GraphVelo · ddHodge · TopoVelo · VeloCycle · velocycle-2024 · veloVI · GioeleLaManno · dynamo · FlowVelo · JuloVelo · physical-time-grounding-across-methods · regvelo-physical-time-critique