When are cell-state dynamics identifiable from single-cell snapshots, and how to estimate them with guarantees
Mixed theory and data: a known impossibility result plus noisy practice means progress needs new assumptions and measurement types, at a difficulty (57) near fold switching (58). Application value 14 because it mainly changes how trajectories are interpreted; leverage 31 as a widely used family of analyses depends on it.
The problem
Can you tell how cells change over time from a single frozen snapshot of many cells?
- 1Cells are destroyed on measurement
- 2Only snapshots of many cells
- 3Different stories fit same photo
- 4Methods add assumptions
- 5Need guarantees and warnings
Model. Suppose cell state follows with possible birth and death. We observe samples from the distributions at one or a few times. Weinreb et al. (PNAS 2018) showed that distinct dynamics can give the same (for example, a stationary cloud can come from a flow with noise or from no flow), so extra assumptions are needed.
Built from
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- Start with
- When are cell-state dynamics identifiable from single-cell snapshots, and how to estimate them with guaranteesThis problem
- Then
- Predicting transcriptome responses to unseen perturbations in unseen cell contexts (virtual cell models)Computational Medicine · D62
Path to understanding
foundations → problemThe research entries this problem rests on, in the order to read them. Each links to its explainer.
- Start with
- Step 2
- PyTorchLibrary
- Step 3
- Single-cell omics analysisAlgorithm · host
- Then
- When are cell-state dynamics identifiable from single-cell snapshots, and how to estimate them with guaranteesThe problem
State of the art
- Fundamental limits. Weinreb et al. (PNAS 2018) showed that multiple dynamics are consistent with the same snapshot distribution, so extra assumptions (or additional data such as lineage barcodes) are needed.
- RNA velocity. Models of splicing kinetics (La Manno 2018; scVelo, Bergen 2020) often give plausible fields, but critiques show identifiability problems: a Bayesian re-analysis (Sabbioni, Bibbona, Mastrantonio, Sanguinetti) reports that the model's time parameter is not identifiable in simulations; a preprint (BayVel, arXiv:2505.03083) reports that scVelo fails to recover parameters even for data simulated from its own assumptions and that its pancreatic results are strongly influenced by post-processing; the reliability and direction on human embryonic forebrain data have been questioned in a separate analysis. The BayVel and forebrain results are preprint-level and partly by competing-method authors.
- Optimal transport and lineage tracing. Waddington-OT (Schiebinger 2019) gives couplings between time points; lineage barcoding (Weinreb et al., Science 2020) provides clonal ground truth and shows that state alone predicts fate only partially.
- No general guarantee. In sources reviewed no estimator has proven consistency for general velocity-style dynamics under realistic noise, nor a validated detector of unidentifiable regimes.
Realistic applications
Reliable dynamics from snapshots would let researchers read developmental and disease trajectories from patient tissue samples, identify fate decision points for differentiation protocols and cell therapies, and decide which datasets support trajectory claims. Presently, trajectory arrows in published figures are often not interpretable as dynamics.
What counts as solved
A refereed theorem (identifiability conditions and consistency of an estimator) combined with a benchmark on at least five datasets that have independent ground truth (lineage barcodes or metabolic labelling) in which the estimator meets the accuracy thresholds above and the diagnostic reliably flags failing datasets.
How it gets verified
ReproductionA training run, experiment or computation rerun by someone else.
A refereed theorem (identifiability conditions and estimator consistency) must be combined with a benchmark on at least five datasets with independent ground truth (lineage barcodes or metabolic labelling), where the estimator meets the accuracy thresholds and the diagnostic flags failing datasets.
Claims under verification
+ add a claimNo claimed results on the Verification board for this problem yet.
Where the work is
Largely a statistical-theory problem about identifiability, with benchmark data from lineage tracing and metabolic labelling.
Bottlenecks
ranked by votes- #1TheoryNon-identifiability of dynamics from marginals
Different drift fields generate the same snapshot distributions; guarantees need explicit assumptions.
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Connected problems
- This problem is needed by
Progress
- May 5, 2025BayVel (preprint)source
Reports scVelo parameter-recovery failures even on simulated data from its model.
- Feb 6, 2020Lineage tracing on transcriptional landscapessource
LARRY barcodes give ground-truth clonal fate for evaluating inference methods.
- Aug 8, 2018RNA velocitysource
La Manno et al. use unspliced/spliced RNA to estimate cell-state velocities.
- Mar 6, 2018Non-identifiability of dynamics from snapshotssource
Weinreb et al. prove that snapshot distributions do not determine dynamics without further assumptions.