Why Cell-Cycle Structure Can Mislead
RNA velocity describes a model-based local expression change, not a direct observation of a cell moving through developmental time. A cell-cycle program can produce strong, coordinated transcriptional changes, and those changes can appear in the same expression measurements used to infer velocity. The resulting vectors may therefore reflect cycling through phases rather than progression along the biological transition of interest.
The diagnostic question is not simply whether cell-cycle genes have nonzero velocity. They may do so because their transcription genuinely changes during the cycle. Instead, ask whether the prominent gene-level patterns and cell-level vector directions are largely organized by cell-cycle phase, and whether a distinct, coherent signal remains after accounting for that organization. These diagnostics support interpretation; by themselves, they do not prove that a vector is developmental or that cell-cycle activity caused a particular inferred pattern.
Gene-Level Phase Portraits Across Cell-Cycle Phases
For a gene \(g\) in cell \(i\), let \(u_{gi}\) and \(s_{gi}\) denote normalized unspliced and spliced expression. Under the standard first-order kinetic interpretation, the instantaneous change in spliced expression is \(v_{gi}=\beta_g u_{gi}-\gamma_g s_{gi}\), where \(\beta_g\) is the splicing rate and \(\gamma_g\) is the degradation rate. The rates must be estimated under an appropriate kinetic model; a phase portrait displays the observed expression values and model fit, not the cell’s history directly.
Inspect the portrait separately by annotated phase, such as G1, S, and G2/M. Look for phase-specific clusters, shifts in the unspliced-to-spliced relationship, or a pattern in which the inferred sign of velocity changes across phases. If phase labels are reliable and each phase has enough cells, this comparison can reveal that a pooled portrait combines distinct phase-associated regimes. It is also useful to inspect whether the apparent pattern is supported by many cells or driven by a few high-count observations.
A phase-associated pattern is not automatically a modeling failure. A cell-cycle-regulated gene may truly be induced or repressed during part of the cycle. The interpretive problem arises when that genuine cyclic signal is read as evidence for a one-way transition, or when it dominates a vector meant to describe another process. Sparse counts, uncertain kinetic parameters, normalization choices, and isoform effects can also distort a portrait; phase separation should be considered alongside those sources of uncertainty.
Worked Example: A Phase-Dependent Sign in One Gene
Suppose a hypothetical gene has fitted rates \(\beta_g=0.80\) per hour and \(\gamma_g=0.50\) per hour. The following are representative normalized expression values for three hypothetical cells, one in each annotated phase. Assume for this calculation that the rates apply to all three cells and that the normalization is comparable across them.
For the G1 cell, \(u=2\) and \(s=8\), so \(v=(0.80)(2)-(0.50)(8)=1.60-4.00=-2.40\) normalized spliced-expression units per hour. For the S-phase cell, \(u=5\) and \(s=6\), so \(v=(0.80)(5)-(0.50)(6)=4.00-3.00=1.00\) units per hour. For the G2/M cell, \(u=3\) and \(s=10\), so \(v=(0.80)(3)-(0.50)(10)=2.40-5.00=-2.60\) units per hour.
The fitted velocity is positive for the example S-phase cell and negative for the G1 and G2/M cells. This phase-associated sign pattern warrants checking the gene’s phase portrait and the reliability of its fitted rates. It does not establish that the gene follows a closed cycle, that these three cells are successive observations of one cell, or that the fitted velocities describe developmental progression.
Cell-Level Vector Coherence
A second diagnostic asks whether cell-level velocity vectors point in a direction associated with cell-cycle variation. Put velocities for a cell into a vector \(\mathbf{v}_i\), with each component corresponding to the same gene and using the same gene order across cells. Let \(\mathbf{c}\) be a unit vector representing a cell-cycle-associated direction in that expression space. For example, it may be estimated from phase-associated expression contrasts using a prespecified set of genes. Its construction should be described, and it should not be defined using the very velocity pattern being tested without acknowledging that circularity.
The cosine between \(\mathbf{v}_i\) and \(\mathbf{c}\) measures directional alignment: values near 1 indicate alignment, values near -1 indicate the opposite direction, and values near 0 indicate little linear alignment. A large cosine is a diagnostic clue, not a probability or a test of causation. Check whether alignment is concentrated in particular phases, whether it persists across reasonable gene sets and scaling choices, and whether a distinct component remains.
Worked Example: Measuring Alignment With a Cycle Direction
Consider a hypothetical cell with velocity vector \(\mathbf{v}=(0.60,0.60,0.20)\), in three consistently scaled gene coordinates. Suppose an independently constructed unit cycle direction is \(\mathbf{c}=(1/\sqrt{2},1/\sqrt{2},0)\). The dot product is \(\mathbf{v}^\mathsf{T}\mathbf{c}=0.60/\sqrt{2}+0.60/\sqrt{2}=0.8485\). The velocity norm is \(\sqrt{0.60^2+0.60^2+0.20^2}=\sqrt{0.76}=0.8718\), and the cycle-direction norm is 1.
Thus the cosine is \(0.8485/0.8718=0.9733\). The vector is strongly aligned with the specified cycle direction. Its projection is \(0.8485\mathbf{c}=(0.600,0.600,0)\); subtracting this from \(\mathbf{v}\) leaves \(\mathbf{r}=(0,0,0.20)\), which is orthogonal to \(\mathbf{c}\). This example shows how to quantify the decomposition. It does not show that the residual is biologically meaningful: its interpretation still depends on gene selection, scaling, uncertainty, and the biological question.
Why Pooled Patterns Can Be Misleading
Cell-cycle phase can be associated both with a coordinate used to order cells and with the inferred velocities. Pooling phases may then produce a trend even if there is no corresponding trend within any phase. This is one reason to compare pooled displays with phase-stratified displays. Stratification is informative only where phases have sufficient overlap in the other variables being compared; if one phase occurs only at one end of a state coordinate, within-phase comparisons may be impossible or unstable.
Worked Example: A Pooled Association Without Within-Phase Trends
Suppose a hypothetical analysis gives the following values for an independently defined state coordinate \(x\) and a velocity summary \(v\): G1 cells have \((x,v)=(0,1)\) and \((1,1)\); S-phase cells have \((2,3)\) and \((3,3)\). Within G1, \(v\) is constant as \(x\) changes, so its within-phase slope is 0. Within S phase, \(v\) is also constant, giving a within-phase slope of 0.
Across all four cells, \(\bar{x}=(0+1+2+3)/4=1.5\) and \(\bar{v}=(1+1+3+3)/4=2\). The pooled least-squares slope is \((\sum_i(x_i-\bar{x})(v_i-\bar{v}))/(\sum_i(x_i-\bar{x})^2)\). The numerator is \((-1.5)(-1)+(-0.5)(-1)+(0.5)(1)+(1.5)(1)=4\). The denominator is \(2.25+0.25+0.25+2.25=5\). Therefore the pooled slope is \(4/5=0.80\) velocity units per unit of \(x\).
The pooled positive slope arises because the S-phase cells have both larger \(x\) and larger \(v\) in this example; neither phase has a within-phase slope. This is a constructed illustration of phase composition creating an apparent pooled relationship. It does not establish that any real pooled association is spurious: actual data may contain within-phase trends as well.
A Practical Diagnostic Sequence
Use the following checks together rather than treating any one as decisive. Phase labels and scores are imperfect measurements, and adjustment for phase can remove genuine cycle-related transcription that is itself biologically relevant.
Confirm how phases were assigned, inspect uncertain or mixed assignments, and verify that expression values and gene coordinates are comparably normalized across phases.
Compare distributions of spliced and unspliced expression, model fit, and inferred velocity signs. Look for phase-specific structure, not just an aggregate loop or pooled trend.
Compare velocity vectors with a clearly defined cycle-associated direction. Examine the distribution by phase and test sensitivity to the gene set and scaling.
Where there is adequate overlap, assess whether the pattern remains within phases or after an explicitly stated adjustment. Report what was adjusted and what biological variation that adjustment may remove.
Describe a pattern as phase-associated or cycle-aligned when that is what the diagnostics show. Do not label the remaining component as a validated fate transition on these checks alone.
Choosing Among Diagnostic Approaches
| Approach | What it helps reveal | Main limitation |
|---|---|---|
| Phase-stratified gene phase portraits | Whether a gene’s spliced–unspliced pattern or velocity sign differs across phases | Can be sparse within phase and still depends on the fitted kinetic model |
| Cell-level vector coherence | Whether inferred directions align with a defined cycle-associated direction | Depends on gene selection, scaling, and how the direction is constructed |
| Within-phase comparison | Whether a pooled association is also present among cells in the same phase | Requires adequate sample size and overlap within phases |
| Covariate adjustment | Whether a modeled association persists conditional on measured phase or cycle score | Can remove genuine cycle biology and cannot correct unmeasured or misclassified phase effects by itself |
These approaches answer related but different questions. Portraits focus on gene-level kinetic structure; coherence summarizes a multigene direction; stratification and adjustment ask whether an association persists after accounting for measured phase. Agreement across them strengthens a cautious diagnosis, but does not establish a causal mechanism or validate a transition independently.
Common Mistakes and Limits
- Calling every cycle-associated velocity an artifact. Cell-cycle transcription can be real. The concern is interpreting it as another process without evidence that separates the signals.
- Treating phase separation as proof of a cycle. Different phase-specific point clouds do not show that the sampled cells trace a closed trajectory or that the fitted rates are correct.
- Using a high cosine as a significance result. A cosine is a descriptive alignment measure. Its value depends on the direction, gene set, and scaling; it is not a p-value.
- Assuming adjustment always improves interpretation. Conditioning on phase can remove meaningful variation, and poor phase overlap can make adjusted comparisons unstable.
- Ignoring uncertainty and sparse counts. A visually sharp pattern can be driven by a small number of cells or uncertain rates. Recheck model fit and sensitivity rather than relying on the plot alone.
The central limitation is that cell-cycle diagnostics can identify alignment and phase dependence, but they cannot, by themselves, distinguish every possible biological source of a velocity vector. A careful report states the phase information used, the diagnostics performed, the assumptions they require, and the uncertainty that remains.
Check Your Understanding
Answer each question, then compare your reasoning with the solutions.
- If \(\beta_g=0.6\), \(\gamma_g=0.2\), \(u=4\), and \(s=8\), what is the fitted velocity and its sign?
- A velocity vector has cosine 0.05 with a specified unit cycle direction. What does this say, and what does it not say?
- Why can a pooled association between a state coordinate and velocity occur when the within-phase slopes are zero?
- Name two reasons that phase adjustment could fail to clarify velocity interpretation.
Solutions. (1) \(v=(0.6)(4)-(0.2)(8)=2.4-1.6=0.80\) normalized spliced-expression units per unit time, positive under the stated model. (2) The vector has little linear alignment with that particular cycle direction. This does not show that cell-cycle effects are absent; another direction, gene set, or nonlinear phase pattern may matter. (3) If phases differ in both their average coordinate and their average velocity, pooling combines those between-phase differences. The pooled slope can be nonzero even when velocity does not vary with the coordinate within either phase. (4) Adjustment may remove genuine cycle-related transcription, and poor overlap or few cells within phases can make conditional comparisons unstable. Incorrect phase assignments are another possible limitation.