Why a Single Label Can Be Too Certain
A cell-type annotation often assigns each cell one label, such as cell type A or cell type B. That is useful when the observed programs are clearly separated, but a hard label can conceal meaningful structure when cells express markers associated with both types or vary gradually between their characteristic programs. Such observations may be consistent with a transitional state or a continuous phenotype. They do not, by themselves, establish that cells are moving from one state to another over time.
The central interpretive task is therefore to describe what the expression data support without claiming more than they show. Mixed marker programs can reflect biological continuity, a stable hybrid phenotype, or a technical artifact. Evidence that a cell expresses markers from two programs should prompt investigation, not an automatic new label or a claim of transition.
Representing Mixed Programs With Scores
For a focused comparison, let \(G_A\) and \(G_B\) be prespecified marker sets for two cell programs. Let \(Y_{ig}\) denote the normalized, transformed expression value for gene \(g\) in cell \(i\). A simple descriptive score for program A is the mean of the values for its marker genes; define the score for program B in the same way. If genes have first been standardized against a suitable reference population, the scores are on a scale that makes a relative comparison easier.
Here \(Z_{ig}\) is the standardized expression value, and \(|G_A|\) and \(|G_B|\) are the numbers of genes in the two marker sets. A score is a summary of expression, not a probability that the cell belongs to a type. Its meaning depends on the marker selection, normalization, standardization reference, and the genes' behavior in the tissue under study. Scores should not be compared as though they were calibrated probabilities.
A useful descriptive summary separates the balance between programs from their joint level. Define a contrast \(t_i\) and a common-activation coordinate \(m_i\). The contrast is positive when program A has the larger score and negative when B has the larger score. The common-activation coordinate is larger when both scores tend to be high together. Examining both can help distinguish a balanced mixed profile from a cell in which neither signature is strongly expressed.
These coordinates are descriptive, and their assumptions are practical rather than a formal sampling model: the marker sets must be biologically relevant, the expression values must be processed comparably, and the standardization reference must make sense for the cells being compared. If these conditions are not credible, the scores can misrepresent the programs. A cell with low counts, for example, may have unreliable scores even if the arithmetic is correct.
Worked Example: A Cell With Two Elevated Programs
Suppose a hypothetical cell has three standardized markers for each of two programs. Its A-marker values are \(1.4\), \(0.8\), and \(1.0\); its B-marker values are \(1.1\), \(0.9\), and \(0.7\). Assume the marker sets were specified in advance and the standardization reference is appropriate for these cells.
The program scores are:
The contrast and common-activation coordinate are:
The contrast is close to zero, so neither program clearly dominates by this summary; the common coordinate is positive, consistent with both scores being elevated relative to their standardization reference. This is evidence for a mixed expression profile in this scoring scheme, not proof that the cell is transitioning. A comparison with canonical cells, examination of the individual markers, and checks for technical artifacts are still needed.
Why Thresholding Can Hide a Continuum
A hard assignment might label a cell A whenever \(t_i>0\) and B whenever \(t_i<0\). That rule can be useful for a required categorical output, but it changes a graded measurement into a category. Cells with \(t_i=0.02\) and \(t_i=2.0\) receive the same A label, despite very different contrasts. The boundary does not show that the biology itself has a boundary.
The coordinate transformation above makes this loss of information explicit. It is an orthogonal rotation of the pair of scores, so retaining both coordinates preserves the original information. A sign-only label retains much less.
The inverse equations recover both original scores when \(m_i\) and \(t_i\) are kept. Replacing \(t_i\) with only its sign cannot recover its magnitude; it also cannot show how close a cell was to the boundary. Thus, a discrete label may be a convenient summary, but should not be presented as a complete description of cells whose scores vary smoothly.
Worked Example: A Graded Pattern Across Cells
Consider five hypothetical cells in a local neighborhood, summarized by standardized program scores. Assume their ordering is based on their observed expression profiles, not on time.
| Cell | \(S_{iA}\) | \(S_{iB}\) | \(t_i=(S_{iA}-S_{iB})/\sqrt{2}\) |
|---|---|---|---|
| 1 | 2.0 | -1.0 | 2.121 |
| 2 | 1.5 | -0.2 | 1.202 |
| 3 | 0.8 | 0.4 | 0.283 |
| 4 | 0.1 | 1.0 | -0.636 |
| 5 | -0.5 | 1.7 | -1.556 |
For cell 3, for example, \(t_3=(0.8-0.4)/\sqrt{2}=0.283\). Its scores are both positive, and its contrast is smaller than those of cells 1 and 2. Across the five cells, the contrast declines from \(2.121\) to \(-1.556\), with intermediate values rather than an abrupt jump. A sign-based rule assigns cells 1–3 to A and cells 4–5 to B; it hides how close cell 3 is to the boundary and how graded the scores are.
If similarly ordered cells show smooth changes in several relevant genes, this pattern supports describing a graded phenotype in this neighborhood. It still does not establish a temporal transition: the ordering is an expression-based arrangement, not a clock. It is also important to inspect the common-activation coordinate and the underlying genes, because a contrast can change when both programs are weak or when only one marker drives the score.
Checking Whether the Mixed Pattern Is Credible
Before interpreting mixed expression biologically, check whether it is present across multiple markers in individual cells and whether it persists after plausible technical explanations are considered. A score averaged across a cluster can be misleading: one subset may express program A and another subset program B, even if no individual cell expresses both. Conversely, a single high marker can inflate a module score without a coherent program.
Relevant checks include inspecting gene-level expression, library size and other quality measures, known ambient-RNA signatures, and doublet indicators. Also consider whether the markers are specific in the tissue and whether activation, stress, or cell-cycle programs could affect them. These checks do not prove a biological interpretation; they help determine whether the observed pattern is robust enough to describe as a candidate mixed phenotype.
Worked Example: Co-Expression After a Doublet Check
In a hypothetical group of 10 candidate cells, six express multiple detectable markers from both programs. Two of those six also have high doublet indicators. Suppose those two are excluded for a sensitivity check; four of the remaining eight cells still show both programs.
Before exclusion, the observed co-expression fraction is \(6/10=0.60\), or 60%. After exclusion, it is \(4/8=0.50\), or 50%. The mixed pattern therefore remains among the cells without high doublet indicators in this example. This makes a purely doublet-based explanation less compelling, but does not eliminate other explanations, such as ambient RNA or non-specific markers.
The calculation is descriptive, not a population estimate with a stated confidence interval. Ten cells are a small group, and the cells may not be independent biological replicates. The appropriate conclusion is that co-expression persists in this hypothetical check, not that half of a broader cell population has a confirmed transitional state. Replication across donors or samples and examination of the specific marker genes would strengthen the interpretation.
Distinguishing Interpretations and Common Failure Modes
Several descriptions can fit overlapping marker expression, and they should not be treated as interchangeable. A continuum describes graded variation in observed features. A hybrid phenotype describes concurrent programs without requiring a direction of change. A transitional-state interpretation adds a claim that the cells are in the process of changing. Cross-sectional RNA measurements can support the first two kinds of description more directly than the third.
| Approach | What it communicates | Main limitation |
|---|---|---|
| Single discrete label | A concise category, such as A or B | Can conceal intermediate scores and force a boundary |
| Continuous scores or contrasts | Relative program strength and graded differences | Depends on marker choice, scaling, and score quality |
| Hybrid or mixed description | Concurrent evidence for more than one program | Needs cell-level and technical checks; may not imply a stable type |
| Transitional-state interpretation | A proposed biological change between states | Expression snapshots alone do not establish temporal direction |
A common mistake is to call every cell with two detectable marker sets “transitional.” The reasoning is that markers of A and B are both present, therefore the cell must be moving from A to B. The conclusion does not follow: the pattern could instead reflect a stable hybrid, non-specific markers, ambient RNA, or a doublet. The correction is to report the observation first, test plausible alternatives, and reserve the temporal claim for evidence that supports change over time or a well-supported biological progression.
Another failure is to define marker programs and a threshold after inspecting the same cells, then treat the resulting categories as independent confirmation. Marker selection and thresholds should be justified biologically or evaluated in separate data where feasible. Results should also be checked for sensitivity to reasonable choices of markers and preprocessing. A pattern that disappears when one gene is removed may be a fragile signature rather than a coherent program.
Check Your Understanding
Answer each question, then compare your reasoning with the solutions.
- A cell has \(S_{iA}=1.2\) and \(S_{iB}=0.8\). Calculate \(t_i\) to three significant figures and state what its sign indicates.
- Why can a rule that assigns A for \(t_i>0\) conceal meaningful differences between cells?
- Four of eight cells show markers from both programs. What fraction is this, and what can you conclude from it without additional checks?
- Does a smooth change in marker scores across cells establish that the cells changed states over time? Explain.
Solutions: 1. \(t_i=(1.2-0.8)/\sqrt{2}=0.283\). The positive sign means the A score exceeds the B score; it does not establish a definitive A identity. 2. The rule retains only the sign, not the magnitude, so cells with contrasts just above zero and far above zero get the same label. 3. The fraction is \(4/8=0.50\), or 50%. It describes those cells; gene-level checks, technical diagnostics, and appropriate replication are needed before making a broader biological claim. 4. No. A smooth cross-sectional pattern supports graded variation in measured expression, but does not by itself provide temporal direction or prove a transition.