99 SMALL PROBLEMS · No. 02 EXTENSION PREVIEW · v0.2.0-alpha
Coexpression Check
Two targets. Same cells?
Audit what “expression-matched” actually preserves. Compare same-cell pairing, bound what separate measurements cannot identify, and locate the next mechanistic question.
What the measurements establish
| Marginal quantity | A | B | CDF separation |
|---|
| Quadrant / fraction | A | B | B − A |
|---|
Same marginals. Inspect the pairing.
Population A · circles
Population B · squares
Log₁₀(value + 1) display only. Marker area encodes event weight in display bins; exact input pairs, not bins, drive calculations. Coordinates do not represent physical cell positions.
Where the cutoff choice matters
Exact calculations at 51 × 51 selected cutoffs. A grid is not a global equivalence test.
What the response assumption changes
| Dimensionless hypothetical score | A | B |
|---|
Independence removes same-cell association; mean-only scoring also removes marginal heterogeneity. Neither is a measured response. Product-score pairing effect = Cov(u,v); either-route pairing effect = −Cov(u,v).
Keep the result reproducible
JSON includes original event multiplicities, settings, evidence notes and limitations. Exports may contain sensitive user-supplied data. No p-values, confidence intervals or efficacy estimates.
Why the pairing matters
A synthetic schematic, not observed cells. Both populations have 50% X-high and 50% Y-high.
Only A places both targets on the same cells. Separate histograms permit either arrangement; they cannot select between them.
WHY THIS SMALL PROBLEM MATTERS
Different pairing is not yet a therapeutic advantage.
In the synthetic example above, A has more double-high cells; B has more either-high cells. A joint-required rule favors A, an either-sufficient rule favors B, and an additive rule with matched marginal contributions gives a tie. The value of the audit is exposing that dependence, not choosing a winner without a mechanism.
When the audit should change your next experiment
- Matched marginals, different pairing: same-cell organization remains an alternative explanation for a response difference. Test engagement in the relevant subpopulations before attributing the difference solely to construct activity.
- Separate measurements, wide bounds: collect paired observations if coexistence matters. More unpaired events do not identify the missing pairing.
- Cutoff-sensitive conclusions: investigate calibration and cutoff purpose. A positivity gate is not a demonstrated functional threshold.
- Comparable expression, different response: examine engagement, processing, active payload and susceptibility. This audit does not distinguish those downstream causes.
Proposed experimental decision rules, not automated biological diagnoses. No significant difference, equivalence margin or efficacy ranking is inferred.
When pairing does not add information
For an exactly additive response a(X) + b(Y), matched marginal distributions imply matched expected scores regardless of pairing. Nonlinear single-axis behavior is not enough: a nonseparable interaction is what makes the joint distribution potentially consequential.
The optional product and either-route scores test two such assumptions. Neither is assigned by the word “bispecific,” and neither establishes the physical engagement state.
Read the scientific argument, mathematical decomposition and literature synthesis. This is a descriptive comparability audit with mechanistic context, not a dynamic ADC model.
Challenge the next inference in the separate lower-uptake, higher-productive-delivery worked example. It follows invented input fluxes through routing, processing and cytosolic escape, without inferring rates from expression or predicting efficacy.
THE TOOL, NOT THE ORACLE
Recognition is an address, not a completed delivery.
This analysis compares target distributions. It does not establish productive delivery or cell killing.
Conceptual route map, not a complete kinetic model. Alternative release routes and construct-specific antibody effects require separate evidence. Solid paths show a possible delivery sequence; dashed paths show competing or additional routes. No arrow is a measured rate.
Record the evidence behind the proposed mechanism
Optional, user-reported metadata only. “User-reported measurement” is not software verification. Missing evidence is not evidence of biological failure. This panel never produces a confidence or efficacy score.
Trafficking and susceptibility: Hunter et al., 2020. Specific lysosomal catabolite transport: Tomabechi et al., 2022. Distribution versus per-cell uptake: Cilliers et al., 2018. Extracellular release: Dal Corso et al., 2017.
What the next model must explain
For intracellular processing, spatial transport, population-specific payload exposure and bispecific engagement, read the annotated mechanistic modeling guide. It distinguishes calibration from independent testing and maps each paper to a possible future module.
Start with Maass et al., 2016, Khera et al., 2018 and Scheuher et al., 2024 (online 2023). These dynamic models are not implemented by this descriptive audit.
A small calculation.
A deliberately large boundary.
Matched antigen distributions do not establish matched accessible epitopes, tissue exposure, productive processing, payload susceptibility or response history. A more elaborate claim needs more than another expression column.
Read the paired model and mathematics · Download the calculation code · Read the full extension specification
Product = uv and either-route = u + v − uv are declared mathematical scenarios. Neither is assigned automatically to a bispecific format. Biparatopic binding to one receptor is not two independently measured antigen axes.
Useful models for assumptions with expensive ambitions.