PerturbMap: Cross-Context Transfer of Single-Cell Perturbation Responses

Technical Summary of PerturbMap: Cross-Context Transfer of Single-Cell Perturbation Responses

1. Problem Definition

The paper addresses a specific gap in single-cell perturbation atlases: the "source-observed, recipient-unmeasured" scenario. In many biological screens, a genetic perturbation $p$ is measured in one or more source contexts (e.g., specific cell states or conditions) but is missing in a target "recipient" context where a researcher needs to understand its effect.

The core challenge is selective trust. Simply copying the measured source response to the recipient context ignores context-specific rewiring of transcriptional programs. Conversely, ignoring the source data discards valuable experimental evidence about the specific query intervention. The goal is to predict the control-relative response vector $y_r(q)$ in a recipient context $r$ for a query perturbation $q$, given:

1. Measured source responses $\{y_s(q)\}$ for the same $q$ in source contexts $s$.
2. Paired training data of other perturbations observed in both source and recipient contexts.
3. Strict constraints where the recipient outcome for the query is sealed (unavailable) during model training and inference.

This differs from standard unseen perturbation prediction (e.g., scGen, GEARS) which generalizes from perturbation identifiers; here, the input includes the actual measured response of the query in a different context.

2. Methodology: PerturbMap

PerturbMap is a train-only reliability-weighted response transport framework. It operates under a strict identity-held split, ensuring that no information from the test identities leaks into the model fitting. The workflow consists of four main modules:

A. Train-Only Response Coordinates
The method first constructs a shared, low-rank coordinate system using only training perturbations. It fits a rank-$K$ basis (via QR iterations) to the training response matrix $Y^{tr}$, excluding held recipient rows. This shared basis serves as the coordinate system for the base predictor, source tokens, and route maps.
$$z_c(p) = (y_c(p) - \mu)U^\top$$

B. Recipient-Local Base Predictor
A local base predictor $b_r(p)$ is trained on the recipient context using only the perturbation descriptor (e.g., correlations with control-anchor genes) and the shared low-rank basis. Crucially, this base model receives no query-specific source-response tokens. It serves as the fallback prediction if source transport is deemed unreliable.

C. Source-to-Recipient Experts
For each observed source context $s$, an affine ridge regression map is fitted to transform source coordinates to recipient coordinates using paired training perturbations.
$$A_{s \to r} = \arg \min_A \| \tilde{Z}_s A - \tilde{Z}_r \|_F^2 + \lambda \eta_s \|A\|_F^2$$
This creates an "expert" that can project a query's measured source response $y_s(q)$ into the recipient coordinate space.

D. Train-Only Reliability Calibration
Before predicting held queries, the method estimates the reliability of each source-to-recipient route using a disjoint set of validation anchors (training perturbations held out for validation).

1. Interpolation Coefficient ($\alpha$): Determines how much to blend the expert prediction with the base prediction.
2. Route Score ($\rho$): Calculates the relative reduction in validation MSE achieved by the route compared to the base.
3. Harm-Control Gate (Ablation): A secondary low-capacity logistic model estimates the probability that a specific route will reduce error for a specific query, based on features like query distance to training descriptors and route residuals.

Final Prediction:
The final prediction is a weighted combination of the base predictor and accepted source experts. The weights are determined by the validation-derived route scores ($\rho$) and, in the ablation version, the query-adaptive harm-control probability.
$$\hat{y}_r(q) = \sum_{s} w_{s \to r}(q) \cdot c_{s \to r}(q)$$
where $c_{s \to r}(q)$ is the blended prediction from source $s$.

3. Key Contributions

1. Problem Formulation: Defined "source-observed, recipient-unmeasured" perturbation response prediction as an identity-held test, distinguishing it from standard unseen perturbation generalization.
2. PerturbMap Algorithm: Introduced a method that maps source response tokens into recipient coordinates using train-only reliability weighting. It decides which routes influence a query based on validation residuals rather than query identity.
3. Rigorous Evaluation: Evaluated the method on a manifest-backed Perturb-CITE-seq melanoma cohort (Frangieh et al.) with:
   • Identity-held outer folds (40 test identities per fold).
   • Information-matched controls (zero-response, raw-copy, calibrated-copy, shuffled-affine).
   • A stronger centralized reference (TokPool) for performance ceiling comparison.
   • Explicit reporting of "harm rates" (instances where the method performs worse than the baseline).
4. Ablation Studies: Investigated query-adaptive harm control and operating point sensitivity (rank, anchor caps, aggregation rules).

4. Experimental Results

The primary evaluation was conducted on the Frangieh et al. melanoma cohort with three contexts (Co-culture, Control, IFN$\gamma$).

• Performance Gain: PerturbMap-GR (Global Route reliability) reduced the full-effect Mean Squared Error (MSE) by 4.1% (from $1.649 \times 10^{-3}$ to $1.581 \times 10^{-3}$) compared to the recipient-local LowRank base.
• Statistical Significance: The paired 95% confidence interval for the MSE reduction was $[-1.16, -0.33] \times 10^{-4}$, excluding zero. It improved predictions for 161 out of 200 held identities.
• Comparison to Baselines:
  • Outperformed FedAvg, Zero-response, Raw-copy, and Calibrated-copy.
  • Outperformed Shuffled-affine controls, confirming that the gain comes from aligned source-recipient pairing, not just marginal calibration.
  • Remained within $2.82 \times 10^{-6}$ MSE of the centralized TokPool reference, which has access to a stronger training interface.
• Secondary Metrics:
  • Top-20 absolute-effect MSE improved by ~12% over copy controls.
  • Cosine-based top-10 retrieval (relative to LowRank) increased from 74.5% to 80.5%.
  • Harm rate (relative to LowRank) was 19.5%, significantly lower than 49.5% for raw copy.
• Secondary Check: On a separate Jiang et al. multi-source Perturb-seq cohort, reliability weighting showed a small but significant gain over uniform expert fusion, validating the approach in a richer source setting.

5. Significance and Claims

The paper modestly claims that measured source responses can serve as query-time evidence to fill missing recipient effects, provided the transfer is guided by train-only reliability estimates.

• Core Claim: Identity-aligned source responses provide predictive information beyond recipient-only behavior, direct copying, or marginal calibration.
• Limitations: The authors explicitly state that PerturbMap does not eliminate negative transfer (it still harms ~19.5% of identities relative to the base) and is not a state-of-the-art virtual-cell generator for full distributional counterfactuals. It predicts condition-mean effects, not within-condition single-cell distributions.
• Implication: The method demonstrates that "reuse without erasing context" is possible through selective, validation-driven transport, offering a practical solution for incomplete perturbation atlases without requiring a centralized pooled training interface.