scDRP: Disentangled representation learning for predicting single-cell responses to perturbations and estimating individual treatment effects

Technical Summary of scDRP: Disentangled Representation Learning for Predicting Single-Cell Responses to Perturbations

1. Problem Statement

Single-cell sequencing technologies (e.g., Perturb-seq, sci-Plex) enable large-scale profiling of gene regulatory circuits under various chemical or genetic perturbations. However, these experiments are inherently destructive, providing only unmatched snapshots of cells under different conditions. Consequently, it is impossible to observe the same cell before and after a perturbation, creating a fundamental barrier to estimating Individual Treatment Effects (ITEs)—the specific causal response of a single cell to a treatment.

Existing methods face two primary limitations:

• Population-Average Focus: Frameworks like scGEN predict average population responses, obscuring the heterogeneity crucial for understanding complex systems like organoids where subpopulations respond differently.
• Overly Strong Assumptions: Methods like CINEMA-OT assume perturbation-induced signals are completely independent of confounders (e.g., cell type) and rely on linear combinations, neglecting complex nonlinear relationships and interactions governing cellular responses.

The challenge is to infer counterfactual states (how a control cell would respond to a perturbation) and estimate ITEs from unmatched population data while accounting for cell-type-specific heterogeneity and nonlinear dynamics.

2. Methodology: The scDRP Framework

The authors propose scDRP, a generative framework that combines disentangled representation learning with conditional optimal transport (OT) to infer ITEs.

A. Disentangled Latent Representation
scDRP models the high-dimensional gene expression profile ($x$) as a function of low-dimensional latent variables ($z$), structured into two conditionally independent subspaces:

1. Perturbation-Invariant Identity ($z_u$): Captures stable intrinsic properties (e.g., cell type, maturation stage) and confounders ($w$).
2. Perturbation-Induced Response ($z_d$): Captures variation induced by the perturbation ($a$) and confounders.

To learn this separation, scDRP employs a $\beta$-Variational Autoencoder ($\beta$-VAE) regularized by:

• Hilbert–Schmidt Conditional Independence Criterion (HSCIC): Enforces strict conditional independence between $z_u$ and $z_d$ given confounders $w$.
• Gated $L_0$ Norm: Encourages sparsity to select optimal latent dimensions and ensure identifiability.

B. Conditional Optimal Transport for Counterfactual Matching
To generate counterfactual predictions, scDRP must match control cells to their "twin" counterparts in the perturbed group. The framework operates under the rank-preserving assumption: within a homogeneous subpopulation (conditioned on $w$ or $z_u$), a perturbation shifts the distribution of responses but preserves the relative rank (quantile) of individual cells.

This matching is formulated as a Conditional Optimal Transport problem in the disentangled latent space. The goal is to find an optimal coupling matrix $\Gamma^*$ that minimizes the transport cost:
$$C(z_s, z_t) = \alpha \|z_s^u - z_t^u\|_2^2 + \beta \|z_s^d - z_t^d\|_2^2$$

• The first term ($\alpha$) acts as a soft constraint ensuring matched cells share similar intrinsic identities.
• The second term ($\beta$) is the transport cost on the response space, equivalent to quantile matching in one dimension.

Once the optimal coupling is found, barycentric projection is used to generate counterfactual latent states ($\tilde{z}$), which are then decoded to estimate the ITE ($\hat{\tau} = \tilde{x} - x$).

C. Downstream Analysis and Generalization

• Biclustering: The estimated ITE matrix is analyzed using biclustering (BCPlaid) to identify Functional Gene Modules (FGMs)—groups of genes and cells exhibiting specific response patterns.
• Unseen Doses: For unobserved perturbation doses, scDRP uses Gaussian Process regression on the latent space to interpolate mean and variance of $z_d$, followed by residual correction to generate counterfactuals.
• Combinatorial Effects: The framework infers the magnitude of combined perturbation effects by treating individual ITEs as vectors and applying vector composition (parallelogram law), though it can only estimate the absolute magnitude, not the direction (up/down-regulation).

3. Key Results

The paper validates scDRP through simulations and four real-world datasets (Kang et al., Dong et al., Hagai et al., Norman et al.):

• Simulation Performance: scDRP consistently outperforms CINEMA-OT and scGEN in estimating ITEs and Conditional Average Treatment Effects (CATEs), particularly in nonlinear settings and when cell-type labels are unknown. It accurately recovers ground-truth pairings and latent disentanglement.
• Real Data Prediction: On real datasets, scDRP generates counterfactual distributions that closely overlap with observed treatment distributions (high PCC, low RMSE, low MMD), whereas other methods show substantial gaps.
• Biological Insights:
  • Rhinovirus & Cigarette Smoke: Re-analysis of bronchial organoid data revealed fine-grained patterns, identifying distinct FGMs for ciliary biogenesis and cell-cycle progression that were missed by previous linear analyses.
  • Interferon Stimulation: In PBMCs, scDRP resolved heterogeneous immune responses, linking specific cell types (e.g., CD4+ T cells, monocytes) to distinct functional modules (e.g., antiviral defense, apoptosis, metabolic regulation).
  • CRISPR Perturbations: In K562 leukemia cells, the method identified dominant functional modules (MHC I antigen presentation) and specific gene-driven divergences (e.g., KLF1 linking oxidative stress to differentiation).
• Generalization: The model successfully interpolated dose-response curves for unseen chemical doses and estimated the magnitude of combinatorial treatment effects.

4. Significance and Claims

The authors claim that scDRP provides a principled computational approach to extracting heterogeneous causal relationships from single-cell perturbation data. Its significance lies in:

• Theoretical Rigor: It establishes rigorous assumptions for counterfactual matching using conditional OT, moving beyond heuristic approaches.
• Biological Resolution: By disentangling identity from response, it enables the discovery of cell-type-specific functional gene modules and heterogeneous mechanisms that population-average methods obscure.
• Versatility: The framework generalizes to unseen perturbation doses and combinations, facilitating in silico perturbation screening and rational therapeutic target discovery.

The paper acknowledges limitations, noting that the disentanglement relies on identifying assumptions (conditional independence) that cannot be verified from observational data alone, and that combinatorial inference currently recovers only effect magnitude, not direction. Future work is suggested to incorporate temporal/spatial modalities and extend to other data types like scATAC-seq.