PaperlayerView exact revision on arXiv

Source-linked AI summary

PopPert: Population-level Joint-Distribution Modeling for Single-Cell Perturbation Prediction

Handong Wang, Jiaxin Qi, Haochen Feng, Baisheng Lai

arXiv:2609.01357v1q-bio.GNcs.AI

TL;DR

Single-cell perturbation prediction must operate on unpaired control and perturbed populations, while independent-gene modeling misses coordinated regulation. PopPert learns perturbation-induced changes in population-level joint distributions with a low-rank Gaussian Copula, and it consistently outperforms competing approaches across core benchmark objectives.

  • Problem

    Single-cell RNA sequencing produces unpaired populations, conflicting with methods that assume cell-to-cell correspondence; accurate prediction of unseen perturbation responses remains important for extending experimental screens.

  • Method

    PopPert predicts shifts in population-level marginal and joint gene-expression distribution parameters using a low-rank Gaussian Copula, then samples synthetic perturbed profiles.

  • Results

    PopPert consistently outperforms state-of-the-art approaches across differential-expression recovery, perturbation-effect estimation, and population-level distribution matching on genetic and chemical benchmarks.

  • Takeaways & Limitations

    Population-level joint distribution learning provides an effective paradigm for predicting transcriptional responses from unpaired single-cell populations.

  • Takeaways & Limitations

    The framework requires population-level pairing between input and target populations, although it eliminates cell-to-cell correspondence.

Abstract

from arXiv · show

Predicting transcriptional responses to specific perturbations is critical for understanding cellular regulatory mechanisms and accelerating drug discovery. Single-cell RNA sequencing destroys each measured cell, yielding only unpaired populations of control and perturbed cells. However, existing methods typically model perturbation prediction at the single-cell level and assume cell-to-cell correspondence, which conflicts with the unpaired nature of the observed data. To address this challenge, we propose PopPert, a framework that explicitly parameterizes population-level joint gene expression distributions for collective transcriptional state modeling. Given a control population distribution and a perturbation condition, PopPert predicts perturbation-induced changes in distribution parameters, eliminating the need for cell-level correspondence and reducing sensitivity to single-cell noise. To effectively capture gene co-expression patterns, PopPert leverages a low-rank Gaussian Copula to model cross-gene statistical dependencies and construct the joint gene expression distribution, additionally allowing sampling of synthetic perturbed single-cell profiles. Across multiple single-cell benchmarks spanning both genetic and chemical perturbations, PopPert achieves superior overall performance in differential expression recovery, perturbation effect estimation, and population-level distribution matching. These results establish population-level joint distribution learning as an effective paradigm for predicting transcriptional responses from unpaired single-cell populations. Code for PopPert is publicly available at https://github.com/whd1125/PopPert.

1 Introduction

PopPert addresses the unpaired nature of single-cell perturbation data and the need to model coordinated gene regulation. It predicts population-level joint-distribution changes and uses a low-rank Gaussian Copula to represent gene dependencies.

  • Motivation: Single-cell RNA sequencing destroys measured cells, so most single-cell prediction methods cannot rely on true cell-to-cell matched data.Existing approaches use random pairing, soft cell-level mappings, or population-level losses, but still require learning single-cell perturbation mappings.
  • Motivation: Treating genes independently can destroy perturbation-induced correlation structures and increase overfitting to technical noise.Coordinated gene regulation produces inter-gene dependencies associated with distinct biological processes.
  • PopPert: PopPert predicts perturbation-induced changes in population-level joint gene expression distributions rather than cell-level correspondences.It parameterizes marginal and joint distributions, predicts their shifts under treatment, and samples perturbed profiles from the predicted state.
  • PopPert: A full G × G Gaussian-Copula correlation matrix has O(G^2) complexity, so PopPert introduces a low-rank representation for practical scRNA-seq datasets.The low-rank Gaussian Copula compactly encodes dependence while coupling gene-level marginal distributions.
  • Evaluation: PopPert is evaluated on genetic and chemical perturbation benchmarks using differential-expression recovery, perturbation-effect estimation, and population-level distribution matching.The paper reports consistent outperformance across most evaluated metrics and methods.

2 Related Work

Related work primarily predicts perturbation responses through single-cell latent transformations, population alignment, transport maps, or conditional generative processes. These approaches differ in how they represent perturbations and supervise prediction.

  • Single-cell approaches: scGen, CPA, and GEARS learn single-cell state shifts using latent-space arithmetic, disentangled perturbation representations, or gene-network knowledge.GEARS specifically targets generalization to unseen genetic perturbations.
  • Population and generative approaches: STATE and scDFM combine perturbation prediction with population-distribution alignment objectives.STATE uses a distributional discrepancy, while scDFM combines conditional flow matching with population alignment.
  • Population and generative approaches: CellOT learns an optimal-transport map, whereas CellFlow uses conditional flow matching to generate perturbed cells.The related methods therefore span both transport-based and generative-process formulations.

3 Method

PopPert represents each cell population with gene-wise marginal distributions and a low-rank cross-gene dependence state, then predicts perturbation-induced state changes from population-level controls and context. It trains on context-matched population batches and can generate synthetic perturbed profiles from the predicted joint distribution.

  • Population-state construction: PopPert maps a control expression matrix into a population state containing gene-wise marginal distributions and a low-rank cross-gene dependence state.The state is written as Sctrl = (Θctrl, sctrl), with Θ representing gene-wise marginals and s encoding joint dependence.
  • Population-level perturbation prediction: A Transformer Decoder predicts perturbed marginal and dependence states from the control population state, perturbation, cellular context, and pretrained gene information.Gene marginal states and the dependence state are encoded as tokens, while perturbation and context information are fused through cross-attention with separate prediction heads.
  • Gene expression generation: The generator samples synthetic perturbed cells by combining predicted marginal and dependence states through the Gaussian copula.It produces a virtual perturbed population with M generated cells by sampling correlated quantiles and applying inverse marginal CDFs.
  • Population-state construction: Each gene’s marginal state is fitted with a zero-inflated K-component truncated Gaussian mixture, while alternative families such as ZINB are also supported.A point mass models zero expression and truncated Gaussian components model positive expression values.
  • Population-state construction: PopPert uses a low-rank Gaussian copula to couple gene marginals and represent cross-gene dependence compactly instead of retaining an O(G^2) correlation matrix.The model transforms observations through fitted marginal CDFs and Gaussian quantiles, then estimates factor strengths for shared dependence directions.
  • Population-level perturbation prediction: Training groups cells by perturbation and context into fixed-size batches and requires only population-level pairing between perturbed batches and context-matched controls.The combined training loss matches predicted marginal and dependence states to target population states, eliminating reliance on cell-to-cell correspondences.

4 Experiments

PopPert is evaluated on held-out genetic and chemical perturbations using gene-recovery, effect-estimation, and distributional metrics, with strong performance across benchmarks and design variants.

  • Datasets, baselines, and metrics: Evaluation uses held-out perturbations across Replogle, Adamson, Norman, and sci-Plex3, comparing PopPert with competitive genetic and chemical-perturbation baselines.Metrics include DE-gene overlap, PR-AUC, Pearson-∆, EMD, Energy Distance, MAE, and MSE.
  • Genetic perturbation results: PopPert achieves the best performance in 18 of 24 dataset–metric combinations on unseen genetic perturbation prediction.The comparison covers the Replogle, Adamson, and Norman datasets.
  • Genetic perturbation results: 36.0% lower MSE and 14.1% lower MAE on Replogle accompany a Pearson-∆ increase from 0.407 to 0.966.The corresponding MSE changes from 0.00788 to 0.00504, and MAE from 0.0548 to 0.04706.
  • Chemical perturbation generalization: PopPert ranks first on four of eight chemical-perturbation metrics and second on the remaining four for nine held-out sci-Plex3 drugs.It ranks first for Overlap@200, Pearson-∆, EMD, and MSE.
  • Ablation study: K = 2 performs best on five of six metrics, nonzero copula ranks outperform the marginal-only variant, and residual prediction consistently improves results.Performance differences among ranks 8, 16, 32, and 64 are small and non-monotonic.

5 Conclusion

PopPert reframes perturbation prediction as population-level joint distribution learning for unpaired single-cell populations and combines marginal modeling with a low-rank Gaussian copula.

  • Conclusion: PopPert eliminates the need for unobserved cell-level one-to-one correspondence by learning population-level joint gene expression distributions.The framework models transcriptional heterogeneity and pairwise gene dependencies while using control-referenced residual updates.
  • Conclusion: Experiments on genetic and chemical benchmarks show consistent gains in DE-gene recovery, perturbation effect estimation, and multivariate population alignment.The conclusion identifies these as the three core evaluation objectives.
  • Conclusion: Future work includes context-dependent factor loadings, more expressive copulas for nonlinear dependencies, and calibrated uncertainty estimates.These directions extend the model beyond fixed shared loadings and its current copula family.

A.1 Datasets and Splits

The experiments use fixed held-out perturbation splits across genetic and chemical benchmarks, with expression-space-specific marginal models and matched control batches.

  • Splits: Fixed partitions keep held-out perturbations identical across preprocessing runs and competing methods.
  • Datasets: The benchmarks include Replogle, Adamson, Norman, and sci-Plex3, covering genetic and chemical perturbations.
  • Chemical benchmark: The chemical comparison evaluates nine held-out drugs across A549, K562, and MCF7 using the same held-out conditions, genes, contexts, and target-cell count.
  • Expression spaces: Main experiments fit ZI-GMM marginals to normalized log-transformed expression, while the alternative Norman experiment fits ZINB directly to raw counts.
  • Population state: Each gene’s marginal state is fitted independently from batches of 128 cells, with control and target summaries fixed before neural-network training.
  • Control pairing: PopPert predicts relative to one compatible pre-fitted control batch rather than pooling controls or averaging mixture parameters.
  • Computational boundary: The low-rank formulation reduces population-specific storage and repeated prediction and generation costs, but dense O(G2) storage remains necessary during offline correlation preprocessing.

B.4 Training Loss Function

Training uses pre-fitted target population summaries and jointly optimizes marginal-distribution and dependence objectives.

  • Target cells are summarized through pre-fitted ZI-GMMs, then M = 256 pseudo-observations per gene are drawn for marginal training.
  • The marginal objective averages negative log-likelihood across items, genes, and pseudo-observations to estimate cross-entropies against fitted target ZI-GMMs.
  • The dependence loss is mean squared error between predicted log dependence states and target-population log states, optimized jointly from the first epoch.
  • The reported main results use dependence-loss weight λdep = 0.2 with AdamW optimization and a learning rate of 10^-4.

C Metrics

The evaluation combines differential-expression recovery, perturbation-effect agreement, direct profile errors, and population-distribution distances, aggregated over valid held-out perturbations.

  • Differential expression: Overlap@100/200 and PR-AUC evaluate recovery and ranking of differentially expressed genes.
  • Perturbation effects: Pearson-∆ measures agreement between predicted and observed control-referenced perturbation effects across the matched gene set.
  • Profile errors: MAE and MSE compare predicted and observed perturbed pseudobulk profiles directly without subtracting the control profile.
  • Distribution matching: Gene-averaged EMD measures marginal agreement across genes, whereas Energy Distance measures multivariate population agreement.
  • Aggregation: Dataset-level scores are arithmetic means over perturbations with finite valid scores, with distribution distances requiring at least five cells per population.

D.1 Ablation Study

The ablations show metric-dependent sensitivity to population-batch size and dependence-loss weight rather than a single uniformly optimal configuration.

  • Population-batch size: Population-batch-size performance does not vary monotonically around the default batch size of 128.
  • Dependence-loss weight: Dependence-loss weight rankings vary across all six metrics, so no weight is uniformly dominant.
  • Dependence-loss weight: λdep = 0.2 gives the highest Overlap@200 and lowest MSE and EMD, λdep = 0.5 gives the highest PR-AUC and lowest Energy Distance, and λdep = 0.1 gives the highest Pearson-∆.

D.2 Qualitative Results

The qualitative results compare PopPert-generated perturbed populations with observed populations across representative genetic and drug conditions. They also provide gene-level views of population expression shifts for selected perturbations.

  • Joint-distribution comparisons: The representative comparisons span Replogle genetic perturbations and sci-Plex3 drug conditions.These qualitative examples complement aggregate distributional metrics.
  • Joint-distribution comparisons: Figure D.1 compares control, real perturbed, and PopPert-generated cells in a shared two-dimensional embedding.The figure covers Replogle perturbations in HepG2 and sci-Plex3 drug conditions in MCF7, with generated cells sampled from the predicted joint distribution.
  • Gene-level expression shifts: Figure D.2 orders 20 genes by decreasing absolute observed change from the control mean for UTP15 and CUDC-101.The examples correspond to one Replogle perturbation and one sci-Plex3 drug condition.
  • Gene-level expression shifts: The gene-level plots juxtapose real perturbed distributions and medians with PopPert-predicted means and control means.Blue boxplots show real perturbed distributions, red bars their medians, blue diamonds predicted means, and black dashed lines control means.
Loading 2609.01357v1…