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Cross-modality Matching and Prediction of Perturbation Responses with Labeled Gromov-Wasserstein Optimal Transport

Jayoung Ryu, Charlotte Bunne, Luca Pinello, Aviv Regev, Romain Lopez

TL;DR

This work addresses cross-modality alignment and predictive modeling of perturbation responses in single-cell data. It extends Gromov-Wasserstein OT (GWOT) and Co-Optimal Transport (COOT) to incorporate perturbation labels, defining labeled GWOT (Labeled EGWOT) and labeled COOT with label-compatible couplings and Sinkhorn-based optimization. The authors provide definitions, algorithmic updates, and complexity analyses showing substantial per-iteration speedups when using $L$ perturbation labels, enabling scalable cross-modality matching and prediction. Applied to a multi-modal perturbation dataset (RNA and protein), the approach achieves improved cross-modality alignment and RNA-perturbation prediction, enabling unified causal models of cell biology across readouts.

Abstract

It is now possible to conduct large scale perturbation screens with complex readout modalities, such as different molecular profiles or high content cell images. While these open the way for systematic dissection of causal cell circuits, integrated such data across screens to maximize our ability to predict circuits poses substantial computational challenges, which have not been addressed. Here, we extend two Gromov-Wasserstein Optimal Transport methods to incorporate the perturbation label for cross-modality alignment. The obtained alignment is then employed to train a predictive model that estimates cellular responses to perturbations observed with only one measurement modality. We validate our method for the tasks of cross-modality alignment and cross-modality prediction in a recent multi-modal single-cell perturbation dataset. Our approach opens the way to unified causal models of cell biology.

Cross-modality Matching and Prediction of Perturbation Responses with Labeled Gromov-Wasserstein Optimal Transport

TL;DR

This work addresses cross-modality alignment and predictive modeling of perturbation responses in single-cell data. It extends Gromov-Wasserstein OT (GWOT) and Co-Optimal Transport (COOT) to incorporate perturbation labels, defining labeled GWOT (Labeled EGWOT) and labeled COOT with label-compatible couplings and Sinkhorn-based optimization. The authors provide definitions, algorithmic updates, and complexity analyses showing substantial per-iteration speedups when using perturbation labels, enabling scalable cross-modality matching and prediction. Applied to a multi-modal perturbation dataset (RNA and protein), the approach achieves improved cross-modality alignment and RNA-perturbation prediction, enabling unified causal models of cell biology across readouts.

Abstract

It is now possible to conduct large scale perturbation screens with complex readout modalities, such as different molecular profiles or high content cell images. While these open the way for systematic dissection of causal cell circuits, integrated such data across screens to maximize our ability to predict circuits poses substantial computational challenges, which have not been addressed. Here, we extend two Gromov-Wasserstein Optimal Transport methods to incorporate the perturbation label for cross-modality alignment. The obtained alignment is then employed to train a predictive model that estimates cellular responses to perturbations observed with only one measurement modality. We validate our method for the tasks of cross-modality alignment and cross-modality prediction in a recent multi-modal single-cell perturbation dataset. Our approach opens the way to unified causal models of cell biology.
Paper Structure (45 sections, 3 theorems, 78 equations, 7 figures, 7 tables, 3 algorithms)

This paper contains 45 sections, 3 theorems, 78 equations, 7 figures, 7 tables, 3 algorithms.

Table of Contents

  1. INTRODUCTION
  2. RELATED WORK
  3. Gromov-Wasserstein Optimal Transport
  4. Optimal Transport with Additional Structure
  5. Domain Adaptation via Representation Matching
  6. METHOD
  7. Notation
  8. Labeled Entropic-regularized GWOT
  9. Definition
  10. Algorithm
  11. Computational Complexity
  12. Labeled COOT
  13. Definition
  14. Algorithm
  15. Computational Complexity
  16. ...and 30 more sections

Key Result

Lemma 3.0

For a label-identity matrix $B^l$, the $l$-compatible entropic optimal transport plan can be expressed as $\textrm{diag}(u)(e^{-C/\epsilon}\odot B^l) \textrm{diag}(v)$, where $\odot$ denotes element-wise multiplication.

Figures (7)

  • Figure 1: Schematic of the proposed computational workflow.
  • Figure 2: UMAPs of cells treated with one of the kinase inhibitors (AZD1480) with varying dosages
  • Figure 3: UMAPs of predicted RNA modality of AZD1480 with varying dosages.
  • Figure 4: Examples of EOT and $l$-compatible EOT coupling matrices through Sinkhorn iterations. (a) Histogram of $x$ and $y$ (b) Cost matrix (c) Coupling matrices along EOT Sinkhorn iterations (b) Coupling matrices along Sinkhorn iterations for $l$-compatible EOT where $l^x=\{\mathbf{1}(x_i>0)\}, l^y=\{\mathbf{1}(y_j>0)\}$ (d) Coupling matrices along Sinkhorn iterations for $l$-compatible EOT where $l^x=\{\mathbf{1}(x_i<2)\}, l^y=\{\mathbf{1}(y_j>0)\}$.
  • Figure 5: UMAPs of each modality for the cells treated with the selected 13 kinase inhibitors.
  • ...and 2 more figures

Theorems & Definitions (6)

  • Lemma 3.0
  • Corollary 3.1
  • Remark 3.2
  • Remark 3.3
  • Lemma B.0
  • proof