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Cited by 202Single-cell and spatial transcriptomicsGene Regulatory Network AnalysisGene expression and cancer classification

Learning single-cell perturbation responses using neural optimal transport

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Bunne, Charlotte, Stark, Stefan G., Gut, Gabriele, del Castillo, Jacobo Sarabia, Levesque, Mitch, Lehmann, Kjong-Van, Pelkmans, Lucas, Krause, Andreas +1 more·2023·Nature Methods
DOI 10.1038/s41592-023-01969-xPMC PMC10630137

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Abstract

Understanding and predicting molecular responses in single cells upon chemical, genetic or mechanical perturbations is a core question in biology. Obtaining single-cell measurements typically requires the cells to be destroyed. This makes learning heterogeneous perturbation responses challenging as we only observe unpaired distributions of perturbed or non-perturbed cells. Here we leverage the theory of optimal transport and the recent advent of input convex neural architectures to present CellOT, a framework for learning the response of individual cells to a given perturbation by mapping these unpaired distributions. CellOT outperforms current methods at predicting single-cell drug responses, as profiled by scRNA-seq and a multiplexed protein-imaging technology. Further, we illustrate that CellOT generalizes well on unseen settings by (1) predicting the scRNA-seq responses of holdout patients with lupus exposed to interferon-β and patients with glioblastoma to panobinostat; (2) inferring lipopolysaccharide responses across different species; and (3) modeling the hematopoietic developmental trajectories of different subpopulations.

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  • Single-cell foundation models and perturbation predictors support cellular-response forecasting.

    “Single-cell foundation models and perturbation predictors support cellular-response forecasting [48-51].”

    From RSI-Anything: Unlocking Recursive Self-Improvement with World Models (2026) · cites this paper as [51]

    The Main and Methods > Model passages describe CellOT as a single-cell perturbation predictor that forecasts cellular responses. They do not identify it as a foundation model or establish the foundation-model part of the sentence. No page numbers are available in our copy. (LLM, conf=0.85)

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References 74 · Cited by 202

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  1. [2]Liberali P Snijder B Pelkmans L A hierarchical map of regulatory genetic interactions in membrane trafficking Cell 2014 157 1473 1487 10.1016/j.cell.2014.04.029 24906158 · DOI
  2. [3]Battich N Stoeger T Pelkmans L Image-based transcriptomics in thousands of single human cells at single-molecule resolution Nat. Methods 2013 10 1127 1133 10.1038/nmeth.2657 24097269 · DOI
  3. [4]Battich N Stoeger T Pelkmans L Control of transcript variability in single mammalian cells Cell 2015 163 1596 1610 10.1016/j.cell.2015.11.018 26687353 · DOI · Paper page
  4. [5]Gut G Herrmann MD Pelkmans L Multiplexed protein maps link subcellular organization to cellular states Science 2018 361 eaar7042 10.1126/science.aar7042 30072512 · DOI · Paper page
  5. [7]Kramer BA Sarabia del Castillo J Pelkmans L Multimodal perception links cellular state to decision-making in single cells Science 2022 377 642 648 10.1126/science.abf4062 35857483 · DOI
  6. [8]Snijder B Population context determines cell-to-cell variability in endocytosis and virus infection Nature 2009 461 520 523 10.1038/nature08282 19710653 · DOI
  7. [9]Wu F Single-cell profiling of tumor heterogeneity and the microenvironment in advanced non-small cell lung cancer Nat. Commun. 2021 12 2540 10.1038/s41467-021-22801-0 33953163 PMC8100173 · DOI
  8. [10]González-Silva L Quevedo L Varela I Tumor functional heterogeneity unraveled by scRNA-seq technologies Trends Cancer 2020 6 13 19 10.1016/j.trecan.2019.11.010 31952776 · DOI
  9. [11]Li C Single-cell transcriptomics reveals cellular heterogeneity and molecular stratification of cervical cancer Commun. Biol. 2022 5 1208 10.1038/s42003-022-04142-w 36357663 PMC9649750 · DOI
  10. [13]Lotfollahi M Wolf FA Theis FJ scGen predicts single-cell perturbation responses Nat. Methods 2019 16 715 721 10.1038/s41592-019-0494-8 31363220 · DOI · Paper page
  11. [14]Yang KD Predicting cell lineages using autoencoders and optimal transport PLoS Comput. Biol. 2020 16 e1007828 10.1371/journal.pcbi.1007828 32343706 PMC7209334 · DOI
  12. [15]Villani, C. Optimal transport: Old and New Vol. 338 (Springer, 2009).
  13. [16]Lavenant, H., Zhang, S., Kim, Y.-H. & Schiebinger, G. Towards a mathematical theory of trajectory inference. Preprint at https://arxiv.org/abs/2102.09204 (2021). · arXiv
  14. [17]Schiebinger G Optimal-transport analysis of single-cell gene expression identifies developmental trajectories in reprogramming Cell 2019 176 928 943 10.1016/j.cell.2019.01.006 30712874 PMC6402800 · DOI · Paper page
  15. [18]Makkuva, A., Taghvaei, A., Oh, S. & Lee, J. Optimal transport mapping via input convex neural networks. In Proc. 37th International Conference on Machine Learning (eds Daumé III, H. & Singh, A.) 6672–6681 (PMLR, 2020).
  16. [19]Jacob, L., She, J., Almahairi, A., Rajeswar, S. & Courville, A. Adversarial computation of optimal transport maps. Preprint at https://arxiv.org/abs/1906.09691 (2019). · arXiv
  17. [20]Yang, K. D. & Uhler, C. Scalable unbalanced optimal transport using generative adversarial networks. In International Conference on Learning Representations (ICLR, 2019).
  18. [21]Prasad, N., Yang, K. & Uhler, C. Optimal Transport using GANs for Lineage Tracing. Preprint at https://arxiv.org/abs/2007.12098 (2020). · arXiv
  19. [22]Amos, B., Xu, L. & Kolter, J. Z. Input convex neural networks. In Proc. 34th International Conference on Machine Learning (eds Precup, D. & Teh, Y. W.) 146–155 (PMLR, 2017).
  20. [23]Villani, C. Topics in Optimal Transportation Vol. 58 (American Mathematical Soc., 2003).
  21. [25]Cang Z Nie Q Inferring spatial and signaling relationships between cells from single cell transcriptomic data Nat. Commun. 2020 11 2084 10.1038/s41467-020-15968-5 32350282 PMC7190659 · DOI
  22. [26]Demetci P Santorella R Sandstede B Noble WS Singh R SCOT: single-cell multi-omics alignment with optimal transport J. Comput. Biol. 2022 29 3 18 10.1089/cmb.2021.0446 35050714 PMC8812493 · DOI
  23. [27]Huizing G-J Peyré G Cantini L Optimal transport improves cell–cell similarity inference in single-cell omics data Bioinformatics 2022 38 2169 2177 10.1093/bioinformatics/btac084 35157031 PMC9004651 · DOI
  24. [28]Zhang S Afanassiev A Greenstreet L Matsumoto T Schiebinger G Optimal transport analysis reveals trajectories in steady-state systems PLoS Comput. Biol. 2021 17 e1009466 10.1371/journal.pcbi.1009466 34860824 PMC8691649 · DOI
  25. [29]Korotin, A., Egiazarian, V., Asadulaev, A., Safin, A. & Burnaev, E. Wasserstein-2 generative networks. Preprint at https://arxiv.org/abs/1909.13082 (2021). · arXiv
  26. [30]Raaijmakers MI A new live-cell biobank workflow efficiently recovers heterogeneous melanoma cells from native biopsies Exp. Dermatol. 2015 24 377 380 10.1111/exd.12683 25739758 · DOI
  27. [32]Chen S Dissecting heterogeneous cell populations across drug and disease conditions with PopAlign Proc. Natl Acad. Sci. USA 2020 117 28784 28794 10.1073/pnas.2005990117 33127759 PMC7682438 · DOI
  28. [35]Smith MP Inhibiting drivers of non-mutational drug tolerance is a salvage strategy for targeted melanoma therapy Cancer Cell 2016 29 270 284 10.1016/j.ccell.2016.02.003 26977879 PMC4796027 · DOI
  29. [36]Kun E Tsang Y Ng C Gershenson D Wong K MEK inhibitor resistance mechanisms and recent developments in combination trials Cancer Treat. Rev. 2021 92 102137 10.1016/j.ctrv.2020.102137 33340965 · DOI
  30. [39]Hedrich CM Tsokos GC Epigenetic mechanisms in systemic lupus erythematosus and other autoimmune diseases Trends Mol. Med. 2011 17 714 724 10.1016/j.molmed.2011.07.005 21885342 PMC3225699 · DOI
  31. [40]Perez-Bercoff D Sustained high expression of multiple APOBEC3 cytidine deaminases in systemic lupus erythematosus Sci. Rep. 2021 11 7893 10.1038/s41598-021-87024-1 33846459 PMC8041901 · DOI
  32. [41]Mathian A Hie M Cohen-Aubart F Amoura Z Targeting interferons in systemic lupus erythematosus: current and future prospects Drugs 2015 75 835 846 10.1007/s40265-015-0394-x 25940912 · DOI
  33. [42]Rani MS Characterization of β-R1, a gene that is selectively induced by interferon β (IFN-β) compared with IFN-α J. Biol. Chem. 1996 271 22878 22884 10.1074/jbc.271.37.22878 8798467 · DOI
  34. [43]Flier J Differential expression of CXCR3 targeting chemokines CXCL10, CXCL9, and CXCL11 in different types of skin inflammation J. Pathol. 2001 194 398 405 10.1002/1096-9896(200108)194:4<397::AID-PATH899>3.0.CO;2-S 11523046 · DOI
  35. [44]Zhao W Deconvolution of cell type-specific drug responses in human tumor tissue with single-cell RNA-seq Genom. Med. 2021 13 82 10.1186/s13073-021-00894-y PMC8114529 33975634 · DOI
  36. [45]Hagai T Gene expression variability across cells and species shapes innate immunity Nature 2018 563 197 202 10.1038/s41586-018-0657-2 30356220 PMC6347972 · DOI · Paper page
  37. [48]Bunne, C., Krause, A. & Cuturi, M. Supervised training of conditional Monge maps. In Advances in Neural Information Processing Systems (NeurIPS, 2022).
  38. [49]Wilkinson DJ Stochastic modelling for quantitative description of heterogeneous biological systems Nat. Rev. Genet. 2009 10 122 133 10.1038/nrg2509 19139763 · DOI
  39. [51]Bunne, C., Hsieh, Y.-P., Cuturi, M. & Krause, A. The Schrödinger bridge between Gaussian measures has a closed form. In International Conference on Artificial Intelligence and Statistics (AISTATS, 2023).
  40. [52]Somnath, V. R. et al. Aligned diffusion Schrödinger bridges. In Conference on Uncertainty in Artificial Intelligence (UAI, 2023).
  41. [54]Kantorovich, L. On the transfer of masses (in Russian). In Doklady Akademii Nauk, vol. 37 (1942).
  42. [55]Cuturi, M. Sinkhorn Distances: Lightspeed Computation of Optimal Transport. Adv. Neural Inf. Process. Syst. (2013).
  43. [56]Chen, Y., Shi, Y. & Zhang, B. Optimal Control Via Neural Networks: A Convex Approach. International Conference on Learning Representations (2019).
  44. [57]Huang, C.-W., Chen, R. T. Q., Tsirigotis, C. & Courville, A. Convex Potential Flows: Universal Probability Distributions with Optimal Transport and Convex Optimization. International Conference on Learning Representations (2021).
  45. [58]Bunne, C., Meng-Papaxanthos, L., Krause, A. & Cuturi, M. Proximal Optimal Transport Modeling of Population Dynamics. International Conference on Artificial Intelligence and Statistics (2022).
  46. [60]Mokrov, P. et al. Large-Scale Wasserstein Gradient Flows. Adv. Neural Inf. Process. Syst. (2021).
  47. [61]Fan, J., Taghvaei, A. & Chen, Y. Scalable Computations of Wasserstein Barycenter via Input Convex Neural Networks. International Conference on Machine Learning (2021).
  48. [62]Knott M Smith CS On the optimal mapping of distributions J. Optim. Theory Appl. 1984 43 39 49 10.1007/BF00934745 · DOI
  49. [63]Brenier Y Polar factorization and monotone rearrangement of vector-valued functions Commun. Pure Appl. Math. 1991 44 375 417 10.1002/cpa.3160440402 · DOI
  50. [64]Taghvaei, A. & Jalali, A. 2-Wasserstein approximation via restricted convex potentials with application to improved training for GANs. arXiv Preprint arXiv:1902.07197 (2019). · arXiv
  51. [66]Heydari T IQCELL: A platform for predicting the effect of gene perturbations on developmental trajectories using single-cell RNA-seq data PLOS Comput. Biol. 2022 18 e1009907 10.1371/journal.pcbi.1009907 35213533 PMC8906617 · DOI
  52. [67]Tritschler S Concepts and limitations for learning developmental trajectories from single cell genomics Development 2019 146 dev170506 10.1242/dev.170506 31249007 · DOI
  53. [68]Weinreb C Wolock S Tusi BK Socolovsky M Klein AM Fundamental limits on dynamic inference from single-cell snapshots Proc. Natl. Acad. Sci. USA 2018 115 E2467 E2476 10.1073/pnas.1714723115 29463712 PMC5878004 · DOI · Paper page
  54. [69]Lübeck, F. et al. Neural unbalanced optimal transport via cycle-consistent semi-couplings. arXiv preprint arXiv:2209.15621 (2022). · arXiv
  55. [70]Chen W Live-seq enables temporal transcriptomic recording of single cells Nature 2022 608 733 740 10.1038/s41586-022-05046-9 35978187 PMC9402441 · DOI
  56. [71]Shi, Y., De Bortoli, V., Campbell, A. & Doucet, A. Diffusion Schrödinger Bridge Matching. arXiv preprint arXiv:2303.16852 (2023). · arXiv
  57. [72]Tong, A. et al. Conditional flow matching: simulation-free dynamic optimal transport. arXiv preprint arXiv:2302.00482 (2023). · arXiv
  58. [73]Carpenter AE CellProfiler: image analysis software for identifying and quantifying cell phenotypes Genome Biol. 2006 7 1 11 10.1186/gb-2006-7-10-r100 PMC1794559 17076895 · DOI
  59. [74]Snijder B Single-cell analysis of population context advances RNAi screening at multiple levels Mol. Syst. Biol. 2012 8 579 10.1038/msb.2012.9 22531119 PMC3361004 · DOI
  60. [75]Guizar-Sicairos M Thurman ST Fienup JR Efficient subpixel image registration algorithms Opt. Lett. 2008 33 156 158 10.1364/OL.33.000156 18197224 · DOI
  61. [76]Stoeger T Battich N Herrmann MD Yakimovich Y Pelkmans L Computer vision for image-based transcriptomics Methods 2015 85 44 53 10.1016/j.ymeth.2015.05.016 26014038 · DOI
  62. [77]Van der Walt S scikit-image: image processing in Python PeerJ 2014 2 e453 10.7717/peerj.453 25024921 PMC4081273 · DOI
  63. [79]Rybakov, S., Lotfollahi, M., Theis, F. J. & Wolf, F. A. Learning interpretable latent autoencoder representations with annotations of feature sets. bioRxiv (2020).
  64. [80]Peidli, S. et al. scPerturb: Information resource for harmonized single-cell perturbation data. bioRxiv (2022).
  65. [81]Kingma, D. P. & Ba, J. Adam: A Method for Stochastic Optimization. International Conference on Learning Representations (2014).

Authors
Bunne, C., Stark, S. G., Gut, G., del Castillo, J. S., Levesque, M., Lehmann, K.-V., Pelkmans, L., Krause, A., & Rätsch, G.
Affiliations
  • ETH Zurich (CH)
  • SIB Swiss Institute of Bioinformatics (CH)
  • University of Zurich (CH)
Corresponding author
  • Lehmann, Kjong-Van
  • Pelkmans, Lucas
  • Krause, Andreas
  • Rätsch, Gunnar
ORCID
Venue
Nature Methods
Publisher
Springer Science and Business Media LLC
Published
2023-09-28
Volume
20
Issue
11
Pages
1759-1768
ISSN
  • 1548-7091 (ISSN-L)
  • 1548-7105
DOI
10.1038/s41592-023-01969-x
PMC
PMC10630137
OpenAlex
W4387130479
Cited by
202
References
74
Citations by year
2026: 83 · 2025: 81 · 2024: 29 · 2023: 8 · 2022: 1
FWCI
17.91
Type
journal article
Language
en
Update notices
correction (2023-10-30)
Open access
Licence
Locations
  • Nature Methods (publishedVersion, cc-by)
  • bioRxiv (Cold Spring Harbor Laboratory) (acceptedVersion, cc-by-nc)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • Repository for Publications and Research Data (ETH Zurich) (submittedVersion, cc-by-nc)
  • Repository for Publications and Research Data (ETH Zurich) (submittedVersion, cc-by)
  • Zurich Open Repository and Archive (University of Zurich) (submittedVersion, cc-by)
  • ETH Zürich Research Collection
Funders
  • National Science Foundation
  • Chan Zuckerberg Initiative
  • Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (180544, 51NF40, 192622, 310030)
  • Eidgenössische Technische Hochschule Zürich (180544)
  • Universität Zürich
  • Innosuisse - Schweizerische Agentur für Innovationsförderung
  • H2020 European Research Council (885579)
  • NCCR Catalysis
Topics
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Single-cell and spatial transcriptomics
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Gene Regulatory Network Analysis
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Gene expression and cancer classification
Keywords
optimal transport, input convex neural networks, single-cell RNA sequencing, interferon-beta, lupus, panobinostat, glioblastoma, lipopolysaccharide response, hematopoietic development, cross-species generalization
MeSH terms
Humans, Sequence Analysis, RNA, Gene Expression Profiling, Single-Cell Analysis

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