Villani, C. Topics in Optimal Transportation Vol. 58 (American Mathematical Society, 2003).Santambrogio, F. Optimal transport for applied mathematicians. Birkhäuser 55, 94 (2015).
Google ScholarÂ
Figalli, A. The Monge–Ampère Equation and Its Applications (Zurich Lectures in Advanced Mathematics, 2017).Caffarelli, L. A. in Optimal Transportation and Applications. Lecture Notes in Mathematics Vol. 1813 (Springer, 2003).Schiebinger, G. et al. Optimal-transport analysis of single-cell gene expression identifies developmental trajectories in reprogramming. Cell 176, 928–943.e22 (2019). By computing consecutive optimal transport plans between measurement snapshots, this work reconstructs developmental processes from single-cell data.ArticleÂ
Google ScholarÂ
Bunne, C. et al. Learning single-cell perturbation responses using neural optimal transport. Nat. Methods 20, 1759–1768 (2023). Using neural optimal transport based on Brenier’s theorem, this work allows us to predict the perturbation responses of heterogeneous cell populations to chemical drugs, developmental signals or genetic perturbations.ArticleÂ
Google ScholarÂ
Uscidda, T. & Cuturi, M. The Monge gap: a regularizer to learn all transport maps. In Int. Conf. Machine Learning (ICML, 2023). This paper introduces the Monge gap, a regularizer for neural optimal transport (OT) methods that quantifies how far a map T deviates from the ideal properties we expect from an OT map.Uhler, C. & Shivashankar, G. Machine learning approaches to single-cell data integration and translation. Proc. IEEE 110, 557–576 (2022).ArticleÂ
Google ScholarÂ
Bunne, C., Meng-Papaxanthos, L., Krause, A. & Cuturi, M. Proximal optimal transport modeling of population dynamics. In Int. Conf. Artificial Intelligence and Statistics Vol. 25 (AISTATS, 2022). Building on the connection of optimal transport, gradient flows and partial differential equations, this work learns an energy potential that explains the continuous differentiation of single cells over time.Forrow, A. & Schiebinger, G. LineageOT is a unified framework for lineage tracing and trajectory inference. Nat. Commun. 12, 4940 (2021).ArticleÂ
ADSÂ
Google ScholarÂ
Bunne, C., Hsieh, Y.-P., Cuturi, M. & Krause, A. The Schrödinger bridge between Gaussian measures has a closed form. In Int. Conf. Artificial Intelligence and Statistics Vol. 206 (AISTATS, 2023).Lavenant, H., Zhang, S., Kim, Y.-H. & Schiebinger, G. Towards a mathematical theory of trajectory inference. Ann. Appl. Probab. 34, 428–500 (2024).ArticleÂ
MathSciNetÂ
Google ScholarÂ
Tong, A., Huang, J., Wolf, G., Van Dijk, D. & Krishnaswamy, S. TrajectoryNet: a dynamic optimal transport network for modeling cellular dynamics. In Int. Conf. Machine Learning (ICML, 2020). This paper parameterizes dynamic optimal transport and in particular the Benamou–Brenier formulation using normalizing flows and enables to generate representative single-cell trajectories from snapshot measurements.Yang, K. D. et al. Predicting cell lineages using autoencoders and optimal transport. PLoS Comput. Biol. 16, e1007828 (2020).ArticleÂ
Google ScholarÂ
Zhang, S., Afanassiev, A., Greenstreet, L., Matsumoto, T. & Schiebinger, G. Optimal transport analysis reveals trajectories in steady-state systems. PLoS Comput. Biol. 17, e1009466 (2021).ArticleÂ
ADSÂ
Google ScholarÂ
Chizat, L., Zhang, S., Heitz, M. & Schiebinger, G. Trajectory inference via mean-field Langevin in path space. In Advances in Neural Information Processing Systems (NeurIPS, 2022).Yang, K. D. & Uhler, C. Scalable unbalanced optimal transport using generative adversarial networks. In Int. Conf. Learning Representations (ICLR, 2019).Lübeck, F. et al. Neural unbalanced optimal transport via cycle-consistent semi-couplings. Preprint at https://arxiv.org/abs/2209.15621 (2022).Moriel, N. et al. NovoSpaRc: flexible spatial reconstruction of single-cell gene expression with optimal transport. Nat. Protocols 16, 4177–4200 (2021).ArticleÂ
Google ScholarÂ
Nitzan, M., Karaiskos, N., Friedman, N. & Rajewsky, N. Gene expression cartography. Nature 576, 132–137 (2019). This paper introduces how optimal transport across heterogeneous spaces, that is, the Gromov–Wasserstein distance, can be used to spatially reconstruct tissues or map non-spatially resolved single-cell measurement onto a reference atlas.ArticleÂ
ADSÂ
Google ScholarÂ
Demetci, P., Santorella, R., Sandstede, B., Noble, W. S. & Singh, R. SCOT: single-cell multi-omics alignment with optimal transport. J. Comput. Biol. 29, 3–18 (2022). Building on optimal transport extensions to heterogeneous spaces, this method allows to integrate and translate across multiple data modalities.ArticleÂ
MathSciNetÂ
Google ScholarÂ
Huizing, G.-J., Peyré, G. & Cantini, L. Optimal transport improves cell–cell similarity inference in single-cell omics data. Bioinformatics 38, 2169–2177 (2022).ArticleÂ
Google ScholarÂ
Yang, K. D. & Uhler, C. Multi-domain translation by learning uncoupled autoencoders. Preprint at https://arxiv.org/abs/1902.03515 (2019).Alatkar, S. A. & Wang, D. CMOT: cross-modality optimal transport for multimodal inference. Genome Biol. 24, 163 (2023). The study presents cross-modality optimal transport, a computational approach that aligns multimodal single-cell sequencing data into a common latent space, effectively inferring missing modalities and enhancing biological interpretations across various applications.ArticleÂ
Google ScholarÂ
Cuturi, M. Sinkhorn distances: lightspeed computation of optimal transport. In Advances in Neural Information Processing Systems Vol. 26 (NeurIPS, 2013).Cuturi, M. et al. Optimal Transport Tools (OTT): A JAX Toolbox for all things Wasserstein. Preprint at https://arxiv.org/abs/2201.12324; https://github.com/ott-jax/ott (2022). A Python library build on JAX to compute optimal transport (OT) at scale, also providing implementations of various neural-network-based OT approaches.Bunne, C., Krause, A. & Cuturi, M. Supervised training of conditional Monge maps. In Advances in Neural Information Processing Systems Vol. 35 (NeurIPS, 2022).Peyré, G. & Cuturi, M. in Foundations and Trends in Machine Learning Vol. 11 (Now Publishers, Inc., 2019). A book introducing in-depth optimal transport concepts and algorithms, with a particular focus on computational aspects.Cai, S., Georgakilas, G. K., Johnson, J. L. & Vahedi, G. A cosine similarity-based method to infer variability of chromatin accessibility at the single-cell level. Front. Genet. 9, 319 (2018).ArticleÂ
Google ScholarÂ
Watson, E. R., Mora, A., Taherian Fard, A. & Mar, J. C. How does the structure of data impact cell–cell similarity? Evaluating how structural properties influence the performance of proximity metrics in single cell RNA-seq data. Brief. Bioinform. 23, bbac387 (2022).ArticleÂ
Google ScholarÂ
Cuturi, M., Klein, M. & Ablin, P. Monge, Bregman and Occam: interpretable optimal transport in high-dimensions with feature-sparse maps. In Proc. 40th Int. Con. Mach. Learn. Vol. 202, 6671–6682 (PMLR, 2023).Liu, R., Balsubramani, A. & Zou, J. Learning transport cost from subset correspondence. In Int. Conf. Learning Representations (ICLR, 2020).Stuart, A. M. & Wolfram, M.-T. Inverse optimal transport. SIAM J. Appl. Math. 80, 19M1261122 (2020).ArticleÂ
MathSciNetÂ
Google ScholarÂ
Li, R., Ye, X., Zhou, H. & Zha, H. Learning to match via inverse optimal transport. J. Mach. Learn. Res. 20, 1–37 (2019).MathSciNetÂ
Google ScholarÂ
Monge, G. Mémoire sur la théorie des déblais et des remblais (Histoire de l’Académie Royale des Sciences, 1781).Kantorovich, L. On the transfer of masses [Russian]. In Dokl. Akad. Nauk SSSR 37, 227–229 (1942).
Google ScholarÂ
Kuhn, H. W. The Hungarian method for the assignment problem. Nav. Res. Logist. Q. 2, 83–97 (1955).ArticleÂ
MathSciNetÂ
Google ScholarÂ
Dantzig, G. Linear Programming and Extensions (Princeton Univ. Press, 1963).Hitchcock, F. L. The distribution of a product from several sources to numerous localities. J. Math. Phys. 20, 224–230 (1941).ArticleÂ
MathSciNetÂ
Google ScholarÂ
Koopmans, T. C. Optimum utilization of the transportation system. Econ. J. Econ. Soc. 17, 136–146 (1949).
Google ScholarÂ
Ahuja, R. K., Magnanti, T. L. & Orlin, J. B. Network Flows: Theory, Algorithms, and Applications (Prentice Hall, 1993).Bertsekas, D. P. The auction algorithm: a distributed relaxation method for the assignment problem. Ann. Oper. Res. 14, 105–123 (1988).ArticleÂ
MathSciNetÂ
Google ScholarÂ
Benamou, J.-D. & Brenier, Y. A computational fluid mechanics solution to the Monge–Kantorovich mass transfer problem. Numer. Math. 84, 375–393 (2000).ArticleÂ
MathSciNetÂ
Google ScholarÂ
Brenier, Y. Polar factorization and monotone rearrangement of vector-valued functions. Commun. Pure Appl. Math. 44, 375–417 (1991).ArticleÂ
MathSciNetÂ
Google ScholarÂ
Scetbon, M., Cuturi, M. & Peyré, G. Low-rank Sinkhorn factorization. In Int. Conf. Machine Learning Vol. 139 (ICML, 2021).Scetbon, M. & Cuturi, M. Low-rank optimal transport: approximation, statistics and debiasing. In Advances in Neural Information Processing Systems (NeurIPS) Vol. 35 (NeurIPS, 2022).Forrow, A. et al. Statistical optimal transport via factored couplings. In Int. Conf. Artificial Intelligence and Statistics (AISTATS) 2454–2465 (PMLR, 2019).Dudley, R. M. et al. Weak convergence of probabilities on nonseparable metric spaces and empirical measures on Euclidean spaces. Ill. J. Math. 10, 109–126 (1966).MathSciNetÂ
Google ScholarÂ
Boissard, E. & Le Gouic, T. On the mean speed of convergence of empirical and occupation measures in Wasserstein distance. Annales de l’IHP Probabilités et statistiques 50, 539–563 (2014).ADSÂ
MathSciNetÂ
Google ScholarÂ
Pooladian, A.-A. & Niles-Weed, J. Entropic estimation of optimal transport maps. Preprint at https://arxiv.org/abs/2109.12004 (2021).Finlay, C., Gerolin, A., Oberman, A. M. & Pooladian, A.-A. Learning normalizing flows from entropy-Kantorovich potentials. Preprint at https://arxiv.org/abs/2006.06033 (2020).Wilfrid, G. & Robert, J. M. The geometry of optimal transportation. Acta Math. 177, 113–161 (1996).ArticleÂ
MathSciNetÂ
Google ScholarÂ
Goodfellow, I. et al. Generative adversarial networks. In Advances in Neural Information Processing Systems Vol. 63 (NeurIPS, 2014).Arjovsky, M., Chintala, S. & Bottou, L. Wasserstein generative adversarial networks. In Int. Conf. Machine Learning (ICML, 2017).Chen, R. T., Rubanova, Y., Bettencourt, J. & Duvenaud, D. Neural ordinary differential equations. In Advances in Neural Information Processing Systems (NeurIPS, 2018).Makkuva, A., Taghvaei, A., Oh, S. & Lee, J. Optimal transport mapping via input convex neural networks. In Int. Conf. Machine Learning Vol. 119 (ICML, 2020).Korotin, A., Egiazarian, V., Asadulaev, A., Safin, A. & Burnaev, E. Wasserstein-2 generative networks. Preprint at https://arxiv.org/abs/1909.13082 (2019).Alvarez-Melis, D., Schiff, Y. & Mroueh, Y. Optimizing functionals on the space of probabilities with input convex neural networks. Trans. Mach. Learn. Res. (2022).Mokrov, P. et al. Large-scale Wasserstein gradient flows. In Advances in Neural Information Processing Systems (NeurIPS, 2021).Vaswani, A. et al. Attention is all you need. In Advances in Neural Information Processing Systems (NeurIPS, 2017).Eyring, L. V. et al. Modeling single-cell dynamics using unbalanced parameterized Monge maps. In International Conference on Learning Representations (ICLR, 2024).Pariset, M., Hsieh, Y.-P., Bunne, C., Krause, A. & De Bortoli, V. Unbalanced diffusion Schrödinger bridge. Preprint at https://arxiv.org/abs/2306.09099 (2023).Frogner, C., Zhang, C., Mobahi, H., Araya, M. & Poggio, T. A. Learning with a Wasserstein loss. In Advances in Neural Information Processing Systems Vol. 28 (NeurIPS, 2015).Chizat, L., Peyré, G., Schmitzer, B. & Vialard, F.-X. Scaling algorithms for unbalanced optimal transport problems. Math. Comput. 87, 2563–2609 (2018).ArticleÂ
MathSciNetÂ
Google ScholarÂ
Mémoli, F. Gromov–Wasserstein distances and the metric approach to object matching. Found. Comput. Math. 11, 417–487 (2011).ArticleÂ
MathSciNetÂ
Google ScholarÂ
Peyré, G., Cuturi, M. & Solomon, J. Gromov–Wasserstein averaging of kernel and distance matrices. In Int. Conf. Machine Learning (ICML, 2016).Scetbon, M., Peyré, G. & Cuturi, M. Linear-time Gromov–Wasserstein distances using low rank couplings and costs. In Int. Conf. Machine Learning Vol. 162 (ICML, 2022).Klein, D. et al. Mapping cells through time and space with moscot. Preprint at bioRxiv https://doi.org/10.1101/2023.05.11.540374 (2023). A Python library based on Optimal Transport Toolbox that implements representative optimal transport applications in single-cell genomics in JAX.Vargas, F., Thodoroff, P., Lawrence, N. D. & Lamacraft, A. Solving Schrödinger bridges via maximum likelihood. Entropy 23, 1134 (2021).ArticleÂ
ADSÂ
Google ScholarÂ
Ji, Y. et al. Optimal distance metrics for single-cell RNA-seq populations. Preprint at bioRxiv https://doi.org/10.1101/2023.12.26.572833 (2023).Dixit, A. et al. Perturb-Seq: dissecting molecular circuits with scalable single-cell RNA profiling of pooled genetic screens. Cell 167, 1853–1866.e17 (2016).ArticleÂ
Google ScholarÂ
Replogle, J. M. et al. Mapping information-rich genotype–phenotype landscapes with genome-scale Perturb-seq. Cell 185, 2559–2575.e28 (2022).ArticleÂ
Google ScholarÂ
Srivatsan, S. R. et al. Massively multiplex chemical transcriptomics at single-cell resolution. Science. 367, 45–51 (2020).ArticleÂ
ADSÂ
Google ScholarÂ
Norman, T. M. et al. Exploring genetic interaction manifolds constructed from rich single-cell phenotypes. Science 365, 786–793 (2019).ArticleÂ
ADSÂ
Google ScholarÂ
Gut, G., Herrmann, M. D. & Pelkmans, L. Multiplexed protein maps link subcellular organization to cellular states. Science 361, eaar7042 (2018).ArticleÂ
Google ScholarÂ
Chen, W. S. et al. Uncovering axes of variation among single-cell cancer specimens. Nat. Methods 17, 302–310 (2020).ArticleÂ
Google ScholarÂ
Lähnemann, D. et al. Eleven grand challenges in single-cell data science. Genome Biol. 21, 31 (2020).ArticleÂ
Google ScholarÂ
Rood, J. E., Maartens, A., Hupalowska, A., Teichmann, S. A. & Regev, A. Impact of the Human Cell Atlas on medicine. Nat. Med. 8, 2486–2496 (2022).ArticleÂ
Google ScholarÂ
Blondel, V. D., Guillaume, J.-L., Lambiotte, R. & Lefebvre, E. Fast unfolding of communities in large networks. J. Statist. Mech. Theory Exp. 2008, P10008 (2008).ArticleÂ
Google ScholarÂ
Duò, A., Robinson, M. D. & Soneson, C. A systematic performance evaluation of clustering methods for single-cell RNA-seq data. F1000 Res. 7, 1141 (2018).ArticleÂ
Google ScholarÂ
Traag, V. A., Waltman, L. & Van Eck, N. J. From Louvain to Leiden: guaranteeing well-connected communities. Sci. Rep. 9, 5233 (2019).ArticleÂ
ADSÂ
Google ScholarÂ
Wolf, F. A. et al. PAGA: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome Biol. 20, 59 (2019).ArticleÂ
Google ScholarÂ
Weber, L. M. & Robinson, M. D. Comparison of clustering methods for high-dimensional single-cell flow and mass cytometry data. Cytometry Pt A 89, 1084–1096 (2016).ArticleÂ
Google ScholarÂ
Wagner, A., Regev, A. & Yosef, N. Revealing the vectors of cellular identity with single-cell genomics. Nat. Biotechnol. 34, 1145–1160 (2016).ArticleÂ
Google ScholarÂ
McInnes, L., Healy, J., Saul, N. & Großberger, L. UMAP: uniform manifold approximation and projection. J. Open Source Softw. 3, 861 (2018).ArticleÂ
Google ScholarÂ
Wilson, N. K. et al. Combined single-cell functional and gene expression analysis resolves heterogeneity within stem cell populations. Cell Stem Cell 16, 712–724 (2015).ArticleÂ
Google ScholarÂ
Van der Maaten, L. & Hinton, G. Visualizing data using t-SNE. J. Mach. Learn. Res. 9, 2579–2605 (2008).
Google ScholarÂ
Gaublomme, J. T. et al. Single-cell genomics unveils critical regulators of Th17 cell pathogenicity. Cell 163, 1400–1412 (2015).ArticleÂ
Google ScholarÂ
Huizing, G.-J., Cantini, L. & Peyré, G. Unsupervised ground metric learning using Wasserstein singular vectors. In Proc. 39th Int. Conf. Mach. Learn. (ICML, 2022).Dou, J. X. et al. Learning more effective cell representations efficiently. In NeurIPS Workshop on Learning Meaningful Representations of Life (LMRL) (NeurIPS, 2022).Cang, Z. & Nie, Q. Inferring spatial and signaling relationships between cells from single cell transcriptomic data. Nat. Commun. 11, 2084 (2020). This article introduces a method using structured optimal transport to incorporate lost spatial information into single-cell RNA-sequencing data, enabling the reconstruction of spatial cellular dynamics and improved understanding of cell–cell communications across tissues.ArticleÂ
ADSÂ
Google ScholarÂ
Cang, Z. et al. Screening cell–cell communication in spatial transcriptomics via collective optimal transport. Nat. Methods 20, 218–228 (2023). This paper introduces a collective optimal transport method to infer cell–cell communication in spatial transcriptomics data, able to trade-off complex molecular interactions and spatial constraints.ArticleÂ
Google ScholarÂ
Yuan, Z. et al. SOTIP is a versatile method for microenvironment modeling with spatial omics data. Nat. Commun. 13, 7330 (2022).ArticleÂ
ADSÂ
Google ScholarÂ
Sun, D., Liu, Z., Li, T., Wu, Q. & Wang, C. STRIDE: accurately decomposing and integrating spatial transcriptomics using single-cell RNA sequencing. Nucleic Acids Res. 50, e42 (2022).ArticleÂ
Google ScholarÂ
Mani, S., Haviv, D., Kunes, R. & Pe’er, D. SPOT: spatial optimal transport for analyzing cellular microenvironments. In NeurIPS Workshop on Learning Meaningful Representations of Life (LMRL) (NeurIPS, 2022).Haviv, D. et al. The covariance environment defines cellular niches for spatial inference. Nat. Biotechnol. https://doi.org/10.1038/s41587-024-02193-4 (2024). The study introduces an optimal-transport-based tool to effectively analyse high-resolution spatial profiling data by capturing complex cellular interactions and enhancing gene expression imputation through the gene–gene covariate structure across cells in the niche.ArticleÂ
Google ScholarÂ
Nguyen, N. D. et al. Optimal transport for mapping senescent cells in spatial transcriptomics. Preprint at bioRxiv https://doi.org/10.1101/2023.08.16.553591 (2023).Mages, S. et al. TACCO unifies annotation transfer and decomposition of cell identities for single-cell and spatial omics. Nat. Biotechnol. 41, 1465–1473 (2023).ArticleÂ
Google ScholarÂ
Held, M. et al. CellCognition: time-resolved phenotype annotation in high-throughput live cell imaging. Nat. Methods 7, 747–754 (2010).ArticleÂ
Google ScholarÂ
Briggs, J. A. et al. The dynamics of gene expression in vertebrate embryogenesis at single-cell resolution. Science 360, eaar5780 (2018).ArticleÂ
Google ScholarÂ
Mittnenzweig, M. et al. A single-embryo, single-cell time-resolved model for mouse gastrulation. Cell 184, 2825–2842.e22 (2021).ArticleÂ
Google ScholarÂ
Farrell, J. A. et al. Single-cell reconstruction of developmental trajectories during zebrafish embryogenesis. Science 360, eaar3131 (2018).ArticleÂ
Google ScholarÂ
Raue, A. et al. Data2dynamics: a modeling environment tailored to parameter estimation in dynamical systems. Bioinformatics 31, 3558–3560 (2015).ArticleÂ
Google ScholarÂ
Ding, J. et al. Reconstructing differentiation networks and their regulation from time series single-cell expression data. Genome Res. 28, 38–395 (2018).ArticleÂ
Google ScholarÂ
Chen, Y., Georgiou, T. T. & Pavon, M. The most likely evolution of diffusing and vanishing particles: Schrödinger bridges with unbalanced marginals. SIAM J. Control Optimiz. 60, 21M1447672 (2022).ArticleÂ
Google ScholarÂ
Massri, A. J. et al. Developmental single-cell transcriptomics in the Lytechinus variegatus sea urchin embryo. Development 148, dev198614 (2021).ArticleÂ
Google ScholarÂ
Weinreb, C., Rodriguez-Fraticelli, A., Camargo, F. D. & Klein, A. M. Lineage tracing on transcriptional landscapes links state to fate during differentiation. Science 367, eaaw3381 (2020).ArticleÂ
Google ScholarÂ
Chen, W. et al. Live-seq enables temporal transcriptomic recording of single cells. Nature 608, 733–740 (2022).ArticleÂ
ADSÂ
Google ScholarÂ
Somnath, V. R. et al. Aligned diffusion Schrödinger bridges. In Proc. 39th Conf. Uncertainty in Artificial Intelligence Vol. 216, 1985–1995 (PMLR, 2023). Building on the connections of optimal transport to control theory, this method allows to reconstruct cellular dynamics that respects and integrates known trajectories, for example, obtained from DNA-barcoding technologies.Kobayashi-Kirschvink, K. J. et al. Prediction of single-cell RNA expression profiles in live cells by Raman microscopy with Raman2RNA. Nat. Biotechnol. https://doi.org/10.1038/s41587-023-02082-2 (2024).ArticleÂ
Google ScholarÂ
Vayer, T., Chapel, L., Flamary, R., Tavenard, R. & Courty, N. Fused Gromov–Wasserstein distance for structured objects. Algorithms 13, 212 (2020).ArticleÂ
MathSciNetÂ
Google ScholarÂ
Zeira, R., Land, M., Strzalkowski, A. & Raphael, B. J. Alignment and integration of spatial transcriptomics data. Nat. Methods 19, 567–575 (2022). Using optimal transport methods for heterogeneous spaces known as the Gromov–Wasserstein problem, this paper allows the integration and alignment of spatial transcriptomics tissue slices.ArticleÂ
Google ScholarÂ
Ma, Q. & Xu, D. Deep learning shapes single-cell data analysis. Nat. Rev. Mol. Cell Biol. 23, 303–304 (2022).ArticleÂ
Google ScholarÂ
Ji, Y., Lotfollahi, M., Wolf, F. A. & Theis, F. J. Machine learning for perturbational single-cell omics. Cell Systems 12, 522–537 (2021).ArticleÂ
Google ScholarÂ
Raimundo, F., Meng-Papaxanthos, L., Vallot, C. & Vert, J.-P. Machine learning for single-cell genomics data analysis. Curr. Opin. Syst. Biol. 26, 64–71 (2021).ArticleÂ
Google ScholarÂ
Roohani, Y., Huang, K. & Leskovec, J. GEARS: predicting transcriptional outcomes of novel multi-gene perturbations. Nat. Biotechnol. 42, 927–935 (2023).ArticleÂ
Google ScholarÂ
Amos, B. On amortizing convex conjugates for optimal transport. In Int. Conf. Learning Representations (ICLR, 2023).Taghvaei, A. & Jalali, A. 2-Wasserstein approximation via restricted convex potentials with application to improved training for GANs. Preprint at https://arxiv.org/abs/1902.07197 (2019).Lopez, R., Regier, J., Cole, M. B., Jordan, M. I. & Yosef, N. Deep generative modeling for single-cell transcriptomics. Nat. Methods 15, 1053–1058 (2018).ArticleÂ
Google ScholarÂ
Lotfollahi, M., Wolf, F. A. & Theis, F. J. scGen predicts single-cell perturbation responses. Nat. Methods. 16, 715–721 (2019).ArticleÂ
Google ScholarÂ
Lotfollahi, M. et al. Predicting cellular responses to complex perturbations in high-throughput screens. Mol. Syst. Biol. 19, e11517 (2023).ArticleÂ
Google ScholarÂ
Waddington, C. H. The Strategy of the Genes: A Discussion of Some Aspects of Theoretical Biology (G. Allen and Unwin, 1957).Schiebinger, G. Reconstructing developmental landscapes and trajectories from single-cell data. Curr. Opin. Syst. Biol. 27, 100351 (2021).ArticleÂ
Google ScholarÂ
Lange, M. et al. Mapping lineage-traced cells across time points with moslin. Preprint at bioRxiv https://doi.org/10.1101/2023.04.14.536867 (2023). Building on the fused Gromov–Wasserstein distance, this paper introduces a method to reconstruct developmental processes based on both single-cell gene expressions and lineage information.Prasad, N., Yang, K. & Uhler, C. Optimal transport using GANs for lineage tracing. Preprint at https://arxiv.org/abs/2007.12098 (2020).Grathwohl, W., Chen, R. T., Bettencourt, J., Sutskever, I. & Duvenaud, D. FFJORD: free-form continuous dynamics for scalable reversible generative models. In Int. Conf. Learning Representations (ICLR, 2019).Moon, K. R. et al. Visualizing structure and transitions in high-dimensional biological data. Nat. Biotechnol. 37, 1482–1492 (2019).ArticleÂ
Google ScholarÂ
Schrödinger, E. Ãœber die Umkehrung der Naturgesetze (Verlag der Akademie der Wissenschaften in Kommission bei Walter De Gruyter u. Company, 1931).Schrödinger, E. Sur la théorie relativiste de l’électron et l’interprétation de la mécanique quantique. Annales de l’institut Henri Poincaré 2, 269–310 (1932).MathSciNetÂ
Google ScholarÂ
De Bortoli, V., Thornton, J., Heng, J. & Doucet, A. Diffusion Schrödinger bridge with applications to score-based generative modeling. In Advances in Neural Information Processing Systems Vol. 34 (NeurIPS, 2021).Chen, T., Liu, G.-H. & Theodorou, E. A. Likelihood training of Schrödinger bridge using forward-backward SDEs theory. In Int. Conf. Learning Representations (ICLR, 2022).Winkler, L., Ojeda, C. & Opper, M. A score-based approach for training Schrödinger bridges for data modelling. Entropy 25, 316 (2023).ArticleÂ
ADSÂ
Google ScholarÂ
Tong, A. et al. Improving and generalizing flow-based generative models with minibatch optimal transport. Trans. Mach. Learn. Res. (2024). By combining optimal transport and known concepts from optimal control, this paper presents a flow matching approach that allows to model cellular dynamics over time.Chen, T., Liu, G.-H., Tao, M. & Theodorou, E. A. Deep momentum multi-marginal Schrödinger bridge. In Advances in Neural Information Processing Systems (NeurIPS, 2023).Di Marino, S. & Chizat, L. A tumor growth model of Hele-Shaw type as a gradient flow. EESAIM Control Optim. Calc. Var. 26, 103 (2020).ArticleÂ
MathSciNetÂ
Google ScholarÂ
Jiang, Q., Zhang, S. & Wan, L. Dynamic inference of cell developmental complex energy landscape from time series single-cell transcriptomic data. PLoS Comput. Biol. 18, e1009821 (2022).ArticleÂ
ADSÂ
Google ScholarÂ
Ambrosio, L., Gigli, N. & Savaré, G. Gradient Flows in Metric Spaces and in the Space of Probability Measures (Springer, 2006).Risken, H. The Fokker–Planck Equation (Springer, 1996).Jordan, R., Kinderlehrer, D. & Otto, F. The variational formulation of the Fokker–Planck equation. SIAM J. Math. Anal. 29, S0036141096303359 (1998).ArticleÂ
MathSciNetÂ
Google ScholarÂ
Benamou, J.-D., Carlier, G. & Laborde, M. An augmented Lagrangian approach to Wasserstein gradient flows and applications. ESAIM Proc. Surv. 54, hal-01245184 (2016).ArticleÂ
MathSciNetÂ
Google ScholarÂ
Carrillo, J. A., Craig, K., Wang, L. & Wei, C. Primal dual methods for Wasserstein gradient flows. Found. Computat. Math. 22, 389–443 (2021).ArticleÂ
MathSciNetÂ
Google ScholarÂ
Peyré, G. Entropic approximation of Wasserstein gradient flows. SIAM J. Imaging Sci. 8, 15M1010087 (2015).ArticleÂ
MathSciNetÂ
Google ScholarÂ
Otto, F. The geometry of dissipative evolution equations: the porous medium equation. Commun. Partial Differ. Equ. 26, 101–174 (2001).ArticleÂ
MathSciNetÂ
Google ScholarÂ
Hashimoto, T., Gifford, D. & Jaakkola, T. Learning population-level diffusions with generative recurrent networks. In Int. Conf. Machine Learning Vol. 33 (ICML, 2016).Huguet, G. et al. Manifold interpolating optimal-transport flows for trajectory inference. In Advances in Neural Information Processing Systems Vol. 35 (NeurIPS, 2022).Lotfollahi, M., Naghipourfar, M., Theis, F. J. & Wolf, F. A. Conditional out-of-distribution generation for unpaired data using transfer VAE. Bioinformatics 36, i610–i617 (2020).ArticleÂ
Google ScholarÂ
Torous, W., Gunsilius, F. & Rigollet, P. An optimal transport approach to causal inference. Preprint at https://arxiv.org/abs/2108.05858 (2021).Tu, R., Zhang, K., Kjellström, H. & Zhang, C. Optimal transport for causal discovery. In Int. Conf. Learning Representations (ICLR, 2022).Abadie, A. Semiparametric difference-in-differences estimators. Rev. Econ. Stud. 72, 1–19 (2005).ArticleÂ
MathSciNetÂ
Google ScholarÂ
Singh, R. et al. Prioritizing transcription factor perturbations from single-cell transcriptomics. Preprint at bioRxiv https://doi.org/10.1101/2022.06.27.497786 (2022).Yang, K. D. et al. Multi-domain translation between single-cell imaging and sequencing data using autoencoders. Nat. Commun. 12, 31 (2021).ArticleÂ
ADSÂ
Google ScholarÂ
Amodio, M. et al. Exploring single-cell data with deep multitasking neural networks. Nat. Methods 16, 1139–1145 (2019).ArticleÂ
Google ScholarÂ
Luecken, M. D. et al. Benchmarking atlas-level data integration in single-cell genomics. Nat. Methods 19, 41–50 (2022).ArticleÂ
Google ScholarÂ
Cao, K., Gong, Q., Hong, Y. & Wan, L. A unified computational framework for single-cell data integration with optimal transport. Nat. Commun. 13, 7419 (2022).ArticleÂ
ADSÂ
Google ScholarÂ
Ryu, J., Lopez, R., Bunne, C. & Regev, A. Cross-modality matching and prediction of perturbation responses with labeled Gromov–Wasserstein optimal transport. Preprint at https://arxiv.org/abs/2405.00838 (2024).Demetci, P., Santorella, R., Sandstede, B. & Singh, R. Unsupervised integration of single-cell multi-omics datasets with disproportionate cell-type representation. In Research in Computational Molecular Biology: 26th Annual International Conference, RECOMB (Springer, 2022).Tran, Q. H. et al. Unbalanced CO-optimal transport. In AAAI Conf. Artificial Intelligence Vol. 37 (AAAI, 2023).Ma, S. et al. Chromatin potential identified by shared single-cell profiling of RNA and chromatin. Cell 183, 1103–1116.e20 (2020).ArticleÂ
Google ScholarÂ
Novershtern, N. et al. Densely interconnected transcriptional circuits control cell states in human hematopoiesis. Cell 144, 296–309 (2011).ArticleÂ
Google ScholarÂ
Lara-Astiaso, D. et al. Chromatin state dynamics during blood formation. Science 345, 943–949 (2014).ArticleÂ
ADSÂ
Google ScholarÂ
Huizing, G.-J., Deutschmann, I. M., Peyre, G. & Cantini, L. Paired single-cell multi-omics data integration with Mowgli. Nat. Commun. 14, 7711 (2023).ArticleÂ
ADSÂ
Google ScholarÂ
Haghverdi, L., Lun, A. T., Morgan, M. D. & Marioni, J. C. Batch effects in single-cell RNA-sequencing data are corrected by matching mutual nearest neighbors. Nat. Biotechnol. 36, 421–427 (2018).ArticleÂ
Google ScholarÂ
Joodaki, M. et al. Detection of PatIent-Level distances from single cell genomics and pathomics data with optimal transport (PILOT). Mol. Syst. Biol. 20, 57–74 (2024).ArticleÂ
Google ScholarÂ
Weinberger, E., Lopez, R., Huetter, J.-C. & Regev, A. Disentangling shared and group-specific variations in single-cell transcriptomics data with multiGroupVI. In Proc. 17th Machine Learning in Computational Biology Meeting Vol. 200 (PMLR, 2022).Tong, A. Y. et al. Diffusion Earth mover’s distance and distribution embeddings. In Int. Conf. Machine Learning (ICML, 2021).Tong, A. et al. Embedding signals on graphs with unbalanced diffusion Earth mover’s distance. In IEEE Int. Conf. Acoustics, Speech and Signal Processing (ICASSP) (IEEE, 2022).Wang, Z. et al. QOT: efficient computation of sample level distance matrix from single-cell omics data through quantized optimal transport. Preprint at bioRxiv https://doi.org/10.1101/2024.02.06.578032 (2024).Zapatero, M. R. et al. Trellis tree-based analysis reveals stromal regulation of patient-derived organoid drug responses. Cell 186, 5606–5619 (2023).ArticleÂ
Google ScholarÂ
Rodriques, S. G. et al. Slide-seq: a scalable technology for measuring genome-wide expression at high spatial resolution. Science 363, 1463–1467 (2019).ArticleÂ
ADSÂ
Google ScholarÂ
Chen, K. H., Boettiger, A. N., Moffitt, J. R., Wang, S. & Zhuang, X. Spatially resolved, highly multiplexed RNA profiling in single cells. Science 348, aaa6090 (2015).ArticleÂ
Google ScholarÂ
Shah, S., Lubeck, E., Zhou, W. & Cai, L. In situ transcription profiling of single cells reveals spatial organization of cells in the mouse hippocampus. Neuron 92, 342–357 (2016).ArticleÂ
Google ScholarÂ
Rahimi, A., Vale-Silva, L. A., Savitski, M. F., Tanevski, J. & Saez-Rodriguez, J. DOT: a flexible multi-objective optimization framework for transferring features across single-cell and spatial omics. Nat. Commun. 15, 4994 (2024).ArticleÂ
ADSÂ
Google ScholarÂ
Alvarez-Melis, D., Jaakkola, T. & Jegelka, S. Structured optimal transport. In Int. Conf. Artificial Intelligence and Statistics (AISTATS, 2018).Bradbury, J. et al. JAX: composable transformations of Python+NumPy programs. GitHub http://github.com/google/jax (2018).Flamary, R. et al. POT: Python optimal transport. J. Mach. Learn. Res. 22, 1–8 (2021). A Python library providing both NumPy-based and PyTorch-based implementations of various optimal transport algorithms.
Google ScholarÂ
Harris, C. R. et al. Array programming with NumPy. Nature 585, 357–362 (2020).ArticleÂ
ADSÂ
Google ScholarÂ
Paszke, A. et al. PyTorch: an imperative style, high-performance deep learning library. In Advances in Neural Information Processing Systems Vol. 32 (NeurIPS, 2019).Feydy, J. et al. Interpolating between optimal transport and MMD using Sinkhorn divergences. In Int. Conf. Artificial Intelligence and Statistics Vol. 22 (AISTATS, 2019).Chen, A. et al. Spatiotemporal transcriptomic atlas of mouse organogenesis using DNA nanoball-patterned arrays. Cell 185, 1777–1792.e21 (2022).ArticleÂ
Google ScholarÂ
Weinreb, C., Wolock, S., Tusi, B. K., Socolovsky, M. & Klein, A. M. Fundamental limits on dynamic inference from single-cell snapshots. Proc. Natl Acad. Sci. USA 115, E2467–E2476 (2018).ArticleÂ
ADSÂ
Google ScholarÂ
Pan, X., Li, H. & Zhang, X. TedSim: temporal dynamics simulation of single-cell RNA sequencing data and cell division history. Nucleic Acids Res. 50, 272–4288 (2022).ArticleÂ
Google ScholarÂ
Packer, J. S. et al. A lineage-resolved molecular atlas of C. elegans embryogenesis at single-cell resolution. Science 365, eaax1971 (2019).ArticleÂ
Google ScholarÂ
Hu, B. et al. Origin and function of activated fibroblast states during zebrafish heart regeneration. Nat. Genet. 54, 1227–1237 (2022).ArticleÂ
ADSÂ
Google ScholarÂ
Hagai, T. et al. Gene expression variability across cells and species shapes innate immunity. Nature 563, 197–202 (2018).ArticleÂ
ADSÂ
Google ScholarÂ
Zhao, W. et al. Deconvolution of cell type-specific drug responses in human tumor tissue with single-cell RNA-seq. Genome Med. 13, 82 (2021).ArticleÂ
Google ScholarÂ
Kang, H. M. et al. Multiplexed droplet single-cell RNA-sequencing using natural genetic variation. Nat. Biotechnol. 36, 89–94 (2018).ArticleÂ
Google ScholarÂ
Luecken, M. D. et al. A sandbox for prediction and integration of DNA, RNA, and proteins in single cells. In Proc. Neural Information Processing Systems Track on Datasets and Benchmarks 1 (Round 2) (NeurIPS, 2021).Lance, C. et al. Multimodal single cell data integration challenge: results and lessons learned. Proceedings of the NeurIPS 2021 Competitions and Demonstrations Track Vol. 176, 162–176 (PMLR, 2022).Codeluppi, S. et al. Spatial organization of the somatosensory cortex revealed by osmFISH. Nat. Methods 15, 932–935 (2018).ArticleÂ
Google ScholarÂ
Liu, L. et al. Deconvolution of single-cell multi-omics layers reveals regulatory heterogeneity. Nat. Commun. 10, 470 (2019).ArticleÂ
ADSÂ
Google ScholarÂ
Luo, C. et al. Single-cell methylomes identify neuronal subtypes and regulatory elements in mammalian cortex. Science 357, 600–604 (2017).ArticleÂ
ADSÂ
Google ScholarÂ
Regev, A. et al. The Human Cell Atlas. eLife 6, e27041 (2017).ArticleÂ
Google ScholarÂ
Abdulla, S. et al. CZ CELL×GENE Discover: a single-cell data platform for scalable exploration, analysis and modeling of aggregated data. Preprint at bioRxiv https://doi.org/10.1101/2023.10.30.563174 (2023).Megill, C. et al. CELL×GENE: a performant, scalable exploration platform for high dimensional sparse matrices. Preprint at bioRxiv https://doi.org/10.1101/2021.04.05.438318 (2021).Peidli, S. et al. scPerturb: information resource for harmonized single-cell perturbation data. Nat. Methods 21, 531–540 (2024).ArticleÂ
Google ScholarÂ
Sinkhorn, R. A relationship between arbitrary positive matrices and doubly stochastic matrices. Ann. Math. Statist. 35, 876–879 (1964).ArticleÂ
MathSciNetÂ
Google ScholarÂ
Heydari, T. et al. IQCELL: a platform for predicting the effect of gene perturbations on developmental trajectories using single-cell RNA-seq data. PLoS Comput. Biol. 18, e1009907 (2022).ArticleÂ
Google ScholarÂ
Busch, K. et al. Fundamental properties of unperturbed haematopoiesis from stem cells in vivo. Nature 518, 542–546 (2015).ArticleÂ
ADSÂ
Google ScholarÂ
Xiong, Y.-X. & Zhang, X.-F. scdot: enhancing single-cell RNA-seq data annotation and uncovering novel cell types through multi-reference integration. Brief. Bioinform. 25, bbae072 (2024).ArticleÂ
Google ScholarÂ
Lipman, Y., Chen, R. T., Ben-Hamu, H., Nickel, M. & Le, M. Flow matching for generative modeling. In Int. Conf. Learning Representations (ICLR, 2023).Liu, X., Wu, L., Ye, M. & Liu, Q. Flow straight and fast: learning to generate and transfer data with rectified flow. In International Conference on Learning Representations (ICLR) (2023).Pooladian, A.-A. et al. Multisample flow matching: straightening flows with minibatch couplings. In Int. Conf. Machine Learning (ICML, 2023).Albergo, M. S., Boffi, N. M. & Vanden-Eijnden, E. Stochastic interpolants: a unifying framework for flows and diffusions. Preprint at https://arxiv.org/abs/2303.08797 (2023).Liu, G.-H. et al. I2 SB: image-to-image Schrödinger bridge. In Int. Conf. Machine Learning (ICML, 2023).Liu, G.-H., Chen, T., So, O. & Theodorou, E. A. Deep generalized Schrödinger bridge. In Advances in Neural Information Processing Systems (NeurIPS, 2022).Brandstetter, J., Worrall, D. & Welling, M. Message passing neural PDE solvers. In Int. Conf. Learning Representations (ICLR, 2022).Raissi, M., Perdikaris, P. & Karniadakis, G. E. Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys. 378, 686–707 (2019).ArticleÂ
ADSÂ
MathSciNetÂ
Google ScholarÂ
Song, Y. et al. Score-based generative modeling through stochastic differential equations. In Int. Conf. Learning Representations (ICLR, 2021).Daniels, M., Maunu, T. & Hand, P. Score-based generative neural networks for large-scale optimal transport. In Advances in Neural Information Processing Systems Vol. 34 (NeurIPS, 2021).Kong, Z., Ping, W., Huang, J., Zhao, K. & Catanzaro, B. DiffWave: a versatile diffusion model for audio synthesis. In Int. Conf. Learning Representations (ICLR, 2021).Song, Y. & Ermon, S. Generative modeling by estimating gradients of the data distribution. In Advances in Neural Information Processing Systems (NeurIPS, 2019).Comiter, C. et al. Inference of single cell profiles from histology stains with the single-cell omics from histology analysis framework (SCHAF). Preprint at bioRxiv https://doi.org/10.1101/2023.03.21.533680 (2023).Rosen, Y. et al. Universal cell embeddings: a foundation model for cell biology. Preprint at bioRxiv https://doi.org/10.1101/2023.11.28.568918 (2023).Cui, H. et al. scGPT: toward building a foundation model for single-cell multi-omics using generative AI. Nat. Methods https://doi.org/10.1038/s41592-024-02201-0 (2024).ArticleÂ
Google ScholarÂ
Chan, E. M. et al. Live cell imaging distinguishes bona fide human iPS cells from partially reprogrammed cells. Nat. Biotechnol. 27, 1033–1037 (2009).ArticleÂ
Google ScholarÂ
Shi, Y., De Bortoli, V., Campbell, A. & Doucet, A. Diffusion Schrödinger bridge matching. In Advances in Neural Information Processing Systems (NeurIPS, 2024).Irmisch, A. et al. The Tumor Profiler Study: integrated, multi-omic, functional tumor profiling for clinical decision support. Cancer Cell 39, 288–293 (2021).ArticleÂ
Google ScholarÂ
Santinha, A. J. et al. Transcriptional linkage analysis with in vivo AAV-Perturb-seq. Nature 622, 367–375 (2023).ArticleÂ
ADSÂ
Google ScholarÂ
Cleary, B., Cong, L., Cheung, A., Lander, E. S. & Regev, A. Efficient generation of transcriptomic profiles by random composite measurements. Cell 171, 1424–1436.e18 (2017).ArticleÂ
Google ScholarÂ
Cleary, B. & Regev, A. The necessity and power of random, under-sampled experiments in biology. Preprint at https://arxiv.org/abs/2012.12961 (2020).Frangieh, C. J. et al. Multimodal pooled Perturb-CITE-seq screens in patient models define mechanisms of cancer immune evasion. Nat. Genet. 53, 332–341 (2021).ArticleÂ
Google ScholarÂ
Wu, F. et al. Single-cell profiling of tumor heterogeneity and the microenvironment in advanced non-small cell lung cancer. Nat. Commun. 12, 2540 (2021).ArticleÂ
ADSÂ
Google ScholarÂ
González-Silva, L., Quevedo, L. & Varela, I. Tumor functional heterogeneity unraveled by scRNA-seq technologies. Trends Cancer 6, 13–19 (2020).ArticleÂ
Google ScholarÂ
Li, C. et al. Single-cell transcriptomics reveals cellular heterogeneity and molecular stratification of cervical cancer. Commun. Biol. 5, 1208 (2022).ArticleÂ
Google ScholarÂ
Bertsimas, D. & Tsitsiklis, J. Introduction to Linear Optimization (Athena Scientific, 1997).Franklin, J. & Lorenz, J. On the scaling of multidimensional matrices. Linear Algebra Appl. 114, 717–735 (1989).ArticleÂ
MathSciNetÂ
Google ScholarÂ