Studies with temporal or spatial resolution are crucial to understand the molecular dynamics and spatial dependencies underlying a biological process or system. With advances in high-throughput omic technologies, time- and space-resolved molecular measurements at scale are increasingly accessible, providing new opportunities to study the role of timing or structure in a wide range of biological questions. At the same time, analyses of the data being generated in the context of spatiotemporal studies entail new challenges that need to be considered, including the need to account for temporal and spatial dependencies and compare them across different scales, biological samples or conditions. In this Review, we provide an overview of common principles and challenges in the analysis of temporal and spatial omics data. We discuss statistical concepts to model temporal and spatial dependencies and highlight opportunities for adapting existing analysis methods to data with temporal and spatial dimensions.
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Rozenblatt-Rosen, O., Stubbington, M. J. T., Regev, A. & Teichmann, S. A. The Human Cell Atlas: from vision to reality. Nature 550, 451–453 (2017).
Janssens, J. et al. Decoding gene regulation in the fly brain. Nature 601, 630–636 (2022).
Li, H. et al. Fly Cell Atlas: a single-nucleus transcriptomic atlas of the adult fruit fly. Science 375, eabk2432 (2022).
Karczewski, K. J. & Snyder, M. P. Integrative omics for health and disease. Nat. Rev. Genet. 19, 299–310 (2018).
Sunagawa, S. et al. Tara Oceans: towards global ocean ecosystems biology. Nat. Rev. Microbiol. 18, 428–445 (2020).
Van Emon, J. M. The omics revolution in agricultural research. J. Agric. Food Chem. 64, 36–44 (2016).
Larsson, L., Frisén, J. & Lundeberg, J. Spatially resolved transcriptomics adds a new dimension to genomics. Nat. Methods 18, 15–18 (2021).
Lewis, S. M. et al. Spatial omics and multiplexed imaging to explore cancer biology. Nat. Methods 18, 997–1012 (2021).
Palla, G., Fischer, D. S., Regev, A. & Theis, F. J. Spatial components of molecular tissue biology. Nat. Biotechnol. 40, 308–318 (2022).
Seferbekova, Z., Lomakin, A., Yates, L. R. & Gerstung, M. Spatial biology of cancer evolution. Nat. Rev. Genet. 24, 295–313 (2023).
Rao, A., Barkley, D., França, G. S. & Yanai, I. Exploring tissue architecture using spatial transcriptomics. Nature 596, 211–220 (2021).
Jackson, H. W. et al. The single-cell pathology landscape of breast cancer. Nature 578, 615–620 (2020).
Wu, S. Z. et al. A single-cell and spatially resolved atlas of human breast cancers. Nat. Genet. 53, 1334–1347 (2021).
Bar-Joseph, Z., Gitter, A. & Simon, I. Studying and modelling dynamic biological processes using time-series gene expression data. Nat. Rev. Genet. 13, 552–564 (2012).
Cardoso-Moreira, M. et al. Developmental gene expression differences between humans and mammalian models. Cell Rep. 33, 108308 (2020).
Dries, R. et al. Advances in spatial transcriptomic data analysis. Genome Res. 31, 1706–1718 (2021).
Atta, L. & Fan, J. Computational challenges and opportunities in spatially resolved transcriptomic data analysis. Nat. Commun. 12, 5283 (2021).
Lederer, A. R. & La Manno, G. The emergence and promise of single-cell temporal-omics approaches. Curr. Opin. Biotechnol. 63, 70–78 (2020).
Crowell, H. L. et al. muscat detects subpopulation-specific state transitions from multi-sample multi-condition single-cell transcriptomics data. Nat. Commun. 11, 6077 (2020).
Büttner, M., Ostner, J., Müller, C. L., Theis, F. J. & Schubert, B. scCODA is a Bayesian model for compositional single-cell data analysis. Nat. Commun. 12, 6876 (2021).
Lun, A. T. L. & Marioni, J. C. Overcoming confounding plate effects in differential expression analyses of single-cell RNA-seq data. Biostatistics 18, 451–464 (2017).
Schüssler-Fiorenza Rose, S. M. et al. A longitudinal big data approach for precision health. Nat. Med. 25, 792–804 (2019).
Bernardes, J. P. et al. Longitudinal multi-omics analyses identify responses of megakaryocytes, erythroid cells, and plasmablasts as hallmarks of severe COVID-19. Immunity 53, 1296–1314 (2020).
Zhou, W. et al. Longitudinal multi-omics of host–microbe dynamics in prediabetes. Nature 569, 663–671 (2019).
Mishra, N. et al. Longitudinal multi-omics analysis identifies early blood-based predictors of anti-TNF therapy response in inflammatory bowel disease. Genome Med. 14, 110 (2022).
Cardoso-Moreira, M. et al. Gene expression across mammalian organ development. Nature 571, 505–509 (2019).
Haghverdi, L., Büttner, M., Wolf, F. A., Buettner, F. & Theis, F. J. Diffusion pseudotime robustly reconstructs lineage branching. Nat. Methods 13, 845–848 (2016).
Trapnell, C. et al. The dynamics and regulators of cell fate decisions are revealed by pseudotemporal ordering of single cells. Nat. Biotechnol. 32, 381–386 (2014).
Moignard, V. et al. Decoding the regulatory network of early blood development from single-cell gene expression measurements. Nat. Biotechnol. 33, 269–276 (2015).
Street, K. et al. Slingshot: cell lineage and pseudotime inference for single-cell transcriptomics. BMC Genomics 19, 477 (2018).
Saelens, W., Cannoodt, R., Todorov, H. & Saeys, Y. A comparison of single-cell trajectory inference methods. Nat. Biotechnol. 37, 547–554 (2019).
Lange, M. et al. CellRank for directed single-cell fate mapping. Nat. Methods 19, 159–170 (2022).
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).
Qiu, X. et al. Inferring causal gene regulatory networks from coupled single-cell expression dynamics using Scribe. Cell Syst. 10, 265–274 (2020).
Ding, J., Sharon, N. & Bar-Joseph, Z. Temporal modelling using single-cell transcriptomics. Nat. Rev. Genet. 23, 355–368 (2022).
Franken, H. et al. Thermal proteome profiling for unbiased identification of direct and indirect drug targets using multiplexed quantitative mass spectrometry. Nat. Protoc. 10, 1567–1593 (2015).
Leuenberger, P. et al. Cell-wide analysis of protein thermal unfolding reveals determinants of thermostability. Science 355, eaai7825 (2017).
Perrin, R. J., Fagan, A. M. & Holtzman, D. M. Multimodal techniques for diagnosis and prognosis of Alzheimer’s disease. Nature 461, 916–922 (2009).
Yoon, B.-J. Hidden Markov models and their applications in biological sequence analysis. Curr. Genomics 10, 402–415 (2009).
Stegle, O. et al. Discovering temporal patterns of differential gene expression in microarray time series. In German Conference on Bioinformatics 2009 (eds Grosse, I. et al.) 133–142 (Gesellschaft für Informatik, 2009).
Svensson, V., Teichmann, S. A. & Stegle, O. SpatialDE: identification of spatially variable genes. Nat. Methods 15, 343–346 (2018). This method uses GPs to identify spatially variable genes, translating ideas from temporal data analysis to spatial transcriptomics.
BinTayyash, N. et al. Non-parametric modelling of temporal and spatial counts data from RNA-seq experiments. Bioinformatics 37, 3788–3795 (2021).
Sun, S., Zhu, J. & Zhou, X. Statistical analysis of spatial expression patterns for spatially resolved transcriptomic studies. Nat. Methods 17, 193–200 (2020).
Kats, I., Vento-Tormo, R. & Stegle, O. SpatialDE2: fast and localized variance component analysis of spatial transcriptomics. Preprint at bioRxiv https://doi.org/10.1101/2021.10.27.466045 (2021).
Conesa, A., Nueda, M. J., Ferrer, A. & Talón, M. maSigPro: a method to identify significantly differential expression profiles in time-course microarray experiments. Bioinformatics 22, 1096–1102 (2006). This is a widely used parametric method based on polynomial regression to identify temporally variable genes.
Song, M. et al. A review of integrative imputation for multi-omics datasets. Front. Genet. 11, 570255 (2020).
Velten, B. et al. Identifying temporal and spatial patterns of variation from multimodal data using MEFISTO. Nat. Methods 19, 179–186 (2022). This dimension-reduction and latent variable model for multiomics data explicitly models temporal and spatial dependencies in the latent embedding.
Townes, F. W. & Engelhardt, B. E. Nonnegative spatial factorization applied to spatial genomics. Nat. Methods 20, 229–238 (2023).
Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nat. Biotechnol. 40, 661–671 (2022).
Andersson, A. et al. Single-cell and spatial transcriptomics enables probabilistic inference of cell type topography. Commun. Biol. 3, 565 (2020).
Dong, R. & Yuan, G.-C. SpatialDWLS: accurate deconvolution of spatial transcriptomic data. Genome Biol. 22, 145 (2021).
Cable, D. M. et al. Robust decomposition of cell type mixtures in spatial transcriptomics. Nat. Biotechnol. 40, 517–526 (2022).
Lopez, R. et al. DestVI identifies continuums of cell types in spatial transcriptomics data. Nat. Biotechnol. 40, 1360–1369 (2022).
Elosua-Bayes, M., Nieto, P., Mereu, E., Gut, I. & Heyn, H. SPOTlight: seeded NMF regression to deconvolute spatial transcriptomics spots with single-cell transcriptomes. Nucleic Acids Res. 49, e50 (2021).
Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nat. Biotechnol. 40, 1349–1359 (2022). This cell type-deconvolution method for spatial transcriptomics data explicitly models spatial dependencies to obtain better estimates of cell type proportions.
Bodein, A., Scott-Boyer, M.-P., Perin, O., Lê Cao, K.-A. & Droit, A. timeOmics: an R package for longitudinal multi-omics data integration. Bioinformatics 38, 577–579 (2021).
Duncker, L. & Sahani, M. Temporal alignment and latent Gaussian process factor inference in population spike trains. In Advances in Neural Information Processing Systems 31 (eds Bengio, S. et al.) 10445–10455 (Curran Associates, 2018).
Childs, D. et al. Nonparametric analysis of thermal proteome profiles reveals novel drug-binding proteins. Mol. Cell. Proteomics 18, 2506–2515 (2019).
Creswell, R. et al. High-resolution temporal profiling of the human gut microbiome reveals consistent and cascading alterations in response to dietary glycans. Genome Med. 12, 59 (2020).
Karlebach, G. & Shamir, R. Modelling and analysis of gene regulatory networks. Nat. Rev. Mol. Cell Biol. 9, 770–780 (2008).
Maini, P. K., Woolley, T. E., Baker, R. E., Gaffney, E. A. & Lee, S. S. Turing’s model for biological pattern formation and the robustness problem. Interface Focus 2, 487–496 (2012).
Van den Berge, K. et al. Trajectory-based differential expression analysis for single-cell sequencing data. Nat. Commun. 11, 1201 (2020).
Bodein, A., Chapleur, O., Droit, A. & Lê Cao, K.-A. A generic multivariate framework for the integration of microbiome longitudinal studies with other data types. Front. Genet. 10, 963 (2019).
Ma, C., Chitra, U., Zhang, S. & Raphael, B. J. Belayer: modeling discrete and continuous spatial variation in gene expression from spatially resolved transcriptomics. Cell Syst. 13, 786–797 (2022).
Rasmussen, C. E. & Williams, C. K. I. Gaussian Processes for Machine Learning (MIT, 2006).
Arnol, D., Schapiro, D., Bodenmiller, B., Saez-Rodriguez, J. & Stegle, O. Modeling cell–cell interactions from spatial molecular data with spatial variance component analysis. Cell Rep. 29, 202–211 (2019).
Äijö, T., Müller, C. L. & Bonneau, R. Temporal probabilistic modeling of bacterial compositions derived from 16S rRNA sequencing. Bioinformatics 34, 372–380 (2018).
Hensman, J., Lawrence, N. D. & Rattray, M. Hierarchical Bayesian modelling of gene expression time series across irregularly sampled replicates and clusters. BMC Bioinformatics 14, 252 (2013).
Walter, F. C., Stegle, O. & Velten, B. FISHFactor: a probabilistic factor model for spatial transcriptomics data with subcellular resolution. Bioinformatics 39, btad183 (2023).
Fang, S., Kirk, P. D. W., Bantscheff, M., Lilley, K. S. & Crook, O. M. A Bayesian semi-parametric model for thermal proteome profiling. Commun. Biol. 4, 810 (2021).
Eddy, S. R. Multiple alignment using hidden Markov models. Proc. Int. Conf. Intell. Syst. Mol. Biol. 3, 114–120 (1995).
Shin, J. et al. Single-cell RNA-seq with waterfall reveals molecular cascades underlying adult neurogenesis. Cell Stem Cell 17, 360–372 (2015).
Schliep, A., Schönhuth, A. & Steinhoff, C. Using hidden Markov models to analyze gene expression time course data. Bioinformatics 19, i255–i263 (2003).
Bar-Joseph, Z. Analyzing time series gene expression data. Bioinformatics 20, 2493–2503 (2004).
Zhu, Q., Shah, S., Dries, R., Cai, L. & Yuan, G.-C. Identification of spatially associated subpopulations by combining scRNAseq and sequential fluorescence in situ hybridization data. Nat. Biotechnol. 36, 1183–1190 (2018). This paper makes use of hidden MRFs to detect spatial domains in sequential fluorescence in situ hybridization data of the mouse visual cortex region.
Dries, R. et al. Giotto: a toolbox for integrative analysis and visualization of spatial expression data. Genome Biol. 22, 78 (2021).
Zhou, J. et al. Graph neural networks: a review of methods and applications. AI Open 1, 57–81 (2020).
Elman, J. L. Finding structure in time. Cogn. Sci. 14, 179–211 (1990).
Lecun, Y., Bottou, L., Bengio, Y. & Haffner, P. Gradient-based learning applied to document recognition. Proc. IEEE 86, 2278–2324 (1998).
Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks. Preprint at arXiv https://doi.org/10.48550/arXiv.1609.02907 (2016).
Fischer, D. S., Schaar, A. C. & Theis, F. J. Modeling intercellular communication in tissues using spatial graphs of cells. Nat. Biotechnol. 41, 332–336 (2023).
Hu, J. et al. SpaGCN: integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nat. Methods 18, 1342–1351 (2021). This method uses a graph convolutional network approach to identify spatial domains and spatially variable genes.
Partel, G. & Wählby, C. Spage2vec: unsupervised representation of localized spatial gene expression signatures. FEBS J. 288, 1859–1870 (2021).
Zhou, Y. et al. CGC-Net: cell graph convolutional network for grading of colorectal cancer histology images. In Proceedings of the IEEE/CVF International Conference on Computer Vision Workshops (2019).
Pati, P. et al. HACT-Net: a hierarchical cell-to-tissue graph neural network for histopathological image classification. In Uncertainty for Safe Utilization of Machine Learning in Medical Imaging, and Graphs in Biomedical Image Analysis 208–219 (Springer International, 2020).
Hetzel, L., Fischer, D. S., Günnemann, S. & Theis, F. J. Graph representation learning for single-cell biology. Curr. Opin. Syst. Biol. 28, 100347 (2021).
Muzio, G., O’Bray, L. & Borgwardt, K. Biological network analysis with deep learning. Brief. Bioinform. 22, 1515–1530 (2021).
Komura, D. & Ishikawa, S. Machine learning methods for histopathological image analysis. Comput. Struct. Biotechnol. J. 16, 34–42 (2018).
Tan, X., Su, A., Tran, M. & Nguyen, Q. SpaCell: integrating tissue morphology and spatial gene expression to predict disease cells. Bioinformatics 36, 2293–2294 (2020).
Ronneberger, O., Fischer, P. & Brox, T. U-Net: convolutional networks for biomedical image segmentation. In Medical Image Computing and Computer-Assisted Intervention—MICCAI 2015: 18th International Conference (eds Navab, N. et al.) 234–241 (Springer International, 2015).
Beeksma, M. et al. Predicting life expectancy with a long short-term memory recurrent neural network using electronic medical records. BMC Med. Inform. Decis. Mak. 19, 36 (2019).
Alley, E. C., Khimulya, G., Biswas, S., AlQuraishi, M. & Church, G. M. Unified rational protein engineering with sequence-based deep representation learning. Nat. Methods 16, 1315–1322 (2019).
Li, S., Chen, J. & Liu, B. Protein remote homology detection based on bidirectional long short-term memory. BMC Bioinformatics 18, 443 (2017).
Almagro Armenteros, J. J., Sønderby, C. K., Sønderby, S. K., Nielsen, H. & Winther, O. DeepLoc: prediction of protein subcellular localization using deep learning. Bioinformatics 33, 3387–3395 (2017).
Angermueller, C., Lee, H. J., Reik, W. & Stegle, O. DeepCpG: accurate prediction of single-cell DNA methylation states using deep learning. Genome Biol. 18, 67 (2017).
Li, Q., Han, Z. & Wu, X.-M. Deeper insights into graph convolutional networks for semi-supervised learning. In Proceedings of the AAAI Conference on Artificial Intelligence 32(1) (AAAI Press, Palo Alto, California USA, 2018).
Srivatsan, S. R. et al. Embryo-scale, single-cell spatial transcriptomics. Science 373, 111–117 (2021).
Miller, B. F., Bambah-Mukku, D., Dulac, C., Zhuang, X. & Fan, J. Characterizing spatial gene expression heterogeneity in spatially resolved single-cell transcriptomic data with nonuniform cellular densities. Genome Res. 31, 1843–1855 (2021).
Ghazanfar, S. et al. Investigating higher-order interactions in single-cell data with scHOT. Nat. Methods 17, 799–806 (2020). This method uses local spatial or temporal summary statistics to identify changes in (co)variation of features in time or space.
Kalaitzis, A. A. & Lawrence, N. D. A simple approach to ranking differentially expressed gene expression time courses through Gaussian process regression. BMC Bioinformatics 12, 180 (2011).
Stegle, O. et al. A robust Bayesian two-sample test for detecting intervals of differential gene expression in microarray time series. J. Comput. Biol. 17, 355–367 (2010).
Qian, X. et al. Probabilistic cell typing enables fine mapping of closely related cell types in situ. Nat. Methods 17, 101–106 (2020).
Argelaguet, R. et al. Multi-Omics Factor Analysis—a framework for unsupervised integration of multi-omics data sets. Mol. Syst. Biol. 14, e8124 (2018).
Welch, J. D., Hartemink, A. J. & Prins, J. F. MATCHER: manifold alignment reveals correspondence between single cell transcriptome and epigenome dynamics. Genome Biol. 18, 138 (2017).
Codeluppi, S. et al. Spatial organization of the somatosensory cortex revealed by osmFISH. Nat. Methods 15, 932–935 (2018).
Chen, K. H., Boettiger, A. N., Moffitt, J. R., Wang, S. & Zhuang, X. RNA imaging. Spatially resolved, highly multiplexed RNA profiling in single cells. Science 348, aaa6090 (2015).
Cuomo, A. S. E. et al. Single-cell RNA-sequencing of differentiating iPS cells reveals dynamic genetic effects on gene expression. Nat. Commun. 11, 810 (2020).
Risom, T. et al. Transition to invasive breast cancer is associated with progressive changes in the structure and composition of tumor stroma. Cell 185, 299–310 (2022).
Olsson, L. M. et al. Dynamics of the normal gut microbiota: a longitudinal one-year population study in Sweden. Cell Host Microbe 30, 726–739 (2022).
Schapiro, D. et al. histoCAT: analysis of cell phenotypes and interactions in multiplex image cytometry data. Nat. Methods 14, 873–876 (2017).
Keren, L. et al. A structured tumor-immune microenvironment in triple negative breast cancer revealed by multiplexed ion beam imaging. Cell 174, 1373–1387 (2018).
Friston, K. J. et al. Spatial registration and normalization of images. Hum. Brain Mapp. 3, 165–189 (1995).
Rood, J. E. et al. Toward a common coordinate framework for the human body. Cell 179, 1455–1467 (2019).
Wang, Q. et al. The Allen Mouse Brain Common Coordinate Framework: a 3D reference atlas. Cell 181, 936–953 (2020).
Giorgino, T. et al. Computing and visualizing dynamic time warping alignments in R: the dtw package. J. Stat. Softw. 31, 1–24 (2009).
Jones, A., Townes, F. W., Li, D. & Engelhardt, B. E. Alignment of spatial genomics and histology data using deep Gaussian processes. Preprint at bioRxiv https://doi.org/10.1101/2022.01.10.475692 (2022).
Zeira, R., Land, M., Strzalkowski, A. & Raphael, B. J. Alignment and integration of spatial transcriptomics data. Nat. Methods 19, 567–575 (2022). This method aligns spatial transcriptomics data from adjacent tissue slices based on an optimal transport problem.
Andersson, A. et al. A landmark-based common coordinate framework for spatial transcriptomics data. Preprint at bioRxiv https://doi.org/10.1101/2021.11.11.468178 (2021).
Metwally, A. A. et al. Robust identification of temporal biomarkers in longitudinal omics studies. Bioinformatics 38, 3802–3811 (2022).
Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nat. Biotechnol. 40, 476–479 (2022).
Mukhopadhyay, N. D. & Chatterjee, S. Causality and pathway search in microarray time series experiment. Bioinformatics 23, 442–449 (2007).
Shojaie, A. & Michailidis, G. Discovering graphical Granger causality using the truncating lasso penalty. Bioinformatics 26, i517–i523 (2010).
Finkle, J. D., Wu, J. J. & Bagheri, N. Windowed Granger causal inference strategy improves discovery of gene regulatory networks. Proc. Natl Acad. Sci. USA 115, 2252–2257 (2018).
Papili Gao, N., Ud-Dean, S. M. M., Gandrillon, O. & Gunawan, R. SINCERITIES: inferring gene regulatory networks from time-stamped single cell transcriptional expression profiles. Bioinformatics 34, 258–266 (2018).
Wu, A. P., Singh, R. & Berger, B. Granger causal inference on DAGs identifies genomic loci regulating transcription. In International Conference on Learning Representations (ICLR, 2022).
Matsumoto, H. et al. SCODE: an efficient regulatory network inference algorithm from single-cell RNA-seq during differentiation. Bioinformatics 33, 2314–2321 (2017).
Ocone, A., Haghverdi, L., Mueller, N. S. & Theis, F. J. Reconstructing gene regulatory dynamics from high-dimensional single-cell snapshot data. Bioinformatics 31, i89–i96 (2015).
Sanchez-Castillo, M., Blanco, D., Tienda-Luna, I. M., Carrion, M. C. & Huang, Y. A Bayesian framework for the inference of gene regulatory networks from time and pseudo-time series data. Bioinformatics 34, 964–970 (2018).
Aubin-Frankowski, P.-C. & Vert, J.-P. Gene regulation inference from single-cell RNA-seq data with linear differential equations and velocity inference. Bioinformatics 36, 4774–4780 (2020).
Pham, D. et al. stLearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell–cell interactions and spatial trajectories within undissociated tissues. Preprint at bioRxiv https://doi.org/10.1101/2020.05.31.125658 (2020).
Efremova, M., Vento-Tormo, M., Teichmann, S. A. & Vento-Tormo, R. CellPhoneDB: inferring cell–cell communication from combined expression of multi-subunit ligand–receptor complexes. Nat. Protoc. 15, 1484–1506 (2020).
Palla, G. et al. Squidpy: a scalable framework for spatial omics analysis. Nat. Methods 19, 171–178 (2022).
Yuan, Y. & Bar-Joseph, Z. GCNG: graph convolutional networks for inferring gene interaction from spatial transcriptomics data. Genome Biol. 21, 300 (2020).
Asp, M. et al. A spatiotemporal organ-wide gene expression and cell atlas of the developing human heart. Cell 179, 1647–1660 (2019).
Maniatis, S. et al. Spatiotemporal dynamics of molecular pathology in amyotrophic lateral sclerosis. Science 364, 89–93 (2019).
Biancalani, T. et al. Deep learning and alignment of spatially resolved single-cell transcriptomes with Tangram. Nat. Methods 18, 1352–1362 (2021).
Baker, E. A. G., Schapiro, D., Dumitrascu, B., Vickovic, S. & Regev, A. In silico tissue generation and power analysis for spatial omics. Nat. Methods 20, 424–431 (2023).
Bost, P., Schulz, D., Engler, S., Wasserfall, C. & Bodenmiller, B. Optimizing multiplexed imaging experimental design through tissue spatial segregation estimation. Nat. Methods 20, 418–423 (2023).
We thank S. Ghazanfar, R. Argelaguet, L. Marconato and I. Kats for providing feedback on the manuscript. The work was supported by the BMBF (COMPLS project MOFA no. 031L0171B), the European Commission (ERC project DECODE, 810296) and core support from the European Molecular Biology Laboratory and the German Cancer Research Center.
O.S. is a paid advisor of Insitro. The remaining author declares no competing interests.
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Velten, B., Stegle, O. Principles and challenges of modeling temporal and spatial omics data. Nat Methods 20, 1462–1474 (2023). https://doi.org/10.1038/s41592-023-01992-y