{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,28]],"date-time":"2026-08-28T00:13:09Z","timestamp":1787875989622,"version":"build-2784847793"},"reference-count":77,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T00:00:00Z","timestamp":1767571200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T00:00:00Z","timestamp":1767571200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Nat Comput Sci"],"DOI":"10.1038\/s43588-025-00934-2","type":"journal-article","created":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T10:02:11Z","timestamp":1767607331000},"page":"193-207","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Decoding cell state transitions driven by dynamic cell\u2013cell communication in spatial transcriptomics"],"prefix":"10.1038","volume":"6","author":[{"given":"Lulu","family":"Yan","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dongyan","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3399-7260","authenticated-orcid":false,"given":"Xiaoqiang","family":"Sun","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,1,5]]},"reference":[{"key":"934_CR1","doi-asserted-by":"publisher","first-page":"975","DOI":"10.1038\/s41586-022-05194-y","volume":"609","author":"OS Rukhlenko","year":"2022","unstructured":"Rukhlenko, O. S. et al. Control of cell state transitions. Nature 609, 975\u2013985 (2022).","journal-title":"Nature"},{"key":"934_CR2","doi-asserted-by":"publisher","DOI":"10.1242\/dev.199950","volume":"148","author":"C Mulas","year":"2021","unstructured":"Mulas, C., Chaigne, A., Smith, A. & Chalut, K. J. Cell state transitions: definitions and challenges. Development 148, dev199950 (2021).","journal-title":"Development"},{"key":"934_CR3","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1038\/nature21350","volume":"541","author":"A Tanay","year":"2017","unstructured":"Tanay, A. & Regev, A. Scaling single-cell genomics from phenomenology to mechanism. Nature 541, 331\u2013338 (2017).","journal-title":"Nature"},{"key":"934_CR4","doi-asserted-by":"publisher","first-page":"1535","DOI":"10.1016\/j.cell.2018.03.074","volume":"173","author":"JD Buenrostro","year":"2018","unstructured":"Buenrostro, J. D. et al. Integrated single-cell analysis maps the continuous regulatory landscape of human hematopoietic differentiation. Cell 173, 1535\u20131548.e16 (2018).","journal-title":"Cell"},{"key":"934_CR5","doi-asserted-by":"publisher","first-page":"1145","DOI":"10.1038\/nbt.3711","volume":"34","author":"A Wagner","year":"2016","unstructured":"Wagner, A., Regev, A. & Yosef, N. Revealing the vectors of cellular identity with single-cell genomics. Nat. Biotechnol. 34, 1145\u20131160 (2016).","journal-title":"Nat. Biotechnol."},{"key":"934_CR6","doi-asserted-by":"publisher","DOI":"10.1186\/s13059-019-1663-x","volume":"20","author":"FA Wolf","year":"2019","unstructured":"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).","journal-title":"Genome Biol."},{"key":"934_CR7","doi-asserted-by":"publisher","DOI":"10.1186\/s12864-018-4772-0","volume":"19","author":"K Street","year":"2018","unstructured":"Street, K. et al. Slingshot: cell lineage and pseudotime inference for single-cell transcriptomics. BMC Genom. 19, 477 (2018).","journal-title":"BMC Genom."},{"key":"934_CR8","doi-asserted-by":"publisher","first-page":"496","DOI":"10.1038\/s41586-019-0969-x","volume":"566","author":"J Cao","year":"2019","unstructured":"Cao, J. et al. The single-cell transcriptional landscape of mammalian organogenesis. Nature 566, 496\u2013502 (2019).","journal-title":"Nature"},{"key":"934_CR9","doi-asserted-by":"publisher","first-page":"979","DOI":"10.1038\/nmeth.4402","volume":"14","author":"X Qiu","year":"2017","unstructured":"Qiu, X. et al. Reversed graph embedding resolves complex single-cell trajectories. Nat. Methods 14, 979\u2013982 (2017).","journal-title":"Nat. Methods"},{"key":"934_CR10","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1038\/s41587-019-0068-4","volume":"37","author":"M Setty","year":"2019","unstructured":"Setty, M. et al. Characterization of cell fate probabilities in single-cell data with Palantir. Nat. Biotechnol. 37, 451\u2013460 (2019).","journal-title":"Nat. Biotechnol."},{"key":"934_CR11","doi-asserted-by":"publisher","first-page":"3509","DOI":"10.1093\/bioinformatics\/btab364","volume":"37","author":"G Weng","year":"2021","unstructured":"Weng, G., Kim, J. & Won, K. J. VeTra: a tool for trajectory inference based on RNA velocity. Bioinformatics 37, 3509\u20133513 (2021).","journal-title":"Bioinformatics"},{"key":"934_CR12","doi-asserted-by":"publisher","first-page":"1408","DOI":"10.1038\/s41587-020-0591-3","volume":"38","author":"V Bergen","year":"2020","unstructured":"Bergen, V., Lange, M., Peidli, S., Wolf, F. A. & Theis, F. J. Generalizing RNA velocity to transient cell states through dynamical modeling. Nat. Biotechnol. 38, 1408\u20131414 (2020).","journal-title":"Nat. Biotechnol."},{"key":"934_CR13","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1038\/s41592-021-01346-6","volume":"19","author":"M Lange","year":"2022","unstructured":"Lange, M. et al. CellRank for directed single-cell fate mapping. Nat. Methods 19, 159\u2013170 (2022).","journal-title":"Nat. Methods"},{"key":"934_CR14","doi-asserted-by":"publisher","DOI":"10.1186\/s13059-023-03148-9","volume":"25","author":"H Cui","year":"2024","unstructured":"Cui, H. et al. DeepVelo: deep learning extends RNA velocity to multi-lineage systems with cell-specific kinetics. Genome Biol. 25, 27 (2024).","journal-title":"Genome Biol."},{"key":"934_CR15","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-022-34188-7","volume":"13","author":"M Gao","year":"2022","unstructured":"Gao, M., Qiao, C. & Huang, Y. UniTVelo: temporally unified RNA velocity reinforces single-cell trajectory inference. Nat. Commun. 13, 6586 (2022).","journal-title":"Nat. Commun."},{"key":"934_CR16","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1038\/s41592-023-01994-w","volume":"21","author":"A Gayoso","year":"2024","unstructured":"Gayoso, A. et al. Deep generative modeling of transcriptional dynamics for RNA velocity analysis in single cells. Nat. Methods 21, 50\u201359 (2024).","journal-title":"Nat. Methods"},{"key":"934_CR17","doi-asserted-by":"publisher","first-page":"494","DOI":"10.1038\/s41586-018-0414-6","volume":"560","author":"G La Manno","year":"2018","unstructured":"La Manno, G. et al. RNA velocity of single cells. Nature 560, 494\u2013498 (2018).","journal-title":"Nature"},{"key":"934_CR18","doi-asserted-by":"publisher","DOI":"10.1016\/j.crmeth.2022.100359","volume":"2","author":"R Gupta","year":"2022","unstructured":"Gupta, R., Cerletti, D., Gut, G., Oxenius, A. & Claassen, M. Simulation-based inference of differentiation trajectories from RNA velocity fields. Cell Rep. Methods 2, 100359 (2022).","journal-title":"Cell Rep. Methods"},{"key":"934_CR19","doi-asserted-by":"publisher","DOI":"10.1016\/j.crmeth.2021.100095","volume":"1","author":"Z Zhang","year":"2021","unstructured":"Zhang, Z. & Zhang, X. Inference of high-resolution trajectories in single-cell RNA-seq data by using RNA velocity. Cell Rep. Methods 1, 100095 (2021).","journal-title":"Cell Rep. Methods"},{"key":"934_CR20","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1126\/science.aaf2403","volume":"353","author":"PL Stahl","year":"2016","unstructured":"Stahl, P. L. et al. Visualization and analysis of gene expression in tissue sections by spatial transcriptomics. Science 353, 78\u201382 (2016).","journal-title":"Science"},{"key":"934_CR21","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1038\/s41592-020-01033-y","volume":"18","author":"V Marx","year":"2021","unstructured":"Marx, V. Method of the Year: spatially resolved transcriptomics. Nat. Methods 18, 9\u201314 (2021).","journal-title":"Nat. Methods"},{"key":"934_CR22","doi-asserted-by":"publisher","DOI":"10.1093\/bioinformatics\/btac805","volume":"39","author":"L Yan","year":"2023","unstructured":"Yan, L. & Sun, X. Benchmarking and integration of methods for deconvoluting spatial transcriptomic data. Bioinformatics 39, btac805 (2023).","journal-title":"Bioinformatics"},{"key":"934_CR23","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-022-31739-w","volume":"13","author":"H Ren","year":"2022","unstructured":"Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with SpaceFlow. Nat. Commun. 13, 4076 (2022).","journal-title":"Nat. Commun."},{"key":"934_CR24","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-023-43120-6","volume":"14","author":"D Pham","year":"2023","unstructured":"Pham, D. et al. Robust mapping of spatiotemporal trajectories and cell\u2013cell interactions in healthy and diseased tissues. Nat. Commun. 14, 7739 (2023).","journal-title":"Nat. Commun."},{"key":"934_CR25","doi-asserted-by":"publisher","DOI":"10.34133\/research.0390","volume":"7","author":"H Wang","year":"2024","unstructured":"Wang, H., Zhao, J., Nie, Q., Zheng, C. & Sun, X. Dissecting spatiotemporal structures in spatial transcriptomics via diffusion-based adversarial learning. Research 7, 0390 (2024).","journal-title":"Research"},{"key":"934_CR26","doi-asserted-by":"publisher","DOI":"10.1016\/j.cels.2025.101194","volume":"16","author":"X Shen","year":"2025","unstructured":"Shen, X. et al. Inferring cell trajectories of spatial transcriptomics via optimal transport analysis. Cell Syst. 16, 101194 (2025).","journal-title":"Cell Syst."},{"key":"934_CR27","doi-asserted-by":"publisher","first-page":"1053","DOI":"10.1038\/s41592-024-02266-x","volume":"21","author":"P Zhou","year":"2024","unstructured":"Zhou, P., Bocci, F., Li, T. & Nie, Q. Spatial transition tensor of single cells. Nat. Methods 21, 1053\u20131062 (2024).","journal-title":"Nat. Methods"},{"key":"934_CR28","doi-asserted-by":"publisher","first-page":"1484","DOI":"10.1038\/s41596-020-0292-x","volume":"15","author":"M Efremova","year":"2020","unstructured":"Efremova, M., Vento-Tormo, M., Teichmann, S. A. & Vento-Tormo, R. CellPhoneDB: inferring cell\u2013cell communication from combined expression of multi-subunit ligand\u2013receptor complexes. Nat. Protoc. 15, 1484\u20131506 (2020).","journal-title":"Nat. Protoc."},{"key":"934_CR29","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-021-21246-9","volume":"12","author":"S Jin","year":"2021","unstructured":"Jin, S. et al. Inference and analysis of cell\u2013cell communication using CellChat. Nat. Commun. 12, 1088 (2021).","journal-title":"Nat. Commun."},{"key":"934_CR30","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1038\/s41592-019-0667-5","volume":"17","author":"R Browaeys","year":"2020","unstructured":"Browaeys, R., Saelens, W. & Saeys, Y. NicheNet: modeling intercellular communication by linking ligands to target genes. Nat. Methods 17, 159\u2013162 (2020).","journal-title":"Nat. Methods"},{"key":"934_CR31","doi-asserted-by":"publisher","first-page":"988","DOI":"10.1093\/bib\/bbaa327","volume":"22","author":"JY Cheng","year":"2021","unstructured":"Cheng, J. Y., Zhang, J., Wu, Z. D. & Sun, X. Q. Inferring microenvironmental regulation of gene expression from single-cell RNA sequencing data using scMLnet with an application to COVID-19. Brief. Bioinform. 22, 988\u20131005 (2021).","journal-title":"Brief. Bioinform."},{"key":"934_CR32","doi-asserted-by":"publisher","DOI":"10.1126\/sciadv.abl5165","volume":"8","author":"X Ni","year":"2022","unstructured":"Ni, X. et al. Interrogating glioma\u2013M2 macrophage interactions identifies Gal-9\/Tim-3 as a viable target against PTEN-null glioblastoma. Sci. Adv. 8, eabl516 (2022).","journal-title":"Sci. Adv."},{"key":"934_CR33","doi-asserted-by":"publisher","first-page":"1788","DOI":"10.1101\/gr.278001.123","volume":"33","author":"J Luo","year":"2023","unstructured":"Luo, J., Deng, M., Zhang, X. & Sun, X. ESICCC as a systematic computational framework for evaluation, selection, and integration of cell\u2013cell communication inference methods. Genome Res. 33, 1788\u20131805 (2023).","journal-title":"Genome Res."},{"key":"934_CR34","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1038\/s41576-020-00292-x","volume":"22","author":"E Armingol","year":"2021","unstructured":"Armingol, E., Officer, A., Harismendy, O. & Lewis, N. E. Deciphering cell\u2013cell interactions and communication from gene expression. Nat. Rev. Genet. 22, 71\u201388 (2021).","journal-title":"Nat. Rev. Genet."},{"key":"934_CR35","doi-asserted-by":"publisher","first-page":"627","DOI":"10.1038\/s41576-021-00370-8","volume":"22","author":"SK Longo","year":"2021","unstructured":"Longo, S. K., Guo, M. G., Ji, A. L. & Khavari, P. A. Integrating single-cell and spatial transcriptomics to elucidate intercellular tissue dynamics. Nat. Rev. Genet. 22, 627\u2013644 (2021).","journal-title":"Nat. Rev. Genet."},{"key":"934_CR36","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1038\/s41576-023-00685-8","volume":"25","author":"E Armingol","year":"2024","unstructured":"Armingol, E., Baghdassarian, H. M. & Lewis, N. E. The diversification of methods for studying cell\u2013cell interactions and communication. Nat. Rev. Genet. 25, 381\u2013400 (2024).","journal-title":"Nat. Rev. Genet."},{"key":"934_CR37","doi-asserted-by":"publisher","first-page":"218","DOI":"10.1038\/s41592-022-01728-4","volume":"20","author":"Z Cang","year":"2023","unstructured":"Cang, Z. et al. Screening cell\u2013cell communication in spatial transcriptomics via collective optimal transport. Nat. Methods 20, 218\u2013228 (2023).","journal-title":"Nat. Methods"},{"key":"934_CR38","doi-asserted-by":"publisher","first-page":"1400","DOI":"10.1101\/gr.279857.124","volume":"35","author":"L Yan","year":"2025","unstructured":"Yan, L., Cheng, J., Nie, Q. & Sun, X. Dissecting multilayer cell\u2013cell communications with signaling feedback loops from spatial transcriptomics data. Genome Res. 35, 1400\u20131414 (2025).","journal-title":"Genome Res."},{"key":"934_CR39","doi-asserted-by":"publisher","unstructured":"Liu, J. et al. CytoSignal detects locations and dynamics of ligand\u2013receptor signaling at cellular resolution from spatial transcriptomic data. Preprint at bioRxiv https:\/\/doi.org\/10.1101\/2024.03.08.584153 (2024).","DOI":"10.1101\/2024.03.08.584153"},{"key":"934_CR40","doi-asserted-by":"publisher","DOI":"10.15252\/msb.202110282","volume":"17","author":"V Bergen","year":"2021","unstructured":"Bergen, V., Soldatov, R. A., Kharchenko, P. V. & Theis, F. J. RNA velocity\u2014current challenges and future perspectives. Mol. Syst. Biol. 17, e10282 (2021).","journal-title":"Mol. Syst. Biol."},{"key":"934_CR41","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1010492","volume":"18","author":"G Gorin","year":"2022","unstructured":"Gorin, G., Fang, M., Chari, T. & Pachter, L. RNA velocity unraveled. PLoS Comput. Biol. 18, e1010492 (2022).","journal-title":"PLoS Comput. Biol."},{"key":"934_CR42","doi-asserted-by":"publisher","first-page":"19490","DOI":"10.1073\/pnas.1912459116","volume":"116","author":"C Xia","year":"2019","unstructured":"Xia, C., Fan, J., Emanuel, G., Hao, J. & Zhuang, X. Spatial transcriptome profiling by MERFISH reveals subcellular RNA compartmentalization and cell cycle-dependent gene expression. Proc. Natl Acad. Sci. USA 116, 19490\u201319499 (2019).","journal-title":"Proc. Natl Acad. Sci. USA"},{"key":"934_CR43","doi-asserted-by":"publisher","DOI":"10.1126\/science.aat5691","volume":"361","author":"X Wang","year":"2018","unstructured":"Wang, X. et al. Three-dimensional intact-tissue sequencing of single-cell transcriptional states. Science 361, eaat5691 (2018).","journal-title":"Science"},{"key":"934_CR44","doi-asserted-by":"publisher","first-page":"360","DOI":"10.1038\/nmeth.2892","volume":"11","author":"E Lubeck","year":"2014","unstructured":"Lubeck, E., Coskun, A. F., Zhiyentayev, T., Ahmad, M. & Cai, L. Single-cell in situ RNA profiling by sequential hybridization. Nat. Methods 11, 360\u2013361 (2014).","journal-title":"Nat. Methods"},{"key":"934_CR45","doi-asserted-by":"publisher","DOI":"10.1126\/science.aaa6090","volume":"348","author":"KH Chen","year":"2015","unstructured":"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).","journal-title":"Science"},{"key":"934_CR46","doi-asserted-by":"publisher","DOI":"10.1126\/science.aau5324","volume":"362","author":"JR Moffitt","year":"2018","unstructured":"Moffitt, J. R. et al. Molecular, spatial, and functional single-cell profiling of the hypothalamic preoptic region. Science 362, eaau5324 (2018).","journal-title":"Science"},{"key":"934_CR47","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1038\/s41586-019-1049-y","volume":"568","author":"CL Eng","year":"2019","unstructured":"Eng, C. L. et al. Transcriptome-scale super-resolved imaging in tissues by RNA seqFISH+. Nature 568, 235\u2013239 (2019).","journal-title":"Nature"},{"key":"934_CR48","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-024-45661-w","volume":"15","author":"J Li","year":"2024","unstructured":"Li, J., Pan, X., Yuan, Y. & Shen, H. B. TFvelo: gene regulation inspired RNA velocity estimation. Nat. Commun. 15, 1387 (2024).","journal-title":"Nat. Commun."},{"key":"934_CR49","doi-asserted-by":"publisher","unstructured":"Qiu, X. et al. Spateo: multidimensional spatiotemporal modeling of single-cell spatial transcriptomics. Preprint at bioRxiv https:\/\/doi.org\/10.1101\/2022.12.07.519417 (2022).","DOI":"10.1101\/2022.12.07.519417"},{"key":"934_CR50","doi-asserted-by":"publisher","first-page":"1176","DOI":"10.1038\/s41588-023-01435-6","volume":"55","author":"AS Kumar","year":"2023","unstructured":"Kumar, A. S. et al. Spatiotemporal transcriptomic maps of whole mouse embryos at the onset of organogenesis. Nat. Genet. 55, 1176\u20131185 (2023).","journal-title":"Nat. Genet."},{"key":"934_CR51","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2105859118","volume":"118","author":"C Qiao","year":"2021","unstructured":"Qiao, C. & Huang, Y. Representation learning of RNA velocity reveals robust cell transitions. Proc. Natl Acad. Sci. USA 118, e2105859118 (2021).","journal-title":"Proc. Natl Acad. Sci. USA"},{"key":"934_CR52","doi-asserted-by":"publisher","first-page":"699","DOI":"10.1146\/annurev-cellbio-100814-125353","volume":"31","author":"S Lodato","year":"2015","unstructured":"Lodato, S. & Arlotta, P. Generating neuronal diversity in the mammalian cerebral cortex. Annu. Rev. Cell. Dev. Biol. 31, 699\u2013720 (2015).","journal-title":"Annu. Rev. Cell. Dev. Biol."},{"key":"934_CR53","doi-asserted-by":"publisher","DOI":"10.1186\/s13059-023-03065-x","volume":"24","author":"SC Zheng","year":"2023","unstructured":"Zheng, S. C., Stein-O\u2019Brien, G., Boukas, L., Goff, L. A. & Hansen, K. D. Pumping the brakes on RNA velocity by understanding and interpreting RNA velocity estimates. Genome Biol. 24, 246 (2023).","journal-title":"Genome Biol."},{"key":"934_CR54","doi-asserted-by":"publisher","first-page":"837","DOI":"10.1016\/S0925-4773(03)00066-2","volume":"120","author":"DL Chapman","year":"2003","unstructured":"Chapman, D. L., Cooper-Morgan, A., Harrelson, Z. & Papaioannou, V. E. Critical role for Tbx6 in mesoderm specification in the mouse embryo. Mech. Dev. 120, 837\u2013847 (2003).","journal-title":"Mech. Dev."},{"key":"934_CR55","doi-asserted-by":"publisher","first-page":"3807","DOI":"10.1242\/dev.00573","volume":"130","author":"S Forlani","year":"2003","unstructured":"Forlani, S., Lawson, K. A. & Deschamps, J. Acquisition of Hox codes during gastrulation and axial elongation in the mouse embryo. Development 130, 3807\u20133819 (2003).","journal-title":"Development"},{"key":"934_CR56","doi-asserted-by":"publisher","first-page":"514","DOI":"10.1016\/j.devcel.2017.07.021","volume":"42","author":"F Koch","year":"2017","unstructured":"Koch, F. et al. Antagonistic activities of Sox2 and Brachyury control the fate choice of neuro-mesodermal progenitors. Dev. Cell 42, 514\u2013526.e7 (2017).","journal-title":"Dev. Cell"},{"key":"934_CR57","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1038\/s41587-020-0739-1","volume":"39","author":"RR Stickels","year":"2021","unstructured":"Stickels, R. R. et al. Highly sensitive spatial transcriptomics at near-cellular resolution with Slide-seqV2. Nat. Biotechnol. 39, 313\u2013319 (2021).","journal-title":"Nat. Biotechnol."},{"key":"934_CR58","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-023-37745-w","volume":"14","author":"T Yabe","year":"2023","unstructured":"Yabe, T., Uriu, K. & Takada, S. Ripply suppresses Tbx6 to induce dynamic-to-static conversion in somite segmentation. Nat. Commun. 14, 2115 (2023).","journal-title":"Nat. Commun."},{"key":"934_CR59","doi-asserted-by":"publisher","first-page":"e33068","DOI":"10.7554\/eLife.33068","volume":"7","author":"W Zhao","year":"2018","unstructured":"Zhao, W. et al. Ripply2 recruits proteasome complex for Tbx6 degradation to define segment border during murine somitogenesis. eLife 7, e33068 (2018).","journal-title":"eLife"},{"key":"934_CR60","doi-asserted-by":"publisher","first-page":"753","DOI":"10.1387\/ijdb.072332sr","volume":"51","author":"S Reijntjes","year":"2007","unstructured":"Reijntjes, S., Stricker, S. & Mankoo, B. S. A comparative analysis of Meox1 and Meox2 in the developing somites and limbs of the chick embryo. Int. J. Dev. Biol. 51, 753\u2013759 (2007).","journal-title":"Int. J. Dev. Biol."},{"key":"934_CR61","doi-asserted-by":"publisher","first-page":"4655","DOI":"10.1242\/dev.00687","volume":"130","author":"BS Mankoo","year":"2003","unstructured":"Mankoo, B. S. et al. The concerted action of Meox homeobox genes is required upstream of genetic pathways essential for the formation, patterning and differentiation of somites. Development 130, 4655\u20134664 (2003).","journal-title":"Development"},{"key":"934_CR62","doi-asserted-by":"publisher","first-page":"632","DOI":"10.1016\/j.stemcr.2015.02.018","volume":"4","author":"ES Lippmann","year":"2015","unstructured":"Lippmann, E. S. et al. Deterministic HOX patterning in human pluripotent stem cell-derived neuroectoderm. Stem Cell Rep. 4, 632\u2013644 (2015).","journal-title":"Stem Cell Rep."},{"key":"934_CR63","doi-asserted-by":"publisher","DOI":"10.3390\/cells13060549","volume":"13","author":"H Kondoh","year":"2024","unstructured":"Kondoh, H. & Takemoto, T. The origin and regulation of neuromesodermal progenitors (NMPs) in embryos. Cells 13, 549 (2024).","journal-title":"Cells"},{"key":"934_CR64","doi-asserted-by":"publisher","first-page":"4243","DOI":"10.1242\/dev.112979","volume":"141","author":"DA Turner","year":"2014","unstructured":"Turner, D. A. et al. Wnt\/beta-catenin and FGF signalling direct the specification and maintenance of a neuromesodermal axial progenitor in ensembles of mouse embryonic stem cells. Development 141, 4243\u20134253 (2014).","journal-title":"Development"},{"key":"934_CR65","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0188842","volume":"12","author":"D Jedroszka","year":"2017","unstructured":"Jedroszka, D., Orzechowska, M., Hamouz, R., Gorniak, K. & Bednarek, A. K. Markers of epithelial-to-mesenchymal transition reflect tumor biology according to patient age and Gleason score in prostate cancer. PLoS ONE 12, e0188842 (2017).","journal-title":"PLoS ONE"},{"key":"934_CR66","doi-asserted-by":"publisher","first-page":"1830","DOI":"10.1038\/s41592-024-02408-1","volume":"21","author":"J Zhu","year":"2024","unstructured":"Zhu, J. et al. Mapping cellular interactions from spatially resolved transcriptomics data. Nat. Methods 21, 1830\u20131842 (2024).","journal-title":"Nat. Methods"},{"key":"934_CR67","doi-asserted-by":"publisher","DOI":"10.1093\/nar\/gkv007","volume":"43","author":"M Ritchie","year":"2015","unstructured":"Ritchie, M. et al. limma powers differential expression analyses for RNA-sequencing and microarray studies. Nucleic Acids Res. 43, e47 (2015).","journal-title":"Nucleic Acids Res."},{"key":"934_CR68","doi-asserted-by":"publisher","DOI":"10.3390\/jcm5040041","volume":"5","author":"J Zhang","year":"2016","unstructured":"Zhang, J., Tian, X. J. & Xing, J. Signal transduction pathways of EMT induced by TGF-\u03b2, SHH, and WNT and their crosstalks. J. Clin. Med. 5, 41 (2016).","journal-title":"J. Clin. Med."},{"key":"934_CR69","doi-asserted-by":"publisher","first-page":"12","DOI":"10.1016\/j.matbio.2023.11.001","volume":"125","author":"S Fernandes","year":"2024","unstructured":"Fernandes, S. et al. TGF-beta induces matrisome pathological alterations and EMT in patient-derived prostate cancer tumoroids. Matrix Biol. 125, 12\u201330 (2024).","journal-title":"Matrix Biol."},{"key":"934_CR70","doi-asserted-by":"publisher","first-page":"838","DOI":"10.1137\/24M1663077","volume":"23","author":"H Lin","year":"2025","unstructured":"Lin, H., Zhang, J., Nie, Q. & Sun, X. Multiscale modeling of tumor\u2013macrophage interactions underlying immunotherapy resistance in glioblastoma. Multiscale Model. Simul. 23, 838\u2013863 (2025).","journal-title":"Multiscale Model. Simul."},{"key":"934_CR71","doi-asserted-by":"publisher","DOI":"10.1126\/sciadv.adv3316","volume":"11","author":"Z Liu","year":"2025","unstructured":"Liu, Z., Zhang, J., Liu, H. & Sun, X. Multiscale mathematical model-informed reinforcement learning optimizes combination treatment scheduling in glioblastoma evolution. Sci. Adv. 11, eadv3316 (2025).","journal-title":"Sci. Adv."},{"key":"934_CR72","doi-asserted-by":"publisher","first-page":"7045","DOI":"10.1016\/j.cell.2024.11.015","volume":"187","author":"B Charlotte","year":"2024","unstructured":"Charlotte, B. et al. How to build the virtual cell with artificial intelligence: priorities and opportunities. Cell 187, 7045\u20137063 (2024).","journal-title":"Cell"},{"key":"934_CR73","doi-asserted-by":"crossref","unstructured":"Ainsworth, S. In Steady-State Enzyme Kinetics 43\u201373 (Macmillan, 1977).","DOI":"10.1007\/978-1-349-01959-5_3"},{"key":"934_CR74","doi-asserted-by":"publisher","first-page":"686","DOI":"10.1016\/j.jcp.2018.10.045","volume":"378","author":"M Raissi","year":"2019","unstructured":"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\u2013707 (2019).","journal-title":"J. Comput. Phys."},{"key":"934_CR75","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0315762","volume":"19","author":"D Viet Cuong","year":"2024","unstructured":"Viet Cuong, D., Lalic, B., Petric, M., Thanh Binh, N. & Roantree, M. Adapting physics-informed neural networks to improve ODE optimization in mosquito population dynamics. PLoS ONE 19, e0315762 (2024).","journal-title":"PLoS ONE"},{"key":"934_CR76","doi-asserted-by":"publisher","first-page":"111260","DOI":"10.1016\/j.jcp.2022.111260","volume":"462","author":"L Yuan","year":"2022","unstructured":"Yuan, L., Ni, Y., Deng, X. & Hao, S. A-PINN: auxiliary physics informed neural networks for forward and inverse problems of nonlinear integro-differential equations. J. Comput. Phys. 462, 111260 (2022).","journal-title":"J. Comput. Phys."},{"key":"934_CR77","doi-asserted-by":"publisher","unstructured":"Yan, L., Zhang, D., Sun, X. CCCvelo. Zenodo https:\/\/doi.org\/10.5281\/zenodo.17384457 (2025).","DOI":"10.5281\/zenodo.17384457"}],"container-title":["Nature Computational Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s43588-025-00934-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s43588-025-00934-2","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s43588-025-00934-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T23:02:17Z","timestamp":1772060537000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s43588-025-00934-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,5]]},"references-count":77,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2026,2]]}},"alternative-id":["934"],"URL":"https:\/\/doi.org\/10.1038\/s43588-025-00934-2","relation":{},"ISSN":["2662-8457"],"issn-type":[{"value":"2662-8457","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,5]]},"assertion":[{"value":"8 June 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 November 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 January 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no competing interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}]}}