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We propose OTVelo, a methodology that takes time-stamped single-cell gene expression data as input and predicts gene regulation across two time points. It is known that the rate of change of gene expression, which we will refer to as gene velocity, provides crucial information that enhances such inference; however, this information is not always available due to the limitations in sequencing depth. Our algorithm overcomes this limitation by estimating gene velocities using optimal transport. We then infer gene regulation using time-lagged correlation and Granger causality via regularized linear regression. Instead of providing an aggregated network across all time points, our method uncovers the underlying dynamical mechanism across time points. We validate our algorithm on 13 simulated datasets with both synthetic and curated networks and demonstrate its efficacy on 9 experimental data sets.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1012476","type":"journal-article","created":{"date-parts":[[2025,5,8]],"date-time":"2025-05-08T16:12:57Z","timestamp":1746720777000},"page":"e1012476","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":6,"title":["Optimal transport reveals dynamic gene regulatory networks via gene velocity estimation"],"prefix":"10.1371","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7499-0084","authenticated-orcid":true,"given":"Wenjun","family":"Zhao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Erica","family":"Larschan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5432-1235","authenticated-orcid":true,"given":"Bj\u00f6rn","family":"Sandstede","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ritambhara","family":"Singh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2025,5,8]]},"reference":[{"key":"pcbi.1012476.ref001","article-title":"Single-cell transcriptome sequencing: recent advances and remaining challenges","volume":"5","author":"S Liu","year":"2016","journal-title":"F1000Res"},{"issue":"1","key":"pcbi.1012476.ref002","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1186\/s12864-018-4772-0","article-title":"Slingshot: cell lineage and pseudotime inference for single-cell transcriptomics","volume":"19","author":"K Street","year":"2018","journal-title":"BMC Genomics"},{"issue":"9","key":"pcbi.1012476.ref003","article-title":"Inferring regulatory networks from expression data using tree-based methods","volume":"5","author":"VA Huynh-Thu","year":"2010","journal-title":"PLoS One"},{"issue":"11","key":"pcbi.1012476.ref004","doi-asserted-by":"crossref","first-page":"1083","DOI":"10.1038\/nmeth.4463","article-title":"SCENIC: single-cell regulatory network inference and clustering","volume":"14","author":"S Aibar","year":"2017","journal-title":"Nat Methods"},{"issue":"5","key":"pcbi.1012476.ref005","doi-asserted-by":"crossref","first-page":"764","DOI":"10.1093\/bioinformatics\/btw729","article-title":"LEAP: constructing gene co-expression networks for single-cell RNA-sequencing data using pseudotime ordering","volume":"33","author":"AT Specht","year":"2017","journal-title":"Bioinformatics"},{"issue":"3","key":"pcbi.1012476.ref006","article-title":"Gene Regulatory Network Inference from Single-Cell Data Using Multivariate Information Measures","volume":"5","author":"TE Chan","year":"2017","journal-title":"Cell Syst"},{"issue":"2","key":"pcbi.1012476.ref007","doi-asserted-by":"crossref","first-page":"258","DOI":"10.1093\/bioinformatics\/btx575","article-title":"SINCERITIES: inferring gene regulatory networks from time-stamped single cell transcriptional expression profiles","volume":"34","author":"N Papili Gao","year":"2018","journal-title":"Bioinformatics"},{"issue":"3","key":"pcbi.1012476.ref008","article-title":"Inferring Causal Gene Regulatory Networks from Coupled Single-Cell Expression Dynamics Using Scribe","volume":"10","author":"X Qiu","year":"2020","journal-title":"Cell Syst"},{"issue":"15","key":"pcbi.1012476.ref009","doi-asserted-by":"crossref","first-page":"2314","DOI":"10.1093\/bioinformatics\/btx194","article-title":"SCODE: an efficient regulatory network inference algorithm from single-cell RNA-Seq during differentiation","volume":"33","author":"H Matsumoto","year":"2017","journal-title":"Bioinformatics"},{"key":"pcbi.1012476.ref010","doi-asserted-by":"crossref","DOI":"10.1101\/2024.05.24.595731","article-title":"Gene regulatory network inference from single-cell data using optimal transport","author":"F Lamoline","year":"2024"},{"key":"pcbi.1012476.ref011","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-031-42697-1","article-title":"Computational Methods in Systems Biology","author":"J Pang","year":"2023"},{"key":"pcbi.1012476.ref012","doi-asserted-by":"crossref","DOI":"10.1101\/2022.06.19.496754","article-title":"One model fits all: combining inference and simulation of gene regulatory networks","author":"E Ventre","year":"2022"},{"key":"pcbi.1012476.ref013","doi-asserted-by":"crossref","DOI":"10.1101\/2023.09.11.557102","article-title":"scEGOT: Single-cell trajectory inference framework based on entropic Gaussian mixture optimal transport","author":"T Yachimura","year":"2023"},{"key":"pcbi.1012476.ref014","unstructured":"Guan V, Janssen J, Rahmani H, Warren A, Zhang S, Robeva E. Identifying drift, diffusion, and causal structure from temporal snapshots. 2024. https:\/\/arxiv.org\/abs\/2410.22729"},{"key":"pcbi.1012476.ref015","unstructured":"Zhang SY. Joint trajectory and network inference via reference fitting. arXiv preprint 2024. https:\/\/arxiv.org\/abs\/2409.06879"},{"key":"pcbi.1012476.ref016","doi-asserted-by":"crossref","DOI":"10.1101\/642926","article-title":"Benchmarking algorithms for gene regulatory network inference from single-cell transcriptomic data","author":"A Pratapa","year":"2019"},{"issue":"3","key":"pcbi.1012476.ref017","article-title":"SERGIO: A Single-Cell Expression Simulator Guided by Gene Regulatory Networks","volume":"11","author":"P Dibaeinia","year":"2020","journal-title":"Cell Syst"},{"key":"pcbi.1012476.ref018","doi-asserted-by":"crossref","DOI":"10.1101\/820936","article-title":"Generalizing RNA velocity to transient cell states through dynamical modeling","author":"V Bergen","year":"2019"},{"key":"pcbi.1012476.ref019","doi-asserted-by":"crossref","DOI":"10.1101\/206052","article-title":"RNA velocity in single cells","author":"G La Manno","year":"2017"},{"issue":"5","key":"pcbi.1012476.ref020","article-title":"Causal gene regulatory analysis with RNA velocity reveals an interplay between slow and fast transcription factors","volume":"15","author":"R Singh","year":"2024","journal-title":"Cell Syst"},{"issue":"4","key":"pcbi.1012476.ref021","doi-asserted-by":"crossref","DOI":"10.1016\/j.cell.2019.01.006","article-title":"Optimal-Transport Analysis of Single-Cell Gene Expression Identifies Developmental Trajectories in Reprogramming","volume":"176","author":"G Schiebinger","year":"2019","journal-title":"Cell"},{"key":"pcbi.1012476.ref022","first-page":"29705","article-title":"Manifold Interpolating Optimal-Transport Flows for Trajectory Inference","volume":"35","author":"G Huguet","year":"2022","journal-title":"Adv Neural Inf Process Syst"},{"issue":"1","key":"pcbi.1012476.ref023","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1038\/s42256-023-00763-w","article-title":"Reconstructing growth and dynamic trajectories from single-cell transcriptomics data","volume":"6","author":"Y Sha","year":"2024","journal-title":"Nat Mach Intell"},{"issue":"9","key":"pcbi.1012476.ref024","doi-asserted-by":"crossref","first-page":"212","DOI":"10.3390\/a13090212","article-title":"Fused Gromov-Wasserstein Distance for Structured Objects","volume":"13","author":"T Vayer","year":"2020","journal-title":"Algorithms"},{"issue":"1","key":"pcbi.1012476.ref025","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1089\/cmb.2021.0446","article-title":"SCOT: Single-Cell Multi-Omics Alignment with Optimal Transport","volume":"29","author":"P Demetci","year":"2022","journal-title":"J Comput Biol"},{"key":"pcbi.1012476.ref026","unstructured":"Titouan V, Courty N, Tavenard R, Laetitia C, Flamary R. Optimal transport for structured data with application on graphs. In: Proceedings of the 36th International Conference on Machine Learning. 6275\u201384."},{"issue":"12","key":"pcbi.1012476.ref027","doi-asserted-by":"crossref","DOI":"10.1242\/dev.173849","article-title":"Comprehensive single cell mRNA profiling reveals a detailed roadmap for pancreatic endocrinogenesis","volume":"146","author":"A Bastidas-Ponce","year":"2019","journal-title":"Development"},{"issue":"3","key":"pcbi.1012476.ref028","doi-asserted-by":"crossref","first-page":"424","DOI":"10.2307\/1912791","article-title":"Investigating Causal Relations by Econometric Models and Cross-spectral Methods","volume":"37","author":"CWJ Granger","year":"1969","journal-title":"Econometrica"},{"issue":"2","key":"pcbi.1012476.ref029","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1111\/j.1467-9868.2005.00503.x","article-title":"Regularization and Variable Selection Via the Elastic Net","volume":"67","author":"H Zou","year":"2005","journal-title":"Journal of the Royal Statistical Society 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