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Monod: model-based discovery and integration through fitting stochastic transcriptional dynamics to single-cell sequencing data

Nature Methods volume 22, pages 2286–2300 (2025)Cite this article

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Abstract

Single-cell RNA sequencing analysis centers on illuminating cell diversity and understanding the transcriptional mechanisms underlying cellular function. These datasets are large, noisy and complex. Current analyses prioritize noise removal and dimensionality reduction to tackle these challenges and extract biological insight. We propose an alternative, physical approach to leverage the stochasticity, size and multimodal nature of these data to explicitly distinguish their biological and technical facets while revealing the underlying regulatory processes. With the Python package Monod, we demonstrate how nascent and mature RNA counts, present in most published datasets, can be meaningfully ‘integrated’ under biophysical models of transcription. By using variation in these modalities, we can identify transcriptional modulation not discernible through changes in average gene expression, quantitatively compare mechanistic hypotheses of gene regulation, analyze transcriptional data from different technologies within a common framework and minimize the use of opaque or distortive normalization and transformation techniques.

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Fig. 1: Monod inference for biophysical representation.
Fig. 2: Resistance and proliferation in malignant PDAC cells.
Fig. 3: Monod analysis of mechanisms of T cell recovery after radiation treatment.
Fig. 4: Monod facilitates the comparison of different biophysical models on a per-gene basis for thousands of genes across cell types.
Fig. 5: Monod’s quantification of parameter estimate uncertainty supports a biophysically meaningful approach to integrating data from different modalities.
Fig. 6: Monod enables quantitative assessment of common data transformations.

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Data availability

The datasets released by the Allen Institute for Brain Science were downloaded from http://data.nemoarchive.org/biccn/grant/u19_zeng/zeng/transcriptome/scell/10x_v3/mouse/raw/MOp/ and filtered according to the metadata annotations at http://data.nemoarchive.org/biccn/grant/u19_zeng/zeng/transcriptome/scell/10x_v3/mouse/processed/analysis/10X_cells_v3_AIBS/ refs. 56,136,155. The paired single-cell and single-nucleus mouse brain datasets as well as the human PBMC datasets were obtained from the 10x Genomics website. Control and IdU-perturbed mESC data47 were obtained from GSE176044 at the Gene Expression Omnibus. The mouse germ cell dataset57 was obtained from Gene Expression Omnibus repository GSE136220, the patient-derived PDAC tumor sample dataset61 was from GSE202051, and intestinal radiation therapy data60 were from GSE165318. Single-nucleus mESC data108 were obtained using Sequence Read Archive run accession number SRR18364193. Fluorescent intensity values for seqFISH+ experiments on mESCs107 were obtained from Zenodo (package 7693825)156. The prebuilt GRCh38 or mm10 genome from https://support.10xgenomics.com/single-cell-gene-expression/software/downloads/latest (2020-A version) was used for quantification of datasets. All loom files with nascent and mature count matrices for the datasets used in this study and all Monod fits have been deposited in Zenodo (package 15051840)157,158.

Code availability

Notebooks that reproduce all the filtering, fitting and analysis procedures have been deposited also in Zenodo (package 15051840)157 and are available at https://github.com/pachterlab/monod_examples/tree/main/manuscript_computation. This GitHub repository also contains a Google Colaboratory notebook that illustrates the Monod workflow with a small dataset. The Monod software used for all analysis is available as a pip installable package with an API available at https://monod-examples.readthedocs.io.

References

  1. Shekhar, K. et al. Comprehensive classification of retinal bipolar neurons by single-cell transcriptomics. Cell 166, 1308–1323 (2016).

    CAS  PubMed  PubMed Central  Google Scholar 

  2. Yao, Z. et al. A high-resolution transcriptomic and spatial atlas of cell types in the whole mouse brain. Nature 624, 317–332 (2023).

    CAS  PubMed  PubMed Central  Google Scholar 

  3. Wagner, D. E. et al. Single-cell mapping of gene expression landscapes and lineage in the zebrafish embryo. Science 360, 981–987 (2018).

    CAS  PubMed  PubMed Central  Google Scholar 

  4. Regev, A. et al. Science forum: the human cell atlas. eLife 6, e27041 (2017).

    PubMed  PubMed Central  Google Scholar 

  5. Chari, T. et al. Whole-animal multiplexed single-cell RNA-seq reveals transcriptional shifts across Clytia medusa cell types. Sci. Adv. 7, eabh1683 (2021).

    CAS  PubMed  PubMed Central  Google Scholar 

  6. Luecken, M. D. & Theis, F. J. Current best practices in single cell RNA seq analysis: a tutorial. Mol. Syst. Biol. 15, e8746 (2019).

    PubMed  PubMed Central  Google Scholar 

  7. Kharchenko, P. V. The triumphs and limitations of computational methods for scRNA-seq. Nat. Methods 18, 723–732 (2021).

    CAS  PubMed  Google Scholar 

  8. Heumos, L. et al. Best practices for single-cell analysis across modalities. Nat. Rev. Genet. 24, 550–572 (2023).

    CAS  PubMed  Google Scholar 

  9. Kobak, D. & Berens, P. The art of using t-SNE for single-cell transcriptomics. Nat. Commun. 10, 5416 (2019).

    PubMed  PubMed Central  Google Scholar 

  10. Hu, Q. & Greene, C. S. Parameter tuning is a key part of dimensionality reduction via deep variational autoencoders for single cell RNA transcriptomics. Pac. Symp. Biocomput. 24, 362–373 (2019).

  11. Raimundo, F., Vallot, C. & Vert, J.-P. Tuning parameters of dimensionality reduction methods for single-cell RNA-seq analysis. Genome Biol. 21, 212 (2020).

    CAS  PubMed  PubMed Central  Google Scholar 

  12. Cooley, S. M., Hamilton, T., Aragones, S. D., Ray, J. C. J. & Deeds, E. J. A novel metric reveals previously unrecognized distortion in dimensionality reduction of scRNA-seq data. Preprint at bioRxiv https://doi.org/10.1101/689851 (2020).

  13. Chamberlin, J. T., Lee, Y., Marth, G. T. & Quinlan, A. R. Differences in molecular sampling and data processing explain variation among single-cell and single-nucleus RNA-seq experiments. Genome Res. 34, 179–188 (2024).

    CAS  PubMed  PubMed Central  Google Scholar 

  14. Ahlmann-Eltze, C. & Huber, W. Comparison of transformations for single-cell RNA-seq data. Nat. Methods 20, 665–672 (2023).

    CAS  PubMed  PubMed Central  Google Scholar 

  15. Chari, T. & Pachter, L. The specious art of single-cell genomics. PLoS Comput. Biol. 19, e1011288 (2023).

    CAS  PubMed  PubMed Central  Google Scholar 

  16. Gorin, G., Fang, M., Chari, T. & Pachter, L. RNA velocity unraveled. PLoS Comput. Biol. 18, e1010492 (2022).

    CAS  PubMed  PubMed Central  Google Scholar 

  17. Kiselev, V. Y., Andrews, T. S. & Hemberg, M. Challenges in unsupervised clustering of single-cell RNA-seq data. Nat. Rev. Genet. 20, 273–282 (2019).

    CAS  PubMed  Google Scholar 

  18. Mimitou, E. P. et al. Scalable, multimodal profiling of chromatin accessibility, gene expression and protein levels in single cells. Nat. Biotechnol. 39, 1246–1258 (2021).

    CAS  PubMed  PubMed Central  Google Scholar 

  19. Elowitz, M. B., Levine, A. J., Siggia, E. D. & Swain, P. S. Stochastic gene expression in a single cell. Science 297, 1183–1186 (2002).

    CAS  PubMed  Google Scholar 

  20. Raser, J. M. & O’Shea, E. K. Noise in gene expression: origins, consequences, and control. Science 309, 2010–2013 (2005).

    CAS  PubMed  PubMed Central  Google Scholar 

  21. Gillespie, D. T. Stochastic simulation of chemical kinetics. Annu. Rev. Phys. Chem. 58, 35–55 (2007).

    CAS  PubMed  Google Scholar 

  22. Guillemin, A. & Stumpf, M. P. H. Noise and the molecular processes underlying cell fate decision-making. Phys. Biol. 18, 011002 (2020).

    Google Scholar 

  23. Gorin, G., Vastola, J. J., Fang, M. & Pachter, L. Interpretable and tractable models of transcriptional noise for the rational design of single-molecule quantification experiments. Nat. Commun. 13, 7620 (2022).

    CAS  PubMed  PubMed Central  Google Scholar 

  24. Gorin, G. & Pachter, L. Length biases in single-cell RNA sequencing of pre-mRNA. Biophys. Rep. 3, 100097 (2023).

    CAS  Google Scholar 

  25. Gorin, G., Vastola, J. J. & Pachter, L. Studying stochastic systems biology of the cell with single-cell genomics data. Cell Syst. 14, 822–843 (2023).

    CAS  PubMed  PubMed Central  Google Scholar 

  26. Gorin, G. & Pachter, L. New and notable: revisiting the ‘two cultures’ through extrinsic noise. Biophys. J. 123, 1–3 (2024).

    CAS  PubMed  Google Scholar 

  27. Raj, A., Peskin, C. S., Tranchina, D., Vargas, D. Y. & Tyagi, S. Stochastic mRNA synthesis in mammalian cells. PLoS Biol. 4, e309 (2006).

    PubMed  PubMed Central  Google Scholar 

  28. Bokes, P., King, J. R., Wood, A. T. A. & Loose, M. Exact and approximate distributions of protein and mRNA levels in the low-copy regime of gene expression. J. Math. Biol. 64, 829–854 (2012).

    PubMed  Google Scholar 

  29. Xu, H., Skinner, S. O., Sokac, A. M. & Golding, I. Stochastic kinetics of nascent RNA. Phys. Rev. Lett. 117, 128101 (2016).

    PubMed  PubMed Central  Google Scholar 

  30. Golding, I., Paulsson, J., Zawilski, S. M. & Cox, E. C. Real-time kinetics of gene activity in individual bacteria. Cell 123, 1025–1036 (2005).

    CAS  PubMed  Google Scholar 

  31. Chari, T., Gorin, G. & Pachter, L. Biophysically interpretable inference of cell types from multimodal sequencing data. Nat. Comput. Sci. 4, 677–689 (2024).

    CAS  PubMed  Google Scholar 

  32. Sullivan, D. K. et al. Accurate quantification of nascent and mature RNAs from single-cell and single-nucleus RNA-seq. Nucleic Acids Res. 53, gkae1137 (2024).

    PubMed Central  Google Scholar 

  33. Sullivan, D. K. kallisto, bustools and kb-python for quantifying bulk, single-cell and single-nucleus RNA-seq. Nat. Protoc. 20, 587–607 (2025).

    CAS  PubMed  Google Scholar 

  34. Jahnke, T. & Huisinga, W. Solving the chemical master equation for monomolecular reaction systems analytically. J. Math. Biol. 54, 1–26 (2006).

    PubMed  Google Scholar 

  35. Vastola, J. J. Solving the chemical master equation for monomolecular reaction systems and beyond: a Doi–Peliti path integral view. J. Math. Biol. 83, 48 (2021).

    PubMed  Google Scholar 

  36. Svensson, V. Droplet scRNA-seq is not zero-inflated. Nat. Biotechnol. 38, 147–150 (2020).

    CAS  PubMed  Google Scholar 

  37. Singh, A. & Bokes, P. Consequences of mRNA transport on stochastic variability in protein levels. Biophys. J. 103, 1087–1096 (2012).

    CAS  PubMed  PubMed Central  Google Scholar 

  38. Dar, R. D. et al. Transcriptional burst frequency and burst size are equally modulated across the human genome. Proc. Natl Acad. Sci. USA 109, 17454–17459 (2012).

    CAS  PubMed  PubMed Central  Google Scholar 

  39. Halpern, K. B. et al. Bursty gene expression in the intact mammalian liver. Mol. Cell 58, 147–156 (2015).

    PubMed Central  Google Scholar 

  40. Corrigan, A. M., Tunnacliffe, E., Cannon, D. & Chubb, J. R. A continuum model of transcriptional bursting. eLife 5, e13051 (2016).

    PubMed  PubMed Central  Google Scholar 

  41. Fukaya, T., Lim, B. & Levine, M. Enhancer control of transcriptional bursting. Cell 166, 358–368 (2016).

    CAS  PubMed  PubMed Central  Google Scholar 

  42. Nicolas, D., Phillips, N. E. & Naef, F. What shapes eukaryotic transcriptional bursting? Mol. Biosyst. 13, 1280–1290 (2017).

    CAS  PubMed  Google Scholar 

  43. Rodriguez, J. & Larson, D. R. Transcription in living cells: molecular mechanisms of bursting. Annu. Rev. Biochem. 89, 189–212 (2020).

    CAS  PubMed  Google Scholar 

  44. Ham, L., Brackston, R. D. & Stumpf, M. P. H. Extrinsic noise and heavy-tailed laws in gene expression. Phys. Rev. Lett. 124, 108101 (2020).

    CAS  PubMed  Google Scholar 

  45. Gorin, G., Yoshida, S. & Pachter, L. Assessing Markovian and delay models for single-nucleus RNA sequencing. Bull. Math. Biol. 85, 114 (2023).

    PubMed  Google Scholar 

  46. Leier, A. & Marquez-Lago, T. T. Delay chemical master equation: direct and closed-form solutions. Proc. R. Soc. Math. Phys. Eng. Sci. 471, 20150049 (2015).

    Google Scholar 

  47. Desai, R. V. et al. A DNA repair pathway can regulate transcriptional noise to promote cell fate transitions. Science 373, eabc6506 (2021).

    CAS  PubMed  PubMed Central  Google Scholar 

  48. Hilfinger, A. & Paulsson, J. Separating intrinsic from extrinsic fluctuations in dynamic biological systems. Proc. Natl Acad. Sci. USA 108, 12167–12172 (2011).

    CAS  PubMed  PubMed Central  Google Scholar 

  49. Robinson, M. D., McCarthy, D. J. & Smyth, G. K. edgeR: a Bioconductor package for differential expression analysis of digital gene expression data. Bioinformatics 26, 139–140 (2010).

    CAS  PubMed  Google Scholar 

  50. Anders, S. & Huber, W. Differential expression analysis for sequence count data. Genome Biol. 11, R106 (2010).

    CAS  PubMed  PubMed Central  Google Scholar 

  51. Love, M. I., Huber, W. & Anders, S. Moderated estimation of fold change and dispersion for RNA-seq data with DESeq2. Genome Biol. 15, 550 (2014).

    PubMed  PubMed Central  Google Scholar 

  52. Hansen, M. M. K., Desai, R. V., Simpson, M. L. & Weinberger, L. S. Cytoplasmic amplification of transcriptional noise generates substantial cell-to-cell variability. Cell Syst. 7, 384–397 (2018).

    CAS  PubMed  PubMed Central  Google Scholar 

  53. García-Blay, Ó. et al. Multimodal screen identifies noise-regulatory proteins. Dev. Cell 60, 133–151 (2025).

    PubMed  Google Scholar 

  54. Calia, G. P., Chen, X., Zuckerman, B. & Weinberger, L. S. Comparative analysis between single-cell RNA-seq and single-molecule RNA FISH indicates that the pyrimidine nucleobase idoxuridine (IdU) globally amplifies transcriptional noise. Preprint at bioRxiv https://doi.org/10.1101/2023.03.14.532632 (2023).

  55. Huang, Z. et al. Deep learning linking mechanistic models to single-cell transcriptomics data reveals transcriptional bursting in response to DNA damage. eLife https://doi.org/10.7554/eLife.100623.2 (2024).

  56. Yao, Z. et al. A transcriptomic and epigenomic cell atlas of the mouse primary motor cortex. Nature 598, 103–110 (2021).

    CAS  PubMed  PubMed Central  Google Scholar 

  57. Mayère, C. et al. Single-cell transcriptomics reveal temporal dynamics of critical regulators of germ cell fate during mouse sex determination. FASEB J. 35, e21452 (2021).

    PubMed  Google Scholar 

  58. Stelzer, G. et al. The GeneCards suite: from gene data mining to disease genome sequence analyses. Curr. Protoc. Bioinformatics 54, 1.30.1–1.30.33 (2016).

    PubMed  Google Scholar 

  59. Lee, S. C.-W. & Abdel-Wahab, O. Therapeutic targeting of splicing in cancer. Nat. Med. 22, 976–986 (2016).

    CAS  PubMed  PubMed Central  Google Scholar 

  60. Lu, H. et al. Single-cell map of dynamic cellular microenvironment of radiation-induced intestinal injury. Commun. Biol. 6, 1248 (2023).

    CAS  PubMed  PubMed Central  Google Scholar 

  61. Hwang, W. L. et al. Single-nucleus and spatial transcriptome profiling of pancreatic cancer identifies multicellular dynamics associated with neoadjuvant treatment. Nat. Genet. 54, 1178–1191 (2022).

    CAS  PubMed  PubMed Central  Google Scholar 

  62. Dyson, N. J. RB1: a prototype tumor suppressor and an enigma. Genes Dev. 30, 1492–1502 (2016).

    CAS  PubMed  PubMed Central  Google Scholar 

  63. Touil, Y. et al. Colon cancer cells escape 5FU chemotherapy-induced cell death by entering stemness and quiescence associated with the c-Yes/YAP axis. Clin. Cancer Res. 20, 837–846 (2014).

    CAS  PubMed  Google Scholar 

  64. Huang, X. et al. Identification of genes related to 5-fluorouracil based chemotherapy for colorectal cancer. Front. Immunol. 13, 887048 (2022).

    CAS  PubMed  PubMed Central  Google Scholar 

  65. Sahebnasagh, R., Azizi, Z., Komeili-Movahhed, T., Zendehdel, K. & Ghahremani, M. H. In-silico and in-vitro investigation of key long non-coding RNAs involved in 5-fluorouracil resistance in colorectal cancer cells: analyses highlighting NEAT1 and MALAT1 as contributors. Cureus 16, e66393 (2024).

    PubMed  PubMed Central  Google Scholar 

  66. Machkalyan, G., Hèbert, T. E. & Miller, G. J. PPIP5K1 suppresses etoposide-triggered apoptosis. J. Mol. Signal. 11, 4 (2016).

    PubMed  PubMed Central  Google Scholar 

  67. Bhandari, K. & Ding, W.-Q. Protein arginine methyltransferases in pancreatic ductal adenocarcinoma: new molecular targets for therapy. Int. J. Mol. Sci. 25, 3958 (2024).

    CAS  PubMed  PubMed Central  Google Scholar 

  68. Wang, X. et al. Characterization of LIMA1 and its emerging roles and potential therapeutic prospects in cancers. Front. Oncol. 13, 1115943 (2023).

    CAS  PubMed  PubMed Central  Google Scholar 

  69. Hashemzehi, M. et al. Angiotensin receptor blocker losartan inhibits tumor growth of colorectal cancer. EXCLI J. 20, 506–521 (2021).

    PubMed  PubMed Central  Google Scholar 

  70. Pothula, S. P. et al. Targeting HGF/c-MET axis in pancreatic cancer. Int. J. Mol. Sci. 21, 9170 (2020).

    CAS  PubMed  PubMed Central  Google Scholar 

  71. Leclerc, G. J., Leclerc, G. M. & Barredo, J. C. Real-time RT–PCR analysis of mRNA decay: half-life of β-actin mRNA in human leukemia CCRF-CEM and Nalm-6 cell lines. Cancer Cell Int. 2, 1 (2002).

    PubMed  PubMed Central  Google Scholar 

  72. Izdebska, M., Zielińska, W., Hałas-Wiśniewska, M. & Grzanka, A. Involvement of actin and actin-binding proteins in carcinogenesis. Cells 9, 2245 (2020).

    CAS  PubMed  PubMed Central  Google Scholar 

  73. Arina, A. et al. Tumor-reprogrammed resident T cells resist radiation to control tumors. Nat. Commun. 10, 3959 (2019).

    PubMed  PubMed Central  Google Scholar 

  74. Shadad, A. K., Sullivan, F. J., Martin, J. D. & Egan, L. J. Gastrointestinal radiation injury: symptoms, risk factors and mechanisms. World J. Gastroenterol. 19, 185–198 (2013).

    PubMed  PubMed Central  Google Scholar 

  75. Augustin, R. C., Bao, R. & Luke, J. J. Targeting Cbl-b in cancer immunotherapy. J. Immunother. Cancer 11, e006007 (2023).

    PubMed  PubMed Central  Google Scholar 

  76. Yu, M. et al. CD73 on cancer-associated fibroblasts enhanced by the A2B-mediated feedforward circuit enforces an immune checkpoint. Nat. Commun. 11, 515 (2020).

    CAS  PubMed  PubMed Central  Google Scholar 

  77. Qu, L. et al. NCAPD3 is a prognostic biomarker and is correlated with immune infiltrates in glioma. Histol. Histopathol. 39, 1473–1484 (2024).

    CAS  PubMed  Google Scholar 

  78. Zhong, Y. et al. Insulin-like growth factor 2 receptor is a key immune-related gene that is correlated with a poor prognosis in patients with triple-negative breast cancer: a bioinformatics analysis. Front. Oncol. 12, 871786 (2022).

    CAS  PubMed  PubMed Central  Google Scholar 

  79. Xu, X. et al. Pan-cancer analysis of the role of MPP7 in human tumors. Heliyon 10, e36148 (2024).

    CAS  PubMed  PubMed Central  Google Scholar 

  80. Dittmer, J. The biology of the Ets1 proto-oncogene. Mol. Cancer 2, 29 (2003).

    PubMed  PubMed Central  Google Scholar 

  81. Phee, H., Mollenauer, M. N. & Weiss, A. Role of GIT2 in T cell migration and development (95.8). J. Immunol. 182, 95.8 (2009).

    Google Scholar 

  82. O’Hagan, K. L., Miller, S. & Phee, H. Pak2 is essential for the function of Foxp3+ regulatory T cells through maintaining a suppressive Treg phenotype. Sci. Rep. 7, 17097 (2017).

    PubMed  PubMed Central  Google Scholar 

  83. Belenguer, G. et al. RNF43/ZNRF3 loss predisposes to hepatocellular-carcinoma by impairing liver regeneration and altering the liver lipid metabolic ground-state. Nat. Commun. 13, 334 (2022).

    CAS  PubMed  PubMed Central  Google Scholar 

  84. Yue, F. et al. Loss of ZNRF3/RNF43 unleashes EGFR in cancer. eLife https://doi.org/10.7554/eLife.95639.2 (2024).

  85. Wei, J.-L. et al. GCH1 induces immunosuppression through metabolic reprogramming and IDO1 upregulation in triple-negative breast cancer. J. Immunother. Cancer 9, e002383 (2021).

    PubMed  PubMed Central  Google Scholar 

  86. Zeng, Q. et al. LCP1 is a prognostic biomarker correlated with immune infiltrates in gastric cancer. Cancer Biomark. 30, 105–125 (2021).

    CAS  PubMed  Google Scholar 

  87. Pan, S. et al. Decreased expression of ARHGAP15 promotes the development of colorectal cancer through PTEN/AKT/FOXO1 axis. Cell Death Dis. 9, 673 (2018).

    PubMed  PubMed Central  Google Scholar 

  88. Dou, B., Jiang, G., Peng, W. & Liu, C. OTULIN deficiency: focus on innate immune system impairment. Front. Immunol. 15, 1371564 (2024).

    CAS  PubMed  PubMed Central  Google Scholar 

  89. Wang, W.-Y. et al. Interaction of FUS and HDAC1 regulates DNA damage response and repair in neurons. Nat. Neurosci. 16, 1383–1391 (2013).

    CAS  PubMed  PubMed Central  Google Scholar 

  90. Martínez, D. et al. Discovery of BbX transcription factor in the Patagonian blennie: exploring expression changes following combined bacterial and thermal stress exposure. Dev. Comp. Immunol. 149, 105056 (2023).

    PubMed  Google Scholar 

  91. Kim, T. H., Zhou, X. & Chen, M. Demystifying ‘drop-outs’ in single-cell UMI data. Genome Biol. 21, 196 (2020).

    PubMed  PubMed Central  Google Scholar 

  92. Ding, J. et al. Systematic comparison of single-cell and single-nucleus RNA-sequencing methods. Nat. Biotechnol. 38, 737–746 (2020).

    CAS  PubMed  PubMed Central  Google Scholar 

  93. Habib, N. et al. Massively parallel single-nucleus RNA-seq with DroNc-seq. Nat. Methods 14, 955–958 (2017).

    CAS  PubMed  PubMed Central  Google Scholar 

  94. Eng, C.-H. L. et al. Transcriptome-scale super-resolved imaging in tissues by RNA seqFISH+. Nature 568, 235–239 (2019).

    CAS  PubMed  PubMed Central  Google Scholar 

  95. Bennett, H. M., Stephenson, W., Rose, C. M. & Darmanis, S. Single-cell proteomics enabled by next-generation sequencing or mass spectrometry. Nat. Methods 20, 363–374 (2023).

    CAS  PubMed  Google Scholar 

  96. Stoeckius, M. et al. Simultaneous epitope and transcriptome measurement in single cells. Nat. Methods 14, 865–868 (2017).

    CAS  PubMed  PubMed Central  Google Scholar 

  97. Buenrostro, J. D., Wu, B., Chang, H. Y. & Greenleaf, W. J. ATAC-seq: a method for assaying chromatin accessibility genome-wide. Curr. Protoc. Mol. Biol. 109, 21.29.1–21.29.9 (2015).

    PubMed  Google Scholar 

  98. Buenrostro, J. D. et al. Single-cell chromatin accessibility reveals principles of regulatory variation. Nature 523, 486–490 (2015).

    CAS  PubMed  PubMed Central  Google Scholar 

  99. Minnoye, L. et al. Chromatin accessibility profiling methods. Nat. Rev. Methods Primers 1, 10 (2021).

    CAS  PubMed  PubMed Central  Google Scholar 

  100. Butler, A., Hoffman, P., Smibert, P., Papalexi, E. & Satija, R. Integrating single-cell transcriptomic data across different conditions, technologies, and species. Nat. Biotechnol. 36, 411–420 (2018).

    CAS  PubMed  PubMed Central  Google Scholar 

  101. Stuart, T. et al. Comprehensive integration of single-cell data. Cell 177, 1888–1902 (2019).

    CAS  PubMed  PubMed Central  Google Scholar 

  102. Korsunsky, I. et al. Fast, sensitive and accurate integration of single-cell data with Harmony. Nat. Methods 16, 1289–1296 (2019).

    CAS  PubMed  PubMed Central  Google Scholar 

  103. Ashuach, T., Reidenbach, D. A., Gayoso, A. & Yosef, N. PeakVI: a deep generative model for single-cell chromatin accessibility analysis. Cell Rep. Methods 2, 100182 (2022).

    CAS  PubMed  PubMed Central  Google Scholar 

  104. Ashuach, T. et al. MultiVI: deep generative model for the integration of multimodal data. Nat. Methods 20, 1222–1231 (2023).

    CAS  PubMed  PubMed Central  Google Scholar 

  105. Tyler, S. R., Guccione, E. & Schadt, E. E. Erasure of biologically meaningful signal by unsupervised scRNAseq batch-correction methods. Preprint at bioRxiv https://doi.org/10.1101/2021.11.15.468733 (2023).

  106. Shah, S. et al. Dynamics and spatial genomics of the nascent transcriptome by intron seqFISH. Cell 174, 363–376 (2018).

    CAS  PubMed  PubMed Central  Google Scholar 

  107. Takei, Y. et al. High-resolution spatial multi-omics reveals cell-type specific nuclear compartments. Preprint at bioRxiv https://doi.org/10.1101/2023.05.07.539762 (2023).

  108. Khateb, M. et al. Transcriptomics, regulatory syntax, and enhancer identification in mesoderm-induced ESCs at single-cell resolution. Cell Rep. 40, 111219 (2022).

    CAS  PubMed  PubMed Central  Google Scholar 

  109. 10x Genomics. 30k Mouse E18 Combined Cortex, Hippocampus and Subventricular Zone Cells Multiplexed, 12 CMOs, Brain 4 https://www.10xgenomics.com/datasets/30-k-mouse-e-18-combined-cortex-hippocampus-and-subventricular-zone-cells-multiplexed-12-cm-os-3-1-standard-6-0-0 (2021).

  110. 10x Genomics. 30k Mouse E18 Combined Cortex, Hippocampus and Subventricular Zone Nuclei Multiplexed, 12 CMOs, Brain Nuclei 4 https://www.10xgenomics.com/datasets/30-k-mouse-e-18-combined-cortex-hippocampus-and-subventricular-zone-nuclei-multiplexed-12-cm-os-3-1-standard-6-0-0 (2021).

  111. Swain, P. S., Elowitz, M. B. & Siggia, E. D. Intrinsic and extrinsic contributions to stochasticity in gene expression. Proc. Natl Acad. Sci. USA 99, 12795–12800 (2002).

    CAS  PubMed  PubMed Central  Google Scholar 

  112. McInnes, L., Healy, J. & Melville, J. UMAP: uniform manifold approximation and projection for dimension reduction. Preprint at arxiv.org/abs/1802.03426 (2018).

  113. Grima, R. & Esmenjaud, P.-M. Quantifying and correcting bias in transcriptional parameter inference from single-cell data. Biophys. J. 123, 4–30 (2024).

    CAS  PubMed  Google Scholar 

  114. Cao, Z. & Grima, R. Linear mapping approximation of gene regulatory networks with stochastic dynamics. Nat. Commun. 9, 3305 (2018).

    PubMed  PubMed Central  Google Scholar 

  115. Gorin, G. & Pachter, L. Modeling bursty transcription and splicing with the chemical master equation. Biophys. J. 121, 1056–1069 (2022).

    CAS  PubMed  PubMed Central  Google Scholar 

  116. Felce, C., Gorin, G. & Pachter, L. Biophysical model for joint analysis of chromatin and RNA sequencing data. Phys. Rev. E 110, 064405 (2024).

    CAS  PubMed  Google Scholar 

  117. Alpert, T., Herzel, L. & Neugebauer, K. M. Perfect timing: splicing and transcription rates in living cells. Wiley Interdiscip. Rev. RNA 8, e1401 (2017).

    Google Scholar 

  118. Herzog, V. A. et al. Thiol-linked alkylation of RNA to assess expression dynamics. Nat. Methods 14, 1198–1204 (2017).

    CAS  PubMed  PubMed Central  Google Scholar 

  119. Gorin, G., Carilli, M., Chari, T. & Pachter, L. Spectral neural approximations for models of transcriptional dynamics. Biophys. J. 123, 2892–2901 (2024).

    CAS  PubMed  PubMed Central  Google Scholar 

  120. Sukys, A., Öcal, K. & Grima, R. Approximating solutions of the chemical master equation using neural networks. iScience 25, 105010 (2022).

    CAS  PubMed  PubMed Central  Google Scholar 

  121. Cao, Z. et al. Efficient and scalable prediction of stochastic reaction–diffusion processes using graph neural networks. Math. Biosci. 375, 109248 (2024).

    CAS  PubMed  Google Scholar 

  122. Carilli, M. T., Gorin, G., Choi, Y., Chari, T. & Pachter, L. Biophysical modeling with variational autoencoders for bimodal, single-cell RNA sequencing data. Nat. Methods 21, 1466–1469 (2024).

    PubMed  Google Scholar 

  123. Fang, M., Gorin, G. & Pachter, L. Trajectory inference from single-cell genomics data with a process time model. PLoS Comp. Biol. 21, e1012752 (2024).

    Google Scholar 

  124. Harris, C. R. et al. Array programming with NumPy. Nature 585, 357–362 (2020).

    CAS  PubMed  PubMed Central  Google Scholar 

  125. Virtanen, P. et al. SciPy 1.0: fundamental algorithms for scientific computing in Python. Nat. Methods 17, 261–272 (2020).

    CAS  PubMed  PubMed Central  Google Scholar 

  126. Brodtkorb, P. A. & D’Errico, J. numdifftools https://pypi.org/project/numdifftools/ (2021).

  127. Melsted, P. et al. Modular, efficient and constant-memory single-cell RNA-seq preprocessing. Nat. Biotechnol. 39, 813–818 (2021).

    CAS  PubMed  Google Scholar 

  128. Gorin, F. & Pachter, L. Intrinsic and extrinsic noise are distinguishable in a synthesis – export – degradation model of mRNA production. Preprint at bioRxiv https://doi.org/10.1101/2020.09.25.312868 (2020).

  129. Ham, L., Schnoerr, D., Brackston, R. D. & Stumpf, M. P. H. Exactly solvable models of stochastic gene expression. J. Chem. Phys. 152, 144106 (2020).

    CAS  PubMed  Google Scholar 

  130. Ham, L., Jackson, M. & Stumpf, M. P. H. Pathway dynamics can delineate the sources of transcriptional noise in gene expression. eLife 10, e69324 (2021).

    CAS  PubMed  PubMed Central  Google Scholar 

  131. Jiang, Q. et al. Neural network aided approximation and parameter inference of non-Markovian models of gene expression. Nat. Commun. 12, 2618 (2021).

    CAS  PubMed  PubMed Central  Google Scholar 

  132. The MathWorks. MATLAB R2022a Symbolic Math Toolbox (MathWorks, 2022).

  133. The MathWorks. MATLAB R2022a (MathWorks, 2022).

  134. Tang, W., Jørgensen, A. C. S., Marguerat, S., Thomas, P. & Shahrezaei, V. Modelling capture efficiency of single cell RNA-sequencing data improves inference of transcriptome-wide burst kinetics. Bioinformatics 39, btad395 (2023).

    CAS  PubMed  PubMed Central  Google Scholar 

  135. Munsky, B., Li, G., Fox, Z. R., Shepherd, D. P. & Neuert, G. Distribution shapes govern the discovery of predictive models for gene regulation. Proc. Natl Acad. Sci. USA 115, 7533–7538 (2018).

    CAS  PubMed  PubMed Central  Google Scholar 

  136. Allen Institute for Brain Science. FASTQ Files for Allen v3 Mouse MOp Samples http://data.nemoarchive.org/biccn/grant/u19_zeng/zeng/transcriptome/scell/10x_v3/mouse/raw/MOp (2020).

  137. Melsted, P. áll., Ntranos, V. & Pachter, L. The barcode, UMI, set format and BUStools. Bioinformatics 35, 4472–4473 (2019).

    CAS  PubMed  Google Scholar 

  138. Burnham, K. P. & Anderson, D. R. Model Selection and Multimodel Inference: a Practical Information–Theoretic Approach 2nd edn (Springer, 2002).

  139. Ly, A., Marsman, M., Verhagen, J., Grasman, R. P. P. P. & Wagenmakers, E.-J. A tutorial on Fisher information. J. Math. Psychol. 80, 40–55 (2017).

    Google Scholar 

  140. 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).

    CAS  PubMed  PubMed Central  Google Scholar 

  141. Halpern, K. B. et al. Nuclear retention of mRNA in mammalian tissues. Cell Rep. 13, 2653–2662 (2015).

    Google Scholar 

  142. McKellar, D. W. et al. Large-scale integration of single-cell transcriptomic data captures transitional progenitor states in mouse skeletal muscle regeneration. Commun. Biol. 4, 1280 (2021).

    CAS  PubMed  PubMed Central  Google Scholar 

  143. Jew, B. et al. Accurate estimation of cell composition in bulk expression through robust integration of single-cell information. Nat. Commun. 11, 1971 (2020).

    CAS  PubMed  PubMed Central  Google Scholar 

  144. Pedregosa, F. et al. Scikit-learn: machine learning in Python. J. Mach. Learn. Res. 12, 2825–2830 (2011).

    Google Scholar 

  145. La Manno, G. et al. RNA velocity of single cells. Nature 560, 494–498 (2018).

    PubMed  PubMed Central  Google Scholar 

  146. Montserrat Ayuso, T. & Esteve-Codina, A. Revealing the prevalence of suboptimal cells and organs in reference cell atlases: an imperative for enhanced quality control. BMC Genomics 25, 1124 (2024).

    CAS  PubMed  PubMed Central  Google Scholar 

  147. Clarke, Z. A. & Bader, G. MALAT1 expression indicates cell quality in single-cell RNA sequencing data. Preprint at bioRxiv https://doi.org/10.1101/2024.07.14.603469 (2024).

  148. Pratapa, A., Jalihal, A. P., Law, J. N., Bharadwaj, A. & Murali, T. M. Benchmarking algorithms for gene regulatory network inference from single-cell transcriptomic data. Nat. Methods 17, 147–154 (2020).

    CAS  PubMed  PubMed Central  Google Scholar 

  149. Kim, D. et al. Gene regulatory network reconstruction: harnessing the power of single-cell multi-omic data. NPJ Syst. Biol. Appl. 9, 51 (2023).

    PubMed  PubMed Central  Google Scholar 

  150. Stumpf, M. P. H. Statistical and computational challenges for whole cell modelling. Curr. Opin. Syst. Biol. 26, 58–63 (2021).

    CAS  Google Scholar 

  151. Saint-Antoine, M. M. & Singh, A. Network inference in systems biology: recent developments, challenges, and applications. Curr. Opin. Biotechnol. 63, 89–98 (2020).

    CAS  PubMed  PubMed Central  Google Scholar 

  152. Stumpf, M. P. H. Inferring better gene regulation networks from single-cell data. Curr. Opin. Syst. Biol. 27, 100342 (2021).

    CAS  Google Scholar 

  153. 10x Genomics. 1k PBMCs from a Healthy Donor (v2 Chemistry), Single Cell Gene Expression Dataset by Cell Ranger 3.0.0 https://www.10xgenomics.com/datasets/1-k-pbm-cs-from-a-healthy-donor-v-2-chemistry-3-standard-3-0-0 (2018).

  154. 10x Genomics. 1k PBMCs from a Healthy Donor (v3 Chemistry), Single Cell Gene Expression Dataset by Cell Ranger 3.0.0 https://www.10xgenomics.com/datasets/1-k-pbm-cs-from-a-healthy-donor-v-3-chemistry-3-standard-3-0-0 (2018).

  155. Allen Institute for Brain Science. Analyses for Allen v3 Mouse MOp Samples http://data.nemoarchive.org/biccn/grant/u19_zeng/zeng/transcriptome/scell/10x_v3/mouse/processed/analysis/10X_cells_v3_AIBS/ (2020).

  156. Takei, Y., Yang, Y. & Cai, L. High-resolution spatial multi-omics datasets. Zenodo https://doi.org/10.5281/zenodo.7693825 (2023).

  157. Gorin, G., Pachter, L., Chari, T., Carilli, M. & Vastola, J. Monod supporting data. Zenodo https://doi.org/10.5281/zenodo.15051840 (2025).

  158. Jayakumar, K. & Mundassery, D. A. On Moran’s bivariate gamma and bivariate negative binomial distribution. Calcutta Stat. Assoc. Bull. 59, 15–28 (2007).

    Google Scholar 

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Acknowledgements

We thank S. Booeshaghi and M. Fang for useful discussions in the course of developing Monod. G.G. and L.P. were partially funded by NIH U19MH114830 and NIH 5UM1HG012077-02. M.C. is supported by the National Science Foundation Graduate Research Fellowship Program under grant no. 2139433. T.C. was supported by the Eric and Wendy Schmidt Center at the Broad Institute of MIT and Harvard. Part of this work was performed during G.G.’s Data Sciences Co-op with Celsius Therapeutics.

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Authors and Affiliations

  1. Fauna Bio, Emeryville, CA, USA

    Gennady Gorin

  2. Eric and Wendy Schmidt Center, Broad Institute of MIT and Harvard, Cambridge, MA, USA

    Tara Chari

  3. Division of Biology and Biological Engineering, California Institute of Technology, Pasadena, CA, USA

    Maria Carilli & Lior Pachter

  4. Department of Neurobiology, Harvard Medical School, Boston, MA, USA

    John J. Vastola

  5. Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA, USA

    Lior Pachter

Authors
  1. Gennady Gorin
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  2. Tara Chari
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  3. Maria Carilli
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  4. John J. Vastola
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  5. Lior Pachter
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Contributions

All authors contributed extensively to the work presented in this paper. The first draft of the paper was conceptualized and written by G.G. and L.P. ‘Assumptions and approach of Monod’ was predominantly conceptualized by G.G., J.J.V. and L.P. ‘Monod generalizes differential expression analyses’ was predominantly conceptualized and executed by G.G., T.C. and L.P. ‘Monod identifies strategies of resistance and recovery’ and ‘Model selection and insight about gene regulation strategies’ were predominantly conceptualized and executed by M.C. and L.P. ‘Principled integration of multiple modalities’ was predominantly conceptualized and executed by G.G., J.J.V., M.C. and L.P. ‘Assessing loss of biological signal after preprocessing’ was predominantly conceptualized and executed by G.G., J.J.V. and L.P.

Corresponding author

Correspondence to Lior Pachter.

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Competing interests

G.G. is an employee of Fauna Bio. The remaining authors declare no competing interests.

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Nature Methods thanks the anonymous reviewers for their contribution to the peer review of this work. Primary Handling Editor: Lin Tang, in collaboration with the Nature Methods team.

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Supplementary Methods, Tables 1–10 and Figs. 1–19

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Gorin, G., Chari, T., Carilli, M. et al. Monod: model-based discovery and integration through fitting stochastic transcriptional dynamics to single-cell sequencing data. Nat Methods 22, 2286–2300 (2025). https://doi.org/10.1038/s41592-025-02832-x

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