Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Modeling gene regulatory networks using neural network architectures


Gene regulatory networks (GRNs) encode the complex molecular interactions that govern cell identity. Here we propose DeepSEM, a deep generative model that can jointly infer GRNs and biologically meaningful representation of single-cell RNA sequencing (scRNA-seq) data. In particular, we developed a neural network version of the structural equation model (SEM) to explicitly model the regulatory relationships among genes. Benchmark results show that DeepSEM achieves comparable or better performance on a variety of single-cell computational tasks, such as GRN inference, scRNA-seq data visualization, clustering and simulation, compared with the state-of-the-art methods. In addition, the gene regulations predicted by DeepSEM on cell-type marker genes in the mouse cortex can be validated by epigenetic data, which further demonstrates the accuracy and efficiency of our method. DeepSEM can provide a useful and powerful tool to analyze scRNA-seq data and infer a GRN.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Overview of DeepSEM.
Fig. 2: The neural network architecture of DeepSEM.
Fig. 3: Summary of the GRN prediction performance in terms of EPR.
Fig. 4: Validating GRN prediction using epigenetic data.
Fig. 5: Single-cell clustering and embedding.
Fig. 6: Simulation performance of DeepSEM compared with cscGAN and scGAN.

Data availability

We provide all datasets generated or analyzed during this study. The gene experimental scRNA-seq datasets were downloaded from Gene Expression Omnibus with the accession numbers GSE81252 (hHEP dataset65), GSE75748 (hESC dataset66), GSE98664 (mESC dataset62), GSE48968 (mDC dataset63), GSE81682 (mHSC dataset64), GSE115746 (mouse cortex dataset33), GSE60361 (Zeisel dataset41), GSE85241 (Muraro dataset78), GSE81861 (Li dataset79), and GSE45719 (Deng dataset80). The other experimental scRNA-seq dataset were downloaded from ArrayExpress with the accession number E-MTAB-5061 (Segerstolpe dataset81), NCBI Sequence Read Archive (SRA) with accession number SRP041736 (Pollen dataset42), GitHub repositories ( (CellBench dataset82) and the website for x10genomics ( (PBMC dataset43). The scATAC-seq and snmC-seq for mouse cortex were downloaded from Gene Expression Omnibus with the accession numbers GSE126724 (scATAC-seq35) and GSE97179 (snmC-seq34). More information for these datasets could be found in Methods. We also summarize the accession and download links in Supplementary Tables 1, 2, 5 and 9. Source Data for Figs. 36 are available with this manuscript.

Code availability

The codes generated during this study are available on GitHub ( and in Zenodo83.


  1. 1.

    Picelli, S. et al. Smart-seq2 for sensitive full-length transcriptome profiling in single cells. Nat. Methods 10, 1096–1098 (2013).

    Google Scholar 

  2. 2.

    Macosko, E. Z. et al. Highly parallel genome-wide expression profiling of individual cells using nanoliter droplets. Cell 161, 1202–1214 (2015).

    Google Scholar 

  3. 3.

    Hashimshony, T. et al. CEL-Seq2: sensitive highly-multiplexed single-cell RNA-seq. Genome Biol. 17, 77 (2016).

    Google Scholar 

  4. 4.

    Wagner, A., Regev, A. & Yosef, N. Revealing the vectors of cellular identity with single-cell genomics. Nat. Biotechnol. 34, 1145–1160 (2016).

    Google Scholar 

  5. 5.

    Kharchenko, P. V., Silberstein, L. & Scadden, D. T. Bayesian approach to single-cell differential expression analysis. Nat. Methods 11, 740–742 (2014).

    Google Scholar 

  6. 6.

    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).

    Google Scholar 

  7. 7.

    Eraslan, G., Simon, L. M., Mircea, M., Mueller, N. S. & Theis, F. J. Single-cell RNA-seq denoising using a deep count autoencoder. Nat. Commun. 10, 390 (2019).

    Google Scholar 

  8. 8.

    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).

    Google Scholar 

  9. 9.

    Olsson, A. et al. Single-cell analysis of mixed-lineage states leading to a binary cell fate choice. Nature 537, 698–702 (2016).

    Google Scholar 

  10. 10.

    Sharma, A. et al. Onco-fetal reprogramming of endothelial cells drives immunosuppressive macrophages in hepatocellular carcinoma. Cell 183, 377–394.e21 (2020).

    Google Scholar 

  11. 11.

    Arisdakessian, C., Poirion, O., Yunits, B., Zhu, X. & Garmire, L. X. DeepImpute: an accurate, fast, and scalable deep neural network method to impute single-cell RNA-seq data. Genome Biol. 20, 211 (2019).

    Google Scholar 

  12. 12.

    Wang, T. et al. BERMUDA: a novel deep transfer learning method for single-cell RNA sequencing batch correction reveals hidden high-resolution cellular subtypes. Genome Biol. 20, 165 (2019).

    Google Scholar 

  13. 13.

    Li, X. et al. Deep learning enables accurate clustering with batch effect removal in single-cell RNA-seq analysis. Nat. Commun. 11, 2338 (2020).

    Google Scholar 

  14. 14.

    Huynh-Thu, V. A., Irrthum, A., Wehenkel, L. & Geurts, P. Inferring regulatory networks from expression data using tree-based methods. PLoS ONE 5, e12776 (2010).

    Google Scholar 

  15. 15.

    Chan, T. E., Stumpf, M. P. H. & Babtie, A. C. Gene regulatory network inference from single-cell data using multivariate information measures. Cell Syst. 5, 251–267.e3 (2017).

    Google Scholar 

  16. 16.

    Matsumoto, H. et al. SCODE: an efficient regulatory network inference algorithm from single-cell RNA-seq during differentiation. Bioinformatics 33, 2314–2321 (2017).

    Google Scholar 

  17. 17.

    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).

    Google Scholar 

  18. 18.

    Moerman, T. et al. GRNBoost2 and Arboreto: efficient and scalable inference of gene regulatory networks. Bioinformatics 35, 2159–2161 (2019).

    Google Scholar 

  19. 19.

    Kamimoto, K., Hoffmann, C. M. & Morris, S. A. CellOracle: dissecting cell identity via network inference and in silico gene perturbation. Preprint at bioRxiv (2020).

  20. 20.

    Kim, S. ppcor: an R package for a fast calculation to semi-partial correlation coefficients. Commun. Stat. Appl. Methods 22, 665–674 (2015).

    Google Scholar 

  21. 21.

    Yu, Y., Jie, C., Tian, G. & Mo, Y. DAG-GNN: DAG structure learning with graph neural networks. In Proceedings of the 36th International Conference on Machine Learning 7154–7163 (ICML, 2019).

  22. 22.

    Lin, C., Jain, S., Kim, H. & Bar-Joseph, Z. Using neural networks for reducing the dimensions of single-cell RNA-seq data. Nucleic Acids Res. 45, e156 (2017).

    Google Scholar 

  23. 23.

    Higgins, I. et al. beta-VAE: learning basic visual concepts with a constrained variational framework. In Proceedings of the 5th International Conference on Learning Representations (ICML, 2017).

  24. 24.

    Zhao, A., Balakrishnan, G., Durand, F., Guttag, J. V. & Dalca, A. V. Data augmentation using learned transformations for one-shot medical image segmentation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition 8543–8553 (IEEE, 2019).

  25. 25.

    Lotfollahi, M., Wolf, F. A. & Theis, F. J. scGen predicts single-cell perturbation responses. Nat. Methods 16, 715–721 (2019).

    Google Scholar 

  26. 26.

    Wang, X., Ghasedi Dizaji, K. & Huang, H. Conditional generative adversarial network for gene expression inference. Bioinformatics 34, i603–i611 (2018).

    Google Scholar 

  27. 27.

    Marouf, M. et al. Realistic in silico generation and augmentation of single-cell RNA-seq data using generative adversarial networks. Nat. Commun. 11, 166 (2020).

    Google Scholar 

  28. 28.

    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).

    Google Scholar 

  29. 29.

    Moore, L. D., Le, T. & Fan, G. DNA methylation and its basic function. Neuropsychopharmacology (2013).

  30. 30.

    Thurman, R. E. et al. The accessible chromatin landscape of the human genome. Nature 489, 75–82 (2012).

    Google Scholar 

  31. 31.

    Keilwagen, J., Posch, S. & Grau, J. Accurate prediction of cell type-specific transcription factor binding. Genome Biol. 20, 9 (2019).

    Google Scholar 

  32. 32.

    Funk, C. C. et al. Atlas of transcription factor binding sites from ENCODE DNase hypersensitivity data across 27 tissue types. Cell Rep. 32, 108029 (2020).

    Google Scholar 

  33. 33.

    Tasic, B. et al. Shared and distinct transcriptomic cell types across neocortical areas. Nature 563, 72–78 (2018).

    Google Scholar 

  34. 34.

    Luo, C. et al. Single-cell methylomes identify neuronal subtypes and regulatory elements in mammalian cortex. Science 357, 600–604 (2017).

    Google Scholar 

  35. 35.

    Fang, R. et al. Comprehensive analysis of single cell ATAC-seq data with SnapATAC. Nat. Commun. 12, 1337 (2021).

    Google Scholar 

  36. 36.

    Dong, J. et al. Enhancing single-cell cellular state inference by incorporating molecular network features. Preprint at bioRxiv (2019).

  37. 37.

    Aibar, S. et al. SCENIC: single-cell regulatory network inference and clustering. Nat. Methods 14, 1083–1086 (2017).

    Google Scholar 

  38. 38.

    Li, X. et al. Network embedding-based representation learning for single cell RNA-seq data. Nucleic Acids Res. 45, e166–e166 (2017).

    Google Scholar 

  39. 39.

    Cahan, P. et al. CellNet: network biology applied to stem cell engineering. Cell 158, 903–915 (2014).

    Google Scholar 

  40. 40.

    Morris, S. A. et al. Dissecting engineered cell types and enhancing cell fate conversion via CellNet. Cell 158, 889–902 (2014).

    Google Scholar 

  41. 41.

    Zeisel, A. et al. Brain structure. Cell types in the mouse cortex and hippocampus revealed by single-cell RNA-seq. Science 347, 1138–1142 (2015).

    Google Scholar 

  42. 42.

    Pollen, A. A. et al. Low-coverage single-cell mRNA sequencing reveals cellular heterogeneity and activated signaling pathways in developing cerebral cortex. Nat. Biotechnol. 32, 1053–1058 (2014).

    Google Scholar 

  43. 43.

    Zheng, G. X. Y. et al. Massively parallel digital transcriptional profiling of single cells. Nat. Commun. 8, 14049 (2017).

    Google Scholar 

  44. 44.

    Pierson, E. & Yau, C. ZIFA: dimensionality reduction for zero-inflated single-cell gene expression analysis. Genome Biol. 16, 241 (2015).

    Google Scholar 

  45. 45.

    Jolliffe, I. T. in Principal Component Analysis (ed. Jolliffe, I. T.) 115–128 (Springer, 1986).

  46. 46.

    Blondel, V. D., Guillaume, J.-L., Lambiotte, R. & Lefebvre, E. Fast unfolding of communities in large networks. J. Stat. Mech. 2008, P10008 (2008).

    MATH  Google Scholar 

  47. 47.

    Becht, E. et al. Dimensionality reduction for visualizing single-cell data using UMAP. Nat. Biotechnol. (2019).

  48. 48.

    Heiser, C. N. & Lau, K. S. A quantitative framework for evaluating single-cell data structure preservation by dimensionality reduction techniques. Cell Rep. 31, 107576 (2020).

    Google Scholar 

  49. 49.

    Viñas, R., Andrés-Terré, H., Liò, P. & Bryson, K. Adversarial generation of gene expression data. Bioinformatics (2021).

  50. 50.

    Bollen, K. A. Structural Equations with Latent Variables (John Wiley & Sons, 1989).

  51. 51.

    Haavelmo, T. The statistical implications of a system of simultaneous equations. Econometrica 11, 1–12 (1943).

    MathSciNet  MATH  Google Scholar 

  52. 52.

    King, M., Goldberger, A. S. & Duncan, O. D. Structural equation models in the social sciences. Econ. J. 84, 212–214 (1974).

    Google Scholar 

  53. 53.

    Duarte, C. W., Klimentidis, Y. C., Harris, J. J., Cardel, M. & Fernández, J. R. A hybrid Bayesian network/structural equation (BN/SEM) modeling approach for detecting physiological networks for obesity-related genetic variants. In Proceedings of the IEEE International Conference on Bioinformatics and Biomedicine 696–702 (IEEE, 2012).

  54. 54.

    Yoo, C. & Oh, S. Combining structure equation model with Bayesian networks for predicting with high accuracy of recommending surgery for better survival in Benign prostatic hyperplasia patients. In 20th International Congress on Modelling and Simulation-Adapting to Change 2029–2033 (Modelling and Simulation Society of Australia and New Zealand, 2013).

  55. 55.

    Zheng, X., Aragam, B., Ravikumar, P. & Xing, E. P. DAGs with NO TEARS: continuous optimization for structure learning. In Proceedings of the 32nd International Conference on Neural Information Processing Systems 9492–9503 (IEEE, 2018).

  56. 56.

    Luo, Y., Peng, J. & Ma, J. When causal inference meets deep learning. Nat. Mach. Intell. 2, 426–427 (2020).

    Google Scholar 

  57. 57.

    Kingma, D. P. & Welling, M. An introduction to variational autoencoders. Found Trends Mach. Learn. 12, 307–392 (2019).

    MATH  Google Scholar 

  58. 58.

    Kingma, D. P. & Ba, J. Adam: a method for stochastic optimization. In Proceedings of the 3th International Conference on Learning Representations (ICLR, 2015).

  59. 59.

    Friedman, J., Hastie, T. & Tibshirani, R. Sparse inverse covariance estimation with the graphical lasso. Biostatistics 9, 432–441 (2008).

    MATH  Google Scholar 

  60. 60.

    Tieleman, T. & Hinton, G. Lecture 6.5-rmsprop, Coursera: Neural Networks for Machine Learning Technical Report (Univ. Toronto, 2012).

  61. 61.

    He, K., Zhang, X., Ren, S. & Sun, J. Delving deep into rectifiers: surpassing human-level performance on ImageNet classification. In Proceedings of the IEEE International Conference on Computer Vision 1026–1034 (IEEE, 2015).

  62. 62.

    Hayashi, T. et al. Single-cell full-length total RNA sequencing uncovers dynamics of recursive splicing and enhancer RNAs. Nat. Commun. 9, 619 (2018).

    Google Scholar 

  63. 63.

    Shalek, A. K. et al. Single-cell RNA-seq reveals dynamic paracrine control of cellular variation. Nature 510, 363–369 (2014).

    Google Scholar 

  64. 64.

    Nestorowa, S. et al. A single-cell resolution map of mouse hematopoietic stem and progenitor cell differentiation. Blood 128, e20–e31 (2016).

    Google Scholar 

  65. 65.

    Camp, J. G. et al. Multilineage communication regulates human liver bud development from pluripotency. Nature 546, 533–538 (2017).

    Google Scholar 

  66. 66.

    Chu, L.-F. et al. Single-cell RNA-seq reveals novel regulators of human embryonic stem cell differentiation to definitive endoderm. Genome Biol. 17, 173 (2016).

    Google Scholar 

  67. 67.

    ENCODE Project Consortium An integrated encyclopedia of DNA elements in the human genome. Nature 489, 57–74 (2012).

  68. 68.

    Davis, C. A. et al. The encyclopedia of DNA elements (ENCODE): data portal update. Nucleic Acids Res. 46, D794–D801 (2018).

    Google Scholar 

  69. 69.

    Oki, S. et al. ChIP-Atlas: a data-mining suite powered by full integration of public ChIP-seq data. EMBO Rep. 19, e46255 (2018).

    Google Scholar 

  70. 70.

    Xu, H. et al. ESCAPE: database for integrating high-content published data collected from human and mouse embryonic stem cells. Database 2013, bat045 (2013).

    Google Scholar 

  71. 71.

    Garcia-Alonso, L., Holland, C. H., Ibrahim, M. M., Turei, D. & Saez-Rodriguez, J. Benchmark and integration of resources for the estimation of human transcription factor activities. Genome Res. 29, 1363–1375 (2019).

    Google Scholar 

  72. 72.

    Liu, Z.-P., Wu, C., Miao, H. & Wu, H. RegNetwork: an integrated database of transcriptional and post-transcriptional regulatory networks in human and mouse. Database 2015, bav095 (2015).

    Google Scholar 

  73. 73.

    Han, H. et al. TRRUST: a reference database of human transcriptional regulatory interactions. Sci. Rep. 5, 11432 (2015).

    Google Scholar 

  74. 74.

    Szklarczyk, D. et al. STRING v11: protein–protein association networks with increased coverage, supporting functional discovery in genome-wide experimental datasets. Nucleic Acids Res. 47, D607–D613 (2019).

    Google Scholar 

  75. 75.

    Wolf, F. A., Angerer, P. & Theis, F. J. SCANPY: large-scale single-cell gene expression data analysis. Genome Biol. 19, 15 (2018).

    Google Scholar 

  76. 76.

    Fornes, O. et al. JASPAR 2020: update of the open-access database of transcription factor binding profiles. Nucleic Acids Res. 48, D87–D92 (2020).

    Google Scholar 

  77. 77.

    Grant, C. E., Bailey, T. L. & Noble, W. S. FIMO: scanning for occurrences of a given motif. Bioinformatics 27, 1017–1018 (2011).

    Google Scholar 

  78. 78.

    Muraro, M. J. et al. A Single-cell transcriptome atlas of the human pancreas. Cell Syst. 3, 385–394.e3 (2016).

    Google Scholar 

  79. 79.

    Li, H. et al. Reference component analysis of single-cell transcriptomes elucidates cellular heterogeneity in human colorectal tumors. Nat. Genet. 49, 708–718 (2017).

    Google Scholar 

  80. 80.

    Deng, Q., Ramsköld, D., Reinius, B. & Sandberg, R. Single-cell RNA-seq reveals dynamic, random monoallelic gene expression in mammalian cells. Science 343, 193–196 (2014).

    Google Scholar 

  81. 81.

    Segerstolpe, Å. et al. Single-cell transcriptome profiling of human pancreatic islets in health and type 2 diabetes. Cell Metab. 24, 593–607 (2016).

    Google Scholar 

  82. 82.

    Tian, L. et al. Benchmarking single cell RNA-sequencing analysis pipelines using mixture control experiments. Nat. Methods 16, 479–487 (2019).

    Google Scholar 

  83. 83.

    Shu, H. et al. Code for paper ‘Modeling gene regulatory networks using neural network architectures’. Zenodo (2021).

Download references


This work was supported in part by the National Natural Science Foundation of China (61872216, 81630103), the Turing AI Institute of Nanjing to J. Zeng. We also acknowledge the National Natural Science Foundation of China (31900862) for funding support to D.Z..

Author information




J. Zeng and J.M. designed the study and developed the conceptual ideas. H.S. and Q.L. implemented the main algorithms. H.S. performed the model training and experimental validation task. H.S. and J. Zhou collected all the input data sources and interpreted the results. H.S., J. Zhou, H.L., D.Z., J. Zeng and J.M. wrote the manuscript with support from all authors.

Corresponding authors

Correspondence to Jianyang Zeng or Jianzhu Ma.

Ethics declarations

Competing interests

J. Zeng is founder and CTO of Silexon AI Technology Co. Ltd. and has an equity interest. The remaining authors declare no competing interests.

Additional information

Peer review information Nature Computational Science thanks Jun Ding, Yafei Lyu and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Handling editor: Fernando Chirigati, in collaboration with the Nature Computational Science team.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Figs. 1–17, Sections 1–7 and Tables 1–10.

Source data

Source Data Fig. 3

The corresponding raw data file for Fig. 3.

Source Data Fig. 4

The corresponding raw data file for Fig. 4.

Source Data Fig. 5

The corresponding raw data file for Fig. 5.

Source Data Fig. 6

The corresponding raw data file for Fig. 6.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Shu, H., Zhou, J., Lian, Q. et al. Modeling gene regulatory networks using neural network architectures. Nat Comput Sci 1, 491–501 (2021).

Download citation

Further reading


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing