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Tensor decomposition for multiple-tissue gene expression experiments


Genome-wide association studies of gene expression traits and other cellular phenotypes have successfully identified links between genetic variation and biological processes. The majority of discoveries have uncovered cis–expression quantitative trait locus (eQTL) effects via mass univariate testing of SNPs against gene expression in single tissues. Here we present a Bayesian method for multiple-tissue experiments focusing on uncovering gene networks linked to genetic variation. Our method decomposes the 3D array (or tensor) of gene expression measurements into a set of latent components. We identify sparse gene networks that can then be tested for association against genetic variation across the genome. We apply our method to a data set of 845 individuals from the TwinsUK cohort with gene expression measured via RNA-seq analysis in adipose, lymphoblastoid cell lines (LCLs) and skin. We uncover several gene networks with a genetic basis and clear biological and statistical significance. Extensions of this approach will allow integration of different omics, environmental and phenotypic data sets.

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Figure 1: Graphical representation of the method.
Figure 2: MHC class II regulation.
Figure 3: MHC class I regulation.
Figure 4: Histone RNA processing.
Figure 5: Type I interferon response.
Figure 6: Zinc-finger gene network.
Figure 7: Multiple-omics data integration.


  1. Stranger, B.E. et al. Population genomics of human gene expression. Nat. Genet. 39, 1217–1224 (2007).

    Article  CAS  Google Scholar 

  2. Degner, J.F. et al. DNaseI sensitivity QTLs are a major determinant of human expression variation. Nature 482, 390–394 (2012).

    Article  CAS  Google Scholar 

  3. Kasowski, M. et al. Extensive variation in chromatin states across humans. Science 342, 750–752 (2013).

    Article  CAS  Google Scholar 

  4. Battle, A. et al. Impact of regulatory variation from RNA to protein. Science 347, 664–667 (2015).

    CAS  Google Scholar 

  5. Pai, A.A., Pritchard, J.K. & Gilad, Y. The genetic and mechanistic basis for variation in gene regulation. PLoS Genet. 11, e1004857 (2015).

    Article  Google Scholar 

  6. Flutre, T., Wen, X., Pritchard, J. & Stephens, M. A statistical framework for joint eQTL analysis in multiple tissues. PLoS Genet. 9, e1003486 (2013).

    Article  CAS  Google Scholar 

  7. Grundberg, E. et al. Mapping cis- and trans-regulatory effects across multiple tissues in twins. Nat. Genet. 44, 1084–1089 (2012).

    Article  CAS  Google Scholar 

  8. Price, A.L. et al. Single-tissue and cross-tissue heritability of gene expression via identity-by-descent in related or unrelated individuals. PLoS Genet. 7, e1001317 (2011).

    Article  CAS  Google Scholar 

  9. Westra, H.-J. et al. Systematic identification of trans eQTLs as putative drivers of known disease associations. Nat. Genet. 45, 1238–1243 (2013).

    Article  CAS  Google Scholar 

  10. Yao, C. et al. Integromic analysis of genetic variation and gene expression identifies networks for cardiovascular disease phenotypes. Circulation 131, 536–549 (2015).

    Article  CAS  Google Scholar 

  11. Novembre, J. et al. Genes mirror geography within Europe. Nature 456, 98–101 (2008).

    Article  CAS  Google Scholar 

  12. Mitchell, T.J. & Beauchamp, J.J. Bayesian variable selection in linear regression. J. Am. Stat. Assoc. 83, 1023–1032 (1988).

    Article  Google Scholar 

  13. Groves, A.R., Beckmann, C.F., Smith, S.M. & Woolrich, M.W. Linked independent component analysis for multimodal data fusion. Neuroimage 54, 2198–2217 (2011).

    Article  Google Scholar 

  14. Groves, A.R. et al. Benefits of multi-modal fusion analysis on a large-scale dataset: life-span patterns of inter-subject variability in cortical morphometry and white matter microstructure. Neuroimage 63, 365–380 (2012).

    Article  Google Scholar 

  15. Kolda, T.G. & Bader, B.W. Tensor decompositions and applications. SIAM Rev. 51, 455–500 (2009).

    Article  Google Scholar 

  16. Yener, B. et al. Multiway modeling and analysis in stem cell systems biology. BMC Syst. Biol. 2, 63 (2008).

    Article  Google Scholar 

  17. Hoff, P.D. Hierarchical multilinear models for multiway data. Comput. Stat. Data Anal. 55, 530–543 (2011).

    Article  Google Scholar 

  18. Khan, S.A., Leppaaho, E. & Kaski, S. Bayesian multi-tensor factorization. Preprint at (2014).

  19. Buil, A. et al. Gene–gene and gene–environment interactions detected by transcriptome sequence analysis in twins. Nat. Genet. 47, 88–91 (2015).

    Article  CAS  Google Scholar 

  20. Brown, A.A. et al. Genetic interactions affecting human gene expression identified by variance association mapping. eLife 3, e01381 (2014).

    Article  Google Scholar 

  21. GTEx Consortium. The Genotype-Tissue Expression (GTEx) pilot analysis: multitissue gene regulation in humans. Science 348, 648–660 (2015).

  22. Reith, W., LeibundGut-Landmann, S. & Waldburger, J.M. Regulation of MHC class II gene expression by the class II transactivator. Nat. Rev. Immunol. 5, 793–806 (2005).

    Article  CAS  Google Scholar 

  23. Stegle, O., Parts, L., Durbin, R. & Winn, J. A Bayesian framework to account for complex non-genetic factors in gene expression levels greatly increases power in eQTL studies. PLoS Comput. Biol. 6, e1000770 (2010).

    Article  Google Scholar 

  24. Kobayashi, K.S. & van den Elsen, P.J. NLRC5: a key regulator of MHC class I–dependent immune responses. Nat. Rev. Immunol. 12, 813–820 (2012).

    Article  CAS  Google Scholar 

  25. Pillai, R.S. et al. Unique Sm core structure of U7 snRNPs: assembly by a specialized SMN complex and the role of a new component, Lsm11, in histone RNA processing. Genes Dev. 17, 2321–2333 (2003).

    Article  CAS  Google Scholar 

  26. Liu, C. et al. MirSNP, a database of polymorphisms altering miRNA target sites, identifies miRNA-related SNPs in GWAS SNPs and eQTLs. BMC Genomics 13, 661 (2012).

    Article  CAS  Google Scholar 

  27. Melchjorsen, J. et al. Differential regulation of the OASL and OAS1 genes in response to viral infections. J. Interferon Cytokine Res. 29, 199–207 (2009).

    Article  CAS  Google Scholar 

  28. Potu, H., Sgorbissa, A. & Brancolini, C. Identification of USP18 as an important regulator of the susceptibility to IFN-α and drug-induced apoptosis. Cancer Res. 70, 655–665 (2010).

    Article  CAS  Google Scholar 

  29. Malakhova, O.A. et al. UBP43 is a novel regulator of interferon signaling independent of its ISG15 isopeptidase activity. EMBO J. 25, 2358–2367 (2006).

    Article  CAS  Google Scholar 

  30. François-Newton, V. et al. USP18-based negative feedback control is induced by type I and type III interferons and specifically inactivates interferon α response. PLoS One 6, e22200 (2011).

    Article  Google Scholar 

  31. Burkart, C. et al. Usp18 deficient mammary epithelial cells create an antitumour environment driven by hypersensitivity to IFN-λ and elevated secretion of Cxcl10. EMBO Mol. Med. 5, 967–982 (2013).

    Article  CAS  Google Scholar 

  32. Huan, T. et al. Genome-wide identification of microRNA expression quantitative trait loci. Nat. Commun. 6, 6601 (2015).

    Article  CAS  Google Scholar 

  33. Lemire, M. et al. Long-range epigenetic regulation is conferred by genetic variation located at thousands of independent loci. Nat. Commun. 6, 6326 (2015).

    Article  CAS  Google Scholar 

  34. Small, K.S. et al. Identification of an imprinted master trans regulator at the KLF14 locus related to multiple metabolic phenotypes. Nat. Genet. 43, 561–564 (2011).

    Article  CAS  Google Scholar 

  35. Hawrylycz, M.J. et al. An anatomically comprehensive atlas of the adult human brain transcriptome. Nature 489, 391–399 (2012).

    Article  CAS  Google Scholar 

  36. Witten, D.M., Tibshirani, R. & Hastie, T. A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis. Biostatistics 10, 515–534 (2009).

    Article  Google Scholar 

  37. Sun, S. A survey of multi-view machine learning. Neural Comput. Appl. 23, 2031–2038 (2013).

    Article  Google Scholar 

  38. Lucas, J. et al. in Bayesian Inference for Gene Expression and Proteomics (eds. Do, K.-A., Muller, P. & Vannucci, M.) 1–25 (2006).

  39. Jordan, M.I., Ghahramani, Z., Jaakkola, T.S. & Saul, L.K. An introduction to variational methods for graphical models. Machine Learning 37, 183–233 (1999).

    Article  Google Scholar 

  40. Li, H. & Durbin, R. Fast and accurate short read alignment with Burrows–Wheeler transform. Bioinformatics 25, 1754–1760 (2009).

    Article  CAS  Google Scholar 

  41. Howie, B., Marchini, J. & Stephens, M. Genotype imputation with thousands of genomes. G3 (Bethesda) 1, 457–470 (2011).

    Article  Google Scholar 

  42. Zhou, X. & Stephens, M. Genome-wide efficient mixed-model analysis for association studies. Nat. Genet. 44, 821–824 (2012).

    Article  CAS  Google Scholar 

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We are grateful to A. Dahl, W. Kretzschmar, K. Sharp, L. Elliot and S. Myers for helpful discussions about the method and interpretation of the results. The TwinsUK cohort was funded by the Wellcome Trust and the European Community's Seventh Framework Programme (FP7/2007-2013). The study also receives support from the NIHR Clinical Research Facility at Guy's and St Thomas' NHS Foundation Trust and the NIHR Biomedical Research Centre based at Guy's and St Thomas' NHS Foundation Trust and King's College London. SNP genotyping was performed by the Wellcome Trust Sanger Institute and National Eye Institute via NIH/CIDR. A.V. and A.B. were supported by European Union Framework Programme 7 grant EuroBATS (259749). V.H. acknowledges the EPSRC for funding through a studentship at the Life Sciences Interface program of the University of Oxford's Doctoral Training Center. J.M. acknowledges support from the ERC (grant 617306).

Author information

Authors and Affiliations



V.H. and J.M. developed the method. V.H. carried out all analysis. J.M. and V.H. wrote the manuscript. A.V., A.B. and K.S. provided the TwinsUK data set. A.V., A.B., J.K., M.I.M. and K.S. advised on interpretation of the results.

Corresponding author

Correspondence to Jonathan Marchini.

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Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Text and Figures

Supplementary Figures 1–39, Supplementary Tables 1–7 and Supplementary Note. (PDF 19964 kb)

Supplementary Data

Detailed information about components. The first sheet of the spreadsheet contains detailed information for the 236 robust components obtained by clustering across ten runs of the tensor decomposition method. The second sheet of the spreadsheet contains detailed Information for 944 components obtained by taking the run of the tensor decomposition method with the highest value of the model negative free energy. (XLSX 77139 kb)

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Hore, V., Viñuela, A., Buil, A. et al. Tensor decomposition for multiple-tissue gene expression experiments. Nat Genet 48, 1094–1100 (2016).

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