Technical Report | Published:

Tensor decomposition for multiple-tissue gene expression experiments

Nature Genetics volume 48, pages 10941100 (2016) | Download Citation

Abstract

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.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

References

  1. 1.

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

  2. 2.

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

  3. 3.

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

  4. 4.

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

  5. 5.

    , & The genetic and mechanistic basis for variation in gene regulation. PLoS Genet. 11, e1004857 (2015).

  6. 6.

    , , & A statistical framework for joint eQTL analysis in multiple tissues. PLoS Genet. 9, e1003486 (2013).

  7. 7.

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

  8. 8.

    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).

  9. 9.

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

  10. 10.

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

  11. 11.

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

  12. 12.

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

  13. 13.

    , , & Linked independent component analysis for multimodal data fusion. Neuroimage 54, 2198–2217 (2011).

  14. 14.

    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).

  15. 15.

    & Tensor decompositions and applications. SIAM Rev. 51, 455–500 (2009).

  16. 16.

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

  17. 17.

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

  18. 18.

    , & Bayesian multi-tensor factorization. Preprint at (2014).

  19. 19.

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

  20. 20.

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

  21. 21.

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

  22. 22.

    , & Regulation of MHC class II gene expression by the class II transactivator. Nat. Rev. Immunol. 5, 793–806 (2005).

  23. 23.

    , , & 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).

  24. 24.

    & NLRC5: a key regulator of MHC class I–dependent immune responses. Nat. Rev. Immunol. 12, 813–820 (2012).

  25. 25.

    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).

  26. 26.

    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).

  27. 27.

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

  28. 28.

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

  29. 29.

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

  30. 30.

    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).

  31. 31.

    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).

  32. 32.

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

  33. 33.

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

  34. 34.

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

  35. 35.

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

  36. 36.

    , & A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis. Biostatistics 10, 515–534 (2009).

  37. 37.

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

  38. 38.

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

  39. 39.

    , , & An introduction to variational methods for graphical models. Machine Learning 37, 183–233 (1999).

  40. 40.

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

  41. 41.

    , & Genotype imputation with thousands of genomes. G3 (Bethesda) 1, 457–470 (2011).

  42. 42.

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

Download references

Acknowledgements

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

Affiliations

  1. Department of Statistics, University of Oxford, Oxford, UK.

    • Victoria Hore
    •  & Jonathan Marchini
  2. Department of Twin Research and Genetic Epidemiology, King's College London, London, UK.

    • Ana Viñuela
    •  & Kerrin Small
  3. Department of Genetic Medicine and Development, University of Geneva, Geneva, Switzerland.

    • Alfonso Buil
  4. Wellcome Trust Centre for Human Genetics, Oxford, UK.

    • Julian Knight
    • , Mark I McCarthy
    •  & Jonathan Marchini
  5. Oxford Centre for Diabetes, Endocrinology and Metabolism, University of Oxford, Churchill Hospital, Oxford, UK.

    • Mark I McCarthy

Authors

  1. Search for Victoria Hore in:

  2. Search for Ana Viñuela in:

  3. Search for Alfonso Buil in:

  4. Search for Julian Knight in:

  5. Search for Mark I McCarthy in:

  6. Search for Kerrin Small in:

  7. Search for Jonathan Marchini in:

Contributions

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.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Jonathan Marchini.

Supplementary information

PDF files

  1. 1.

    Supplementary Text and Figures

    Supplementary Figures 1–39, Supplementary Tables 1–7 and Supplementary Note.

Excel files

  1. 1.

    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.

About this article

Publication history

Received

Accepted

Published

DOI

https://doi.org/10.1038/ng.3624

Further reading