Technical Report | Published:

Tensor decomposition for multiple-tissue gene expression experiments

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


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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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


  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


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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

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  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.

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