Advertisement

A Robust Bayesian Two-Sample Test for Detecting Intervals of Differential Gene Expression in Microarray Time Series

  • Oliver Stegle
  • Katherine Denby
  • David L. Wild
  • Zoubin Ghahramani
  • Karsten M. Borgwardt
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5541)

Abstract

Understanding the regulatory mechanisms that are responsible for an organism’s response to environmental changes is an important question in molecular biology. A first and important step towards this goal is to detect genes whose expression levels are affected by altered external conditions. A range of methods to test for differential gene expression, both in static as well as in time-course experiments, have been proposed. While these tests answer the question whether a gene is differentially expressed, they do not explicitly address the question when a gene is differentially expressed, although this information may provide insights into the course and causal structure of regulatory programs. In this article, we propose a two-sample test for identifying intervals of differential gene expression in microarray time series. Our approach is based on Gaussian process regression, can deal with arbitrary numbers of replicates and is robust with respect to outliers. We apply our algorithm to study the response of Arabidopsis thaliana genes to an infection by a fungal pathogen using a microarray time series dataset covering 30,336 gene probes at 24 time points. In classification experiments our test compares favorably with existing methods and provides additional insights into time-dependent differential expression.

Keywords

Gaussian Process Reference Dataset Expectation Propagation Gaussian Process Regression Gaussian Process Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Kerr, M., Martin, M., Churchill, G.: Analysis of Variance for Gene Expression Microarray Data. Journal of Computational Biology 7(6), 819–837 (2000)CrossRefPubMedGoogle Scholar
  2. 2.
    Dudoit, S., Yang, Y.H., Callow, M.J., Speed, T.P.: Statistical methods for identifying differentially expressed genes in replicated cDNA microarray experiments. Statistica Sinica 12, 111–140 (2002)Google Scholar
  3. 3.
    Efron, B., Tibshirani, R., Storey, J.D., Tusher, V.: Empirical Bayes Analysis of a Microarray Experiment. Journal of the American Statistical Association 96, 1151–1160 (2001)CrossRefGoogle Scholar
  4. 4.
    Ishwaran, H., Rao, J.: Detecting differentially expressed genes in microarrays using Bayesian model selection. Journal of the American Statistical Association 98, 438–455 (2003)CrossRefGoogle Scholar
  5. 5.
    Lonnstedt, I., Speed, T.: Replicated microarray data. Statistica Sinica 12, 31–46 (2002)Google Scholar
  6. 6.
    Bar-Joseph, Z., Gerber, G., Simon, I., Gifford, D.K., Jaakkola, T.S.: Comparing the continuous representation of time-series expression profiles to identify differentially expressed genes. Proceedings of the National Academy of Sciences of the United States of America 100, 10146–10151 (2003)CrossRefPubMedPubMedCentralGoogle Scholar
  7. 7.
    Storey, J.D., Xiao, W., Leek, J.T., Tompkins, R.G., Davis, R.W.: Significance analysis of time course microarray experiments. Proceedings of the National Academy of Sciences of the United States of America 102, 12837–12842 (2005)CrossRefPubMedPubMedCentralGoogle Scholar
  8. 8.
    Tai, Y.C., Speed, T.P.: A multivariate empirical Bayes statistic for replicated microarray time course data. Annals of Statistics 34, 2387–2412 (2006)CrossRefGoogle Scholar
  9. 9.
    Angelini, C., De Canditiis, D., Mutarelli, M., Pensky, M.: A Bayesian Approach to Estimation and Testing in Time-course Microarray Experiments. Statistical Applications in Genetics and Molecular Biology 6 (September 2007)Google Scholar
  10. 10.
    Yuan, M.: Flexible temporal expression profile modelling using the Gaussian process. Computational Statistics and Data Analysis 51, 1754–1764 (2006)CrossRefGoogle Scholar
  11. 11.
    Lawrence, N.D., Sanguinetti, G., Rattray, M.: Modelling transcriptional regulation using Gaussian Processes. In: Advances in Neural Information Processing Systems, vol. 19, pp. 785–792. MIT Press, Cambridge (2007)Google Scholar
  12. 12.
    Chu, W., Ghahramani, Z., Falciani, F., Wild, D.: Biomarker discovery in microarray gene expression data with Gaussian processes. Bioinformatics 21(16), 3385–3393 (2005)CrossRefPubMedGoogle Scholar
  13. 13.
    Rasmussen, C.E., Williams, C.K.I.: Gaussian Processes for Machine Learning. The MIT Press, Cambridge (2006)Google Scholar
  14. 14.
    Kuss, M., Pfingsten, T., Csato, L., Rasmussen, C.E.: Approximate Inference for Robust Gaussian Process Regression. Technical report, Max Planck Institute for Biological Cybernetics, Tubingen (2005)Google Scholar
  15. 15.
    Minka, T.: Expectation propagation for approximate Bayesian inference. Uncertainty in Artificial Intelligence 17, 362–369 (2001)Google Scholar
  16. 16.
    Stegle, O., Fallert, S.V., MacKay, D.J.C., Brage, S.: Gaussian process robust regression for noisy heart rate data. IEEE Trans. Biomed. Eng. 55, 2143–2151 (2008)CrossRefPubMedGoogle Scholar
  17. 17.
    Fujita, M., Fujita, Y., Noutoshi, Y., Takahashi, F., Narusaka, Y., Yamaguchi-Shinozaki, K., Shinozaki, K.: Crosstalk between abiotic and biotic stress responses: a current view from the points of convergence in the stress signaling networks. Current Opinion in Plant Biology 9, 436–442 (2006)CrossRefPubMedGoogle Scholar
  18. 18.
    Allemeersch, J., Durinck, S., Vanderhaeghen, R., Alard, P., Maes, R., Seeuws, K., Bogaert, T., Coddens, K., Deschouwer, K., Hummelen, P.V., Vuylsteke, M., Moreau, Y., Kwekkeboom, J., Wijfjes, A.H., May, S., Beynon, J., Hilson, P., Kuiper, M.T.: Benchmarking the catma microarray. a novel tool forarabidopsis transcriptome analysis. Plant Physiol. 137, 588–601 (2005)CrossRefPubMedPubMedCentralGoogle Scholar
  19. 19.
    Wu, H., Kerr, M., Cui, X., Churchill, G.: MAANOVA: a software package for the analysis of spotted cDNA microarray experiments. The Analysis of Gene Expression Data: Methods and Software, pp. 313–341Google Scholar
  20. 20.
    Heard, N., Holmes, C., Stephens, D., Hand, D., Dimopoulos, G.: Bayesian coclustering of Anopheles gene expression time series: Study of immune defense response to multiple experimental challenges. Proceedings of the National Academy of Sciences 102(47), 16939–16944 (2005)CrossRefGoogle Scholar
  21. 21.
    Heard, N.A., Holmes, C.C., Stephens, D.A.: A Quantitative Study of Gene Regulation Involved in the Immune Response of Anopheline Mosquitoes: An Application of Bayesian Hierarchical Clustering of Curves. Journal of the American Statistical Association 101(473), 18 (2006)CrossRefGoogle Scholar
  22. 22.
    Falcon, S., Gentleman, R.: Using GOstats to test gene lists for GO term association. Bioinformatics 23(2), 257 (2007)CrossRefPubMedGoogle Scholar
  23. 23.
    Stegle, O., Denby, K., Wild, D.L., Ghahramani, Z., Borgwardt, K.: Supplementary material: A robust Bayesian two-sample test for detecting intervals of differential gene expression in microarray time series (2009), http://www.inference.phy.cam.ac.uk/os252/projects/GPTwoSample
  24. 24.
    Yuan, C., Neubauer, C.: Variational Mixture of Gaussian Process Experts. In: Advances in Neural Information Processing Systems, vol. 19. MIT Press, Cambridge (2008)Google Scholar
  25. 25.
    Rasmussen, C.E., Ghahramani, Z.: Infinite Mixtures of Gaussian Process Experts. In: Advances in Neural Information Processing Systems, vol. 19, pp. 881–888. MIT Press, Cambridge (2001)Google Scholar
  26. 26.
    Jordan, M., Ghahramani, Z., Jaakkola, T., Saul, L.: An introduction to variational methods for graphical models. Machine Learning 37, 183–233 (1999)CrossRefGoogle Scholar
  27. 27.
    Kullback, S., Leibler, R.: On Information and Sufficiency. The Annals of Mathematical Statistics 22(1), 79–86 (1951)CrossRefGoogle Scholar
  28. 28.
    Seeger, M.: Expectation Propagation for Exponential Families. Technical report, University of California at Berkeley (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Oliver Stegle
    • 1
  • Katherine Denby
    • 2
  • David L. Wild
    • 2
  • Zoubin Ghahramani
    • 1
  • Karsten M. Borgwardt
    • 1
    • 3
  1. 1.University of CambridgeUK
  2. 2.University of WarwickUK
  3. 3.Max-Planck-Institutes for Developmental Biology and Biological CyberneticsTübingenGermany

Personalised recommendations