, Volume 183, Issue 3, pp 361–377 | Cite as

Dynamic Bayesian networks in molecular plant science: inferring gene regulatory networks from multiple gene expression time series

  • Frank Dondelinger
  • Dirk HusmeierEmail author
  • Sophie Lèbre


To understand the processes of growth and biomass production in plants, we ultimately need to elucidate the structure of the underlying regulatory networks at the molecular level. The advent of high-throughput postgenomic technologies has spurred substantial interest in reverse engineering these networks from data, and several techniques from machine learning and multivariate statistics have recently been proposed. The present article discusses the problem of inferring gene regulatory networks from gene expression time series, and we focus our exposition on the methodology of Bayesian networks. We describe dynamic Bayesian networks and explain their advantages over other statistical methods. We introduce a novel information sharing scheme, which allows us to infer gene regulatory networks from multiple sources of gene expression data more accurately. We illustrate and test this method on a set of synthetic data, using three different measures to quantify the network reconstruction accuracy. The main application of our method is related to the problem of circadian regulation in plants, where we aim to reconstruct the regulatory networks of nine circadian genes in Arabidopsis thaliana from four gene expression time series obtained under different experimental conditions.


Gene regulatory networks Reverse engineering Dynamic Bayesian networks Data integration Information sharing Arabidopsis thaliana Circadian regulation 



This study was supported by the Scottish Government Rural and Environment Research and Analysis Directorate (RERAD). Frank Dondelinger’s PhD research is partly funded by the Engineering and Physical Sciences Research Council (EPSRC).


  1. Aoki K, Ogata Y, Shibata D (2007) Approaches for extracting practical information from gene co-expression networks in plant biology. Plant Cell Physiol 48(3):381PubMedCrossRefGoogle Scholar
  2. Butte A, Kohane I (2000) Mutual information relevance networks: functional genomic clustering using pairwise entropy measurements. In: Pacific Symposium on Biocomputing. Pacific Symposium on Biocomputing, p 418Google Scholar
  3. Davis J, Goadrich M (2006) The relationship between Precision-Recall and ROC curves. In: Proceedings of the 23rd international conference on Machine learning, ACM, Pittsburgh, Pennsylvania, pp 233–240Google Scholar
  4. Edwards K, Anderson P, Hall A, Salathia N, Locke J, Lynn J, Straume M, Smith J, Millar A (2006) FLOWERING LOCUS C mediates natural variation in the high-temperature response of the Arabidopsis circadian clock. Plant Cell 18(3):639PubMedCrossRefGoogle Scholar
  5. Ferrazzi F, Rinaldi S, Parikh A, Shaulsky G, Zupan B, Bellazzi R (2008) Population models to learn Bayesian networks from multiple gene expression experimentsGoogle Scholar
  6. Friedman N, Murphy K, Russell S (1998) Learning the structure of dynamic probabilistic networks. In: Proceedings of fourteenth conference on uncertainty in artificial intelligence (UAI98), Citeseer, pp 139–147Google Scholar
  7. Friedman N, Linial M, Nachman I, Pe’er D (2000) Using Bayesian networks to analyze expression data. J Comput Biol 7(3-4):601–620PubMedCrossRefGoogle Scholar
  8. Grzegorczyk M, Husmeier D, Edwards K, Ghazal P, Millar A (2008) Modelling non-stationary gene regulatory processes with a non-homogeneous Bayesian network and the allocation sampler. Bioinformatics 24(18):2071PubMedCrossRefGoogle Scholar
  9. Hamada K, Hongo K, Suwabe K, Shimizu A, Nagayama T, Abe R, Kikuchi S, Yamamoto N, Fujii T, Yokoyama K et al (2011) OryzaExpress: an integrated database of gene expression networks and omics annotations in rice. Plant Cell Physiol 52(2):220PubMedCrossRefGoogle Scholar
  10. Husmeier D, Dondelinger F, Lebre S (2010) Inter-time segment information sharing for non-homogeneous dynamic Bayesian networks. Adv Neur Inf Process Syst 23:901–909Google Scholar
  11. Jiao Y, Tausta S, Gandotra N, Sun N, Liu T, Clay N, Ceserani T, Chen M, Ma L, Holford M, et al (2009) A transcriptome atlas of rice cell types uncovers cellular, functional and developmental hierarchies. Nat Genet 41(2):258–263PubMedCrossRefGoogle Scholar
  12. Lèbre S, Becq J, Devaux F, Lelandais G, Stumpf M (2010) Statistical inference of the time-varying structure of gene-regulation networks (submitted)Google Scholar
  13. Locke JCW, Southern MM, Kozma-Bognr L, Hibberd V, Brown PE, Turner MS, Millar AJ (2005) Extension of a genetic network model by iterative experimentation and mathematical analysis. Mol Syst Biol 1(1):E1–E9. doi: 10.1038/msb4100018 CrossRefGoogle Scholar
  14. Ma S, Gong Q, Bohnert H (2007) An Arabidopsis gene network based on the graphical Gaussian model. Genome research 17(11):1614PubMedCrossRefGoogle Scholar
  15. MacKay DJC (1998) Introduction to Monte Carlo methods. In: Jordan MI (ed) Learning in graphical models. Kluwer Academic Publishers, The Netherlands, pp 301–354Google Scholar
  16. Madigan D, York J (1995) Bayesian graphical models for discrete data. Int Stat Rev 63:215–232CrossRefGoogle Scholar
  17. McClung CR (2006) Plant circadian rhythms. Plant Cell 18(4):792–803PubMedCrossRefGoogle Scholar
  18. Mochida K, Uehara-Yamaguchi Y, Yoshida T, Sakurai T, Shinozaki K (2011) Global landscape of a co-expressed gene network in barley and its application to gene discovery in Triticeae crops. Plant Cell Physiol 52(5):785–803PubMedCrossRefGoogle Scholar
  19. Mockler T, Michael T, Priest H, Shen R, Sullivan C, Givan S, McEntee C, Kay S, Chory J (2007) The DIURNAL project: DIURNAL and circadian expression profiling, model-based pattern matching and promoter analysis. Cold Spring Harb Symp Quant Biol 72:353–363PubMedCrossRefGoogle Scholar
  20. Moriyama M, Hoshida Y, Otsuka M, Nishimura S, Kato N, Goto T, Taniguchi H, Shiratori Y, Seki N, Omata M (2003) Relevance network between chemosensitivity and transcriptome in human hepatoma cells1. Mol Cancer Ther 2(2):199PubMedGoogle Scholar
  21. Morohashi K, Grotewold E (2009) A systems approach reveals regulatory circuitry for Arabidopsis trichome initiation by the GL3 and GL1 selectors. PLoS genet 5(2):e1000396PubMedCrossRefGoogle Scholar
  22. Murphy K, Mian S (1999) Modelling gene expression data using dynamic Bayesian networks. Technical report, University of California, BerkeleyGoogle Scholar
  23. Obayashi T, Kinoshita K, Nakai K, Shibaoka M, Hayashi S, Saeki M, Shibata D, Saito K, Ohta H (2006) ATTED-II: a database of co-expressed genes and cis elements for identifying co-regulated gene groups in Arabidopsis. Nucleic Acids Res 35(suppl 1):D863PubMedGoogle Scholar
  24. Okazaki Y, Shimojima M, Sawada Y, Toyooka K, Narisawa T, Mochida K, Tanaka H, Matsuda F, Hirai A, Hirai M et al. (2009) A chloroplastic UDP-glucose pyrophosphorylase from Arabidopsis is the committed enzyme for the first step of sulfolipid biosynthesis. Plant Cell 21(3):892PubMedCrossRefGoogle Scholar
  25. Robinson J, Hartemink A (2010) Learning non-stationary dynamic Bayesian networks. J Mach Learn Res 11:3647–3680Google Scholar
  26. Rogers S, Girolami M (2005) A Bayesian regression approach to the inference of regulatory networks from gene expression data. Bioinformatics 21(14):3131–3137PubMedCrossRefGoogle Scholar
  27. Schäfer J, Strimmer K (2005) An empirical Bayes approach to inferring large-scale gene association networks. Bioinformatics 21(6):754–764PubMedCrossRefGoogle Scholar
  28. van Someren EP, Vaes BLT, Steegenga WT, Sijbers AM, Dechering KJ, Reinders MJT (2006) Least absolute regression network analysis of the murine osterblast differentiation network. Bioinformatics 22(4):477–484PubMedCrossRefGoogle Scholar
  29. Sreenivasulu N, Usadel B, Winter A, Radchuk V, Scholz U, Stein N, Weschke W, Strickert M, Close T, Stitt M et al. (2008) Barley grain maturation and germination: metabolic pathway and regulatory network commonalities and differences highlighted by new MapMan/PageMan profiling tools. Plant Physiol 146(4):1738PubMedCrossRefGoogle Scholar
  30. Werhli AV, Husmeier D (2007) Reconstructing gene regulatory networks with Bayesian networks by combining expression data with multiple sources of prior knowledge. Stat App Genet Mol Biol 6(1). doi: 10.2202/1544-6115.1282
  31. Werhli AV, Husmeier D (2008) Gene regulatory network reconstruction by Bayesian integration of prior knowledge and/or different experimental conditions. J Bioinfor Comput Biol 6(3):543–572CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Frank Dondelinger
    • 1
  • Dirk Husmeier
    • 1
    Email author
  • Sophie Lèbre
    • 2
  1. 1.Biomathematics and Statistics ScotlandEdinburghUK
  2. 2.Université de Strasbourg, LSIIT - UMR 7005IllkirchFrance

Personalised recommendations