Skip to main content

Uncovering Gene Regulatory Networks from Time-Series Microarray Data with Variational Bayesian Structural Expectation Maximization


We investigate in this paper reverse engineering of gene regulatory networks from time-series microarray data. We apply dynamic Bayesian networks (DBNs) for modeling cell cycle regulations. In developing a network inference algorithm, we focus on soft solutions that can provide a posteriori probability (APP) of network topology. In particular, we propose a variational Bayesian structural expectation maximization algorithm that can learn the posterior distribution of the network model parameters and topology jointly. We also show how the obtained APPs of the network topology can be used in a Bayesian data integration strategy to integrate two different microarray data sets. The proposed VBSEM algorithm has been tested on yeast cell cycle data sets. To evaluate the confidence of the inferred networks, we apply a moving block bootstrap method. The inferred network is validated by comparing it to the KEGG pathway map.



  1. Kitano H: Looking beyond that details: a rise in system-oriented approaches in genetics and molecular biology. Current Genetics 2002, 41(1):1-10. 10.1007/s00294-002-0285-z

    Article  MathSciNet  Google Scholar 

  2. D'haeseleer P, Liang S, Somogyi R: Genetic network inference: from co-expression clustering to reverse engineering. Bioinformatics 2000, 16(8):707-726. 10.1093/bioinformatics/16.8.707

    Article  Google Scholar 

  3. Brazhnik P, de la Fuente A, Mendes P: Gene networks: how to put the function in genomics. Trends in Biotechnology 2002, 20(11):467-472. 10.1016/S0167-7799(02)02053-X

    Article  Google Scholar 

  4. Friedman N: Inferring cellular networks using probabilistic graphical models. Science 2004, 303(5659):799-805. 10.1126/science.1094068

    Article  Google Scholar 

  5. Shmulevich I, Dougherty ER, Kim S, Zhang W: Probabilistic Boolean networks: a rule-based uncertainty model for gene regulatory networks. Bioinformatics 2002, 18(2):261-274. 10.1093/bioinformatics/18.2.261

    Article  Google Scholar 

  6. Zhou X, Wang X, Dougherty ER: Construction of genomic networks using mutual-information clustering and reversible-jump Markov-chain-Monte-Carlo predictor design. Signal Processing 2003, 83(4):745-761. 10.1016/S0165-1684(02)00469-3

    Article  MATH  Google Scholar 

  7. Hartemink AJ, Gifford DK, Jaakkola TS, Young RA: Using graphical models and genomic expression data to statistically validate models of genetic regulatory networks. Proceedings of the 6th Pacific Symposium on Biocomputing (PSB '01), The Big Island of Hawaii, Hawaii, USA, January 2001 422-433.

    Google Scholar 

  8. Moler EJ, Radisky DC, Mian IS: Integrating naive Bayes models and external knowledge to examine copper and iron homeostasis in S. cerevisiae. Physiol Genomics 2000, 4(2):127-135.

    Google Scholar 

  9. Segal E: Rich probabilistic models for genomic data, Ph.D. thesis. Stanford University, Stanford, Calif, USA; 2004.

    Google Scholar 

  10. de Jong H: Modeling and simulation of genetic regulatory systems: a literature review. Journal of Computational Biology 2002, 9(1):67-103. 10.1089/10665270252833208

    Article  Google Scholar 

  11. Bar-Joseph Z: Analyzing time series gene expression data. Bioinformatics 2004, 20(16):2493-2503. 10.1093/bioinformatics/bth283

    Article  Google Scholar 

  12. Simonis N, Wodak SJ, Cohen GN, van Helden J: Combining pattern discovery and discriminant analysis to predict gene co-regulation. Bioinformatics 2004, 20(15):2370-2379. 10.1093/bioinformatics/bth252

    Article  Google Scholar 

  13. Murphy K, Mian S: Modelling gene expression data using dynamic Bayesian networks. Computer Science Division, University of California, Berkeley, Calif, USA; 1999.

    Google Scholar 

  14. Friedman N, Linial M, Nachman I, Pe'er D: Using Bayesian networks to analyze expression data. Journal of Computational Biology 2000, 7(3-4):601-620. 10.1089/106652700750050961

    Article  Google Scholar 

  15. van Berlo RJP, van Someren EP, Reinders MJT: Studying the conditions for learning dynamic Bayesian networks to discover genetic regulatory networks. Simulation 2003, 79(12):689-702.

    Google Scholar 

  16. Beal MJ, Falciani F, Ghahramani Z, Rangel C, Wild DL: A Bayesian approach to reconstructing genetic regulatory networks with hidden factors. Bioinformatics 2005, 21(3):349-356. 10.1093/bioinformatics/bti014

    Article  Google Scholar 

  17. Perrin B-E, Ralaivola L, Mazurie A, Bottani S, Mallet J, d'Alché-Buc F: Gene networks inference using dynamic Bayesian networks. Bioinformatics 2003, 19(2):ii138-ii148. 10.1093/bioinformatics/btg1071

    Google Scholar 

  18. Kim SY, Imoto S, Miyano S: Inferring gene networks from time series microarray data using dynamic Bayesian networks. Briefings in Bioinformatics 2003, 4(3):228-235. 10.1093/bib/4.3.228

    Article  Google Scholar 

  19. Ferrazzi F, Amici R, Sebastiani P, Kohane IS, Ramoni MF, Bellazzi R: Can we use linear Gaussian networks to model dynamic interactions among genes? Results from a simulation study. Proceedings of IEEE International Workshop on Genomic Signal Processing and Statistics (GENSIPS '06), College Station, Tex, USA, May 2006 13-14.

    Google Scholar 

  20. Wang X, Poor HV: Wireless Communication Systems: Advanced Techniques for Signal Reception. Prentice Hall PTR, Englewood Cliffs, NJ, USA; 2004.

    Google Scholar 

  21. Wang J, Huang Y, Sanchez M, Wang Y, Zhang J: Reverse engineering yeast gene regulatory networks using graphical models. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '06), Toulouse, France, May 2006 2: 1088-1091.

    Google Scholar 

  22. Husmeier D: Sensitivity and specificity of inferring genetic regulatory interactions from microarray experiments with dynamic Bayesian networks. Bioinformatics 2003, 19(17):2271-2282. 10.1093/bioinformatics/btg313

    Article  Google Scholar 

  23. Murphy KP: Dynamic Bayesian networks: representation, inference and learning, Ph.D. thesis. University of California, Berkeley, Calif, USA; 2004.

    Google Scholar 

  24. Kay SM: Fundamentals of Statistical Signal Processing: Estimation Theory. Prentice-Hall, Englewood Cliffs, NJ, USA; 1997.

    Google Scholar 

  25. Beal MJ: Variational algorithms for approximate Bayesian inference, Ph.D. thesis. The Gatsby Computational Neuroscience Unit, University College London, London, UK; 2003.

    Google Scholar 

  26. Brooks SP: Markov chain Monte Carlo method and its application. Journal of the Royal Statistical Society: Series D, The Statistician 1998, 47(1):69-100. 10.1111/1467-9884.00117

    Google Scholar 

  27. Spellman PT, Sherlock G, Zhang MQ, et al.: Comprehensive identification of cell cycle-regulated genes of the yeast Saccharomyces cerevisiae by microarray hybridization. Molecular Biology of the Cell 1998, 9(12):3273-3297.

    Article  Google Scholar 

  28. Cho RJ, Campbell MJ, Winzeler EA, et al.: A genome-wide transcriptional analysis of the mitotic cell cycle. Molecular Cell 1998, 2(1):65-73. 10.1016/S1097-2765(00)80114-8

    Article  Google Scholar 

  29. Efron B, Tibshirani R: An Introduction to Bootstrap, Monographs on Statistics and Applied Probability, no. 57. Chapman & Hall, New York, NY, USA; 1993.

    Book  Google Scholar 

  30. Lahiri SN: Resampling Methods for Dependent Data. Springer, New York, NY, USA; 2003.

    Book  MATH  Google Scholar 

  31. Kegg: Kyoto encyclopedia of genes and genomes

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Isabel Tienda Luna.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Cite this article

Luna, I.T., Huang, Y., Yin, Y. et al. Uncovering Gene Regulatory Networks from Time-Series Microarray Data with Variational Bayesian Structural Expectation Maximization. J Bioinform Sys Biology 2007, 71312 (2007).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI:


  • Gene Regulatory Network
  • Expectation Maximization Algorithm
  • Dynamic Bayesian Network
  • Yeast Cell Cycle
  • Block Bootstrap