Abstract
The extraction of regulatory networks and pathways from postgenomic data is important for drug discovery and development, as the extracted pathways reveal how genes or proteins regulate each other. Following up on the seminal paper of Friedman et al. (J Comput Biol 7:601–620, 2000), Bayesian networks have been widely applied as a popular tool to this end in systems biology research. Their popularity stems from the tractability of the marginal likelihood of the network structure, which is a consistent scoring scheme in the Bayesian context. This score is based on an integration over the entire parameter space, for which highly expensive computational procedures have to be applied when using more complex models based on differential equations; for example, see (Bioinformatics 24:833–839, 2008). This chapter gives an introduction to reverse engineering regulatory networks and pathways with Gaussian Bayesian networks, that is Bayesian networks with the probabilistic BGe scoring metric [see (Geiger and Heckerman 235–243, 1995)]. In the BGe model, the data are assumed to stem from a Gaussian distribution and a normal-Wishart prior is assigned to the unknown parameters. Gaussian Bayesian network methodology for analysing static observational, static interventional as well as dynamic (observational) time series data will be described in detail in this chapter. Finally, we apply these Bayesian network inference methods (1) to observational and interventional flow cytometry (protein) data from the well-known RAF pathway to evaluate the global network reconstruction accuracy of Bayesian network inference and (2) to dynamic gene expression time series data of nine circadian genes in Arabidopsis thaliana to reverse engineer the unknown regulatory network topology for this domain.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Friedman N, Linial M, Nachman I, Pe’er D (2000) Using Bayesian networks to analyze expression data. J Comput Biol 7:601–620
Vyshemirsky V, Girolami MA (2008) Bayesian ranking of biochemical system models. Bioinformatics 24:833–839
Cooper GF, Herskovits E (1992) A Bayesian method for the induction of probabilistic networks from data. Mach Learn 9:309–347
Geiger D, Heckerman D (1995) Learning Gaussian networks. In: Proceedings of the tenth conference on uncertainty in artificial intelligence, 235–243, Seattle, Washington, USA, 29–31 July 1994
Madigan D, York J (1995) Bayesian graphical models for discrete data. Int Stat Rev 63:215–232
Verma T, Pearl J (1990) Equivalence and synthesis of causal models. In: Proceedings of the 6th conference on uncertainty in artificial intelligence, 6, 220–227
Chickering DM (2002) Learning equivalence classes of Bayesian network structures. J Mach Learn Res 2:445–498
Chickering DM (1995) A transformational characterization of equivalent Bayesian network structures. In: International conference on uncertainty in artificial intelligence (UAI), 11, 87–98
Pearl J (2000) Causality: models, reasoning and intelligent systems. Cambridge University Press, London, UK
Heckerman D (1999) A tutorial on learning with Bayesian networks, Learning in Graphical Models. In: Jordan MI (ed) Adaptive computation and machine Learning. MIT Press, Cambridge, pp 301–354
Friedman N, Koller D (2003) Being Bayesian about network structure. Mach Learn 50:95–126
Grzegorczyk M, Husmeier D (2008) Improving the structure MCMC sampler for Bayesian networks by introducing a new edge reversal move. Mach Learn 71:265–305
Werhli AV, Grzegorczyk M, Husmeier D (2006) Comparative evaluation of reverse engineering gene regulatory networks with relevance networks, graphical Gaussian models and Bayesian networks. Bioinformatics 22:2523–2531
Wernisch L, Pournara I (2004) Reconstruction of gene networks using Bayesian learning and manipulation experiments. Bioinformatics 20:2934–2942
Sachs K, Perez O, Pe’er DA, Lauffenburger DA, Nolan GP (2005) Causal protein-signaling networks derived from multiparameter single-cell data. Science 308(5721):523–529
Salome P, McClung C (2004) The Arabidopsis thaliana clock. J Biol Rhythms 19:425–435
Grzegorczyk, M (2006) Comparative evaluation of different Graphical Models for the Analysis of Gene Expression Data. Doctoral Thesis, Department of Statistics, Dortmund University
Grzegorczyk M, Husmeier D, Werhli AV (2008) Reverse engineering gene regulatory networks with various machine learning methods. In: Emmert-Streib F, Dehmer M (eds) Analysis of microarray data: a network-based approach. Wiley-VCH, Weinheim
Grzegorczyk M, Husmeier D, Edwards KD, Ghazal P, Millar AJ (2008) Modelling non-stationary gene regulatory processes with a non-homogeneous Bayesian network and the allocation sampler. Bioinformatics 24:2071–2078
Grzegorczyk M, Husmeier D (2009) Modelling non-stationary gene regulatoy processes with a non-homogeneous Bayesian network and the change point process. In: Manninen et al (eds) Proceedings of the 6th international workshop on computational systems biology (WCSB 2009), TICSP series 48
Grzegorczyk M (2008) Comparison of two different stochastic models for extracting protein regulatory pathways with Bayesian networks. J Toxicol Environ Health A 71:780–787
Acknowledgements
Marco Grzegorczyk is supported by the Graduate school “Statistische Modellbildung” of the Department of Statistics at TU Dortmund University.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer Science+Business Media, LLC
About this protocol
Cite this protocol
Grzegorczyk, M. (2010). An Introduction to Gaussian Bayesian Networks. In: Yan, Q. (eds) Systems Biology in Drug Discovery and Development. Methods in Molecular Biology, vol 662. Humana Press, Totowa, NJ. https://doi.org/10.1007/978-1-60761-800-3_6
Download citation
DOI: https://doi.org/10.1007/978-1-60761-800-3_6
Published:
Publisher Name: Humana Press, Totowa, NJ
Print ISBN: 978-1-60761-799-0
Online ISBN: 978-1-60761-800-3
eBook Packages: Springer Protocols