Abstract
Reconstruction of genetic regulatory networks from gene expression profiles and protein interaction data is a critical problem in systems biology. Boolean networks and their variants have been used for network reconstruction problems due to Boolean networks’ simplicity. In the graph of a Boolean network, nodes represent the statuses of genes while the edges represent relationships between genes. In a Boolean network model, the status of a gene is quantized as ‘on’ or ‘off’, representing the gene as being ‘active’ or ‘inactive’ respectively. In this chapter, we will introduce the basic definitions of Boolean networks and the analysis of their properties. We will also discuss a related model called probabilistic Boolean network, which extends Boolean networks in order to have the advantage of modeling with data uncertainty and model selection. Furthermore, we will also introduce directed acyclic Boolean network and the statistical method of SPAN to reconstruct Boolean networks from noisy array data by assigning an s-p-score for every pair of genes. At last, we will suggest possible directions for future developments on Boolean networks.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Akutsu, T., Kuhara, S., Maruyama, O., & Miyano, S. (1998). Identification of gene regulatory networks by strategic gene disruptions and gene overexpression. In Proceeding 9th ACM-SIAM symposium discrete algorithms (pp. 695–702).
Akutsu, T., & Miyano, S. (1999). Identification of genetic networks from a small number of gene expression patterns under the Boolean network model. Pacific Symposium on Biocomputing, 4, 17–28.
Akutsu, T., Miyano, S., & Kuhara, S. (2000). Inferring qualitative relations genetic networks and metabolic pathways. Bioinformatics, 16, 727–734.
Bornholdt, S. (2005). Less is more in modeling large genetic networks. Science, 310(5747), 449–451.
Dougherty, E. R., Kim, S., & Chen, Y. (2000). Coefficient of determination in nonlinear signal processing. Signal Processing, 80, 2219–2235.
Friedman, N., Linial, M., Nachman, I., & Pe’er, D. (2000). Using Bayesian networks to analyze expression data. Journal of Computational Biology, 7, 601–620.
Harvey, I., & Bossomaier, T. (1997). Time out of joint: Attractors in asynchronous random Boolean network. In Proceedings of the fourth European conference on artificial life (pp. 67–75).
Heckerman, D., Geiger, D., & Chickering, D. M. (1995). Learning Bayesian networks: The combination of knowledge and statistical data. Machine Learning, 20, 197–243.
Huang, S. (1999). Gene expression profiling, genetic networks and cellular states: An integrating concept for tumorigenesis and drug discovery. Journal of Molecular Medicine, 77, 469–480.
Imoto, S., Goto, T., & Miyano, S. (2002). Estimation of genetic networks and functional structures between genes by using Bayesian network and nonparametric regression. Pacific Symposium on Biocomputing, 7, 175–186.
Imoto, S., Higuchi, T., Goto, T., Tashiro, K., Kuhara, S., & Miyano, S. (2004). Combining microarrays and biological knowledge for estimating gene networks via Bayesian networks. Journal of Bioinformatics and Computational Biology, 2, 77–98.
Jensen, F. V. (1996). An introduction to Bayesian networks. London: University College London Press.
Jensen, F. V. (2001). Bayesian networks and decision graphs. New York: Springer.
Kauffman, S. A. (1969). Metabolic stability and epigenesis in randomly constructed genetic nets. Journal of Theoretical Biology, 22(3), 437–467.
Kauffman, S. A. (1993). The origins of order: Self-organization and selection in evolution. New York: Oxford University Press.
Kauffman, S. A., Peterson, C., Samuelsson, B., & Troein, C. (2003). Random Boolean network models and the yeast transcriptional network. Biophysics, 100(25), 14796–14799.
Kim, H., Lee, J. K., & Park, T. (2007). Boolean networks using the chi-square test for inferring large-scale gene regulatory networks. BMC Bioinformatics, 8, 37.
Kim, S., Dougherty, E. R., Chen, Y., Sivakumar, K., Meltzer, P., Trent, J. M., & Bittner, M. (2000). Multivariate measurement of gene expression relationships. Genomics, 67, 201–209.
Laubenbacher, R., & Stigler, B. (2004). A computational algebra approach to the reverse engineering of gene regulatory networks. Journal of Theoretical Biology, 299, 523–537.
Li, L. M., & Lu, H. H.-S. (2005). Explore biological pathways from noisy array data by directed acyclic Boolean networks. Journal of Computational Biology, 12(2), 170–185.
Liang, S., Fuhrman, S., & Somogyi, R. (1998). REVEAL, a general reverse engineering algorithm for inference of genetic network architectures. Pacific Symposium on Biocomputing, 3, 18–29.
Moler, E. J., Radisky, D. C., & Mian, I. S. (2000). Integrating naive Bayes models and external knowledge to examine copper and iron homeostasis in S. cerevisiae. Physiol Genomics, 4(2), 127–135.
Pearl, J. (1988). Probabilistic reasoning in intelligent systems: Networks of plausible inference. San Mateo: Morgan Kaufmann.
Schwarzer, C., & Teuscher C. (2003). The software of teuscher’s Lab: Matlab random Boolean network toolbox. Swiss Federal Institute of Technology Lausanne (EPFL). URL http://www.teuscher.ch/rbntoolbox/
Shannon, C. E., & Weaver, W. (1963). The Mathematical Theory of Communication. University of Illinois Press. ISBN: 0252725484.
Shmulevich, I., Dougherty, E. R., Kim, S., & Zhang, W. (2002). Probabilistic Boolean networks: A rule-based uncertainty model for gene regulatory networks. Bioinformatics, 18(2), 261–274.
Shmulevich, I., Dougherty, E. R., & Zhang, W. (2002). From Boolean to probabilistic Boolean networks as models of genetic regulatory networks. Proceeding of the IEEE, 90(11), 1778–1792.
Shmulevich, I., Dougherty, E. R., & Zhang, W. (2002). Gene perturbation and intervention in probabilistic Boolean networks. Bioinformatics, 18(10), 1319–1331.
Shmulevich, I., Gluhovsky, I., Hashimoto, R. F., Dougherty, E. R., & Zhang, W. (2003). Steady-state analysis of genetic regulatory networks modelled by probabilistic Boolean networks. Comparative and Functional Genomics, 4, 601–608.
Somogyi, R., & Sniegoski, C. A. (1996). Modeling the complexity of genetic networks: Understanding multigene and pleiotropic regulation. Complexity, 1, 45–63.
Sontag, E., Veliz-Cuba, A., Laubenbacher, R., & Jarrah, A. S. (2008). The effect of negative feedback loops on the dynamics of Boolean networks. Biophysical Journal, 95, 518–526.
Spirtes, P., Glymour, C., & Scheines, R. (2000). Causation, prediction and search. Cambridge, MA: MIT.
Szallasi, Z., & Liang, S. (1998). Modeling the normal and neoplastic cell cycle with ‘realistic Boolean genetic networks’: Their application for understanding carcinogenesis and assessing therapeutic strategies. Pacific Symposium on Biocomputing, 3, 66–76.
Thomas, R., Thieffry, D., & Kaufman, M. (1995). Dynamical behaviour of biological regulatory networksXI. Biological role of feedback loops and practical use of the concept of the loop-characteristic state. Bulletin of Mathematical Biology, 57(2), 247–276.
Wegner, K., Knabe, J., Robinson, M., Egri-Nagy, A., Schilstra, M., & Nehaniv, C. (2007). The NetBuilder’project: development of a tool for constructing, simulating, evolving, and analysing complex regulatory networks. BMC Systems Biology, 1(Suppl 1):P72.
Wolfram, S. (1983). Statistical mechanics of cellular automata. Reviews of Modern Physics, 55(3), 601–644.
Wolfram, S. (1984). Universality and complexity in cellular automata. Physica 10D, 10(1), 1–35.
Wuensche, A. (1998). Genomic regulation modeled as a network with basins of attraction. Pacific Symposium on Biocomputing, 3, 89–102.
Acknowledgements
The authors would like to express their gratitude to the English editing of Yang Wang and Arthur Tu. This work was partially supported by the National Science Council (NSC), National Center for Theoretical Sciences (NCTS) and Center of Mathematical Modeling and Scientific Computing (CMMSC) at the National Chiao Tung University in Taiwan.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Chueh, TH., Lu, H.HS. (2011). Boolean Networks. In: Lu, HS., Schölkopf, B., Zhao, H. (eds) Handbook of Statistical Bioinformatics. Springer Handbooks of Computational Statistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16345-6_20
Download citation
DOI: https://doi.org/10.1007/978-3-642-16345-6_20
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-16344-9
Online ISBN: 978-3-642-16345-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)