Summary
We describe a Bayesian network approach to infer genetic regulatory interactions from microarray gene expression data. This problem was introduced in Chapter 7 and an alternative Bayesian network approach was presented in Chapter 8. Our approach is based on a linear dynamical system, which renders the inference problem tractable: the E-step of the EM algorithm draws on the well-established Kalman smoothing algorithm. While the intrinsic linearity constraint makes our approach less suitable for modeling non-linear genetic interactions than the approach of Chapter 8, it has two important advantages over the method of Chapter 8. First, our approach works with continuous expression levels, which avoids the information loss inherent in a discretization of these signals. Second, we include hidden states to allow for the effects that cannot be measured in a microarray experiment, for example: the effects of genes that have not been included on the microarray, levels of regulatory proteins, and the effects of mRNA and protein degradation.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
T. Akutsu, S. Miyano, and S. Kuhara. Identification of genetic networks from a small number of gene expression patterns under the boolean network model. Pac. Symp. Biocomput., pages 17–28, 1999.
M. Aoki. State Space Modeling of Time Series. Springer-Verlag, New York, 1987.
A. Arkin, P. Shen, and J. Ross. A test case of correlation metric construction of a reaction pathway from measurements. Science, 277:1275–1279, 1997.
P. Brockwell and R. Davis. Time Series: Theory and Methods. Springer-Verlag, New York, 1996.
R. G. Brown and P. Y. Hwang. Introduction to Random Signals and Applied Kalman Filtering. John Wiley and Sons, New York, 1997.
G. Cooper and E. Herskovits. A Bayesian method for the induction of probabilistic networks from data. Machine Learning, 9:309–347, 1992.
T. G. Dewey and D. J. Galas. Generalized dynamical models of gene expression and gene classification. Funt. Int. Genomics, 1:269–278, 2000.
P. D’Haeseleer, X. Wen, S. Fuhrman, and R. Somogyi. Linear modeling of mRNA expression levels during CNS development and injury. Pacific Symposium for Biocomputing, 3:41–52, 1999.
J. Dopazo, E. Zanders, I. Dragoni, G. Amphlett, and F. Falciani. Methods and approaches in the analysis of gene expression data. Journal of Immunological Methods, 250:93–112, 2001.
N. Friedman, M. Linial, I. Nachman, and D. Pe’er. Using Bayesian networks to analyze expression data. J. Comput. Biol., 7:601–620, 2000.
Z. Ghahramani and M. Beal. Variational inference for Bayesian mixture of factor analysers. Advances in Neural Information Processing Systems, 12:449–455, 2000.
Z. Ghahramani and M. Beal. Propagation algorithms for variational Bayesian learning. Advances in Neural Information processing Systems, 13, 2001.
E. Hannan and M. Deistler. The Statistical Theory of Linear Systems. John Wiley, New York, 1988.
B. Kholodenko, A. Kiyatkin, F. Bruggeman, E. Sontag, H. Westerhoff, and J. Hoek. Untangling the wires: a strategy to trace functional interactions in signaling and gene networks. Proc. Natl. Acad. Sci., 99:12841–12846, 2002.
S. Liang, S. Fuhrman, and R. Somogyi. Identification of genetic networks from a small number of gene expression patterns under the boolean network model. Pac. Symp. Biocomput., pages 18–29, 1998.
L. Ljung. System Identifiability, 2nd ed. Prentice Hall, New Jersey, 1999.
R. J. Meinhold and N. D. Singpurwalla. Understanding the Kalman Filter. The American Statistician, 37(2):123–127, 1983.
K. Murphy and S. Mian. Modelling gene expression data using dynamic Bayesian networks. Proc. Intelligent Systems for Molecular Biology, August 1999.
I. Ong, J. Glasner, and D. Page. Modelling regulatory pathways in E. coli from time series expression profiles. Bioinformatics, 18(1):S241–S248, 2002.
D. Pe’er, A. Regev, G. Elidan, and N. Friedman. Inferring subnetworks from perturbed expression profiles. Proc. 9th International Conference on Intelligent Systems for Molecular Biology (ISMB), 2001.
C. Rangel, J. Angus, Z. Ghahramani, M. Lioumi, E.A. Sotheran, A. Gaiba, D. L. Wild, and F. Falciani. Modeling T-cell activation using gene expression profiling and state space models. Bioinformatics, 20(9): 1316–1372, 2004.
C. Rangel, D. L. Wild, F. Falciani, Z. Ghahramani, and A. Gaiba. Modelling biological responses using gene expression profiling and linear dynamical systems. In Proceedings of the 2nd International Conference on Systems Biology, pages 248–256. Omipress, Madison, WI, 2001.
S. Roweis and Z. Ghahramani. A unifying review of linear Gaussian models. Neural Computation, 11:305–345, 1999.
V. Smith, E. Jarvis, and A. Hartemink. Evaluating functional network influence using simulations of complex biological systems. Bioinformatics, 18(1):S216–S224, 2002.
P. Spellman, G. Sherlock, M. Zhang, V. Iyer, K. Anders, M. Eisen, P. Brown, D. Botstein, and B. Futcher. Comprehensive identification of cell cycle-regulated genes of the yeast Saccharomyces cerevisiae by microarray hybridization. Mol. Biol. Cell., 9:3273–3297, 1998.
R. Thomas. Boolean formalization of genetic control circuits. J. Theor. Biol., 42(3):563–586, 1973.
E. van Someren, L.F. Wessels, E. Backer, and M. Reinders. Genetic network modeling. Pharmacogenomics, 3:507–525, 2002.
E. van Someren, L.F. Wessels, and M. Reinders. Linear modeling of genetic networks from experimental data. Proc. 9th International Conference on Intelligent Systems for Molecular Biology (ISMB), 8:355–366, 2000.
D. Weaver, C. Workman, and G. Stormo. Modeling regulatory networks with weight matrices. Pacific Symposium for Biocomputing, 4:112–123, 1999.
L. Wessels, E. van Someren, and M. Reinders. A comparison of genetic network models. Pacific Symposium for Biocomputing, 6:508–519, 2001.
M. Yeung, J. Tegner, and J. Collins. Reverse engineering gene networks using singular value decomposition and robust regression. Proc. Natl. Acad. Sci., 99:6163–6168, 2002.
C. Yoo, V. Thorsson, and G. Cooper. Discovery of causal relationships in a gene-regulation pathway from a mixture of experimental and observational DNA microarray data. Pac. Symp. Biocomput., pages 422–433, 2002.
D. Zak, F. Doyle, G. Gonye, and J. Schwaber. Simulation studies for the identification of genetic networks from cDNA array and regulatory activity data. In Proceedings of the 2nd International Conference on Systems Biology, pages 231–238. Omipress, Madison, WI, 2001.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag London Limited
About this chapter
Cite this chapter
Rangel, C., Angus, J., Ghahramani, Z., Wild, D.L. (2005). Modeling Genetic Regulatory Networks using Gene Expression Profiling and State-Space Models. In: Husmeier, D., Dybowski, R., Roberts, S. (eds) Probabilistic Modeling in Bioinformatics and Medical Informatics. Advanced Information and Knowledge Processing. Springer, London. https://doi.org/10.1007/1-84628-119-9_9
Download citation
DOI: https://doi.org/10.1007/1-84628-119-9_9
Publisher Name: Springer, London
Print ISBN: 978-1-85233-778-0
Online ISBN: 978-1-84628-119-8
eBook Packages: Computer ScienceComputer Science (R0)