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. 2003 Dec;4(6):601–608. doi: 10.1002/cfg.342

Steady-State Analysis of Genetic Regulatory Networks Modelled by Probabilistic Boolean Networks

Ilya Shmulevich 1,✉, Ilya Gluhovsky 2, Ronaldo F Hashimoto 4,3, Edward R Dougherty 3,1, Wei Zhang 1
PMCID: PMC2447305  PMID: 18629023

Abstract

Probabilistic Boolean networks (PBNs) have recently been introduced as a promising class of models of genetic regulatory networks. The dynamic behaviour of PBNs can be analysed in the context of Markov chains. A key goal is the determination of the steady-state (long-run) behaviour of a PBN by analysing the corresponding Markov chain. This allows one to compute the long-term influence of a gene on another gene or determine the long-term joint probabilistic behaviour of a few selected genes. Because matrix-based methods quickly become prohibitive for large sizes of networks, we propose the use of Monte Carlo methods. However, the rate of convergence to the stationary distribution becomes a central issue. We discuss several approaches for determining the number of iterations necessary to achieve convergence of the Markov chain corresponding to a PBN. Using a recently introduced method based on the theory of two-state Markov chains, we illustrate the approach on a sub-network designed from human glioma gene expression data and determine the joint steadystate probabilities for several groups of genes.

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Selected References

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  1. Arsura M., Wu M., Sonenshein G. E. TGF beta 1 inhibits NF-kappa B/Rel activity inducing apoptosis of B cells: transcriptional activation of I kappa B alpha. Immunity. 1996 Jul;5(1):31–40. doi: 10.1016/s1074-7613(00)80307-6. [DOI] [PubMed] [Google Scholar]
  2. Cheng S. Y., Huang H. J., Nagane M., Ji X. D., Wang D., Shih C. C., Arap W., Huang C. M., Cavenee W. K. Suppression of glioblastoma angiogenicity and tumorigenicity by inhibition of endogenous expression of vascular endothelial growth factor. Proc Natl Acad Sci U S A. 1996 Aug 6;93(16):8502–8507. doi: 10.1073/pnas.93.16.8502. [DOI] [PMC free article] [PubMed] [Google Scholar]
  3. Fuller G. N., Rhee C. H., Hess K. R., Caskey L. S., Wang R., Bruner J. M., Yung W. K., Zhang W. Reactivation of insulin-like growth factor binding protein 2 expression in glioblastoma multiforme: a revelation by parallel gene expression profiling. Cancer Res. 1999 Sep 1;59(17):4228–4232. [PubMed] [Google Scholar]
  4. Hasty J., McMillen D., Isaacs F., Collins J. J. Computational studies of gene regulatory networks: in numero molecular biology. Nat Rev Genet. 2001 Apr;2(4):268–279. doi: 10.1038/35066056. [DOI] [PubMed] [Google Scholar]
  5. Hayashi S., Yamamoto M., Ueno Y., Ikeda K., Ohshima K., Soma G., Fukushima T. Expression of nuclear factor-kappa B, tumor necrosis factor receptor type 1, and c-Myc in human astrocytomas. Neurol Med Chir (Tokyo) 2001 Apr;41(4):187–195. doi: 10.2176/nmc.41.187. [DOI] [PubMed] [Google Scholar]
  6. Huang S. Gene expression profiling, genetic networks, and cellular states: an integrating concept for tumorigenesis and drug discovery. J Mol Med (Berl) 1999 Jun;77(6):469–480. doi: 10.1007/s001099900023. [DOI] [PubMed] [Google Scholar]
  7. Kim S., Dougherty E. R., Bittner M. L., Chen Y., Sivakumar K., Meltzer P., Trent J. M. General nonlinear framework for the analysis of gene interaction via multivariate expression arrays. J Biomed Opt. 2000 Oct;5(4):411–424. doi: 10.1117/1.1289142. [DOI] [PubMed] [Google Scholar]
  8. Kim S., Dougherty E. R., Chen Y., Sivakumar K., Meltzer P., Trent J. M., Bittner M. Multivariate measurement of gene expression relationships. Genomics. 2000 Jul 15;67(2):201–209. doi: 10.1006/geno.2000.6241. [DOI] [PubMed] [Google Scholar]
  9. Sato T. N., Qin Y., Kozak C. A., Audus K. L. Tie-1 and tie-2 define another class of putative receptor tyrosine kinase genes expressed in early embryonic vascular system. Proc Natl Acad Sci U S A. 1993 Oct 15;90(20):9355–9358. doi: 10.1073/pnas.90.20.9355. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. Shmulevich Ilya, Dougherty Edward R., Kim Seungchan, Zhang Wei. Probabilistic Boolean Networks: a rule-based uncertainty model for gene regulatory networks. Bioinformatics. 2002 Feb;18(2):261–274. doi: 10.1093/bioinformatics/18.2.261. [DOI] [PubMed] [Google Scholar]
  11. Shmulevich Ilya, Dougherty Edward R., Zhang Wei. Gene perturbation and intervention in probabilistic Boolean networks. Bioinformatics. 2002 Oct;18(10):1319–1331. doi: 10.1093/bioinformatics/18.10.1319. [DOI] [PubMed] [Google Scholar]
  12. Smith V. Anne, Jarvis Erich D., Hartemink Alexander J. Evaluating functional network inference using simulations of complex biological systems. Bioinformatics. 2002;18 (Suppl 1):S216–S224. doi: 10.1093/bioinformatics/18.suppl_1.s216. [DOI] [PubMed] [Google Scholar]
  13. Smolen P., Baxter D. A., Byrne J. H. Mathematical modeling of gene networks. Neuron. 2000 Jun;26(3):567–580. doi: 10.1016/s0896-6273(00)81194-0. [DOI] [PubMed] [Google Scholar]
  14. Wang Hua, Wang Huamin, Shen Weiping, Huang Helen, Hu Limei, Ramdas Latha, Zhou Yi-Hong, Liao Warren S-L, Fuller Gregory N., Zhang Wei. Insulin-like growth factor binding protein 2 enhances glioblastoma invasion by activating invasion-enhancing genes. Cancer Res. 2003 Aug 1;63(15):4315–4321. [PubMed] [Google Scholar]
  15. de Jong Hidde. Modeling and simulation of genetic regulatory systems: a literature review. J Comput Biol. 2002;9(1):67–103. doi: 10.1089/10665270252833208. [DOI] [PubMed] [Google Scholar]

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