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Comparative and Functional Genomics
Volume 4, Issue 6, Pages 601-608
Research article

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

1Cancer Genomics Laboratory, University of Texas M. D. Anderson Cancer Center, 1515 Holcombe Blvd., Unit 85, Houston 77030, TX, USA
2Sun Microsystems Laboratories, Palo Alto, CA, USA
3Department of Electrical Engineering, Texas A&M University, College Station 77843, TX, USA
4Departamento de Ciencia de Computacao, Universidade de Sao Paulo, Sao Paulo, Brazil

Received 26 March 2003; Revised 22 September 2003; Accepted 3 October 2003

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.