Probabilistic Boolean networks (PBNs) have recently been introduced as a promising class of models of genetic regulatory networks. The dynamic behaviour of PBNs canbe analysed in the context of Markov chains. A key goal is the determination of thesteady-state (long-run) behaviour of a PBN by analysing the corresponding Markovchain. This allows one to compute the long-term influence of a gene on anothergene 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 tothe stationary distribution becomes a central issue. We discuss several approachesfor determining the number of iterations necessary to achieve convergence of theMarkov chain corresponding to a PBN. Using a recently introduced method based onthe theory of two-state Markov chains, we illustrate the approach on a sub-networkdesigned from human glioma gene expression data and determine the joint steadystateprobabilities for several groups of genes.
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