<p>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.</p> <p>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.</p>
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Comp Funct Genomics. 2003 Dec; 4(6):601-608