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

Author(s): Ilya Shmulevich | Ilya Gluhovsky | Ronaldo F. Hashimoto | Edward R. Dougherty | Wei Zhang

Journal: Comparative and functional genomics.
ISSN 1531-6912

Volume: 4;
Issue: 6;
Start page: 601;
Date: 2006;
Original page

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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