International Journal of Genomics

International Journal of Genomics / 2003 / Article

Research article | Open Access

Volume 4 |Article ID 131563 | https://doi.org/10.1002/cfg.342

Ilya Shmulevich, Ilya Gluhovsky, Ronaldo F. Hashimoto, Edward R. Dougherty, Wei Zhang, "Steady-State Analysis of Genetic Regulatory Networks Modelled by Probabilistic Boolean Networks", International Journal of Genomics, vol. 4, Article ID 131563, 8 pages, 2003. https://doi.org/10.1002/cfg.342

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

Received26 Mar 2003
Revised22 Sep 2003
Accepted03 Oct 2003

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.

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.


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