Steady-state analysis of genetic regulatory networks modelled by probabilistic boolean networks. Academic Article uri icon


  • 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.

published proceedings

  • Comp Funct Genomics

author list (cited authors)

  • Shmulevich, I., Gluhovsky, I., Hashimoto, R. F., Dougherty, E. R., & Zhang, W.

citation count

  • 105

complete list of authors

  • Shmulevich, Ilya||Gluhovsky, Ilya||Hashimoto, Ronaldo F||Dougherty, Edward R||Zhang, Wei

publication date

  • December 2003