title: Steady-state analysis of genetic regulatory networks modelled by probabilistic boolean networks.
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.
authors.affiliation: Cancer Genomics Laboratory, University of Texas, M. D. Anderson Cancer Center, 1515 Holcombe Blvd., Houston, TX 77030, USA.
authors.forename: Ilya
authors.initials: I
authors.lastname: Shmulevich
authors.forename: Ilya
authors.initials: I
authors.lastname: Gluhovsky
authors.forename: Ronaldo F
authors.initials: RF
authors.lastname: Hashimoto
authors.forename: Edward R
authors.initials: ER
authors.lastname: Dougherty
authors.forename: Wei
authors.initials: W
authors.lastname: Zhang