%0 Journal Article %1 Shmulevich:2003:Comp-Funct-Genomics:18629023 %A Shmulevich, I %A Gluhovsky, I %A Hashimoto, R F %A Dougherty, E R %A Zhang, W %D 2003 %J Comp Funct Genomics %K boolean-networks classic probabilistic %N 6 %P 601-608 %R 10.1002/cfg.342 %T Steady-state analysis of genetic regulatory networks modelled by probabilistic boolean networks %U https://www.ncbi.nlm.nih.gov/pubmed/18629023 %V 4 %X 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.

@article{Shmulevich:2003:Comp-Funct-Genomics:18629023, 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.}, added-at = {2019-08-22T13:27:49.000+0200}, author = {Shmulevich, I and Gluhovsky, I and Hashimoto, R F and Dougherty, E R and Zhang, W}, biburl = {https://www.bibsonomy.org/bibtex/2b3f69156edb5e8694269ae121a4ca320/karthikraman}, description = {Steady-state analysis of genetic regulatory networks modelled by probabilistic boolean networks. - PubMed - NCBI}, doi = {10.1002/cfg.342}, interhash = {216e5db286fb03b68724f8ade9a31dd4}, intrahash = {b3f69156edb5e8694269ae121a4ca320}, journal = {Comp Funct Genomics}, keywords = {boolean-networks classic probabilistic}, number = 6, pages = {601-608}, pmid = {18629023}, timestamp = {2019-08-22T13:27:49.000+0200}, title = {Steady-state analysis of genetic regulatory networks modelled by probabilistic boolean networks}, url = {https://www.ncbi.nlm.nih.gov/pubmed/18629023}, volume = 4, year = 2003 }