title: Probabilistic Boolean Networks: a rule-based uncertainty model for gene regulatory networks.
abstract: BACKGROUND
  Our goal is to construct a model for genetic regulatory networks such that the model class: (i) incorporates rule-based dependencies between genes; (ii) allows the systematic study of global network dynamics; (iii) is able to cope with uncertainty, both in the data and the model selection; and (iv) permits the quantification of the relative influence and sensitivity of genes in their interactions with other genes.
  
  
  RESULTS
  We introduce Probabilistic Boolean Networks (PBN) that share the appealing rule-based properties of Boolean networks, but are robust in the face of uncertainty. We show how the dynamics of these networks can be studied in the probabilistic context of Markov chains, with standard Boolean networks being special cases. Then, we discuss the relationship between PBNs and Bayesian networks--a family of graphical models that explicitly represent probabilistic relationships between variables. We show how probabilistic dependencies between a gene and its parent genes, constituting the basic building blocks of Bayesian networks, can be obtained from PBNs. Finally, we present methods for quantifying the influence of genes on other genes, within the context of PBNs. Examples illustrating the above concepts are presented throughout the paper.
authors.affiliation: Cancer Genomics Laboratory, University of Texas M.D. Anderson Cancer Center, 1515 Holcombe Blvd, Box 85, Houston, TX 77030, USA. is@ieee.org
authors.forename: Ilya
authors.initials: I
authors.lastname: Shmulevich
authors.forename: Edward R
authors.initials: ER
authors.lastname: Dougherty
authors.forename: Seungchan
authors.initials: S
authors.lastname: Kim
authors.forename: Wei
authors.initials: W
authors.lastname: Zhang
mesh_terms: D002453:Cell Cycle / Q000235:genetics; D019295:Computational Biology; D005786:Gene Expression Regulation; D008390:Markov Chains; D008957:Models, Genetic; D015233:Models, Statistical