Probabilistic Boolean networks: a rule-based uncertainty model for gene regulatory networks

TLDR

The study aims to construct a rule‑based, uncertainty‑tolerant model of gene regulatory networks that enables global dynamic analysis and quantifies gene influence, and to relate these models to Bayesian networks. The authors model network dynamics as Markov chains, relate PBNs to Bayesian networks, and provide methods to quantify gene influence within this framework. Probabilistic Boolean Networks combine Boolean rule‑based structure with robustness to uncertainty, allow extraction of probabilistic gene dependencies similar to Bayesian networks, and are illustrated with examples. Contact email is [e-mail].

Abstract

Abstract Motivation: 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. Contact: [e-mail]