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.
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.