Automaton models of computational genetic regulatory networks with combinatorial gene-protein interactions

In this paper, we present an approach for modeling computational genetic regulatory networks with multi-threshold protein concentration and combinatorial gene-protein interactions. We first present a gene automata model that describes the activities of a single gene, and discuss the construction of a network automaton model that describes the complete behavior of a gene network. To model the gene-protein interaction in the given gene network, we define the basic interaction, in the form of an automaton, that characterizes the interaction between a protein and a gene. We then define the new concept of an inducible event and propose the AND- and OR-composition operations (based on this concept of an inducible event) for combining the basic interactions into a combinatorial interaction, which is also represented by an automaton. By taking the synchronous product over the combinatorial interaction automata, we obtain a composite interaction automaton describing the overall gene-protein interaction patterns in a given gene network. Subsequent imposition of this composite logical relationship on the network automaton model yields a complete description of the dynamical behavior of the gene network. We illustrate the effectiveness of our proposed approach in the modeling of (i) morphogenesis in Arabidopsis and (ii) regulation in phage λ.