On the number of driver nodes for controlling a Boolean network when the targets are restricted to attractors

On Attractor Detection and Optimal Control of Deterministic Generalized Asynchronous Random Boolean Networks

Deterministic asynchronous Boolean networks play a crucial role in modeling and analysis of gene regulatory networks. In this paper, we focus on a typical type of deterministic asynchronous Boolean networks called deterministic generalized asynchronous random Boolean networks (DGARBNs). We first formulate the extended state transition graph, which captures the whole dynamics of a DGARBN and paves potential ways to analyze this DGARBN. We then propose two SMT-based methods for attractor detection and optimal control of DGARBNs. These methods are implemented in a JAVA tool called DABoolNet. Two experiments are designed to highlight the scalability of the proposed methods. We also formally state and prove several relations between DGARBNs and other models including deterministic asynchronous models, block-sequential Boolean networks, generalized asynchronous random Boolean networks, and mixed-context random Boolean networks. Several case studies are presented to show the applications of our methods.