Context-sensitive probabilistic boolean networks: Steady-state properties, reduction, and steady-state approximation

Context-sensitive probabilistic Boolean networks (PBNs) have been recently introduced as a paradigm for modeling genetic regulatory networks and have served as the main model for the application of intervention methods, including optimal control strategies, to favorably effect system dynamics. Since it is believed that the steady-state behavior of a context-sensitive PBN is indicative of the phenotype, it is important to study the alternation in the steady-state probability distribution due to any variations in the formulations of the context-sensitive PBNs. Furthermore, the huge computational complexity of the context-sensitive PBN model necessitates generation of size-reduction techniques and approximate methods for calculation of the steady-state probability distribution of context-sensitive PBNs. The goal of this paper is threefold: i) to study the effects of the various definitions of context-sensitive PBNs on the steady-state probability distributions and the downstream control policy design; ii) to propose a reduction technique that maintains the steady-state probability distribution; and iii) to provide an approximation method for calculating the steady-state probability distribution of a context-sensitive PBN.