A Graph-Theoretic Approach to Design of Probabilistic Boolean Networks

Abstract

Abstract In this paper, a graph-theoretic design method for a probabilistic Boolean network (PBN) is proposed. A PBN is well known as a mathematical model of complex network systems such as gene regulatory networks. In Boolean networks, interactions between binary states are modeled by Boolean functions. In PBNs, Boolean functions are switched probabilistically. In this paper, after a polynomial representation of a PBN is briefly explained, a simplified representation is proposed. Here, the steady value of the expected value of the state is focused, and is characterized by a minimum feedback vertex set of an interaction graph expressing interactions between states. Using this representation, input selection and stabilization are discussed. The proposed method is demonstrated by a biological example.