A Feedback Vertex Set-Based Approach to Simplifying Probabilistic Boolean Networks

Abstract

A PBN is well known as a mathematical model of complex network systems such as gene regulatory networks. In Boolean networks, interactions between nodes (e.g., genes) are modeled by Boolean functions. In PBNs, Boolean functions are switched probabilistically. In this paper, for a PBN, a simplified representation that is effective in analysis and control is proposed. First, after a polynomial representation of a PBN is briefly explained, a simplified representation is derived. Here, the steady-state 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 nodes. Next, using this representation, input selection and stabilization are discussed. Finally, the proposed method is demonstrated by a biological example.