Total-activity conservation of probabilistic Boolean networks and its applications

Abstract

Conservation law is a basic property of biological networks, which exhibits the total-activity conservation in Boolean networks (BNs). This article analyzes the total-activity conservation of probabilistic Boolean networks (PBNs) based on the algebraic state space representation approach. The concept of total-activity conservation is proposed for PBNs, and a vector-based criterion is presented to verify the total-activity conservation of PBNs. Moreover, the impact of deterministic function perturbation on the total-activity conservation of PBNs is analyzed. Finally, as an application of total-activity conservation for PBNs, the robust total-activity conservation of BNs subject to stochastic function perturbation is explored.