Pinning Stabilization of Logical Networks Based on Deformation of the State Transition Matrix

Abstract

Boolean Networks (BNs) are a powerful model to describe the way in which genes work and holistically interact with one another in system biology. Based on the requirement to guide the systems to a desired state, the stabilization problem becomes an important issue in BNs. Since the normal state feedback control puts controllers to all nodes, the control cost is relatively high. In this paper, we investigate the stabilization problem of BNs under pinning control strategy. Meanwhile, to cut down the cost of control to the most, the set of pinned nodes is minimized. Specifically, a four-procedure method as well as the corresponding computationally feasible algorithms are proposed to determine a minimum set of controlled nodes based on a deformed state transition matrix and a constructed digraph. In comparison with the strategy that is traditionally based on the state transition matrix, the proposed approach can effectively reduce the computational complexity. Finally, gene networks are discussed as simulations, which demonstrate the effectiveness of the proposed method, minimizing the number of controlled nodes with lower time complexity. Note to Practitioners—BNs are commonly used to explore gene interactions and evolutions in modeling and analyzing cellular processes and neural networks. When it comes to biological systems or genetic networks, it’s critical to create therapeutic interventions that guide patients toward and sustain desired states, like health. Thus, the requirement to steer BNs to a preassigned state through control design is what motivates this study. In order to ensure the arbitrariness of the preassigned state and minimize the control cost, pinning control with minimum controlled nodes is a wise option. However, existing pinning strategies based on state transition matrix generally fall short of practice due to the high time complexity. To address the issue, the present work proposes a four-procedure pinning control method via a graph method to seek for the minimum set of pinned nodes with lower time complexity and verifies on different gene networks.