Global stabilization of Boolean networks with applications to biomolecular network control

Boolean networks (BNs) are vital modeling tools in systems biology for biomolecular regulatory networks. After a transient phase, BNs converge to attractors that represent distinct cell types or conditions. Therefore, methods to control the long-term behavior of BNs have important implications for biological and genetic applications. In this paper, we propose a method to enforce convergence of a BN to a desired attractor from any initial state through a simple intervention: fixing a specific subset of network variables at definite values. We refer to this method as the global stabilization of a BN to a target attractor. Utilizing the algebraic state space representation of BNs, we introduce novel matrix tools to formulate this intervention method, as well as develop a foundation for analyzing the stabilizability of BNs. We derive necessary and sufficient conditions for the global stabilizability of BNs and utilize these criteria to identify a minimal subset of network variables—termed the global stabilizing kernel—whose regulation ensures that the BN converges to the desired attractor. Finally, we apply our proposed method to determine the stabilizing kernels of several biomolecular regulatory network models and demonstrate how they can be steered to their target attractors, showcasing the applicability of our approach. We also apply our method to identify the stabilizing kernels of 480 randomly generated BNs. Our experiments suggest that, on average, only a relatively small portion (approximately 25%) of the network nodes need to be manipulated for the networks to converge to their primary attractors.