Stabilizing Control of Complex Biological Networks Based on Attractor-Specific Network Reduction

Global stabilization of complex biological networks means controlling the dynamic state of the network to converge to a desired stable state, or an attractor, irrespective of initial states by perturbing a set of control target nodes. Global stabilization is of paramount importance in systems biology since attractors represent key phenotypes of biological systems. Most of the previous attempts to solve the global stabilization problem resort to either near-brute force or analytical searching with huge computational burden. In this paper, we propose a novel control scheme that can achieve global stabilization of complex biological networks by avoiding such issues. For this purpose, a Boolean network model of biological networks is considered. We reduce the Boolean network using a simple coordinate transformation with respect to the desired attractor without loss of the information on connectivity that is needed for global stabilization. We then identify control inputs by searching for a minimum set of nodes the perturbation of which makes the reduced Boolean network acyclic. Our control scheme ensures global stabilization with modest complexity and scalability.