Driving cellular biological systems to one of desired long-term behaviors, an important subject in systems biology, can be interpreted as the set stabilization problem. This article presents a realistic control approach to set stabilization of complex biological networks modeled by Boolean networks (BNs) wherein only open-loop control is applied. First, the considered BN is transformed into an auxiliary BN having redundant state variables. Based on the similarity between desired attractors and Boolean algebra, a number of reduced BNs are constructed from the auxiliary BN in favor of set stabilization. Next, the feedback vertex set (FVS) control law is applied to reduced BNs for obtaining open-loop control inputs that take partial state variables toward desired values. This procedure continues in a recursive way until ensuring that the controlled BN converges to an unspecified desired attractor. The proposed scheme has the superiority that both fixed-point and cyclic attractors can be included in the problem setting, and that it can tackle complex BNs with moderate computational burdens. Extensive numerical experiments on random BNs and real biological systems are provided to demonstrate the applicability of the proposed scheme.
Yang et al. (Thu,) studied this question.