An efficient algorithm to identify the optimal one-bit perturbation based on the basin-of-state size of Boolean networks

Boolean networks are widely used to model gene regulatory networks and to design therapeutic intervention strategies to affect the long-term behavior of systems. In this paper, we investigate the less-studied one-bit perturbation, which falls under the category of structural intervention. Previous works focused on finding the optimal one-bit perturbation to maximally alter the steady-state distribution (SSD) of undesirable states through matrix perturbation theory. However, the application of the SSD is limited to Boolean networks with about ten genes. In 2007, Xiao et al. proposed to search the optimal one-bit perturbation by altering the sizes of the basin of attractions (BOAs). However, their algorithm requires close observation of the state-transition diagram. In this paper, we propose an algorithm that efficiently determines the BOA size after a perturbation. Our idea is that, if we construct the basin of states for all states, then the size of the BOA of perturbed networks can be obtained just by updating the paths of the states whose transitions have been affected. Results from both synthetic and real biological networks show that the proposed algorithm performs better than the exhaustive SSD-based algorithm and can be applied to networks with about 25 genes.