Structure-based approach to identify driver nodes in ensembles of biologically inspired Boolean networks

Because the attractors of biological networks reflect stable behaviors (e.g., cell phenotypes), identifying control interventions that can drive a system towards its attractors (attractor control) is of particular relevance when controlling biological systems. Driving a network's feedback vertex set (FVS) by node-state override into a state consistent with a target attractor is proven to force every system trajectory to the target attractor, but in biological networks the FVS is typically larger than can be realistically manipulated. External control of a subset of a biological network's FVS was proposed as a strategy to drive the network to its attractors utilizing fewer interventions; however, the effectiveness of this strategy was only demonstrated on a small set of Boolean models of biological networks. Here, we extend this analysis to ensembles of biologically inspired Boolean networks. On these models, we use three structural metrics-PRINCE propagation, modified PRINCE propagation, and CheiRank-to rank FVS subsets by their predicted attractor control strength. We validate the accuracy of these rankings using three dynamical measures: To control, away control, and logical domain of influence. We also calculate the propagation metrics on effective graphs, which incorporate each Boolean model's functional information into edge weights. While this additional information increases the predicting power of structural metrics, we find that the increase with respect to the unweighted network is limited. The propagation metrics in conjunction with the FVS can be used to identify realizable driver node sets by emulating the dynamics that are prevalent in biological networks. This approach only uses the network's structure, and the driver sets are shown to be robust to the specific dynamical model.