  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.
