Attractor landscape recovery under sparse structural intervention in Boolean networks

Attractor landscape recovery in Boolean networks under sparse structural intervention is investigated in this paper. In contrast to conventional stabilization problems, the enlargement of the basin of a prescribed target attractor is considered as the objective, while the target attractor itself is preserved and only a limited set of node update rules is modified. XOR feedback intervention is considered, under which selected update functions are changed into f i ( x ) ⊕ g i ( x ) . For a given intervention set, the admissible transition matrices are characterized by algebraic column constraints. A feasible transition graph is then constructed from these constraints. It is proved that the largest recoverable target basin is exactly the set of states from which the target attractor can be reached in this graph, and this result is used to synthesize an optimal feedback controller. It is further shown that sparse basin recovery is generally not submodular, by which cooperative effects and sudden basin expansion in attractor landscape reshaping are revealed. In the mammalian cell-cycle network, a target basin reduced by structural perturbation is substantially recovered through a sparse single-node intervention. Across modular random Boolean networks, positive cooperative recovery occurs in 40 to 50 percent of the tested instances.