Fig. 2. The ARC framework.

(A) Exact ARC framework for phenotype landscape reversion of small Boolean networks. The algorithm input is the Boolean network. In step 1, exact basins for each attractor are calculated through eigen decomposition of the transpose of the STP transition matrix. In step 2, reached attractors and corresponding phenotypes for each basin under nominal, altered, and controlled conditions are computed. In step 3, the phenotype landscape matrices under nominal, altered, and controlled conditions are compared to identify the reverse control targets. (B) Approximate ARC framework for phenotype landscape reversion of large Boolean networks. The algorithm inputs are the Boolean network, its attractors, and their relative basin size ratios. In step 1, approximated average basins for each attractor are calculated through the backward state transitions. In step 2, reached attractors and corresponding phenotypes for each approximated average basin under nominal, altered, and controlled conditions are computed. In step 3, the phenotype landscape matrices under nominal, altered, and controlled conditions are compared to identify the reverse control targets.