Symbolic Approaches for Finding Control Strategies in Boolean Networks

We present an exact algorithm, based on techniques from the field of Model Checking, for finding control policies for Boolean Networks (BN) with control nodes. Given a BN, a set of starting states, I, a set of goal states, F, and a target time, t, our algorithm automatically finds a sequence of control signals that deterministically drives the BN from I to F at, or before time t, or else guarantees that no such policy exists. Despite recent hardness-results for finding control policies for BNs, we show that, in practice, our algorithm runs in seconds to minutes on over 13,400 BNs of varying sizes and topologies, including a BN model of embryogenesis in Drosophila melanogaster with 15,360 Boolean variables. We then extend our method to automatically identify a set of Boolean transfer functions that reproduce the qualitative behavior of gene regulatory networks. Specifically, we automatically learn a BN model of D. melanogaster embryogenesis in 5.3 seconds, from a space containing 6.9 × 10¹⁰ possible models.