Finding the Logic Backbone of a Boolean Network.

Cellular behaviors, governed by various interaction networks among biomolecules, are often modeled using Boolean networks, where the future state of a node is determined by a logic function of the current states of its regulator nodes. Dynamic simulations of the system's trajectory in state space and methods that link the structure and the dynamics of the network have proven insightful. For example, stable motifs by Zanudo et. al. determine the steady states of the system. Here we propose a complementary method, namely the identification and representation of the backbone logical structure of a network, based on categorizing edges as sufficient or necessary. A sufficient activating (inhibitory) relationship means that the ON state of the regulator implies the ON (OFF) state of the target. A necessary activating (inhibitory) relationship means that the OFF state of the regulator implies the OFF (ON) state of the target. We identify (complex) subnetworks distillable into a causal relationship. This way, we represent a signal transduction network as a backbone network of external signals, stable motifs, and the output nodes. Furthermore, we use this framework to identify crucial nodes that can drive the system from one steady state to another.