Uncertainty-based essentiality in gene regulatory networks

In this paper, we propose a definition for the essentiality of regulatory relationships among molecules in a Boolean network model, which takes the regulatory relationships between the molecules into account, in addition to their connectivity. The proposed definition of essentiality is tightly related to the ultimate goal of designing intervention strategies to achieve beneficial dynamic changes in the network. Focusing on Boolean networks, we define the essentiality of each regulatory relationship as the difference between the expected performance of the Bayesian robust structural intervention over the uncertainty class of networks, which arises from the uncertainty in the given regulatory relationship, and the performance of the optimal structural intervention for the known network in which there is no uncertainty. For a specific regulatory relationship, a large difference in performance implies that the given relationship is critical for designing effective therapeutic strategies. On the other hand, small difference implies that the regulatory relationship under consideration may not be crucial in designing intervention strategies. This new definition of essentiality, grounded on the quantification of uncertainty in network dynamics, may provide a deep understanding of the robustness, adaptability, and controllability of gene regulatory networks.