Supplementary text: Details of the Bayesian formalisms

The model: The global responses of a network node i (to perturbations which do not directly affect node i) have a linear relationship with the global responses of its potential regulators. This relationship was previously derived in [3] and the resulting formulation is known as Modular Response Analsys or MRA. We proposed a modified version of MRA by introducing a binary indicator variable Aij which indicates whether node i is directly regulated by node j. Please note that any interaction routes via unknown elements are also considered as direct interaction. Aij = 1 indicates that the node i is directly regulated by node j and Aij = 0 indicates that node j does not directly regulate node i. We also accounted for biological and measurement noise in the MRA relationship. The resulting equation is shown below. ∑