Advances in functional proteomic technologies have significantly enriched our knowledge of protein functions and their interactions in bio-molecular pathways. We discuss inference for RPPA (reverse phase protein array) data that measure the expression of the protein markers over time. We exploit the dynamical nature of the experiment to build a directed network of protein interactions. For this, we employ a Bayesian graphical model with an informative prior that favors sparsity. Conditional on the network, we model dependence at the level of latent binary indicators rather than the raw expression measurements. One of the key features of the proposed approach is a hierarchical model that allows for the dependence structure to be shared across different experiments, in the case of the motivating application across different drugs and doses. This is critical to facilitate meaningful inference with the limited available sample sizes. The second key feature is a sparsity inducing prior on the dependence structure.