Explicit Representation of Protein Activity States Significantly Improves Causal Discovery of Protein Phosphorylation Networks

Protein phosphorylation networks play an important role in cell signaling. In these networks, phosphorylation of a protein kinase usually leads to its activation, which in turn will phosphorylate its downstream target proteins. A phosphorylation network is essentially a causal network, which can be learned by causal inference algorithms. Prior efforts have applied such algorithms to data measuring protein phosphorylation levels, assuming that the phosphorylation levels represent protein activity states. However, the phosphorylation status of a kinase does not always reflect its activity state, because interventions such as inhibitors or mutations can directly affect its activity state without changing its phosphorylation status. Thus, when cellular systems are subjected to extensive perturbations, the statistical relationships between phosphorylation states of proteins may be disrupted, making it difficult to reconstruct the true protein phosphorylation network. Here, we describe a novel framework to address this challenge. We have developed a causal discovery framework that explicitly represents the activity state of each protein kinase as an unmeasured variable and developed a novel algorithm called “InferA” to infer the protein activity states, which allows us to incorporate the protein phosphorylation level, pharmacological interventions and prior knowledge. We applied our framework to simulated datasets and to a real-world dataset. The simulation experiments demonstrated that explicit representation of activity states of protein kinases allows one to effectively represent the impact of interventions and thus enabled our framework to accurately recover the ground-truth causal network. Results from the real-world dataset showed that the explicit representation of protein activity states allowed an effective and data-driven integration of the prior knowledge by InferA, which further leads to the recovery of a phosphorylation network that is more consistent with experiment results. Explicit representation of the protein activity states by our novel framework significantly enhances causal discovery of protein phosphorylation networks.