Step-wise target controllability to identify dysregulated pathways in molecular networks

Identifying the nodes that have the potential to influence the state of a network is a relevant question for many complex systems. In many applications it is often essential to test the ability of an individual node to control a specific target subset of the network. In biological networks, this might provide precious information on how single genes regulate the expression of specific groups of molecules in the cell. Taking into account these constraints, we propose an optimized heuristic based on the Kalman rank condition to quantify the centrality of a node as the number of target nodes it can control. By introducing a hierarchy among the nodes in the target set, and performing a step-wise research, we ensure for sparse and directed networks the identification of a controllable driver-target configuration in a significantly reduced space and time complexity. We show how the method works for simple network configurations, then we use it to characterize the inflammatory pathways in molecular gene networks associated with macrophage dysfunction in patients with multiple sclerosis. Results indicate that the targeted secreted molecules can in general be controlled by a large number of driver nodes (51%) involved in different cell functions, i.e. sensing, signaling and transcription. However, during the inflammatory response only a moderate fraction of all the possible driver-target pairs are significantly coactivated, as measured by gene expression data obtained from human blood samples. Notably, they differ between multiple sclerosis patients and healthy controls, and we find that this is related to the presence of dysregulated genes along the controllable walks. Our method, that we name step-wise target controllability, represents a practical solution to identify controllable driver-target configurations in directed complex networks and test their relevance from a functional perspective.