Co-controllability of drug-disease-gene network

Controllability of a single network often focuses on the determination of the network's minimum dominating set, which aims to elaborate how to control the whole network with minimum driver nodes. This paper proposes a new framework, co-controllability of multiple networks, which stresses the control of one network by another network as well as the mutual control characteristics of multiple networks based on minimum dominating sets. We take a drug-disease-gene network that consists of a drug-drug network, a disease-disease network and a gene-gene network as an example to study co-controllability of multiple networks. The results show that driver nodes tend to be conserved, e.g. diseases highly associated with driver nodes of the drug-drug network tend to be driver nodes in the disease-disease network compared with random networks. In addition, co-controllability of multiple networks is probably associated with the networks' node degree, which is more stringent than controllability of a single network that is mainly determined by the network's degree distribution. We also find that diseases and drugs tend to be mapped as two different subnetworks of human protein-protein interaction (PPI) network, drugs are inclined to dominate diseases by controlling the PPI network, and the coded proteins of disease-related genes exhibit a low tendency to be drug targets for the control of diseases. The results in this paper not only play an important role in understanding co-controllability of multiple networks, but also are helpful for understanding the mechanisms of drug-disease-gene, disease treatments and drug design in a network-based framework.