Controllability of protein-protein interaction phosphorylation-based networks: Participation of the hub 14-3-3 protein family

Posttranslational regulation of protein function is an ubiquitous mechanism in eukaryotic cells. Here, we analyzed biological properties of nodes and edges of a human protein-protein interaction phosphorylation-based network, especially of those nodes critical for the network controllability. We found that the minimal number of critical nodes needed to control the whole network is 29%, which is considerably lower compared to other real networks. These critical nodes are more regulated by posttranslational modifications and contain more binding domains to these modifications than other kinds of nodes in the network, suggesting an intra-group fast regulation. Also, when we analyzed the edges characteristics that connect critical and non-critical nodes, we found that the former are enriched in domain-to-eukaryotic linear motif interactions, whereas the later are enriched in domain-domain interactions. Our findings suggest a possible structure for protein-protein interaction networks with a densely interconnected and self-regulated central core, composed of critical nodes with a high participation in the controllability of the full network, and less regulated peripheral nodes. Our study offers a deeper understanding of complex network control and bridges the controllability theorems for complex networks and biological protein-protein interaction phosphorylation-based networked systems.