Fig. 1: Schematic demonstration of the cascading failure process in multilayer biological molecular networks.

The multilayer model includes a gene regulatory network in which the genes (ellipses) are linked by regulatory relations (red directed links), a PPI network in which proteins (bone shapes) are linked by physical interactions (black undirected links), and a metabolic network in which metabolites (molecule shapes) are connected by chemical–chemical interactions (purple undirected links). The gene regulatory and PPI networks are connected by bidirectional interdependency links (yellow dashed lines). From the PPI to metabolic networks, there are multiple supporting links (green dashed lines). a Initially perturb a gene in the gene regulatory network causing such gene to stop functioning (represented by a black ellipse). b The target genes of the perturbed genes fail (black ellipses), and their corresponding proteins stop functioning, represented by black bone shapes. c The proteins that disconnected from the largest connected component fail (black bone shapes), and the metabolites losing all supports from the PPI network stop functioning (black molecule shapes).