Petri Net Analysis of the MAPK/ERK Cascade Coupled to the GTP:RAS Complex in the EGFR Signaling Network

The MAP kinase cascade of the epidermal growth factor receptor network is analyzed to further develop and demonstrate the application of Petri net models for the analysis of cellular systems. The mitogen-activated protein kinase/extracellular-regulated kinase (ERK) (subreaction H) model is then coupled to the model previously developed for the GTP:Ras complex (subreaction A) to demonstrate the computational scalability and analytical utility of the Shannon-like partition information entropy metric in the analysis of ever larger biochemical signaling networks. Unique minimal cycles (UMCs) have been shown to provide a natural partitioning of biochemical reaction networks. The complete listing of UMCs for two coupled subnetworks is found to contain all the UMCs of the individual subnetworks plus additional UMCs introduced by the cross-coupling of the two subnetworks by the shared species, in this case, ERK-PP and GTP:Ras, leading to a significant increase in the number and complexity of UMCs available for the control of the coupled subnetworks. The partition information entropy metric is used to rank order the UMCs to provide insight into the most critical pathways, thereby identifying which loops provide the most dynamic controllability over the cell's fate. Analysis of UMCs with some feed-backward transitions is found to be at least as important to the functioning of the network as UMCs with feed-forward only transitions.